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aqua_rat__bYfJFRCLildXzyxp | A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 40 years now, the son's age five years back was: Choose one:
A) A)15 B) B)67 C) C)56 D) D)89 E) E)34 | Let the son's present age be x years. Then, (40 - x) = x 2x = 40. x = 20. Son's age 5 years back (20 - 5)=
<gadget id="calculator">(20 - 5)</gadget>
<output>15</output>
15 years. 15nswer:15
<result>A</result> | A | {
"A": "A)15",
"B": "B)67",
"C": "C)56",
"D": "D)89",
"E": "E)34"
} | A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 40 years now, the son's age five years back was: |
aqua_rat__2cAjAodNvLPkn3nE | If the average of w, b, c, 14 and 15 is 12. What is the average value of w, b, c and 29 Pick one:
A) 12 B) 13 C) 14 D) 15 E) 16 | w+b+c+14+15 = 12*5=
<gadget id="calculator">12*5</gadget>
<output>60</output>
60=>w+b+c = 60-29=
<gadget id="calculator">60-29</gadget>
<output>31</output>
31 w+b+c+29= 31+29=
<gadget id="calculator">31+29</gadget>
<output>60</output>
60 Average= 60/4=
<gadget id="calculator">60/4</gadget>
<output>15</output>
15 Answer 15
<result>D</result> | D | {
"A": "12",
"B": "13",
"C": "14",
"D": "15",
"E": "16"
} | If the average of w, b, c, 14 and 15 is 12. What is the average value of w, b, c and 29 |
aqua_rat__pNHjjUO82OCsdJcP | A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform? Choose the correct choice from the following answers:
A) 120 m B) 240 m C) 300 m D) 500 m E) 550 m | Speed = 54 * 5/18=
<gadget id="calculator">54 * 5/18</gadget>
<output>15</output>
15 m/sec. Length of the train= 15 * 20=
<gadget id="calculator">15 * 20</gadget>
<output>300</output>
300 m. Let the length of the platform be x m . Then, (x + 300)/36= 15 => x = 240 m. ANSWER 240 m
<result>B</result> | B | {
"A": "120 m",
"B": "240 m",
"C": "300 m",
"D": "500 m",
"E": "550 m"
} | A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform? |
aqua_rat__12jN6h3IAxv9VQ1f | n is an integer chosen at random from the set
{5, 7, 9, 11 }
p is chosen at random from the set
{2, 4, 10, 14, 18}
What is the probability that n + p = 13 ? Choose the correct choice from the following choices:
A) 0.15
B) 0.2
C) 0.25
D) 0.3
E) 0.4 | Set N: there is 4 ways to chose a number Set P: there is 5 ways to chose a number so total outcome is 4*5=
<gadget id="calculator"> 4*5</gadget>
<output>20</output>
20 which is represent 20 pairs of number now we have 3 pairs can give us 13 which are (7,6), (9,4) and (11,2) . 3/20=
<gadget id="calculator">3/20</gadget>
<output>3/20 = around 0.15</output>
0.15 0.15nswer 0.15
<result>A</result> | A | {
"A": "0.15",
"B": "0.2",
"C": "0.25",
"D": "0.3",
"E": "0.4"
} | n is an integer chosen at random from the set
{5, 7, 9, 11 }
p is chosen at random from the set
{2, 4, 10, 14, 18}
What is the probability that n + p = 13 ? |
aqua_rat__pzAVaIHLKefdqadK | A tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume. If 3,000 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride?
Choose the correct choice from the following answers: A) 6.28% B) 7.14% C) 7.86% D) 8.25% E) 8.63% | The amount of sodium chloride is 0.05*10,000 = 500 gallons 500/7000 = 1/14 which is about 7.14% The answer is 7.14%.
<result>B</result> | B | {
"A": "6.28%",
"B": "7.14%",
"C": "7.86%",
"D": "8.25%",
"E": "8.63%"
} | A tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume. If 3,000 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride? |
aqua_rat__KgQ7OQAYau8EtYFX | At a dinner party every two guests used a bowl of rice between them, every three guests used a bowl of dal between them and every four used a bowl of meat between them. There were altogether 65 dishes. How many guests were present at the party ? Choose the correct option
A) 60 B) 65 C) 90 D) 95 E) None of these | no. of rice bowl=x no. of dal bowl=y no. of meat bowl=z then, x+y+z=65(eq 1) also, 2x=3y=4z substituting value of y&z in terms of x in eq 1, x=30. as 1 rice bowl is shared between 2 guests, therefore there are 60 guests... 60NSWER:60
<result>A</result> | A | {
"A": "60",
"B": "65",
"C": "90",
"D": "95",
"E": "None of these"
} | At a dinner party every two guests used a bowl of rice between them, every three guests used a bowl of dal between them and every four used a bowl of meat between them. There were altogether 65 dishes. How many guests were present at the party ? |
aqua_rat__K7TBDHAlrAUtgSYZ | Sylvia can buy watches at a price of M dollars per watch, which she marks up by a certain percentage before selling. If she makes a total profit of X by selling Y watches, then in terms of M and X and Y, what is the percent of the markup from her buy price to her sell price? Choose one.
A) 100*(YM)
B) 100X*(YM)
C) 100X/(YM)
D) 100X-(YM)
E) 100X+(YM) | Algebraic Solution:If she makes a total profit of X for Y watches, then that must be a profit of X/Y for each watch. That must be the markup above cost on each watch, the amount of the increase. Well, percent increase = (amount of increase)/(starting amount) x 100% = (X/Y)/M *100 = 100X/(YM) Answer : 100X/(YM)
<result>C</result> | C | {
"A": "100*(YM)",
"B": "100X*(YM)",
"C": "100X/(YM)",
"D": "100X-(YM)",
"E": "100X+(YM)"
} | Sylvia can buy watches at a price of M dollars per watch, which she marks up by a certain percentage before selling. If she makes a total profit of X by selling Y watches, then in terms of M and X and Y, what is the percent of the markup from her buy price to her sell price? |
aqua_rat__IvTJq7UexSFbGAvl | What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 14%? Choose the correct choice from the following answers:
A) 20% B) 29% C) 13 1/30% D) 12% E) 13% | SP2 = 2/3 SP1 CP = 100 SP2 = 86 2/3 SP1 = 86 SP1 = 129 100 --- 29 => 29% ANSWER:29%
<result>B</result> | B | {
"A": "20%",
"B": "29%",
"C": "13 1/30%",
"D": "12%",
"E": "13%"
} | What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 14%? |
aqua_rat__nDEKww2ei7xi1tJw | Find the smallest four-digit number which is a multiple of 112. Choose the correct answer.
A) 896
B) 1008
C) 1120
D) 1024
E) None of these | The smallest four digit number is 1000. If 1000 is divided by 112, the remainder is 104. 112 - 104=
<gadget id="calculator">112 - 104</gadget>
<output>8</output>
8, if 8 is added to 1000, it will become the smallest four digit number and a multiple of 112. ANSWER:1008
<result>B</result> | B | {
"A": "896",
"B": "1008",
"C": "1120",
"D": "1024",
"E": "None of these"
} | Find the smallest four-digit number which is a multiple of 112. |
aqua_rat__24Hjm6x8aFvMAAQW | 25% of 30% of 45% is equal to? Options.
A) 0.03375
B) 0.03372
C) 0.0337
D) 0.03377
E) 0.03376 | (25/100) * (30/100) * (45/100) 1/4 * 3/10 * 9/20 27/800=
<gadget id="calculator">27/800</gadget>
<output>27/800 = around 0.03375</output>
0.03375 0.03375nswer:0.03375
<result>A</result> | A | {
"A": "0.03375",
"B": "0.03372",
"C": "0.0337",
"D": "0.03377",
"E": "0.03376"
} | 25% of 30% of 45% is equal to? |
aqua_rat__r8gZxickzbHA3U4e | A watch which gains uniformly ,is 5 min,slow at 8 o'clock in the morning on sunday and it is 5 min 48 sec.fast at 8 p.m on following sunday. when was it correct? Choose the most appropriate option: A) 28 min past 7pm on wednesday B) 20 min past 7pm on wednesday C) 20 min past 8pm on wednesday D) 29 min past 7pm on wednesday E) 20 min past 5pm on wednesday | Explanation: This sunday morning at 8:00 AM, the watch is 5 min. Slow, and the next sunday at 8:00PM it becomes 5 min 48 sec fast. The watch gains min in a time of (7×24)+12 = 180 hours. To show the correct tine, it has to gain 5 min. Answer: 20 min past 7pm on wednesday) 20 min past 7pm on wednesday So the correct time will be shown on wednesdy at 7:20 PM
<result>B</result> | B | {
"A": "28 min past 7pm on wednesday",
"B": "20 min past 7pm on wednesday",
"C": "20 min past 8pm on wednesday",
"D": "29 min past 7pm on wednesday",
"E": "20 min past 5pm on wednesday"
} | A watch which gains uniformly ,is 5 min,slow at 8 o'clock in the morning on sunday and it is 5 min 48 sec.fast at 8 p.m on following sunday. when was it correct? |
aqua_rat__rC3ZKKMN1Ak3ArvA | Tom, who has 50 math questions, will get 7 points per question if he chooses a correct answer. If he chooses a wrong answer to a question or skips one, he will lose 2 points per question. Then, which of the following can be the score if he solves all the 50 questions? Answers:
A) 192 B) 193 C) 194 D) 195 E) 197 | Let x be the correctly answered questions. y be the wrongly answered/ skipped ones. We have x + y = 50; Score = 7x-2y 2x+2y = 100; 7x-2y = Score; ==> 9x = 100+Score; check for answer choices where 100+Score is divisible by 9 Choice (197) 197 fits the equation !
<result>E</result> | E | {
"A": "192",
"B": "193",
"C": "194",
"D": "195",
"E": "197"
} | Tom, who has 50 math questions, will get 7 points per question if he chooses a correct answer. If he chooses a wrong answer to a question or skips one, he will lose 2 points per question. Then, which of the following can be the score if he solves all the 50 questions? |
aqua_rat__cXJmjhEAxxt1yuPC | In how many different number of ways 5 boys and 3 girls can sit on a bench? Select
A) 700 B) 40320 C) 720 D) 730 E) 740 | npn = n! 8p8 = 8 X 7 X 6 × 5 × 4 × 3 × 2 × 1 = 40320 40320
<result>B</result> | B | {
"A": "700",
"B": "40320",
"C": "720",
"D": "730",
"E": "740"
} | In how many different number of ways 5 boys and 3 girls can sit on a bench? |
aqua_rat__EQfy9muLtMHTs0jV | If selling price of an article is Rs. 250, profit percentage is 25%. Find the ratio of the cost price and the selling price
Select
A) 4:5 B) 3.:2 C) 2:1 D) 9:3 E) 4:2 | selling price = 250 Profit=25% cost price =250*100/125=
<gadget id="calculator">250*100/125</gadget>
<output>200</output>
200 Required ratio=200:250=4:5 4:5nswer: Option 4:5
<result>A</result> | A | {
"A": "4:5",
"B": "3.:2",
"C": "2:1",
"D": "9:3",
"E": "4:2"
} | If selling price of an article is Rs. 250, profit percentage is 25%. Find the ratio of the cost price and the selling price |
aqua_rat__2LKhsKZ18wn1yT1P | If n is a natural number, then 6n^ 2 + 6n is always divisible by? Choose the correct option: A) 6 only B) 6 and 12 C) 12 only D) 18 only E) 20 only | 6n^2 + 6n = 6n(n+1), which is always divisible by 6 and 12 both, since n(n+1) is always even. Answer is 6 and 12
<result>B</result> | B | {
"A": "6 only",
"B": "6 and 12",
"C": "12 only",
"D": "18 only",
"E": "20 only"
} | If n is a natural number, then 6n^ 2 + 6n is always divisible by? |
aqua_rat__NM7PzylUKjut9g0z | If the sum of two numbers is 45 and the H.C.F and the sum of the reciprocals of the numbers are 3 and 103/100 respectively, then the LCM of the numbers is equal to: Choose the correct choice from the following options:
A) 460 B) 300 C) 245 D) 100 E) 200 | Let the numbers be a and b and LCM be x, Then, a + b = 45 and ab = 3 * x = 3x Required sum = 1/a + 1/b = (a + b)/ab = 103/300 103/300=45/3x x=100 ANSWER:100
<result>D</result> | D | {
"A": "460",
"B": "300",
"C": "245",
"D": "100",
"E": "200"
} | If the sum of two numbers is 45 and the H.C.F and the sum of the reciprocals of the numbers are 3 and 103/100 respectively, then the LCM of the numbers is equal to: |
aqua_rat__OeyJeHOrXgK5CDal | A lemonade stand sold only small and large cups of lemonade on Tuesday. 2/5 of the cups sold were small and the rest were large. If the large cups were sold for 7/6 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups? Choose the correct choice from the following answers:
A) (a) 7/16 B) (b) 7/11 C) (c) 10/21 D) (d) 17/35 E) (e) 1/2 | A simpler way i guess would be to think that in total 5 cups were sold. Out of which 2 are small and 3 are large. Now let the small ones cost $6. so the large ones would cost $7. So, 2*6=
<gadget id="calculator">2*6</gadget>
<output>12</output>
12 and 3*7=
<gadget id="calculator"> 3*7</gadget>
<output>21</output>
21. Total revenue was 12+21=
<gadget id="calculator">12+21</gadget>
<output>33</output>
33 and Large cup sales as found above is 21 Therefore answer is 21/33 i.e 7/11 (b) 7/11
<result>B</result> | B | {
"A": "(a) 7/16",
"B": "(b) 7/11",
"C": "(c) 10/21",
"D": "(d) 17/35",
"E": "(e) 1/2"
} | A lemonade stand sold only small and large cups of lemonade on Tuesday. 2/5 of the cups sold were small and the rest were large. If the large cups were sold for 7/6 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups? |
aqua_rat__RynB3G2EgxS09npw | Light glows for every 15 seconds . How many times did it between 1:57:58 and 3:20:47 am Select.
A) 381 B) 332 C) 383 D) 334 E) 385 | the diff in sec between 1:57:58 and 3:20:47 is 4969 sec, 4969/13 = 331. so total 332 times light ll glow ANSWER:332
<result>B</result> | B | {
"A": "381",
"B": "332",
"C": "383",
"D": "334",
"E": "385"
} | Light glows for every 15 seconds . How many times did it between 1:57:58 and 3:20:47 am |
aqua_rat__U2aSc2gNmozop9SK | A 250m long train is travelling at 30km/hr. Another 200m long train travelling at 40km/hr in the same direction overtakes it. How long would it take to pass the first train completely? Choose the correct option.
A) 2min32secs. B) 1min32secs. C) 3min42secs. D) 2min42secs, E) 4min12secs. | Relative speed =x-y x,y are their speeds. Distance =(250+200)=
<gadget id="calculator">(250+200)</gadget>
<output>450</output>
450m Relative speed= (40-30)km/hr =450m =25/9 m/s Time taken to cover 450m = 450*9/25 secs. =162 secs. =2min.42sec. Answer : 2min42secs,
<result>D</result> | D | {
"A": "2min32secs.",
"B": "1min32secs.",
"C": "3min42secs.",
"D": "2min42secs,",
"E": "4min12secs."
} | A 250m long train is travelling at 30km/hr. Another 200m long train travelling at 40km/hr in the same direction overtakes it. How long would it take to pass the first train completely? |
aqua_rat__DPCKB3pd2fXCjbyT | A boy is traveling from his house to school at 3km/hr and reached school 9minutes late. Next day he traveled 4km/hr and reached 6minutes early. Then find the distance between house and school? Choose the correct choice from the following answers:
A) 3km
B) 4.5km
C) 5km
D) 2.5km
E) 6km | Let distance be x S1 = 3km/hr S2 = 4km/hr T1 = x/3hr T2 = x/4hr Difference in time = 9+6=
<gadget id="calculator">9+6</gadget>
<output>15</output>
15m= 1/4hr (x/3)-(x/4) = 1/4 x = 3km 3kmnswer is 3km
<result>A</result> | A | {
"A": "3km",
"B": "4.5km",
"C": "5km",
"D": "2.5km",
"E": "6km"
} | A boy is traveling from his house to school at 3km/hr and reached school 9minutes late. Next day he traveled 4km/hr and reached 6minutes early. Then find the distance between house and school? |
aqua_rat__tyNczaU0xVqQ9RQs | A, B, C, D and E play a game of cards. A says to B, "If you give me three cards, you will have as many as E has and if I give you three cards, you will have as many as D has." A and B together have 10 cards more than what D and E together have. If B has two cards more than what C has and the total number of cards be 133, how many cards does B have ? Choose the correct choice from the following:
A) 37 B) 23 C) 25 D) 29 E) 17 | Clearly, we have : B-3 = E ...(i) B + 3 = D ...(ii) A+B = D + E+10 ...(iii) B = C + 2 ...(iv) A+B + C + D + E= 133 ...(v) From (i) and (ii), we have : 2 B = D + E ...(vi) From (iii) and (vi), we have : A = B + 10 ...(vii) Using (iv), (vi) and (vii) in (v), we get: (B + 10) + B + (B - 2) + 2B = 133 5B = 125 B = 25. Answer: 25
<result>C</result> | C | {
"A": "37",
"B": "23",
"C": "25",
"D": "29",
"E": "17"
} | A, B, C, D and E play a game of cards. A says to B, "If you give me three cards, you will have as many as E has and if I give you three cards, you will have as many as D has." A and B together have 10 cards more than what D and E together have. If B has two cards more than what C has and the total number of cards be 133, how many cards does B have ? |
aqua_rat__XRoyc82Hr7NkpKFq | There are r red ball, b blue ball and w white ball in a bag. What is the ratio of the number of blue ball to the total no. of ball in terms of r, b and w.? Choices: A) (r + b + w) B) r / (r + b + w) C) r * (r + b + w) D) r / (r + b ) E) r / (r + w) | The total number of marbles is r + b + w The total ratio of blue marbles to the total number of marbles is r / (r + b + w) r / (r + b + w)
<result>B</result> | B | {
"A": "(r + b + w)",
"B": "r / (r + b + w)",
"C": "r * (r + b + w)",
"D": "r / (r + b )",
"E": "r / (r + w)"
} | There are r red ball, b blue ball and w white ball in a bag. What is the ratio of the number of blue ball to the total no. of ball in terms of r, b and w.? |
aqua_rat__V2l65jD3rv4URnNZ | What is the total number of X integers between 100 and 200 that are divisible by 3? Choose the correct choice from the following: A) 33 B) 32 C) 31 D) 30 E) 29 | yes there is a different way of arriving at that answer .... u can also use airthmetic progression to get the answer since the first term to be divisble by 3 is 102 ..take that as A .. the starting no and since 198 is the last digit to be divisible by 3 take that as N ... since the difference is 3 take that as D no u have to find what term is 198 take that as nth term the formula for that is N = 33 + (n-1) * d 198 = 102 +(n-1) * 3 from this u get n =33
<result>A</result> | A | {
"A": "33",
"B": "32",
"C": "31",
"D": "30",
"E": "29"
} | What is the total number of X integers between 100 and 200 that are divisible by 3? |
aqua_rat__DwmAKZw2sXBS90Wr | Half of the workers in Palabras bookstore have read the latest book by J. Saramago, and 1/6 of the workers have read the latest book by H. Kureishi. The number of workers that have read neither book is one less than the number of the workers that have read the latest Saramago book and have not read the latest Kureishi book. If there are 42 workers in the Palabras bookstore, how many of them have read both books? Pick
A) 3
B) 12
C) 9
D) 8
E) 7 | There are total 42 workers. Half of the workers in Palabras bookstore have read the latest book by J. Saramago, So 21 have read Saramago. 1/6 of the workers have read the latest book by H. Kureishi. So (1/6) * 42=
<gadget id="calculator">(1/6) * 42</gadget>
<output>7</output>
7 have read Kureishi The number of workers that have read neither book is one less than the number of the workers that have read the latest Saramago book and have not read the latest Kureishi book If B workers have read both books, 20 - B have read Saramago but not Kureishi. So, (21 - B - 1) have read neither. Total= n(3) + n(B) - Both + Neither 42 = 21 + 7 - B + (21 - B - 1) B = 3 3nswer (3)
<result>A</result> | A | {
"A": "3",
"B": "12",
"C": "9",
"D": "8",
"E": "7"
} | Half of the workers in Palabras bookstore have read the latest book by J. Saramago, and 1/6 of the workers have read the latest book by H. Kureishi. The number of workers that have read neither book is one less than the number of the workers that have read the latest Saramago book and have not read the latest Kureishi book. If there are 42 workers in the Palabras bookstore, how many of them have read both books? |
aqua_rat__DZsqxpRhNUuJnZFW | In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women? Answers
A) 33 B) 63 C) 22 D) 29 E) 177 | Explanation: Required number of ways = \inline {\color{63lack}(7C_{5}\times 3C_{2})=(7C_{2}\times 3C_{1})=63} Answer: 63) 63
<result>B</result> | B | {
"A": "33",
"B": "63",
"C": "22",
"D": "29",
"E": "177"
} | In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women? |
aqua_rat__vabulrTOxBzR7Cdl | The surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 12 cm each. The radius of the sphere is: Choose the correct choice from the following answers:
A) 4cm
B) 6cm
C) 8cm
D) 10cm
E) 9cm | Explanation: Curved surface area of sphere =4/πr2Surface area of cylinder =2πrh 4/ 2=
<gadget id="calculator">4/ 2</gadget>
<output>2</output>
2πrh=>4/πr2=2πrh 4/ 2=
<gadget id="calculator">4/ 2</gadget>
<output>2</output>
2πrh=>r2=6∗12/2 =>r2=36 =>r=6 Note: Diameter of cylinder is 12 so radius is taken as 6. Option 6cm
<result>B</result> | B | {
"A": "4cm",
"B": "6cm",
"C": "8cm",
"D": "10cm",
"E": "9cm"
} | The surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 12 cm each. The radius of the sphere is: |
aqua_rat__uO3rbvIBTBHCeJPI | If cost of sugar increases by 52%. How much percent consumption of sugar should be decreased in order to keep expenditure fixed? Pick
A) 34.21 B) 35.15 C) 36.32 D) 28.21 E) 26.54 | 100 152 ----- 152 ----- 52 100 ------ ? => 34.21% 34.21nswer:34.21
<result>A</result> | A | {
"A": "34.21",
"B": "35.15",
"C": "36.32",
"D": "28.21",
"E": "26.54"
} | If cost of sugar increases by 52%. How much percent consumption of sugar should be decreased in order to keep expenditure fixed? |
aqua_rat__kQt5fylRmPqmGPH9 | Three numbers are in the ratio 1:4:8 and their H.C.F is 3. The numbers are? Choose the correct choice from the following options.
A) 3, 15, 24 B) 3, 12, 27 C) 3, 12, 22 D) 3, 12, 24 E) 3, 12, 21 | Let the required numbers be x, 4x and 8x. Then, their H.C.F = x. So, x = 3. The numbers are 3, 12, 24. Answer: 3, 12, 24
<result>D</result> | D | {
"A": "3, 15, 24",
"B": "3, 12, 27",
"C": "3, 12, 22",
"D": "3, 12, 24",
"E": "3, 12, 21"
} | Three numbers are in the ratio 1:4:8 and their H.C.F is 3. The numbers are? |
aqua_rat__LD3NokSgkj8Yhh2h | Compound interest earned on a sum for the second and the third years are Rs.1200 and Rs.1440 respectively. Find the rate of interest? Select: A) 80% p.a B) 10% p.a C) 20% p.a D) 28% p.a E) 30% p.a | Rs.1440 - 1200 = Rs.240 is the interest on Rs.1200 for one year. Rate of interest = (100 * 240) / (100 * 1) = 20% p.a Answer:20% p.a
<result>C</result> | C | {
"A": "80% p.a",
"B": "10% p.a",
"C": "20% p.a",
"D": "28% p.a",
"E": "30% p.a"
} | Compound interest earned on a sum for the second and the third years are Rs.1200 and Rs.1440 respectively. Find the rate of interest? |
aqua_rat__60GAuwGhaqeTkQhS | In a class of 40 students 26 play football and play 20 long tennis, if 17 play above, many play neither? Choose the correct option:
A) 6
B) 8
C) 10
D) 11
E) 14 | 26 + 20 - 17=
<gadget id="calculator">26 + 20 - 17</gadget>
<output>29</output>
29 40 - 29=
<gadget id="calculator">40 - 29</gadget>
<output>11</output>
11 play neither Answer is 11
<result>D</result> | D | {
"A": "6",
"B": "8",
"C": "10",
"D": "11",
"E": "14"
} | In a class of 40 students 26 play football and play 20 long tennis, if 17 play above, many play neither? |
aqua_rat__oormbxcNs1QL83th | Edward is a trail runner who decides to take a day off work to run up and down a local mountain. He runs uphill at an average speed of 6 miles per hour and returns along the same route at an average speed of 9 miles per hour. Of the following, which is the closest to his average speed, in miles per hour, for the trip up and down the mountain? Choose the correct choice: A) 5.5 B) 5.8 C) 6.0 D) 6.3 E) 7.2 | to calculate average of 2 speeds a and b when distance is constant Formula - 2ab/(a+b) Here 7.2dward's uphill speed = 6 mph 7.2dward's downhill speed = 9 mph 2*6*9/(6+9) = 108/15=
<gadget id="calculator">108/15</gadget>
<output>36/5 = around 7.2</output>
7.2 Correct answer - 7.2
<result>E</result> | E | {
"A": "5.5",
"B": "5.8",
"C": "6.0",
"D": "6.3",
"E": "7.2"
} | Edward is a trail runner who decides to take a day off work to run up and down a local mountain. He runs uphill at an average speed of 6 miles per hour and returns along the same route at an average speed of 9 miles per hour. Of the following, which is the closest to his average speed, in miles per hour, for the trip up and down the mountain? |
aqua_rat__jfT1ERDCy3vDyRgd | The length of a room is 5.5 m and width is 3.75 m. Find the cost of paving the floor by slabs at the rate of Rs. 1400 per sq. metre. Pick one: A) Rs. 15000 B) Rs. 15550 C) Rs. 15600 D) Rs. 28875 E) None of these | Solution Area of the floor = (5.5 × 3.75) m2 = 20.625 m2 ∴ Cost of paving = Rs. (1400 × 20.625) = 28875. Answer Rs. 28875
<result>D</result> | D | {
"A": "Rs. 15000",
"B": "Rs. 15550",
"C": "Rs. 15600",
"D": "Rs. 28875",
"E": "None of these"
} | The length of a room is 5.5 m and width is 3.75 m. Find the cost of paving the floor by slabs at the rate of Rs. 1400 per sq. metre. |
aqua_rat__7AUmRr6gWd2p5lNQ | At the time of marriage, a man was 8 years elder to his wife. 15 years after their marriage, his age is 5/4 times the age of his wife. What was wife's age at the time of marriage ? Choose one answer. Choose the correct choice.
A) 15 years B) 30 years C) 18 years D) 17 years E) 26 years | let wifes age= x husband age = x+8 now after 15 years of mrg x+15 wifes age x+8+15 husbands age 5/4(x+15)=x+8+15 after solving x=17 ANSWER:17 years
<result>D</result> | D | {
"A": "15 years",
"B": "30 years",
"C": "18 years",
"D": "17 years",
"E": "26 years"
} | At the time of marriage, a man was 8 years elder to his wife. 15 years after their marriage, his age is 5/4 times the age of his wife. What was wife's age at the time of marriage ? Choose one answer. |
aqua_rat__4zQA9f8x30Lw8u4e | It is being given that (2^32 + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?
Choices:
A) 2^16
B) 7 * 2^23
C) 7 * 2^33
D) 5 * 2^32
E) 2^96 + 1 | Assume 2^32 = x Therefore , (2^32 + 1) = (x + 1) --------eq. 1 2^96 + 1 = (2^32)^3 + 1 = x^3 + 1 = x^3 + 1^3 = (x + 1) (x^2 - x +1)---------eq. 2 From eq. 1 and 2 Option 2^96 + 1 is correct.
<result>E</result> | E | {
"A": "2^16",
"B": "7 * 2^23",
"C": "7 * 2^33",
"D": "5 * 2^32",
"E": "2^96 + 1"
} | It is being given that (2^32 + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number? |
aqua_rat__JuuqWcFnvejUw6hq | List L: ABC, BCA, CAB
In list L above, there are 3 positive integers, where each of A, B, and C is a different nonzero digit. Which of the following is the sum of all the positive integers that MUST be factors of the sum of the integers in list L? Choose the correct choice:
A) 47 B) 114 C) 152 D) 161 E) 488 | Sum = (100A + 10B + C) + (100B + 10C + A) + (100C + 10A + B) = 111*(A + B + C). So, we have that the sum will be a multiple of 111=3*37. As for A + B + C: if A=1, B=2 and C=4, then A + B + C = 7, so the sum will also be divisible by 7 BUT if A=1, B=2 and C=8, then A + B + C = 11, so the sum will also be divisible by 11. This implies that A + B + C will not produce the same factors for all possible values of A, B and C. Therefore, we can say that 111*(A + B + C) MUST be divisible only by 111 --> so, by 1, 3, 37, and 111 --> 1 + 3 + 37 + 111 = 152. Answer: 152.
<result>C</result> | C | {
"A": "47",
"B": "114",
"C": "152",
"D": "161",
"E": "488"
} | List L: ABC, BCA, CAB
In list L above, there are 3 positive integers, where each of A, B, and C is a different nonzero digit. Which of the following is the sum of all the positive integers that MUST be factors of the sum of the integers in list L? |
aqua_rat__jrTNFR3CW2MhuTip | If the cost price of 50 articles is equal to the selling price of 46 articles, then the gain or loss percent is? Choose the correct choice from the following options.
A) 22
B) 65
C) 78
D) 33
E) 8.69 | Given that, cost price of 50 article is equal to selling price of 46 articles. Let cost price of one article = Rs. 1 Selling price of 46 articles = Rs. 50 But Cost price of 46 articles = Rs. 46 Therefore, the trader made profit.\Percentage of profit = 4/46 * 100 = 8.69% Answer:8.69
<result>E</result> | E | {
"A": "22",
"B": "65",
"C": "78",
"D": "33",
"E": "8.69"
} | If the cost price of 50 articles is equal to the selling price of 46 articles, then the gain or loss percent is? |
aqua_rat__gWXsKd2kpNLSL7us | The ratio between the present age of P and Q is 6 : 7. if Q is 4 years old then P, what will be the ratio of the ages of P and Q after 4 year ? Choose the correct answer.
A) 3 : 4
B) 3 : 5
C) 7 : 8
D) 4 : 3
E) None of these | Solution Let P's age and Q's age be 6x years and 7x years respectively. Then, 7x - 6x = 4 ⇔ x = 4. ∴ Required ratio = (6 x + 4) : (7 x + 4) = 28 : 32 = 7 : 8 .Answer 7 : 8
<result>C</result> | C | {
"A": "3 : 4",
"B": "3 : 5",
"C": "7 : 8",
"D": "4 : 3",
"E": "None of these"
} | The ratio between the present age of P and Q is 6 : 7. if Q is 4 years old then P, what will be the ratio of the ages of P and Q after 4 year ? |
aqua_rat__BmvfZpYyDBVWiIMv | A die is thrown twice and the sum of the numbers appearing is observed to be 6.
find the conditional probability that the number 4 has appeared at least once? Choose one: A) 2/5 B) 3/5 C) 3/7 D) 3/11 E) None | Let E be the event that ‘number 4 appears at least once’ and F be the event that ‘the sum of the numbers appearing is 6’. Then, E = {(4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (1,4), (2,4), (3,4), (5,4), (6,4)} and F = {(1,5), (2,4), (3,3), (4,2), (5,1)} We have P(E) = 11/36 and P (F) = 5/36 Also EnF = {(2,4), (4,2)} Therefore P(EnF) = 2/36 the required probability P(E|F) = P(EnF)/P(F) = (2/36)/(5/36) = 2/5. 2/5)
<result>A</result> | A | {
"A": "2/5",
"B": "3/5",
"C": "3/7",
"D": "3/11",
"E": "None"
} | A die is thrown twice and the sum of the numbers appearing is observed to be 6.
find the conditional probability that the number 4 has appeared at least once? |
aqua_rat__9nzO8E16OG76pjdl | A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long? Options.
A) 333 Sec B) 190 Sec C) 176 Sec D) 2687 Sec E) 1876 Sec | L = S*T S= 1200/120=
<gadget id="calculator">1200/120</gadget>
<output>10</output>
10 m/Sec. Total length (D)= 1900 m T = D/S T = 1900/10=
<gadget id="calculator">1900/10</gadget>
<output>190</output>
190 Sec Answer:190 Sec
<result>B</result> | B | {
"A": "333 Sec",
"B": "190 Sec",
"C": "176 Sec",
"D": "2687 Sec",
"E": "1876 Sec"
} | A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long? |
aqua_rat__RSnqSpeyuT8vAZ3K | A, B can Complete a work in 15 days &10 days respectively. They started doing thework together after 2 days B had to leave and A alone completed the remaining work.The whole work wascompleted in how many days? Answers.
A) 8 days
B) 10 days
C) 12 days
D) 14 days
E) 16 days | A and B can complete whole work in 30/(2+3)=
<gadget id="calculator">30/(2+3)</gadget>
<output>6</output>
6 days Part of work completed together in 3 days=2/6=1/3 part Now 2/3 part will be completed by A in 2/3*15=
<gadget id="calculator"> 2/3*15</gadget>
<output>10</output>
10 days Hence, whole work will be completed in 2+10=
<gadget id="calculator"> 2+10</gadget>
<output>12</output>
12 days 12 days
<result>C</result> | C | {
"A": "8 days",
"B": "10 days",
"C": "12 days",
"D": "14 days",
"E": "16 days"
} | A, B can Complete a work in 15 days &10 days respectively. They started doing thework together after 2 days B had to leave and A alone completed the remaining work.The whole work wascompleted in how many days? |
aqua_rat__NtS1Rq2s9eOxQP6c | Baseball's World Series matches 2 teams against each other in a best-of-seven series. The first team to win four games wins the series and no subsequent games are played. If you have no special information about either of the teams, what is the probability E that the World Series will consist of fewer than 7 games?
Select the correct option
A) 12.5% B) 25% C) 31.25% D) 68.75% E) 75% | Your explanation is very close toManhattan GMAT's official answer - it's quite uncanny: "There are many other ways this could happen. Using the permutation formula, there are 6!/(3!)(3!) = 20 ways for the two teams to split the first 6 games (3 wins for each). There are then 2 possible outcomes to break the tie in Game 7. Thus, there are a total of 202 = 40 ways for the World Series to last the full 7 games. The probability that any one of these 40 ways occurs can be calculated from the fact that the probability of a team winning a game equals the probability of a team losing a game = 1/2. Given that 7 distinct events must happen in any 7 game series, and that each of these events has a probability of 1/2, the probability that any one particular 7 game series occurs is. Since there are 40 possible different 7 game series, the probability that the World Series will last exactly 7 games is: (1/2)^7 = 1/128 40*1/128 = 40/128 = 31.25% Thus the probability E that the World Series will last less than 7 games is 100% - 31.25% = 68.75%. The correct answer is 68.75%." 100 - 31.25=
<gadget id="calculator"> 100 - 31.25</gadget>
<output>68.75</output>
68.75%. The correct answer is 68.75%."
<result>D</result> | D | {
"A": "12.5%",
"B": "25%",
"C": "31.25%",
"D": "68.75%",
"E": "75%"
} | Baseball's World Series matches 2 teams against each other in a best-of-seven series. The first team to win four games wins the series and no subsequent games are played. If you have no special information about either of the teams, what is the probability E that the World Series will consist of fewer than 7 games? |
aqua_rat__ep1ZtEHlDdjd5Flh | Find the sum of first 30 natural numbers Choose the correct choice from the following choices.
A) 470
B) 468
C) 465
D) 463
E) 485 | Explanation: Sum of n natural numbers =n(n+1)2 =30(30+1)2=30(31)2=465 Answer: Option 465
<result>C</result> | C | {
"A": "470",
"B": "468",
"C": "465",
"D": "463",
"E": "485"
} | Find the sum of first 30 natural numbers |
aqua_rat__aOrkiBAJn0nav58Z | Tina’s cat weighs 3.2 kilograms. Her dog weighs 5 times as much as her cat. How much does her dog weigh in kilograms? Choose the most appropriate option.
A) A)10.4kg B) B)38kg C) C)22kg D) D)48kg E) E)16kg | 3.2*5=
<gadget id="calculator">3.2*5</gadget>
<output>16</output>
16kg.Answer is 16kg.
<result>E</result> | E | {
"A": "A)10.4kg",
"B": "B)38kg",
"C": "C)22kg",
"D": "D)48kg",
"E": "E)16kg"
} | Tina’s cat weighs 3.2 kilograms. Her dog weighs 5 times as much as her cat. How much does her dog weigh in kilograms? |
aqua_rat__kmCO8I5U8Y2Sof3D | A certain telephone company company charges 3.10 cents for the first 1/5 of a minute plus 0.40 cents for each additional 1/5 of a minute. What would this company charge for a talk time of 8 minutes long? Choices: A) 15.60 B) 16.0 C) 17.8 D) 18.7 E) 19.1 | first 1/5 minute charge = 3.10 cents rest of the minute = 8 - (1/5) = 39/5 charge for the rest of the minute = 39 *0.4=
<gadget id="calculator">39 *0.4</gadget>
<output>15.6</output>
15.6 total charge= 3.10+15.6=
<gadget id="calculator">3.10+15.6</gadget>
<output>18.7</output>
18.7 cents Answer is 18.7.
<result>D</result> | D | {
"A": "15.60",
"B": "16.0",
"C": "17.8",
"D": "18.7",
"E": "19.1"
} | A certain telephone company company charges 3.10 cents for the first 1/5 of a minute plus 0.40 cents for each additional 1/5 of a minute. What would this company charge for a talk time of 8 minutes long? |
aqua_rat__iEpUCXvFj6m9N9fH | How many numbers with 3 different digits can be formed using only the even-numbered digit? Answers: A) 10 B) 24 C) 40 D) 60 E) 120 | Odd digits are 2, 4, 6, 8. We want 3 different digits. First digit can be chosen in 4 ways. Second digit can be chosen in 3 ways. Third digit can be chosen in 2 ways. Total ways = 4*3*2=
<gadget id="calculator">4*3*2</gadget>
<output>24</output>
24 Hence option (24).
<result>B</result> | B | {
"A": "10",
"B": "24",
"C": "40",
"D": "60",
"E": "120"
} | How many numbers with 3 different digits can be formed using only the even-numbered digit? |
aqua_rat__EMDWM4M2HltQwbhF | A list of measurements in increasing order is 4, 5, 6, 8, 15 and x. If the median of these measurements is 3/4 times their arithmetic mean, what is the value of x? Options:
A) 16 B) 18 C) 20 D) 22 E) 24 | The median is (6+8)/2=
<gadget id="calculator">(6+8)/2</gadget>
<output>7</output>
7 The mean is (4+5+6+8+15+x)/6= (38+x)/6 (38+x) /6 * 3/4 = 7 x = 56-38=
<gadget id="calculator">56-38</gadget>
<output>18</output>
18 The answer is 18.
<result>B</result> | B | {
"A": "16",
"B": "18",
"C": "20",
"D": "22",
"E": "24"
} | A list of measurements in increasing order is 4, 5, 6, 8, 15 and x. If the median of these measurements is 3/4 times their arithmetic mean, what is the value of x? |
aqua_rat__LxodLY2OMdZJsTEB | If a boat goes upstream at 5 km/hr and downstream at 7 km/hr what is the speed of the stream?
Choose the correct choice from the following choices.
A) 1.5 kmph B) 1.2 kmph C) 1.1 kmph D) 1.3 kmph E) 1 kmph | Sol. Speed of stream = 1/2(7 -5) kmph = 1 kmph. Answer 1 kmph
<result>E</result> | E | {
"A": "1.5 kmph",
"B": "1.2 kmph",
"C": "1.1 kmph",
"D": "1.3 kmph",
"E": "1 kmph"
} | If a boat goes upstream at 5 km/hr and downstream at 7 km/hr what is the speed of the stream? |
aqua_rat__VAFJgYcUSajiM54C | 4 friends went for a cinema, and everyone decided to contribute equally to the total bill of $60. If one of the friends had a coupon for 8% off the total bill, and if each friend still contributed equally after the coupon was applied to the bill, how much did each friend pay? Choose one:
A) 13 B) 13.1 C) 13.2 D) 13.8 E) 14 | At the non-discounted price, each friend would pay $15, as $60 divided by 4 friends is $15 per friend. But if the bill is 8% off, then each friend would pay 8% less. 8% of $15 is $1.2, so each friend saves $1.2 and pays the remaining 13.8 CORRECT OPTION:OPTION 13.8
<result>D</result> | D | {
"A": "13",
"B": "13.1",
"C": "13.2",
"D": "13.8",
"E": "14"
} | 4 friends went for a cinema, and everyone decided to contribute equally to the total bill of $60. If one of the friends had a coupon for 8% off the total bill, and if each friend still contributed equally after the coupon was applied to the bill, how much did each friend pay? |
aqua_rat__1VHUUJNfcAgEkv9R | A rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m? Choose the correct option.
A) Rs.3990
B) Rs.3967
C) Rs.3927
D) Rs.3900
E) Rs.3282 | Area = (l + b – d) d (80 + 60 – 10)10 => 1300 m2 1300 * 3 = Rs.3900 Answer: Rs.3900
<result>D</result> | D | {
"A": "Rs.3990",
"B": "Rs.3967",
"C": "Rs.3927",
"D": "Rs.3900",
"E": "Rs.3282"
} | A rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m? |
aqua_rat__CscUye27k0uUxyWs | Distance between two stations A and B is 778 km. A train covers the journey from A to B at 84 km per hour and returns back to A with a uniform speed of 56km per hour. Find the average speed of the train during the whole journey?
Choose the correct choice from the following choices.
A) 67.8 B) 67.4 C) 67.2 D) 67.6 E) 67.0 | If a car covers a certain distance at x kmph and an equal distance at y kmph. Then, average speed of the whole journey = (2xy)/x+y kmph. By using the same formula, we can find out the average speed quickly. Average speed =(2×84×56)/(84+56) =(2×84×56)/140 =(2×21×56)/35 =(2×3×56)/5 =3365=67.2 Answer is 67.2.
<result>C</result> | C | {
"A": "67.8",
"B": "67.4",
"C": "67.2",
"D": "67.6",
"E": "67.0"
} | Distance between two stations A and B is 778 km. A train covers the journey from A to B at 84 km per hour and returns back to A with a uniform speed of 56km per hour. Find the average speed of the train during the whole journey? |
aqua_rat__k9rIhoqMMT04s3nb | A reduction of 40% in the price of bananas would enable a man to obtain 64 more for Rs.40. What is the reduced price/dozen?
Choose the correct choice from the following choices:
A) 3 B) 4 C) 5 D) 6 E) 9 | Sol. lie purchases 6a bananas mere for 4096 of Rs 40 or, Rs 16. Reduced price per do 3 3
<result>A</result> | A | {
"A": "3",
"B": "4",
"C": "5",
"D": "6",
"E": "9"
} | A reduction of 40% in the price of bananas would enable a man to obtain 64 more for Rs.40. What is the reduced price/dozen? |
aqua_rat__y3oSU0AMcSTjSsmc | A soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price. During the annual summer sale, everything in the store is an additional 20 percent off the original list price. If a replica jersey's list price is $80, approximately what percent of the list price is the lowest possible sale price? Choose the correct choice from the following options
A) 20 B) 25 C) 30 D) 40 E) 50 | Let the list price be 2x for min sale price, the first discount given should be 50%, 2x becomes x here now, during summer sale additional 20% off is given ie sale price becomes 0.8x it is given lise price is $80 => 2x = 80 => x = 40 and 0.8x = 32 so lowest sale price is 32, which is 40% of 80 hence, 40 is the answer
<result>D</result> | D | {
"A": "20",
"B": "25",
"C": "30",
"D": "40",
"E": "50"
} | A soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price. During the annual summer sale, everything in the store is an additional 20 percent off the original list price. If a replica jersey's list price is $80, approximately what percent of the list price is the lowest possible sale price? |
aqua_rat__qMTVDZrwtuRtrY5G | The probability that a man will be alive for 10more yrs is 1/4 & the probability that his wife will alive for 10 more yrs is 1/3. The probability that none of them will be alive for 10 more yrs, is Pick: A) 1/2 B) 1 C) 2/3 D) 3/5 E) 3/8 | Sol. Required probability = Pg.) x P(B) = (1— D x(1 —I) =: x 1=1/2 1/2ns.(1/2)
<result>A</result> | A | {
"A": "1/2",
"B": "1",
"C": "2/3",
"D": "3/5",
"E": "3/8"
} | The probability that a man will be alive for 10more yrs is 1/4 & the probability that his wife will alive for 10 more yrs is 1/3. The probability that none of them will be alive for 10 more yrs, is |
aqua_rat__AL6B9bAbfVvLfJy9 | A, B, C subscribe Rs. 50,000 for a business, A Subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 35,000, C receives : Choose the correct answer
A) 8400
B) 14703
C) 37798
D) 13777
E) 14778 | Explanation: Let C = x. Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000. So, x + x + 5000 + x + 9000 = 50000 <=> 3x = 36000 <=> x = 12000. A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12. C's share = Rs. (35000 * 12/50 ) = Rs. 8,400. 8400nswer: 8400)
<result>A</result> | A | {
"A": "8400",
"B": "14703",
"C": "37798",
"D": "13777",
"E": "14778"
} | A, B, C subscribe Rs. 50,000 for a business, A Subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 35,000, C receives : |
aqua_rat__6cM7baioV6OekzXP | A computer program generates a single digit by a random process, according to which the probability of generating any digit is directly proportional to the reciprocal of one more than that digit. If all digits are possible to generate, then the probability R of generating an odd prime digit is between Choose the correct choice.
A) 0 and 1/6
B) 1/6 and 1/3
C) 1/3 and 1/2
D) 1/2 and 2/3
E) 2/3 and 5/6 | K (1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9+ 1/10) =1 Note that 1/10 is least value and is equal to 0.1 so we can write above series as K (1+0.5+0.3+0.25+0.2+0.16+0.5+residual) = 1 K=1/3+ P (3 or 5 or 7) =K*13/24 Required probability R= 13/24 × 1/3+ = 4+/24 > 1/6 Answer should be B P.s. 3+ denotes a value little greater than 3 . Same for 4+.
<result>B</result> | B | {
"A": "0 and 1/6",
"B": "1/6 and 1/3",
"C": "1/3 and 1/2",
"D": "1/2 and 2/3",
"E": "2/3 and 5/6"
} | A computer program generates a single digit by a random process, according to which the probability of generating any digit is directly proportional to the reciprocal of one more than that digit. If all digits are possible to generate, then the probability R of generating an odd prime digit is between |
aqua_rat__NQCCBq8efqjmacDK | P and Q invested in a business. The profit earned was divided in the ratio 2 : 3. If P invested Rs 40000, the amount invested by Q is Choose the correct answer:
A) 30000 B) 50000 C) 40000 D) 20000 E) 60000 | Let the amount invested by Q = q 40000:q=2:3 ⇒40000×3=2q ⇒q=(40000×3)/2=60000 Answer is 60000.
<result>E</result> | E | {
"A": "30000",
"B": "50000",
"C": "40000",
"D": "20000",
"E": "60000"
} | P and Q invested in a business. The profit earned was divided in the ratio 2 : 3. If P invested Rs 40000, the amount invested by Q is |
aqua_rat__dBuOB2yw5G9J4xo4 | The speed of a boat in upstream is 70 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?
Pick one
A) 5 kmph B) 13 kmph C) 65 kmph D) 55 kmph E) 14 kmph | Speed of the boat in still water = (70+80)/2=
<gadget id="calculator">(70+80)/2</gadget>
<output>75</output>
75 kmph. Speed of the stream= (80-70)/2=
<gadget id="calculator">(80-70)/2</gadget>
<output>5</output>
5 kmph. 5 kmphnswer: 5 kmph
<result>A</result> | A | {
"A": "5 kmph",
"B": "13 kmph",
"C": "65 kmph",
"D": "55 kmph",
"E": "14 kmph"
} | The speed of a boat in upstream is 70 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream? |
aqua_rat__JVuDWlUcLXGDR4xh | Square X is inscribed in circle Y. If the perimeter of X is 100, what is the circumference of Y? Choose the correct choice from the following options:
A) 30√ 2π B) 2√ 2π C) 5√ 2π D) 4√ 2π E) 25√ 2π | square forms two right angled triangles. Any time we have a right angle triangle inside a circle, the hypotenuse is the diameter. hypotenuse here = diagonal of the square = 25 sqrt(2) = diameter => radius = 12.5 sqrt(2) Circumference of the circle = 2pi r = 25 pi sqrt(2) Answer is 25√ 2π.
<result>E</result> | E | {
"A": "30√ 2π",
"B": "2√ 2π",
"C": "5√ 2π",
"D": "4√ 2π",
"E": "25√ 2π"
} | Square X is inscribed in circle Y. If the perimeter of X is 100, what is the circumference of Y? |
aqua_rat__wShVbDcYe06O63qo | A painting is painted on a cardboard 19 cm and 14 cm wide, such that there is a margin of 1.5 cm along each of its sides. Find the total area of the margin. Pick one:
A) 80
B) 85
C) 88
D) 90
E) 92 | Length of the cardboard = 19 cm Breadth of the cardboard = 14 cm Area of the cardboard = 19 × 14 cm² = 266 cm² Length of the painting excluding the margin = [19 - (1.5 + 1.5)=
<gadget id="calculator">19 - (1.5 + 1.5)</gadget>
<output>16</output>
16 cm Breadth of the painting excluding the margin= 14 - (1.5 + 1.5)=
<gadget id="calculator">14 - (1.5 + 1.5)</gadget>
<output>11</output>
11 cm Area of the painting excluding the margin= (16 × 11) cm² = 176 cm² Therefore, area of the margin = (266 - 176)=
<gadget id="calculator">(266 - 176)</gadget>
<output>90</output>
90 cm² ANSWER : OPTION 90
<result>D</result> | D | {
"A": "80",
"B": "85",
"C": "88",
"D": "90",
"E": "92"
} | A painting is painted on a cardboard 19 cm and 14 cm wide, such that there is a margin of 1.5 cm along each of its sides. Find the total area of the margin. |
aqua_rat__fny6tgWiqN4Uznwt | When processing flower-nectar into honey bees' extract, a considerable amount of water gets reduced. How much flower-nectar must be processed to yield 1kg of honey, if nectar contains 50% water, and the honey obtained from this nectar contains 30% water?
Choose the correct answer:
A) 1.2 kg B) 1.5 kg C) 1.4 kg D) 1.9 kg E) None of these | Explanation : Flower-nectar contains 50% of non-water part. In honey this non-water part constitutes 70% (100-30). Therefore 0.5 X Amount of flower-nectar = 0.70 X Amount of honey = 0.70 X 1 kg Therefore amount of flower-nectar needed = (0.70/0.51)kg=1.4 kgs Answer : 1.4 kg
<result>C</result> | C | {
"A": "1.2 kg",
"B": "1.5 kg",
"C": "1.4 kg",
"D": "1.9 kg",
"E": "None of these"
} | When processing flower-nectar into honey bees' extract, a considerable amount of water gets reduced. How much flower-nectar must be processed to yield 1kg of honey, if nectar contains 50% water, and the honey obtained from this nectar contains 30% water? |
aqua_rat__Gsat11Gtck6kyRg4 | The variables a and b are non-zero integers W. If a = 2b^3/c, what happens to c when a is halved and b is doubled? Pick:
A) c is not changed. B) c is halved. C) c is doubled. D) c is multiplied by 4. E) c is multiplied by 16. | a=2b^3/c c=2b^3/a when a is halved and b is doubled c=2(2b)^3/(a/2) c=16*2b^3/a Ans. c is multiplied by 16. c is multiplied by 16.
<result>E</result> | E | {
"A": "c is not changed.",
"B": "c is halved.",
"C": "c is doubled.",
"D": "c is multiplied by 4.",
"E": "c is multiplied by 16."
} | The variables a and b are non-zero integers W. If a = 2b^3/c, what happens to c when a is halved and b is doubled? |
aqua_rat__6amCf2wAqJlOC22a | A certain psychologist charges $40 more for the first hour of therapy than for each additional hour. If the total charge to a patient who receives 5 hours of therapy is $375, what is the total charge to a patient who receives only 2 hours of therapy ?
Select the correct option
A) $120 B) $135 C) $150 D) $174 E) $192 | Let the charge for first hour = x+40 then charge for each additional hour = x x+40 + 4x = 375 => 5x = 335 => x = 67 Total charge for patient for 3 hours of therapy = x+40 + x = 2x+40 = 174 $ Answer $174
<result>D</result> | D | {
"A": "$120",
"B": "$135",
"C": "$150",
"D": "$174",
"E": "$192"
} | A certain psychologist charges $40 more for the first hour of therapy than for each additional hour. If the total charge to a patient who receives 5 hours of therapy is $375, what is the total charge to a patient who receives only 2 hours of therapy ? |
aqua_rat__ooAvFeLpT49MejDM | 20% of employees are women with fair hair. 40% of fair-haired employees are women. What percent of employees have fair hair? Choose the correct answer: A) 25 B) 30 C) 50 D) 55 E) 60 | 20% of employees are women with fair hair. 40% of fair-haired employees are women. So, 20% * Employees = 40% * Fair Haired Employees (because both are equal to the number of fair haired women employees) (1/2) * Employees = Fair Haired Employees Answer (50)
<result>C</result> | C | {
"A": "25",
"B": "30",
"C": "50",
"D": "55",
"E": "60"
} | 20% of employees are women with fair hair. 40% of fair-haired employees are women. What percent of employees have fair hair? |
aqua_rat__KQ68RhgBJKxKtkuO | At 11:00 a.m., Tom begins traveling on a certain bike path from Riverdale at a constant rate of 10 mph. If, at 1:00 p.m., Jim begins traveling from Riverdale on the same path at a constant rate of 20 mph, at what time will he catch up to Peter? Choices:
A) 3:00 p.m. B) 4:00 p.m. C) 5:00 p.m. D) 6:00 p.m. E) 7:00 p.m. | By the time Jim starts, Tom has already covered = 2 hr * 10 mph = 20 miles Relative speed = 20- 10=
<gadget id="calculator">20- 10</gadget>
<output>10</output>
10mph To catch up, Jim needs to cover 20 miles which can be covered in= 20/10=
<gadget id="calculator">20/10</gadget>
<output>2</output>
2 hours If Jim leaves at 1 pm, he will catch Tom at 3 pm 3:00 p.m.nswer: 3:00 p.m.
<result>A</result> | A | {
"A": "3:00 p.m.",
"B": "4:00 p.m.",
"C": "5:00 p.m.",
"D": "6:00 p.m.",
"E": "7:00 p.m."
} | At 11:00 a.m., Tom begins traveling on a certain bike path from Riverdale at a constant rate of 10 mph. If, at 1:00 p.m., Jim begins traveling from Riverdale on the same path at a constant rate of 20 mph, at what time will he catch up to Peter? |
aqua_rat__C4UoHnmvkhGpURc8 | Students are in cultural program as follows: music-10, Dance-15, and skits -6. No student is in all three cultural program , but 4 are in both music and Dance, 3 are in both music and skits, and 2 are in Dance and skits.
How many different students are in at least one of the three cultural program? Choose one: A) 34 B) 28 C) 26 D) 22 E) 18 | Total students = M + D + S - (sum of 2-group overlaps) + (all three) Total students = 10 + 15 + 6 - (3 + 4 + 2) + 0=
<gadget id="calculator">10 + 15 + 6 - (3 + 4 + 2) + 0</gadget>
<output>22</output>
22 students. Answer is 22
<result>D</result> | D | {
"A": "34",
"B": "28",
"C": "26",
"D": "22",
"E": "18"
} | Students are in cultural program as follows: music-10, Dance-15, and skits -6. No student is in all three cultural program , but 4 are in both music and Dance, 3 are in both music and skits, and 2 are in Dance and skits.
How many different students are in at least one of the three cultural program? |
aqua_rat__YxzbEL0eY43ECubG | You are distributing vegetable oil. there are 21 bottles in total out of which 7 are full, 7 half empty, 7 empty. the oil has to be distributed among three people. how will you distribute so that each person gets equal number of bottles and the same quantity of oil Choose the correct answer.
A) 1st person : 3 full, 1 half, 3 empty , 2nd person: 3 full, 1 half, 3 empty,, 3rd person : 1 full, 5 half, 1 empty B) 1st person : 1 full, 1 empty ,1half , 2nd person: 3 full, 1 half, 2 empty, 3rd person : 1 full, 2 half, 4 empty C) 1st person : 1 full, 2 half, 3 empty , 2nd person: 3 full, 1 empty , 3 empty, 3rd person : 3 full, 5 half, 2 empty D) 1st person : 1 full, 1 half, 2 empty , 2nd person: 2 full, 1 half, 1 empty, 3rd person : 1 full, 5 half, 2 empty E) None | Correct 1st person : 3 full, 1 half, 3 empty , 2nd person: 3 full, 1 half, 3 empty,, 3rd person : 1 full, 5 half, 1 emptynswer : 1st person : 3 full, 1 half, 3 empty , 2nd person: 3 full, 1 half, 3 empty,, 3rd person : 1 full, 5 half, 1 empty
<result>A</result> | A | {
"A": "1st person : 3 full, 1 half, 3 empty , 2nd person: 3 full, 1 half, 3 empty,, 3rd person : 1 full, 5 half, 1 empty",
"B": "1st person : 1 full, 1 empty ,1half , 2nd person: 3 full, 1 half, 2 empty, 3rd person : 1 full, 2 half, 4 empty",
"C": "1st person : 1 full, 2 half, 3 empty , 2nd person: 3 full, 1 empty , 3 empty, 3rd person : 3 full, 5 half, 2 empty",
"D": "1st person : 1 full, 1 half, 2 empty , 2nd person: 2 full, 1 half, 1 empty, 3rd person : 1 full, 5 half, 2 empty",
"E": "None"
} | You are distributing vegetable oil. there are 21 bottles in total out of which 7 are full, 7 half empty, 7 empty. the oil has to be distributed among three people. how will you distribute so that each person gets equal number of bottles and the same quantity of oil |
aqua_rat__JW9XdTVUV8LhzcbE | If 3x=8y=z, what is x+y, in terms of z? Options:
A) z/2
B) 2z
C) 11z/24
D) 3z/5
E) z/9 | 3x=8y=z x = z/3 and y = z/8 x+y = z/3 + z/8 = 11z/24 Answer is 11z/24
<result>C</result> | C | {
"A": "z/2",
"B": "2z",
"C": "11z/24",
"D": "3z/5",
"E": "z/9"
} | If 3x=8y=z, what is x+y, in terms of z? |
aqua_rat__ea8jXTAQpSgL2QU1 | A man walks from B to C, a distance of x miles, at 10 miles per hour and returns at 15 miles per hour. What is his average speed? Answers
A) 10 mph B) 12 mph C) 8.8 mph D) 8.4 mph E) 14 mph | Total distance covered = 2x Time taken12miles / hour = x/15 hrs Time taken @ 8 miles / hour = x/10 hrs Avg speed = 2x / (x/10 + x/15) = 12 mph Ans is 12 mph
<result>B</result> | B | {
"A": "10 mph",
"B": "12 mph",
"C": "8.8 mph",
"D": "8.4 mph",
"E": "14 mph"
} | A man walks from B to C, a distance of x miles, at 10 miles per hour and returns at 15 miles per hour. What is his average speed? |
aqua_rat__qCDu322jfXBit9re | When x is divided by y, the quotient is z with remainder t. Which of the following is equal to t? Choose the correct option:
A) yz – x B) y/x−z C) x – y – z D) x – yz E) zx – y | (x/y)=z(+t) (18/8)=2(+2) x-yz which is 18-(8*2)=
<gadget id="calculator"> 18-(8*2)</gadget>
<output>2</output>
2 Answer is x – yz
<result>D</result> | D | {
"A": "yz – x",
"B": "y/x−z",
"C": "x – y – z",
"D": "x – yz",
"E": "zx – y"
} | When x is divided by y, the quotient is z with remainder t. Which of the following is equal to t? |
aqua_rat__fRnVgO0ySYKZSQ43 | A list of numbers has six positive integers. Three of those integers are known: 4, 5 and 24 and three of those are unknown: x, y and z. The three unknowns are known to be distinct. It is also known that the mean of the list is 10 and the median lies between 7 and 8 (exclusive). Which of the following CANNOT be the value of any one of the unknowns? Choices:
A) 13 B) 12 C) 11 D) 10 E) 5 | Mean = 10 Therefore sum of the 6 digits = 6*10=
<gadget id="calculator">6*10</gadget>
<output>60</output>
60 -------- (1) The 3 digits are 4,5 & 24 -------------- (2) Now, 7 < median < 8 -> 7 < (sum of 2 digits)/2 < 8 -> 14 < (sum of 2 digits) < 16 Therefore the sum of 2 digits= 15. The 2 digits whose sum is 15 & whose median is b/w 7 & 8 can be : 1. 7, 8, 2. 6, 9, 3. 5, 10, or But as soon as we take 4, 11 -> the series becomes 4,4,5,11,12,24 & 11 pairs up with 5 to give median as 8. Hence the number can't be 11 !! Answer : 11
<result>C</result> | C | {
"A": "13",
"B": "12",
"C": "11",
"D": "10",
"E": "5"
} | A list of numbers has six positive integers. Three of those integers are known: 4, 5 and 24 and three of those are unknown: x, y and z. The three unknowns are known to be distinct. It is also known that the mean of the list is 10 and the median lies between 7 and 8 (exclusive). Which of the following CANNOT be the value of any one of the unknowns? |
aqua_rat__9W3Rc0dzjhnGo3J0 | Find the number of ways of arranging the boy and 12 guests at a circular table so that the boy always sits in a particular seat? Pick one.
A) 3! B) 8! C) 11! D) 12! E) 14! | Ans.(D) Sol. Total number of persons = 13 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 12 places => 12! Ways ... The number of required arrangements = 12! x 1= 12! = 12! ways
<result>D</result> | D | {
"A": "3!",
"B": "8!",
"C": "11!",
"D": "12!",
"E": "14!"
} | Find the number of ways of arranging the boy and 12 guests at a circular table so that the boy always sits in a particular seat? |
aqua_rat__SEmct7A9DiYqwViV | A survey was conducted to find out how many people in a housing colony of 144 residents could swim, dance and drive a car. It was found that the number of people who could not swim was 85, the number of people who could not dance was 100 and that the number of people who could not drive a car was 91. If the number of people who could do at least two of these things, was found to be 37 and the number of people who could do all these things was found to be 6, how many people could not do any of these things? Choose the correct choice from the following answers
A) 28 B) 31 C) 33 D) 35 E) 37 | T=n(A)+n(31)+n(C)-n(Exactly two of the events)-2*n(All 3 Events)+n(None of the events) T=144 n(A)=T-n(A')=144-85=
<gadget id="calculator">144-85</gadget>
<output>59</output>
59 n(31)=T-n(31')=144-100=
<gadget id="calculator">144-100</gadget>
<output>44</output>
44 n(C)=T-n(C')=144-91=
<gadget id="calculator">144-91</gadget>
<output>53</output>
53 n(Exactly two of the events)=n(At least 2 Events)-n(All 3 Events)=37-6=
<gadget id="calculator">37-6</gadget>
<output>31</output>
31 n(All 3 Events)=6 144=59+44+53-31-2*6+n(None of the events) n(None of the events)=144-55-44-53+31+12=31 Ans:31
<result>B</result> | B | {
"A": "28",
"B": "31",
"C": "33",
"D": "35",
"E": "37"
} | A survey was conducted to find out how many people in a housing colony of 144 residents could swim, dance and drive a car. It was found that the number of people who could not swim was 85, the number of people who could not dance was 100 and that the number of people who could not drive a car was 91. If the number of people who could do at least two of these things, was found to be 37 and the number of people who could do all these things was found to be 6, how many people could not do any of these things? |
aqua_rat__1JD2RDAIwoElg3qP | Excluding stoppages, the speed of a train is 54 kmph and including stoppages it is 40 kmph. Of how many minutes does the train stop per hour? Choose the correct choice from the following.
A) A)13.55 B) B)14.55 C) C)15.55 D) D)16.55 E) E)17.55 | Explanation: T = 14/54 * 60 = 15.55 Answer: Option 15.55
<result>C</result> | C | {
"A": "A)13.55",
"B": "B)14.55",
"C": "C)15.55",
"D": "D)16.55",
"E": "E)17.55"
} | Excluding stoppages, the speed of a train is 54 kmph and including stoppages it is 40 kmph. Of how many minutes does the train stop per hour? |
aqua_rat__Jjc0CZmk1h18Tk2S | Rajan borrowed Rs.4000 at 5% p.a compound interest. After 2 years, he repaid Rs.2210 and after 2 more year, the balance with interest. What was the total amount that he paid as interest?
Choices.
A) 635.50 B) 635.58 C) 635.52 D) 635.59 E) 635.51 | 4000 200 ---- I 200 10 ---- II --------------- 4410 2210 -------- 2000 110 ---- III 110 5.50 ---- IV ----------- 2425.50 2210 ----------- 4635.50 4000 ---------- 635.50 635.50nswer: 635.50
<result>A</result> | A | {
"A": "635.50",
"B": "635.58",
"C": "635.52",
"D": "635.59",
"E": "635.51"
} | Rajan borrowed Rs.4000 at 5% p.a compound interest. After 2 years, he repaid Rs.2210 and after 2 more year, the balance with interest. What was the total amount that he paid as interest? |
aqua_rat__hrFDOfhwm1PKSqzG | In a group of ducks and cows, the total number of legs are 28 more than twice the number of heads. Find the total number of cows. Choose the correct choice from the following answers:
A) 14
B) 12
C) 16
D) 8
E) 6 | Explanation : Let the number of ducks be d and number of cows be c Then, total number of legs = 2d + 4c = 2(d + 2c) total number of heads = c + d Given that total number of legs are 28 more than twice the number of heads => 2(d + 2c) = 28 + 2(c + d) => d + 2c = 14 + c + d => 2c = 14 + c => c = 14 i.e., total number of cows = 14 14nswer : 14
<result>A</result> | A | {
"A": "14",
"B": "12",
"C": "16",
"D": "8",
"E": "6"
} | In a group of ducks and cows, the total number of legs are 28 more than twice the number of heads. Find the total number of cows. |
aqua_rat__AtJBbTR8HrbJIBaZ | If i is a positive integer and i^2 is divisible by 12, then the largest positive integer that must divide i ^3 is Choose the correct choice from the following: A) 2^3 B) 2^6 C) 3^3 D) 6^3 E) 12^2 | Since i is an integer so i cannot have a 2 and sqrt 3 (because squaring this will give us a 2^2 and 3 (making the product as 12, and making i^2 as a multiple of 12)) i^2 is divisible by 12 (12 = 2*2*3), So, i should have at least one 2 and one 3 so that i^2 has a 2^2 and two 3 So, i will have a 2 and a 3. Or i will be a multiple of 6 So, largest possible integer than should divide i^3 is 6^3 So, Answer will be 6^3
<result>D</result> | D | {
"A": "2^3",
"B": "2^6",
"C": "3^3",
"D": "6^3",
"E": "12^2"
} | If i is a positive integer and i^2 is divisible by 12, then the largest positive integer that must divide i ^3 is |
aqua_rat__xOIxVCurLdqFkiHU | What is the 4 digit number in which the 1st digit is 1/3 of the second, the 3rd is the sum of the 1st and 2nd, & the last is three times the second? Choose the correct choice from the following answers.
A) 1234 B) 1567 C) 1349 D) 1456 E) 1356 | First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9. First + second = third => we can eliminate 3 & 9 since 3 + 9=
<gadget id="calculator"> 3 + 9</gadget>
<output>12</output>
12. Last is 3 times the second=> we can eliminate option 2 & 6 since 3 * 6=
<gadget id="calculator"> 3 * 6</gadget>
<output>18</output>
18. Hence the number is 1349 1349
<result>C</result> | C | {
"A": "1234",
"B": "1567",
"C": "1349",
"D": "1456",
"E": "1356"
} | What is the 4 digit number in which the 1st digit is 1/3 of the second, the 3rd is the sum of the 1st and 2nd, & the last is three times the second? |
aqua_rat__IJ3uSOakvfHrLCny | A number has exactly 32 factors out of which 4 are not composite. Product of these 4 factors (which are not composite) is 30. How many such numbers D are possible? Choose the correct choice from the following
A) 2
B) 4
C) 6
D) 3
E) Not possible | Firstly , we should note that 1 is NEITHER a prime nor a composite number.The first composite number is 4.Thus, when the problem states that there are 4 factors that are not composite, these nos are 1,2,3,5. Thus, the given number = 2^a*3^b*5^c. Also, (a+1)*(b+1)*(c+1) = 32. We can break down 32 into 3 integers as : 2*2*8 or 4*4*2 Also, the only possible combinations for a,b,c are : 3,3,1 OR 1,1,7. Thus, each combination has 3 possible orders and we have a total D of 6 possibilities. 6.
<result>C</result> | C | {
"A": "2",
"B": "4",
"C": "6",
"D": "3",
"E": "Not possible"
} | A number has exactly 32 factors out of which 4 are not composite. Product of these 4 factors (which are not composite) is 30. How many such numbers D are possible? |
aqua_rat__pydFCB2B0mGCClxZ | Pat, kate and mark charged a total of 180 hours to a certain project . If pat charged twice as much time to the project as kate and 1/3 as much times as mark, how many more hours did mark charge to the project than kate. Choose the correct choice
A) 18 B) 36 C) 72 D) 90 E) 100 | Let Kate charge for x hours, then Pat charged for 2x and Mat - for 6x. So, 2x+6x+x = 180 -total hours charged for, x= 20. Mat charged 6x-x or 5x for more hours than kate, or for 100 hours . 100 is correct
<result>E</result> | E | {
"A": "18",
"B": "36",
"C": "72",
"D": "90",
"E": "100"
} | Pat, kate and mark charged a total of 180 hours to a certain project . If pat charged twice as much time to the project as kate and 1/3 as much times as mark, how many more hours did mark charge to the project than kate. |
aqua_rat__8CAXwVORJqQ8S8iB | A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 600 m long? Choose the correct option: A) 266 Sec B) 180 Sec C) 776 Sec D) 166 Sec E) 997 Sec | L = S*T S= 1200/120=
<gadget id="calculator">1200/120</gadget>
<output>10</output>
10 m/Sec. Total length (D)= 1800 m T = D/S T = 1800/10=
<gadget id="calculator">1800/10</gadget>
<output>180</output>
180 Sec Answer: 180 Sec
<result>B</result> | B | {
"A": "266 Sec",
"B": "180 Sec",
"C": "776 Sec",
"D": "166 Sec",
"E": "997 Sec"
} | A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 600 m long? |
aqua_rat__N4TyAZWKGIQ3yrzo | A train 210 m in length crosses a telegraph post in 13 seconds. The speed of the train is?
Choose the correct option:
A) 77 kmph
B) 55 kmph
C) 54 kmph
D) 58 kmph
E) 76 kmph | S = 210/13 * 18/5 = 58 kmph Answer: 58 kmph
<result>D</result> | D | {
"A": "77 kmph",
"B": "55 kmph",
"C": "54 kmph",
"D": "58 kmph",
"E": "76 kmph"
} | A train 210 m in length crosses a telegraph post in 13 seconds. The speed of the train is? |
aqua_rat__cbtAb750i9ACWhwZ | From January 1, 1991, to January 1, 1993, the number of people enrolled in health maintenance organizations increased by 30 percent. The enrollment on January 1, 1993, was 45 million. How many million people, to the nearest million, were enrolled in health maintenance organizations on January 1, 1991 ? Select the correct option:
A) 35
B) 39
C) 40
D) 41
E) 42 | 1.30x=45 --> 13/10*x=45 --> x=45*10/13=450/13=~35. 35nswer: 35.
<result>A</result> | A | {
"A": "35",
"B": "39",
"C": "40",
"D": "41",
"E": "42"
} | From January 1, 1991, to January 1, 1993, the number of people enrolled in health maintenance organizations increased by 30 percent. The enrollment on January 1, 1993, was 45 million. How many million people, to the nearest million, were enrolled in health maintenance organizations on January 1, 1991 ? |
aqua_rat__QA6acZ3oJJ00Clgt | Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. After how much time will the trains meet?
Select: A) 20/8 sec B) 20/4 sec C) 20/7 sec D) 22/7 sec E) 60/7 sec | They are moving in opposite directions, relative speed is equal to the sum of their speeds. Relative speed = (54 + 72)*5/18 = 7*5=
<gadget id="calculator">7*5</gadget>
<output>35</output>
35 mps. The time required= d/s = 100/35 = 20/7 sec.Answer:20/7 sec
<result>C</result> | C | {
"A": "20/8 sec",
"B": "20/4 sec",
"C": "20/7 sec",
"D": "22/7 sec",
"E": "60/7 sec"
} | Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. After how much time will the trains meet? |
aqua_rat__5XGgAopBtU5ifBS6 | A sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 45 paisa and Z gets 30 paisa. If the share of Y is RS. 36, what is the total amount? Choose the correct choice from the following options:
A) 166
B) 140
C) 178
D) 177
E) 169 | x:y:z = 100:45:30 20:9:6 9 --- 36 35 --- ? => 140 Answer: 140
<result>B</result> | B | {
"A": "166",
"B": "140",
"C": "178",
"D": "177",
"E": "169"
} | A sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 45 paisa and Z gets 30 paisa. If the share of Y is RS. 36, what is the total amount? |
aqua_rat__2qVMCgJmv8ArX0WH | If there are ten positive real numbers n1 < n2 < n3 … < n10, how many triplets of these numbers (n1, n2, n3), (n2, n3, n4) … can be generated such that in each triplet the first number is always less than the second number, and the second number is always less than the third number? Choose the correct answer: A) 45 B) 90 C) 120 D) 180 E) 150 | Three numbers can be selected and arranged out of ten numbers in 10P3 ways=10!/7!=10*9*8. Now this arrangement is restricted to a given condition that first number is always less than the second number, and the second number is always less than the third number. Hence three numbers can be arranged among themselves in 3! ways. Required number of arrangements=(10*9*8)/(3*2)=
<gadget id="calculator">(10*9*8)/(3*2)</gadget>
<output>120</output>
120 ANS:120
<result>C</result> | C | {
"A": "45",
"B": "90",
"C": "120",
"D": "180",
"E": "150"
} | If there are ten positive real numbers n1 < n2 < n3 … < n10, how many triplets of these numbers (n1, n2, n3), (n2, n3, n4) … can be generated such that in each triplet the first number is always less than the second number, and the second number is always less than the third number? |
aqua_rat__CyxoMQEQXZ7p3dHN | A man purchased 3 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets?
Choose the most appropriate option
A) 278 B) 277 C) 278 D) 450 E) 272 | 10 * 150=
<gadget id="calculator">10 * 150</gadget>
<output>1_500</output>
1500 3 * 100 + 5 * 150=
<gadget id="calculator">3 * 100 + 5 * 150</gadget>
<output>1_050</output>
1050 1500 – 1050= 450 Answer:450
<result>D</result> | D | {
"A": "278",
"B": "277",
"C": "278",
"D": "450",
"E": "272"
} | A man purchased 3 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets? |
aqua_rat__xXxU6WeUn1NKcIAz | If a tire rotates at 400 revolutions per minute when the car is traveling 48km/h, what is the circumference of the tire? Choose the correct choice from the following choices: A) 7 meters B) 9 meters C) 8 meters D) 2 meters E) 3 meters | 400 rev / minute = 400 * 60 rev / 60 minutes = 24,000 rev / hour 24,000 * C = 48,000 m : C is the circumference C = 2 meters correct answer 2 meters
<result>D</result> | D | {
"A": "7 meters",
"B": "9 meters",
"C": "8 meters",
"D": "2 meters",
"E": "3 meters"
} | If a tire rotates at 400 revolutions per minute when the car is traveling 48km/h, what is the circumference of the tire? |
aqua_rat__IqOMiPvpoANuHj8u | Anil and Suresh are working on a special assignment. Anil needs 6 hours to type 32 pages on a computer and Suresh needs 5 hours to type 40 pages. If both of them work together on two different computers, how much time is needed to type an assignment of 110 pages? Choose one
A) 7 hour 15 minutes B) 7 hour 30 minutes C) 8 hour 15 minutes D) 8 hour 30 minutes E) 8 hour 45 minutes | Explanation : Pages typed by Anil in 1 hour = 32/6 = 16/3 Pages typed by Suresh in 1 hour = 40/5=
<gadget id="calculator">40/5</gadget>
<output>8</output>
8 Pages typed by Anil and Suresh in 1 hour= 16/3 + 8 = 40/3 Time taken to type 110 pages when Anil and Suresh work together = 110 × 3 /40 = 33/4 = 8 ¼ hours = 8 hour 15 minutes Answer : Option 8 hour 15 minutes
<result>C</result> | C | {
"A": "7 hour 15 minutes",
"B": "7 hour 30 minutes",
"C": "8 hour 15 minutes",
"D": "8 hour 30 minutes",
"E": "8 hour 45 minutes"
} | Anil and Suresh are working on a special assignment. Anil needs 6 hours to type 32 pages on a computer and Suresh needs 5 hours to type 40 pages. If both of them work together on two different computers, how much time is needed to type an assignment of 110 pages? |
aqua_rat__DrN4KbsVEBCzpI26 | When positive integer X is divided by positive integer Y, the remainder is 5.76. If X/Y = 96.12, what is the value of Y? Choose the correct choice from the following answers.
A) 96
B) 75
C) 48
D) 25
E) 12 | When positive integer x is divided by positive integer y, the remainder is 5.76 --> x=qy+5.76; x/y=96.12 --> x=96y+0.12y (so q above equals to 96); 0.12y=5.76 --> y=48. Answer: 48.
<result>C</result> | C | {
"A": "96",
"B": "75",
"C": "48",
"D": "25",
"E": "12"
} | When positive integer X is divided by positive integer Y, the remainder is 5.76. If X/Y = 96.12, what is the value of Y? |
aqua_rat__YA14TuT20xIZeMvF | The sum of 33 consecutive integers is 3333. What is the greatest integer in the set?
Pick:
A) 113 B) 115 C) 117 D) 119 E) 121 | Let x be the first integer in the set, then x+32 is the largest integer. The sum is: x+(x+1)+(x+2)+...+(x+32) = 33x + 32*33/2 = 33(x+16) Then x+16=101 x=85 The largest integer in the set is 85+32=
<gadget id="calculator"> 85+32</gadget>
<output>117</output>
117 The answer is 117.
<result>C</result> | C | {
"A": "113",
"B": "115",
"C": "117",
"D": "119",
"E": "121"
} | The sum of 33 consecutive integers is 3333. What is the greatest integer in the set? |
aqua_rat__GhndU8FWaO5qLXPl | Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 2/3 were basic and the rest were deluxe. If it takes 1.3 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos? Choose the correct choice from the following answers:
A) 7/17
B) 13/33
C) 7/15
D) 17/35
E) 1/2 | The easiest way for me is to plug in numbers. Let the number of basic stereos produced be 40, and number of delux stereos produced be 20. Total of 60 stereos. If it takes an hour to produce a basic stereo then it will take 1.3 hours to produce a deluxe stereo. 40 basic stereos = 40 hours. 20 delux stereos = 26 hours. Total hours = 66. Then the fraction would be 26/66 = 13/33. Therefore answer 13/33 13/33.
<result>B</result> | B | {
"A": "7/17",
"B": "13/33",
"C": "7/15",
"D": "17/35",
"E": "1/2"
} | Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 2/3 were basic and the rest were deluxe. If it takes 1.3 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos? |
aqua_rat__ntPUkbT8Nwm7beYa | A profit of Rs. 1000 is divided between X and Y in the ratio of 1/2:1/3 . What is the difference between their profit shares ? Answers: A) s. 200 B) s. 100 C) s. 300 D) s. 50 E) s. 90 | A profit of Rs. 1000 is divided between X and Y in the ratio of 1/2 : 1/3 or 3:2. so profits are 600 and 400. difference in profit share = 600-400=
<gadget id="calculator">600-400</gadget>
<output>200</output>
200 s. 200NSWER:s. 200
<result>A</result> | A | {
"A": "s. 200",
"B": "s. 100",
"C": "s. 300",
"D": "s. 50",
"E": "s. 90"
} | A profit of Rs. 1000 is divided between X and Y in the ratio of 1/2:1/3 . What is the difference between their profit shares ? |
aqua_rat__hZo2lkXPGCGoUvED | A store raised the price of an item by exactly 30 percent. Which of the following could NOT be the resulting price of the item? Choose the correct option.
A) 19.5 B) 195 C) 325 D) 168 E) 18.2 | If it raised the value by 30% then the resulting price is 1.3 times the original price. So the final answer has to be a multiple of 1.3. Check the answers. 19.5 - Yes 195 - Yes 325 - Yes 168 - No 18.2 - Yes Answer : 168
<result>D</result> | D | {
"A": "19.5",
"B": "195",
"C": "325",
"D": "168",
"E": "18.2"
} | A store raised the price of an item by exactly 30 percent. Which of the following could NOT be the resulting price of the item? |
aqua_rat__5vhSSpwG9CckAZkU | A man invested Rs. 14,400 in Rs. 100 shares of a company at 20% premium.If the company declares 8% dividend at the end of the year,then how much does he get ? Choices:
A) Rs. 500 B) Rs. 600 C) Rs. 960 D) Rs. 720 E) None | Solution Number of shares = (14400/120)=
<gadget id="calculator">(14400/120)</gadget>
<output>120</output>
120. Face value= Rs. (100x120 ) = Rs. 12000. Annual income = Rs.(8/100x12000) = Rs. 960. Answer Rs. 960
<result>C</result> | C | {
"A": "Rs. 500",
"B": "Rs. 600",
"C": "Rs. 960",
"D": "Rs. 720",
"E": "None"
} | A man invested Rs. 14,400 in Rs. 100 shares of a company at 20% premium.If the company declares 8% dividend at the end of the year,then how much does he get ? |
aqua_rat__b1ZA42AgEw8UcuUl | Of the following, which is the closest approximation of (50.2*0.49)/199.8 ?
Choose the correct choice from the following options:
A) 0.121 B) 0.125 C) 0.122 D) 0.123 E) 0.124 | Ans: For approximation (50.2$ \times $0.49)/199.8 can be taken as 50$ \times $0.5/200 = 25/200 = 1/8=
<gadget id="calculator">1/8</gadget>
<output>1/8 = around 0.125</output>
0.125 Answer:0.125
<result>B</result> | B | {
"A": "0.121",
"B": "0.125",
"C": "0.122",
"D": "0.123",
"E": "0.124"
} | Of the following, which is the closest approximation of (50.2*0.49)/199.8 ? |
aqua_rat__DtDL9oXfswTbUOnO | At a dinner party, 5 people are to be seated around a circular table. 2 seating arrangements are considered different only when the positions of the people are different relative to each other. what is the total number T of different possible seating arrangements for the group? Choose one.
A) 5 B) 10 C) 24 D) 32 E) 120 | 24ircular arrangements= (n-1)! Hence (4!) = 24=T Answer is 24
<result>C</result> | C | {
"A": "5",
"B": "10",
"C": "24",
"D": "32",
"E": "120"
} | At a dinner party, 5 people are to be seated around a circular table. 2 seating arrangements are considered different only when the positions of the people are different relative to each other. what is the total number T of different possible seating arrangements for the group? |
aqua_rat__Q70wiJiXvnkRvTyL | A trader mixes 80 kg of tea at 15 per kg with 20 kg of tea at cost price of 20 per kg. In order to earn a profit of 35%, what should be the sale price of the mixed tea? Choose the correct choice from the following answers:
A) 23.75 B) 21.6 C) 20 D) 19.2 E) None of these | C.P. of mixture = 80×15+20×20 /80+20=16 ∴ S.P. = (100+35)/100×16=21.6 Answer 21.6
<result>B</result> | B | {
"A": "23.75",
"B": "21.6",
"C": "20",
"D": "19.2",
"E": "None of these"
} | A trader mixes 80 kg of tea at 15 per kg with 20 kg of tea at cost price of 20 per kg. In order to earn a profit of 35%, what should be the sale price of the mixed tea? |
aqua_rat__rEXAnBy02kEFkmOX | A train 125 m long passes a man, running at 8 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
Choose one
A) 36 B) 53 C) 88 D) 66 E) 22 | Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 8) km/hr. x - 8 = 45 ==> x = 53 km/hr. Answer:53
<result>B</result> | B | {
"A": "36",
"B": "53",
"C": "88",
"D": "66",
"E": "22"
} | A train 125 m long passes a man, running at 8 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is? |
aqua_rat__uUpKmMCP8r9xnFta | 2 pipes A and B can separately fill a cistern in 10 and 15 mins respectively. A person opens both the pipes together when the cistern should have beenwas full he finds the waste pipe open. He then closes the waste pipe and in another 4mins the cistern was full. In what time can the waste pipe empty the cistern when fill? Select the correct option:
A) 6
B) 8
C) 9
D) 10
E) 12 | 1/10 + 1/15 = 1/6 * 4 = 2/3 1 - 2/3 = 1/3 1/10 + 1/15 - 1/x = 1/3 x = 8 8
<result>B</result> | B | {
"A": "6",
"B": "8",
"C": "9",
"D": "10",
"E": "12"
} | 2 pipes A and B can separately fill a cistern in 10 and 15 mins respectively. A person opens both the pipes together when the cistern should have beenwas full he finds the waste pipe open. He then closes the waste pipe and in another 4mins the cistern was full. In what time can the waste pipe empty the cistern when fill? |
aqua_rat__jjT7IO8bmmyj0pB4 | An atom's atomic number is determined by the number of: Choose the correct choice from the following answers: A) neutrons minus protons B) protons C) electrons D) neutrons E) WW2 | protons Answer:protons
<result>B</result> | B | {
"A": "neutrons minus protons",
"B": "protons",
"C": "electrons",
"D": "neutrons",
"E": "WW2"
} | An atom's atomic number is determined by the number of: |