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NLP Centre, Faculty of Informatics, Masaryk University 14

aqua_rat__EJdAT1XUiaHXkHyH

In how many ways can the letters of the word CAVERN be arranged in a row so that the vowels appear in alphabetic order? Choose the correct answer A) 360 B) 720 C) 620 D) 180 E) 36

Two letters can be arranged in 2! ways. only one combination EIU is required. 6 letters can be arranged in 6! ways. thus 6!/ 2! * 1 = 360. 360 <result>A</result>

A

In how many ways can the letters of the word CAVERN be arranged in a row so that the vowels appear in alphabetic order?

aqua_rat__g1XwI27PSAO4vQM0

If two letters are chosen at random (without replacement) from the word DANCE, what is the probability that none of the letters are vowels? Options A) 1/5 B) 2/5 C) 3/10 D) 7/20 E) 11/30

The number of ways to choose two letters is 5C2 = 10 The number of ways to choose two consonants is 3C2 = 3. P(no vowels) = 3/10 The answer is 3/10. <result>C</result>

C

If two letters are chosen at random (without replacement) from the word DANCE, what is the probability that none of the letters are vowels?

aqua_rat__UNepl5RyyaJTD3SR

A train running at the speed of 60 km/hr crosses a pole in 15 seconds. Find the length of the train. Choose the correct choice from the following choices: A) 150 m B) 145 m C) 240 m D) 135 m E) 250 m

Speed = 60*(5/18) m/sec = 50/3 m/sec Length of Train (Distance) = Speed * Time (50/3) * 15= <gadget id="calculator"> (50/3) * 15</gadget> <output>250</output> 250 meter ANSW250 mR: 250 m <result>E</result>

E

A train running at the speed of 60 km/hr crosses a pole in 15 seconds. Find the length of the train.

aqua_rat__HVVXEKglS4FvBvPA

Mrs. Rodger got a weekly raise of $147. If she gets paid every other week, write an integer describing how the raise will affect her paycheck. Choose the most appropriate option A) $140 B) $141 C) $142 D) $147 E) $145

Let the 1st paycheck be x (integer). Mrs. Rodger got a weekly raise of $ 147. So after completing the 1st week she will get $ (x+147). Similarly after completing the 2nd week she will get $ (x + 147) + $ 147. = $ (x + 147 + 147) = $ (x + 294) So in this way end of every week her salary will increase by $ 147. correct answer $147)$147 <result>D</result>

D

Mrs. Rodger got a weekly raise of $147. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.

aqua_rat__CqjOPsqz7BnotfkP

Calculate how many seconds it will take for 4 bells to toll together again, given that they begin to toll together respectively at the intervals of 5, 6, 10 and 12 seconds. ? Options: A) 61 B) 60 C) 79 D) 70 E) 78

LCM of 5, 6, 10 and 12 is 60 LCM=60 ANSWER:60 <result>B</result>

B

Calculate how many seconds it will take for 4 bells to toll together again, given that they begin to toll together respectively at the intervals of 5, 6, 10 and 12 seconds. ?

aqua_rat__vUCa1W3j0xDA43zZ

In a certain archery competition, points were awarded as follows: the first place winner receives 11 points, the second place winner receives 7 points, the third place winner receives 5 points and the fourth place winner receives 2 points. No other points are awarded. John participated several times in the competition and finished first, second, third, or fourth each time. The product of all the points he received was 38500. How many times did he participate in the competition? Choose the most appropriate option: A) 6 B) 7 C) 8 D) 9 E) 10

38500 = 2*2*5*5*5*7*11 John participated 7 times. The answer is 7. <result>B</result>

B

In a certain archery competition, points were awarded as follows: the first place winner receives 11 points, the second place winner receives 7 points, the third place winner receives 5 points and the fourth place winner receives 2 points. No other points are awarded. John participated several times in the competition and finished first, second, third, or fourth each time. The product of all the points he received was 38500. How many times did he participate in the competition?

aqua_rat__OyyOfpJhxMovIXyg

What is the area of a square field whose diagonal of length 22 m? Choose one: A) 300 sq m B) 220 sq m C) 200 sq m D) 400 sq m E) 800 sq m

d2/2 = (22 * 22)/2 = 220 ANSWER:220 sq m <result>B</result>

B

What is the area of a square field whose diagonal of length 22 m?

aqua_rat__aO2MfmDnBPffovbr

Two cars are traveling towards each other. If car A is traveling at a speed of 50 mph and car B is traveling 12% slower, how much time will it take the cars to meet if the initial distance between the two is 825 miles? Choose the correct choice from the following answers: A) Six hours and 30 minutes. B) Seven hours and 30 minutes. C) Eight hours and 20 minutes. D) Nine hours and 15 minutes. E) Ten hours and 20 minutes.

Speed of second train= 50*88/100= <gadget id="calculator">50*88/100</gadget> <output>44</output> 44 Time= toral distance /total speed 825/ (50+44)= 825/94= 8.___ Eight hours and 20 minutes. is the answer <result>C</result>

C

Two cars are traveling towards each other. If car A is traveling at a speed of 50 mph and car B is traveling 12% slower, how much time will it take the cars to meet if the initial distance between the two is 825 miles?

aqua_rat__CZSEcn3UA1kQwa2T

The cost of 2 chairs and 3 tables is Rs.1700. The cost of 3 chairs and 2 tables is Rs.1200. The cost of each table is more than that of each chair by? Answers: A) 228 B) 287 C) 277 D) 188 E) 500

500xplanation: 2C + 3T = 1700 --- (1) 3C + 2T = 1200 --- (2) Subtracting 2nd from 1st, we get -C + T = 500 =&gt; T - C = 500 Answer:500 <result>E</result>

E

The cost of 2 chairs and 3 tables is Rs.1700. The cost of 3 chairs and 2 tables is Rs.1200. The cost of each table is more than that of each chair by?

aqua_rat__dLzLNfg3HPYoHw89

Trapezoid JKLM in the x-y plane has coordinates J = (–2, –3), K = (–2, 1), L = (6, 7), and M = (6, –3). What is its perimeter? Choose the correct answer: A) 32 B) 36 C) 38 D) 40 E) (F) 42

JK = 4 LM = 10 KL =using distance formula 10 JM = using distance formula 8 Sum of all is 32 32 <result>A</result>

A

Trapezoid JKLM in the x-y plane has coordinates J = (–2, –3), K = (–2, 1), L = (6, 7), and M = (6, –3). What is its perimeter?

aqua_rat__A4QaIl80O4Y7GLmJ

If 6 (A's capital) = 8 (B's capital) = 16 (C's capital). Then the ratio of their capitals is? Choose the correct choice A) 8:15:16 B) 8:15:68 C) 8:6:3 D) 20:15:11 E) 20:15:19

6A = 8B = 16 8:6:3 A:B:8:6:3 = 1/6:1/8:1/16 = 8:6:3 Answer: 8:6:3 <result>C</result>

C

If 6 (A's capital) = 8 (B's capital) = 16 (C's capital). Then the ratio of their capitals is?

aqua_rat__KFw40nUYarcnCyPj

How many C ways can you group 3 people from 4 sets of twins if no two people from the same set of twins can be chosen? Choices: A) 3 B) 16 C) 28 D) 32 E) 56

Ways to select 3 people from 8 people (4 twins x 2) = 8C3 = 56 Ways to select 1 twin + 1 people = 4C1*6C1 = 24 Ways to select a group 3 people from 4 sets of twins if no two people from the same set of twins can be chosen C = 56 - 24= <gadget id="calculator">56 - 24</gadget> <output>32</output> 32 Ans: 32 <result>D</result>

D

How many C ways can you group 3 people from 4 sets of twins if no two people from the same set of twins can be chosen?

aqua_rat__Jz4bBVkJfwIUVUcu

The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 8 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each? Options: A) s.4529 B) s.4586 C) s.7248 D) s.4530 E) s.4528

Area of the four walls = 2h(l + b) Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft. Total cost = 906 * 8 =Rs.7248 Answer: s.7248 <result>C</result>

C

The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 8 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?

aqua_rat__U0aiEp1PrUWzRd5J

In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is? Choose the correct choice from the following choices: A) 1 hr B) 2 hr C) 6 hr D) 8 hr E) 7 hr

Let the duration of the flight be x hours. Then, 600/x - 600/(x + 1/2) = 200 x(2x + 1) = 3 2x2 + x - 3 (2 + 1)= <gadget id="calculator"> (2 + 1)</gadget> <output>3</output> 3 2x2 + x - 3= 0 (2x + 3)(x - 1) = 0 x = 1 hr. 1 hrnswer: 1 hr <result>A</result>

A

In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is?

aqua_rat__yzTMnMYkawZAJOIY

What is the next number in the sequence. 15 29 56 108 208 ? Choices: A) 450 B) 400 C) 300 D) 500 E) 580

400 400 Explanation: 400egins with 15 2*15-1= <gadget id="calculator">2*15-1</gadget> <output>29</output> &gt; 29 2*29-2= <gadget id="calculator">2*29-2</gadget> <output>56</output> &gt; 56 2*56-4= <gadget id="calculator">2*56-4</gadget> <output>108</output> &gt; 108 2*108-8= <gadget id="calculator">2*108-8</gadget> <output>208</output> &gt; 208 2*208-16= <gadget id="calculator">2*208-16</gadget> <output>400</output> &gt; 400 <result>B</result>

B

What is the next number in the sequence. 15 29 56 108 208 ?

aqua_rat__ND6nbip2WmeOdhTk

There is a 10% chance that Tigers will not win at all during the whole season. There is a 90% chance that Federer will not play at all in the whole season. What is the greatest possible probability that the Tigers will win and Federer will play during the season? Choose the correct answer A) A)55% B) B)60% C) C)70% D) D)72% E) E)10%

There is a 10% chance that Tigers will not win at all during the whole season We can infer that there is 90% chance Tigers will win . Similarly There is a 90% chance that Federer will not play at all in the whole season We can also infer that there is 10% chance that Federer will play. Answer 10% <result>E</result>

E

There is a 10% chance that Tigers will not win at all during the whole season. There is a 90% chance that Federer will not play at all in the whole season. What is the greatest possible probability that the Tigers will win and Federer will play during the season?

aqua_rat__etYzYiQGQuupwlJz

At an upscale fast-food restaurant, Shin can buy 3 burgers, 7 shakes, and one cola for $120. At the same place it would cost $160.50 for 4 burgers, 10 shakes, and one cola. How much would it cost for a meal of one burger, one shake, and one cola? Select: A) $21 B) $27 C) $31 D) $39 E) It cannot be determined

let's suppose that the price of a burger is BB, of a shake - SS and that of a cola is CC. We can then construct these equations: 3B+7S+C=120 4B+10S+C=160.5 Subtracting the first equation from the second gives us B+3S=40.5 Now if we subtract the new equation two times from first or 3 times from second we will get B+S+C=39. In any case, there is no necessity to know each item's price, just the sum. Answer: $39 <result>D</result>

D

At an upscale fast-food restaurant, Shin can buy 3 burgers, 7 shakes, and one cola for $120. At the same place it would cost $160.50 for 4 burgers, 10 shakes, and one cola. How much would it cost for a meal of one burger, one shake, and one cola?

aqua_rat__hRcnkjDtoyqctydj

A sum of Rs. 725 is lent in the beginning of a year at a certain rate of interest. After 8 months, a sum of Rs. 362.50 more is lent but at the rate twice the former. At the end of the year, Rs. 33.50 is earned as interest from both the loans. What was the original rate of interest? Choose the correct choice: A) 3.6% B) 4.5% C) 5% D) 6% E) None of these

(725 x R x 1 /100) + (362.50 x 2R x 1 /100 x 3 ) = 33.50 (725 x 1 /100 + 362.50 x 2 /100 x 3) R = 33.50 (725 x 3 + 725 / 100 x 3) R = 33.50 (2175 + 725 ) R = 33.50 x 100 x 3 (2900) R = 10050 R = 10050/2900 R = 3.46% answer :None of these <result>E</result>

E

A sum of Rs. 725 is lent in the beginning of a year at a certain rate of interest. After 8 months, a sum of Rs. 362.50 more is lent but at the rate twice the former. At the end of the year, Rs. 33.50 is earned as interest from both the loans. What was the original rate of interest?

aqua_rat__1r9oSBpAEx5uld0O

A boat can move upstream at 25 kmph and downstream at 39 kmph, then the speed of the current is? Select: A) 5 B) 6 C) 7 D) 54 E) 3

US = 25 DS = 39 M = (39 - 25)/2= <gadget id="calculator">(39 - 25)/2</gadget> <output>7</output> 7.Answer:7 <result>C</result>

C

A boat can move upstream at 25 kmph and downstream at 39 kmph, then the speed of the current is?

aqua_rat__QdONkPblYhnwyAs1

If x% of y is 100 and y% of z is 200, then find the relation between x and z. Pick one. A) z = x B) 2z = x C) z = 2x D) z =x2 E) None of above

Explanation: It is , y% of z = 2(x% of y) =&gt; yz/100 = 2xy/100 =&gt; z = 2x Answer: Option z = 2x <result>C</result>

C

If x% of y is 100 and y% of z is 200, then find the relation between x and z.

aqua_rat__x9EtkuVfJGLucOyF

The present ages of Reena and Usha are 24 and 36 yr. respectively . What was the ratio between the ages of Usha and Reena respectively 8 yr ago ? Answers: A) 7 : 4 B) 4 : 7 C) 11 : 8 D) 8 : 11 E) 9:12

Required ratio = (36 - 8)/(24 - 8) = 28/16 = 7 : 4 7 : 4NSWER :7 : 4 <result>A</result>

A

The present ages of Reena and Usha are 24 and 36 yr. respectively . What was the ratio between the ages of Usha and Reena respectively 8 yr ago ?

aqua_rat__BZr6sLRkW3jlVSK8

At a certain paint store forest green is made by mixing 4 parts blue paint with 3 parts yellow paint.Verdant green is made by mixing 4 parts yellow paint with 3 parts blue paint.How many liters of yellow paint must be added to 7 liters of forest green to change it to Verdant green? Choose one: A) 5/3 B) 2/7 C) 7/3 D) 1/7 E) 1/4

7 liter of Forset green have 4 liter of blue and 3 liter of yellow Suppose we add x liter of yellow to make it a verdant green so the ratio of blue to yellow in verdant green is ¾ so the equation is Blue/yellow =4/(3+x) = ¾ 9+3x=16 =&gt; x =7/3 Answer : 7/3 <result>C</result>

C

At a certain paint store forest green is made by mixing 4 parts blue paint with 3 parts yellow paint.Verdant green is made by mixing 4 parts yellow paint with 3 parts blue paint.How many liters of yellow paint must be added to 7 liters of forest green to change it to Verdant green?

aqua_rat__I33xpuUbg2HUQMZ2

If a = (1/5)b and c = 9a, then which of the following represents the average (arithmetic mean) of a, b, and c, in terms of a ? Choices A) a + 4 B) (11/3)a C) 4a D) 5a E) (7 1/4)a

Official Answer: D The average of the three variables isa + b + c/3. However, we need to solve in terms of a, which means we must convert b and c into something in terms of a. Were told that a =1/5b, which is equivalent to b = 5a. We can plug that in and simplify the average to:a + 5a + c/3 We also know that c = 9a, which we can plug directly into the average expression: a + 5a + 9a/3 = 15a/3 = 5a, choice5a.15 /3= <gadget id="calculator">15 /3</gadget> <output>5</output> 5a, choice5a. <result>D</result>

D

If a = (1/5)b and c = 9a, then which of the following represents the average (arithmetic mean) of a, b, and c, in terms of a ?

aqua_rat__urwZZMB75ZqzksYl

By selling 50 meters of cloth. I gain the selling price of 15 meters. Find the gain percent? Choose the correct choice from the following choices: A) 42 6/8% B) 42 5/7% C) 49 6/7% D) 42 6/7% E) 42 1/7%

SP = CP + g 50 SP = 50 CP + 15 SP 35 SP = 50 CP 35 --- 15 CP gain 100 --- ? =&gt; 42 6/7% Answer:42 6/7% <result>D</result>

D

By selling 50 meters of cloth. I gain the selling price of 15 meters. Find the gain percent?

aqua_rat__ApfmmWjJpwvkc6yb

The average age of the mother and her six children is 9 years which is reduced by 5 years if the age of the mother is excluded. How old is the mother? Answers: A) 39 B) 41 C) 42 D) 43 E) 44

Total age of mother and 6 children = avg x n = 9 x (6+1)= 63 If mother is excluded new average is (9 - 5)= <gadget id="calculator"> (9 - 5)</gadget> <output>4</output> 4 so for 6 children= 6 x 4 =24 so mother's age is 63 - 24= <gadget id="calculator"> 63 - 24</gadget> <output>39</output> 39 39nswer: Option 39 <result>A</result>

A

The average age of the mother and her six children is 9 years which is reduced by 5 years if the age of the mother is excluded. How old is the mother?

aqua_rat__Js6ZDIiejLpaD7F6

In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the rate in the remaining 40 overs to reach the target of 282 runs? Pick one A) 6.25 B) 6.27 C) 6.23 D) 6.29 E) 6.39

Required run rate = [282 - (3.2 * 10)]/40 = 250/40= <gadget id="calculator">250/40</gadget> <output>25/4 = around 6.25</output> 6.25' 6.25nswer:6.25 <result>A</result>

A

In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the rate in the remaining 40 overs to reach the target of 282 runs?

aqua_rat__q32CKUV7jft1RGb7

A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire? Choose the correct choice from the following choices. A) 45 cm B) 18 cm C) 90 cm D) 180 cm E) None of these

Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere. π(16)2 * h = (4/3)π (12)3 =&gt; h = 9 cm ANSWNone of theseR:None of these <result>E</result>

E

A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire?

aqua_rat__CkF6RoLrMw9pGdQr

The average of 50 numbers id 20. If two numbers, namely 45 and 55 are discarded, the average of the remaining numbers is : Options. A) 22.75 B) 33.25 C) 22.25 D) 11.75 E) 18.75

18.75xplanation: Total of 50 numbers = (50×20)=1000 Total of 48 numbers =(1000-(45+55)]=900 Required average = 900/48= <gadget id="calculator">900/48</gadget> <output>75/4 = around 18.75</output> 18.75 Answer:18.75 <result>E</result>

E

The average of 50 numbers id 20. If two numbers, namely 45 and 55 are discarded, the average of the remaining numbers is :

aqua_rat__n0wTS2OGTWahJ2Mb

John bought 2 shares and sold them for $90 each. If he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share, then on the sale of both shares John had Choose the correct choice from the following choices: A) a profit of $10 B) a profit of $8 C) a loss of $8 D) a loss of $20 E) neither a profit nor a loss

$ Profit of the share sold at 20% profit = 120-90 20-? $10 profit on the sale of 1 share. $ Loss of the share sold at 20% loss= 80-90 20-? $30 loss on the sale of 1 share. 10-30=Loss of $20 Answer: a loss of $20 <result>D</result>

D

John bought 2 shares and sold them for $90 each. If he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share, then on the sale of both shares John had

aqua_rat__8SbAOrFYSDNkG8nD

The manufacturing cost of a shoe is Rs.220 and the transportation lost is Rs.500 for 100 shoes. What will be the selling price if it is sold at 20% gains Choose the correct choice from the following answers: A) s 222 B) s 216 C) s 220 D) s 270 E) s 217

Explanation : Total cost of a watch = 220 + (500/100)= <gadget id="calculator">220 + (500/100)</gadget> <output>225</output> 225. Gain= 20% =&gt; SP = 1.2CP = 1.2 X 225 = 270 Answer : s 270 <result>D</result>

D

The manufacturing cost of a shoe is Rs.220 and the transportation lost is Rs.500 for 100 shoes. What will be the selling price if it is sold at 20% gains

aqua_rat__g2U82ukYEQQvg3Ii

Machine Z takes 2 more hours than machine B to make 20 widgets. If working together, the machines can make 25 widgets in 3 hours, how long will it take machine Z to make 40 widgets? Answers: A) 5 B) 6 C) 8 D) 10 E) 12

i approached this one by plugging in numbers...started with C. if 40 are made in 8 hours, then 20 are made in 4 hours. so time of Z is 4, and time of B is 2. rate together: 20/4 + 20/2 = 5+10= <gadget id="calculator">5+10</gadget> <output>15</output> 15. so in 1 hour, together make 15 widgets. in 3 hours= 45. way too much. we can eliminate right away C, B, and A - because B and A reduces the time - the total # of widgets made will be even higher. now between D and E -&gt; try only one ..if it doesn't work, then the other one is the answer. i picked E: 12h to make 40 widgets, and 6 hours to make 20. this is the time of Z. time of B=4 hours. 20/6 + 20/4 = 10/3 + 20/4 find LCM of 3 and 4 = 12. multiply first by 4, and second by 3: 40+60/12 = 100/12 divide by 4: 25/3 so this is the rate given. 12 is the correct answer <result>E</result>

E

Machine Z takes 2 more hours than machine B to make 20 widgets. If working together, the machines can make 25 widgets in 3 hours, how long will it take machine Z to make 40 widgets?

aqua_rat__0QQR4iE6iJtIhO3Z

In how many different number of ways 8 men and 5 women can sit on a shopa which can accommodate persons? Pick A) 170 B) 180 C) 200 D) 1716 E) 220

Option '1716' 13p3 = 13 × 12 × 11 = 1716 <result>D</result>

D

In how many different number of ways 8 men and 5 women can sit on a shopa which can accommodate persons?

aqua_rat__8yCoqNZVz0tXsnuR

A certain deck of cards contains 2 blue cards, 2 red cards, 2 yellow cards, and 2 green cards. If two cards are randomly drawn from the deck, what is the probability that they will both be not red? Pick A) 15/28 B) 1/4 C) 9/16 D) 1/32 E) 1/16

The question asks they will both be not red. Considering that these are draws without replacement there are following possibilities : draw 1, draw 2 ===== ===== 1) Not Red, Red; 2) Red, Not Red; 3) Red, Red; 4) Not Red, not Red; The answer has to be either P(4) OR all exclusion of the 3 previous conditions i.e. 1- [P(1) + P(2) + P(3)] =&gt; neither of the draws are Red P(4) = 6/8*5/7=15/28 1- [P(1) + P(2) + P(3)] = 1 - [ (6/8 * 2/7) + (2/8*6/7) + (2/8*1/7)] = 1 - [26/8*7] = 1 - [13/28] = 15/28 15/28 <result>A</result>

A

A certain deck of cards contains 2 blue cards, 2 red cards, 2 yellow cards, and 2 green cards. If two cards are randomly drawn from the deck, what is the probability that they will both be not red?

aqua_rat__zLjrPfmTVpSszPh5

Two bus tickets from city A to B and three tickets from city A to C cost Rs. 462 but three tickets from city A to B and two tickets from city A to C cost Rs. 438. What are the fares for cities B and C from A ? Choose the correct choice from the following choices: A) s. 4, Rs. 23 B) s. 13, Rs. 17 C) s. 15, Rs. 14 D) s. 77, Rs. 103 E) s. 78, Rs. 102

If fares for cities B and C from A are x and y respectively, then 2x+3y=462 or 6x+9y= 1386 3x+2y =438 or 6x+4y= 876 subtracting 5y = 510 y= Rs 102 Hence e. Rs. 78, Rs. 102 ANSWs. 78, Rs. 102R:s. 78, Rs. 102 <result>E</result>

E

Two bus tickets from city A to B and three tickets from city A to C cost Rs. 462 but three tickets from city A to B and two tickets from city A to C cost Rs. 438. What are the fares for cities B and C from A ?

aqua_rat__EB57pWSBKgpFNIdb

The cost price of an article is 64% of the marked price. Calculate the gain percent after allowing a discount of 18%? Choose the correct answer: A) 37.5% B) 48% C) 50.5% D) 28.125% E) 56%

Explanation: Let marked price = Rs. 100. Then, C.P. = RS. 64, S.P. = Rs. 82 Gain % = 18/64 * 100= <gadget id="calculator">18/64 * 100</gadget> <output>225/8 = around 28.125</output> 28.125%. Answer: Option 28.125% <result>D</result>

D

The cost price of an article is 64% of the marked price. Calculate the gain percent after allowing a discount of 18%?

aqua_rat__fV27BP19sbf2yRqI

A shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 3.5 a rupee. Find his net profit or loss percent? Answers A) 13.2 % B) 15.2 % C) 14.28 % D) 32 1/3 % E) 33 1/2 %

The total number of mangoes bought by the shopkeeper be 12. If he buys 4 a rupee, his 14.28 %P = 3.5 He selling at 3.5 a rupee, his SP = 4 Profit = SP - 14.28 %P = 4 - 3.5= <gadget id="calculator">4 - 3.5</gadget> <output>0.5</output> 0.5 Profit Percent= 0.5/3.5 * 100 = 14.28 % Answer:14.28 % <result>C</result>

C

A shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 3.5 a rupee. Find his net profit or loss percent?

aqua_rat__lQBxSmplxln8NT90

A positive whole number has factors of 5 and 11. The number MUST be divisible by: I. 55 II. 110 III. 220 Choices. A) I B) II & III C) II D) III * I E) III

55 , 110 is not divisible by 220.But 220 is divisible by 5,11,55,110 So answer is III Answer : III <result>E</result>

E

A positive whole number has factors of 5 and 11. The number MUST be divisible by: I. 55 II. 110 III. 220

aqua_rat__Y0xCPn7KbAW5RRKi

Two cars, one from Austin to Dallas and the other from Dallas to Austin, start simultaneously. After they meet, the cars reach their destinations after 4 hours and 9 hours respectively The ratio of their speeds is Choose the correct choice from the following A) 2 : 3 B) 4 : 3 C) 3 : 6 D) 4 : 5 E) None

Solution Let us name the cars as 2 : 3 and B. = (Car 2 : 3'S speed) : (Car B's speed) =√b : √a = √4 : √9 = 2 : 3 2 : 3nswer 2 : 3 <result>A</result>

A

Two cars, one from Austin to Dallas and the other from Dallas to Austin, start simultaneously. After they meet, the cars reach their destinations after 4 hours and 9 hours respectively The ratio of their speeds is

aqua_rat__VWcId3c18qiToVAR

A scientist has a set of weights {1Kg, 2Kg, 4Kg, 8Kg, 16Kg, 32Kg}. This set is good enough to weight any object having an integral weight between 1Kg and 63Kg (Eg. 19 Kg = 16Kg + 2Kg + 1Kg). If the 4 Kg weight is lost, how many weights between 1Kg & 63Kg can no longer be measured ? Choose the most appropriate option: A) 16 B) 32 C) 48 D) 64 E) 80

Total # of ways to distribute SSEGT among 5 sisters (without restriction) is 5!2!=605!2!=60; The # of ways when the youngest niece gets G is: 4!2!=124!2!=12 (give G to youngest and then distribute SSET among 4 sisters). So, # of ways when youngest niece doesn't get G is: 60−12=4860−12=48. Answer: 48. ANSWER:48 <result>C</result>

C

A scientist has a set of weights {1Kg, 2Kg, 4Kg, 8Kg, 16Kg, 32Kg}. This set is good enough to weight any object having an integral weight between 1Kg and 63Kg (Eg. 19 Kg = 16Kg + 2Kg + 1Kg). If the 4 Kg weight is lost, how many weights between 1Kg & 63Kg can no longer be measured ?

aqua_rat__NhpMIJUmrxrkYhv9

An institute organised a fete and 1/5 of the girls and 1/8 of the boys participated in the same. What fraction of the total number of students took part in the fete ? Choose the correct choice A) 2/13 B) 13/40 C) Data inadequate D) 14/50 E) None of these

Explanation: Data insufficient to solve the question Answer is Data inadequate <result>C</result>

C

An institute organised a fete and 1/5 of the girls and 1/8 of the boys participated in the same. What fraction of the total number of students took part in the fete ?

aqua_rat__WjmNXymKUrngMz74

The profits of QRS company rose 35% from March to April, then dropped 20% from April to May, then rose 50% from May to June. What was the percent increase for the whole quarter, from March to June? Choose the correct option. A) 15% B) 32% C) 40% D) 62% E) 80%

Assume 100 in march , then 135 in April as 35% increase , Then 108 in may as 20% decrease from April , and then 162 in june which is 150% of 108 . So overall increase is from 100 to 162 is 62% Answer 62% <result>D</result>

D

The profits of QRS company rose 35% from March to April, then dropped 20% from April to May, then rose 50% from May to June. What was the percent increase for the whole quarter, from March to June?

aqua_rat__e81OLlkBVx76p3hu

What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit? Choose the correct option: A) 10% B) 30% C) 20% D) 70% E) 45%

D 20% Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69. Number of such number =14 Required percentage =(14x100/70) % = 20%. <result>C</result>

C

What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?

aqua_rat__7mbgpRXfUduuLS1P

What is the dividend. divisor 15, the quotient is 8 and the remainder is 5 Choose the most appropriate option: A) A)145 B) B)148 C) C)150 D) D)125 E) E)158

125 = d * Q + R 125 = 15 * 8 + 5 125 = 120 + 5 125 = 125 Answer : 125 <result>D</result>

D

What is the dividend. divisor 15, the quotient is 8 and the remainder is 5

aqua_rat__dhM3MNrqoDrrVvdK

If 34 men completed 2/5th of a work in 8 days working 9 hours a day. How many more man should be engaged to finish the rest of the work in 6 days working 9 hours a day? Choose the correct answer: A) 100 men B) 101 men C) 102 men D) 103 men E) 104 men

102 men 102 men From the above formula i.e (m1*t1/w1) = (m2*t2/w2) so, (34*8*9/(2/5)) = (x*6*9/(3/5)) so, x = 136 men number of men to be added to finish the work = 136-34= <gadget id="calculator">136-34</gadget> <output>102</output> 102 men <result>C</result>

C

If 34 men completed 2/5th of a work in 8 days working 9 hours a day. How many more man should be engaged to finish the rest of the work in 6 days working 9 hours a day?

aqua_rat__Kdoh8ZeiCzAvArom

If 25% of x is 15 less than 15% of 1500, then x is? Choose the correct answer: A) 720 B) 750 C) 820 D) 840 E) 860

25% of x = x/4 ; 15% of 1500 = 15/100 * 1500= <gadget id="calculator">15/100 * 1500</gadget> <output>225</output> 225 Given that, x/4= 225 - 15 =&gt; x/4 = 210 =&gt; x = 840. ANSWER:840 <result>D</result>

D

If 25% of x is 15 less than 15% of 1500, then x is?

aqua_rat__MHNJPXPEAXfz0uEZ

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 W of generating an odd prime digit is between Choose the correct choice from the following answers: 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 W= 13/24 × 1/3+ = 4+/24 &gt; 1/6 Answer should be B P.s. 3+ denotes a value little greater than 3 . Same for 4+. <result>B</result>

B

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 W of generating an odd prime digit is between

aqua_rat__fJXu9BjucDw1Rjdr

A starts business with a capital of Rs.1200 B and C join with some investments after 3 and 6 months respectively. If the end of a year, the profit is divided in the ratio 2:3:5 respectively. What is B's investment in the business? Pick. A) 2400 B) 2408 C) 2777 D) 29087 E) 27871

1200 * 12: x * 9 = 2:3 x = 2400 2400nswer: a <result>A</result>

A

A starts business with a capital of Rs.1200 B and C join with some investments after 3 and 6 months respectively. If the end of a year, the profit is divided in the ratio 2:3:5 respectively. What is B's investment in the business?

aqua_rat__edUINW4mlM1yYwiC

At a certain amateur bands rock show the ratio of freaks( F) to nerds to geeks is 1:2:3. If these are the only types of people in the crowd, and each person in the crowd has the same chance of yelling rock on!, what are the chances that the next person who yells rock on!will be a geek? Choose the correct choice from the following: A) 1/2 B) 1/3 C) 1/6 D) 1/4 E) 1/8

Another approach is toassign some nice valuesfor the number of freaks, nerds and geeks. Given: the ratio of freaks to nerds to geeks is 1:2:3 So, let's say there is: 1 freak, 2 nerds and3geeks for a TOTAL of6people. P(next person who yellsrock on!is a geek) = (# of geeks in the crowd)/(TOT1/2L # of people in the crowd) =3/6 = 1/2 1/2nswer: 1/2 <result>A</result>

A

At a certain amateur bands rock show the ratio of freaks( F) to nerds to geeks is 1:2:3. If these are the only types of people in the crowd, and each person in the crowd has the same chance of yelling rock on!, what are the chances that the next person who yells rock on!will be a geek?

aqua_rat__q8dSIJZ5ddvObHMt

John is three times as old as Sam. If John will be twice as old as Sam in nine years, how old was Sam two years ago? Choose the correct choice from the following options. A) 2 B) 4 C) 6 D) 8 E) 7

j= 3s after 9 years j +9 = 2(s+9) j= 2s+9 2s +9 = 3s s= 9 two years ago s= 9-2= <gadget id="calculator">9-2</gadget> <output>7</output> 7 7 is the answer <result>E</result>

E

John is three times as old as Sam. If John will be twice as old as Sam in nine years, how old was Sam two years ago?

aqua_rat__6SHpPyIZ5vTacPlI

The sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter? Choose the most appropriate option A) 91.5 cm B) 92.2 cm C) 28.9 cm D) 29.2 cm E) 98.2 cm

Perimeter of the sector = length of the arc + 2(radius) = (135/360 * 2 * 22/7 * 21) + 2(21) = 49.5 + 42= <gadget id="calculator">49.5 + 42</gadget> <output>91.5</output> 91.5 cm 91.5 cmnswer:91.5 cm <result>A</result>

A

The sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter?

aqua_rat__KuICVvMBnfX2znJo

If a dealer wants to earn 50% profit on an article after offering 60% discount to the customer, by what percentage should he increase his marked price to arrive at the label price? Choose the most appropriate option: A) 120% B) 275% C) 250% D) 130% E) 100%

Profit = 50% discount = 60% Required answer = (50+60 / 100-60)*100 = 275 % Answer is 275% <result>B</result>

B

If a dealer wants to earn 50% profit on an article after offering 60% discount to the customer, by what percentage should he increase his marked price to arrive at the label price?

aqua_rat__8aBbonshflgMrqDC

A and B started a business and invested in 4:5 ratio.after 3 month A takes back 1/4 part of his investment and B takes back 1/5 part of his investment.after 10 month there is profit of 76000 rs.calculate the profit share of A. Choose the correct choice from the following answers: A) 35000 B) 43000 C) 33000 D) 46000 E) 38000

let A invested 4x rs. and B invested 5x rs. ratio of A and B investment={(4x*3)+[4x-1/4*4x]*7}:{(5x*3)+[5x-1/5*5x]*7} =(12x+21x):(15x+28x)=33:43. total profit=76000 rs. share profit of A=[76000*33/76]rs.=33000 rs. answer 33000 <result>C</result>

C

A and B started a business and invested in 4:5 ratio.after 3 month A takes back 1/4 part of his investment and B takes back 1/5 part of his investment.after 10 month there is profit of 76000 rs.calculate the profit share of A.

aqua_rat__NKVsnzzhOiso0gHC

If the numbers 19/36, 5/11, 12/25, 6/11, and 8/18 were arranged from least to greatest, which number would be in the middle? Choose the correct choice from the following answers A) 19/36 B) 12/25 C) 6/11 D) 5/11 E) 8/18

All numbers are about 1/2 so you can separate those are bigger from those are smaller: 19/36 bigger than 18/36=1/2 12/25 smaller than 12/24=1/2 6/11 bigger than 6/12=1/2 5/11 smaller than 6/12=1/2 8/18=4/9 smaller than 4/8=1/2 now you have to choose 12/25, 5/11 or 4/9. you compare 4/9 and 5/11: the least common multiple between 9 and 11 is 99---&gt; 44/99 &lt; 45/99 you compare now 5/11 and 12/25: the LCM is 25*11= <gadget id="calculator"> 25*11</gadget> <output>275</output> 275---&gt; 125/275 &lt; 132/275 so answer is 12/25! <result>B</result>

B

If the numbers 19/36, 5/11, 12/25, 6/11, and 8/18 were arranged from least to greatest, which number would be in the middle?

aqua_rat__yCl1ybS8TdoUzSOh

A bag contains nine yellow balls, three white balls and four red balls. In how many ways can two balls be drawn from the bag? Choose the correct choice from the following choices: A) 250 B) 800 C) 740 D) 120 E) 200

Explanation: Total number of balls = 9 + 3 + 4 Two balls can be drawn from 16 balls in 16C2 ways=(16*15/1*2)=120 ways Answer: 120 <result>D</result>

D

A bag contains nine yellow balls, three white balls and four red balls. In how many ways can two balls be drawn from the bag?

aqua_rat__Yi5xMNBAkGXM8EbP

54 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780. The bigger part is Select: A) 24 B) 30 C) 32 D) 34 E) 36

Solution Let the two parts be (54 - x) and x. Then, 10(54-x)+22x=780 = 12x = 240 ‹=›x = 20. Therefore Bigger part = (54-x) = 34. Answer 34 <result>D</result>

D

54 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780. The bigger part is

aqua_rat__67UlEmGOQQUVnnhU

The salary of a typist was at first raised by 10% and then the same was reduced by 5%. If he presently draws Rs.3135.What was his original salary? Choose the correct choice: A) 2277 B) 2999 C) 1000 D) 3000 E) 1971

X * (110/100) * (95/100) = 3135 X * (11/10) * (1/100) = 33 X = 3000 Answer: 3000 <result>D</result>

D

The salary of a typist was at first raised by 10% and then the same was reduced by 5%. If he presently draws Rs.3135.What was his original salary?

aqua_rat__YY6A3znFZrfJnMsh

How many words can be formed using the letters of the word “DRAW”" Select. A) 20 B) 22 C) 24 D) 26 E) 29

There are ‘4’ different letters of the word “DRAW” Number of Permutations taking all the letters at a time = 4P4 4!= 24 24 <result>C</result>

C

How many words can be formed using the letters of the word “DRAW”"

aqua_rat__7O504HEAXdDMuPEO

The length of a rectangular field is 7/5 its width. If the perimeter of the field is 240 meters, what is the width of the field? Choose the most appropriate option: A) 50 B) 60 C) 70 D) 80 E) 90

Let L be the length and W be the width. L = (7/5)W Perimeter: 2L + 2W = 240, 2(7/5)W + 2W = 240 Solve the above equation to find: W = 50 m and L = 70 m. correct answer 50)50 <result>A</result>

A

The length of a rectangular field is 7/5 its width. If the perimeter of the field is 240 meters, what is the width of the field?

aqua_rat__4M52bBlY1lBlRE7q

The average price of 10 books is Rs. 12 while the average price of 8 of these books is Rs. 11.75. Of the remaining two books, if the price of one book is 60% more than the price of the other, what ia the pice of each of these two books ? Choose the correct choice from the following options: A) 10,68 B) 10,16 C) 10,12 D) 10,10 E) 10,11

Explanation: Total pice of the two books = Rs. [(12 x 10) - (11.75 x 8)] = Rs. (120 - 94) = Rs. 26. let the price of one book be Rs. x Then, the price of other book = Rs. (x + 60% of x) = Rs. = Rs. So, The prices of the two books are Rs. 10 and Rs. 16 Answer: 10,16 <result>B</result>

B

The average price of 10 books is Rs. 12 while the average price of 8 of these books is Rs. 11.75. Of the remaining two books, if the price of one book is 60% more than the price of the other, what ia the pice of each of these two books ?

aqua_rat__5EEmwKh9D7ZAH1yL

Find the number of square tiles to cover the floor of a room measuring 4 m * 9 m leaving 0.25 m space around the room. A side of square tile is given to be 25 cms? Choose the correct choice from the following answers: A) 388 B) 476 C) 557 D) 2885 E) 271

3 1/2 * 8 1/2 = 1/4 * 1/4 * x =&gt; x = 476 Answer: 476 <result>B</result>

B

Find the number of square tiles to cover the floor of a room measuring 4 m * 9 m leaving 0.25 m space around the room. A side of square tile is given to be 25 cms?

aqua_rat__TfwlNoxw7rsFyEfN

It takes 5 tons of copper ore and 9 tons of iron ore to make one ton of alloy A. How many tons of alloy A can be made from 60 tons of copper ore and 90 tons of iron ore? Choose the correct choice: A) 18 B) 18 3/4 C) 16 D) 12 E) 10

Yes, you need copper ore:iron ore in the ratio 5:9. Total 14 tons of the mix in this ratio will give 1 ton of alloy A. If you have 60 tons of copper ore, it is enough for 60/5= <gadget id="calculator">60/5</gadget> <output>12</output> 12 tons of alloy A. If you have 90 tons of iron ore, it is enough for 90/9= <gadget id="calculator">90/9</gadget> <output>10</output> 10 tons of alloy A. Since iron ore is available for only 10 tons of alloy A, you can make only 10 tons of alloy A. The leftover copper ore alone cannot make any alloy A and hence will be leftover only. Answer must be 10. (10) <result>E</result>

E

It takes 5 tons of copper ore and 9 tons of iron ore to make one ton of alloy A. How many tons of alloy A can be made from 60 tons of copper ore and 90 tons of iron ore?

aqua_rat__Ye7lqRPWT2dInXRq

4 guys buy same cellphones cost them 250 each. Two guy have 25% of for his first cellphone. What is the total cost all of them pay to seller. Choose the correct answer: A) 1000 B) 850 C) 875 D) 775 E) 750

Solution: C.250*2=500 for 2 guy without discount, for other 2 (250*2) with 25% is 375. total cost 500+375= <gadget id="calculator">500+375</gadget> <output>875</output> 875 <result>C</result>

C

4 guys buy same cellphones cost them 250 each. Two guy have 25% of for his first cellphone. What is the total cost all of them pay to seller.

aqua_rat__vtXw7Fb8TWkr6ZFY

In a public show 45 % of the seats were filled. If there were 600 seats in the hall, how many seats were vacant? Choose the correct choice from the following answers. A) 330 B) 110 C) 120 D) 140 E) 150

75 % of 600 = 45/100 × 600 = 270 Therefore, the number of vacant seats = 600 - 270= <gadget id="calculator">600 - 270</gadget> <output>330</output> 330. 330nswer:330 <result>A</result>

A

In a public show 45 % of the seats were filled. If there were 600 seats in the hall, how many seats were vacant?

aqua_rat__L3SrDef0eYde3EI0

How many three digit numbers B greater than 330 can be formed from the digits 1, 2, 3, 4, 5 and 6, if each digit can only be used once? Choose the correct option: A) 72 B) 48 C) 120 D) 96 E) 76

Find the number of 3 digit numbers greater than 300, and then subtract from them the number of three digit numbers between 300 and 330 formed with the given 6 digits. ABC three digit numbers greater than 300 - total of 4*5*4= <gadget id="calculator"> 4*5*4</gadget> <output>80</output> 80, because a must be greater than 2, so 4 possibilities left; B 5 remaining, and C 4 remaining possibilities to choose from. Between 300 and 330 there are 1*2*4= <gadget id="calculator"> 1*2*4</gadget> <output>8</output> 8 numbers with the given property: A= 3, 1 possibility; B can be only 1 or 2 (ABC &lt; 330), so two possibilities; C the remaining 4 possibilities after choosing A and B. Total possible choice 80 - 8= <gadget id="calculator"> 80 - 8</gadget> <output>72</output> 72=B 72nswer: 72. <result>A</result>

A

How many three digit numbers B greater than 330 can be formed from the digits 1, 2, 3, 4, 5 and 6, if each digit can only be used once?

aqua_rat__Ev437GhgaHuCSk9k

Let the sides of a rectangular prism are consecutive multiples of 5. Which among the following could be the base area Select the correct option A) 360 B) 450 C) 560 D) 670 E) 780

Length=5*a breadth=5*(a+1) or 5*(a+2) 450ase area -&gt; multiple of 25 450=25*18 Answer:450 <result>B</result>

B

Let the sides of a rectangular prism are consecutive multiples of 5. Which among the following could be the base area

aqua_rat__v47Jr3QhUCJNu0cV

Two trains, 250 metres and 150 metres long respectively, are running on parallel lines. If they are running in the same directions, the faster train crosses the slower train in 40 seconds. If they are moving in the opposite direction they pass each other in eight seconds. What is the speed of the slower train? Pick one. A) 108kmph B) 82kmph C) 92 kmph D) 72 kmph E) 87 kmph

Let the speed of faster train be f and slower train be y. Time taken to cross each other traveling in the same direction = 250 +150/ (x-y) = 40………(1) Time taken to cross each other traveling in the opposite direction = 250+150 /(x+y) = 8 …….(2) From (1) and (2) f= 30 m/s and s = 20 m/s Speed of slower train = 20 * 18/5= <gadget id="calculator">20 * 18/5</gadget> <output>72</output> 72 kmph Answer : 72 kmph <result>D</result>

D

Two trains, 250 metres and 150 metres long respectively, are running on parallel lines. If they are running in the same directions, the faster train crosses the slower train in 40 seconds. If they are moving in the opposite direction they pass each other in eight seconds. What is the speed of the slower train?

aqua_rat__MNq2LwqoZr11nao0

If integers ending in zero are excluded, what is the unit digit of the product of the even integers from 502 to 598, inclusive? Choose the most appropriate option: A) 4 B) 6 C) 8 D) 10 E) 12

502 x 504 x 506 x 508 =&gt; unit digit 4 512 x 514 x 516 x 518 =&gt; unit digit 4 592 x 594 x 596 x 598 =&gt; unit digit 4 So we have 10 numbers ending by 4 to multiply. Given that 4 x 4 = 16, we have 5 numbers ending by 6 to multiply Given that 6 x 6 = 36, we have 3 numbers ending by 6 to multiply So the unit digit is 6 Answer: 6. <result>B</result>

B

If integers ending in zero are excluded, what is the unit digit of the product of the even integers from 502 to 598, inclusive?

aqua_rat__1oaYtt28VoVbiBvh

Today is Brian's birthday. In two years from today he will be twice as old as he was 11 years ago. How old is Brian today ? Choose one: A) 24 years B) 22 years C) 19 years D) 26 years E) 28 years

Let Brian's age=x x+2= <gadget id="calculator">+2</gadget> <output>2</output> 2(x-11) x=24 24 yearsNSWER:24 years <result>A</result>

A

Today is Brian's birthday. In two years from today he will be twice as old as he was 11 years ago. How old is Brian today ?

aqua_rat__iRRgNdKOaQowHFkH

The arithmetic mean (average) of a set of 5 numbers is an integer A. Upon being divided by 180, A leaves a remainder of 30. If two of the numbers in the set are decreased by 120 and 180 units respectively, which of the following statements must be true about the new arithmetic mean B of the set? I. The remainder that B leaves upon division by 180 is less than the remainder that A leaves upon division by 180. II. When B is divided by 60, the remainder is 30. III. The value of the decimal digits is greater in the number A/90 than in the number B/90. Options: A) I only B) II only C) III only D) I and II only E) I and III only

A = 180n + 30 (n is any non negative integer) A is 30/210/390... If the total sum is reduced by 300, with 5 numbers, the average will go down by 60. B = A - 60 I. The remainder that B leaves upon division by 180 is less than the remainder that A leaves upon division by 180. B = 180n + 30 - 60 = 180n - 30 = 180(n-1) + 150 Not True. Remainder is 150 II. When B is divided by 60, the remainder is 30. B = 180(n-1) + 150 = 180(n-1) + 120 + 30 True. B leaves remainder 30 on division by 60. III. The value of the decimal digits is greater in the number A/90 than in the number B/90. The decimal part of A is 30/90 = .333 The decimal part of B will be obtained by 150/90 = (90 + 60)/90 =&gt; 60/90 = .666 Not True. Answer (II only) <result>B</result>

B

The arithmetic mean (average) of a set of 5 numbers is an integer A. Upon being divided by 180, A leaves a remainder of 30. If two of the numbers in the set are decreased by 120 and 180 units respectively, which of the following statements must be true about the new arithmetic mean B of the set? I. The remainder that B leaves upon division by 180 is less than the remainder that A leaves upon division by 180. II. When B is divided by 60, the remainder is 30. III. The value of the decimal digits is greater in the number A/90 than in the number B/90.

aqua_rat__2en1a2EieILxkvtE

A light has a rating of 110 watts, it is replaced with a new light that has 30% higher wattage. How many watts does the new light have? Choose the correct answer A) 143 B) 145 C) 156 D) 134 E) 100

Final number = Initial number + 30%(original number) = 110 + 30%(110) = 110 + 33= <gadget id="calculator">110 + 33</gadget> <output>143</output> 143. 143nswer 143 <result>A</result>

A

A light has a rating of 110 watts, it is replaced with a new light that has 30% higher wattage. How many watts does the new light have?

aqua_rat__HjUjH1azLM41Hh1C

In what time will a train 135 m long cross an electric pole, it its speed be 140 km/hr? Choices A) 3.5 B) 2.7 C) 2.9 D) 2.3 E) 2.1

Speed = 140 * 5/18 = 38.8 m/sec Time taken = 135/38.8 = 3.5 sec. 3.5nswer: 3.5 <result>A</result>

A

In what time will a train 135 m long cross an electric pole, it its speed be 140 km/hr?

aqua_rat__YhMYuhS5v6Vm6nHV

A committee of four is to be chosen from seven employees for a special project at ACME Corporation. Two of the seven employees are unwilling to work with each other. How many committees are possible if the two employees do not work together? Choose the correct choice from the following answers: A) 15 B) 20 C) 25 D) 35 E) 50

total combinations =7254 total combinations if 2 persons who dont like each other are selected together= 5253 Ans= 7254-5253 =25 ANSWER:25 <result>C</result>

C

A committee of four is to be chosen from seven employees for a special project at ACME Corporation. Two of the seven employees are unwilling to work with each other. How many committees are possible if the two employees do not work together?

aqua_rat__ZGsVmpL6Q34k7wQs

The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team? Pick one. A) 23 Years B) 20 Years C) 25 Years D) 22 Years E) 28 Years

A 23 Years Let the average age of the whole team by x years. 11x - (26 + 29) = 9(x -1) 11x - 9x = 46 2x = 46 x = 23. So, average age of the team is 23 years <result>A</result>

A

The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?

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The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle? Options: A) 30 B) 31 C) 32 D) 34 E) 35

Area of a triangle = r * s Where r is the inradius and s is the semi perimeter of the triangle. Area of triangle = 2.5 * 28/2= <gadget id="calculator">2.5 * 28/2</gadget> <output>35</output> 35 cm2 Answer: Option 35 <result>E</result>

E

The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?

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CONVERT 1.3 hectares in ares Select. A) 130 ares. B) 160 ares. C) 180 ares. D) 230 ares. E) 250 ares.

1.3 hectares in ares 1 hectare = 100 ares Therefore, 1.3 hectares = 1.3 × 100 ares = 130 ares. 130 ares.NSWER- 130 ares. <result>A</result>

A

CONVERT 1.3 hectares in ares

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Lorna invests $8000, with some at 6% annual interest and some at 11% annual interest. If she receives a total of $580 from these investments at the end of a year, how much was invested at the 6% interest rate? Choose the correct choice: A) $160 B) $1,700 C) $2,200 D) $4,400 E) $5,840

We have that 'x' invested at 6% We also have that '8000-x' invested at 11% Now then 580/8000 is approx 10% Therefore, -4x+8000-x=0 5x=8000 x=1600 approximately. Probably higher Only $1,700 matches <result>B</result>

B

Lorna invests $8000, with some at 6% annual interest and some at 11% annual interest. If she receives a total of $580 from these investments at the end of a year, how much was invested at the 6% interest rate?

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It would take one machine 8 hours to complete a large production order and another machine 7 hours to complete the same order. How many hours would it take both machines, working simultaneously at their respective constant rates, to complete the order? Choose the correct choice from the following. A) A 15/56 B) B 14/45 C) C 24/56 D) D 45/56 E) E 56/15

The rate of the first machine is 1/8 job per hour; The rate of the second machine is 1/7 job per hour; Thus, the combined rate of the machines is 1/8+1/7=15/56 job per hour, which means that it takes 1/(15/56)=56/15 hours both machines to do the job. Answer: E 56/15. <result>E</result>

E

It would take one machine 8 hours to complete a large production order and another machine 7 hours to complete the same order. How many hours would it take both machines, working simultaneously at their respective constant rates, to complete the order?

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An airplane travels 4362 km against the wind in 6 hours and 5322 km with the wind in the same amount of time. what is the rate of the wind? Choose the correct answer A) 60km/hr B) 70km/hr C) 80km/hr D) 90km/hr E) 100km/hr

Let the speed of the air plane in still air be x km/hr And the speed of the wind be y km/hr. Then speed of the airplane going with the wind = (x + y) km/hr and speed of the airplane going against the wind = (x - y) km/hr. We know that, Distance = Speed ? Time or, Speed = Distance Time According to the problem, An airplane travels 4362 km against the wind in 6 hours x - y = 4362/6 or, x - y = 727 ----------- (1) Again, the airplane travels 5322 km with the wind in the same amount of time i.e. 6 hours x + y = 5322/6 or, x + y = 887 ----------- (2) Now add (1) and (2) we get, x - y = 727 x + y = 887 2x = 1614 or, 2x/2 = 1614/2, (Divide both sides by 2) or, x = 807 Now substitute the value of value of x = 807 in equation (2) we get, 807 + y = 887 -807 -807, (Subtract 407 from both sides) y = 80 Answer:Rate of the wind = 80km/hr correct answer 80km/hr <result>C</result>

C

An airplane travels 4362 km against the wind in 6 hours and 5322 km with the wind in the same amount of time. what is the rate of the wind?

aqua_rat__PnDODvbWucM2WTSM

5^2010 what will be the sum of digits? Choose the correct choice from the following choices A) 6028 B) 6029 C) 6031 D) 3021 E) 6032

5^2=25 sum of digits =2+5= <gadget id="calculator">2+5</gadget> <output>7</output> 7 now if we take the power of 5 and do 2*3+1= <gadget id="calculator"> 2*3+1</gadget> <output>7</output> 7 similarly for 5^4=625 and sum=6+2+5= <gadget id="calculator">6+2+5</gadget> <output>13</output> 13 now do 4*3+1= <gadget id="calculator"> 4*3+1</gadget> <output>13</output> 13 similarly, 5^2010 sum of the digits would be 2010*3+1= <gadget id="calculator"> 2010*3+1</gadget> <output>6_031</output> 6031 ANSWER:6031 <result>C</result>

C

5^2010 what will be the sum of digits?

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If the true discount on s sum due 2 years hence at 14% per annum be Rs. 210, the sum due is: Choose one: A) s. 768 B) s. 960 C) s. 1960 D) s. 2400 E) s. 2800

td=pw*r*t/100 so 210=pw*14*2/100 so pw=750 sum=pw+td.. sum=750+210= <gadget id="calculator">750+210</gadget> <output>960</output> 960 ANSWER:s. 960 <result>B</result>

B

If the true discount on s sum due 2 years hence at 14% per annum be Rs. 210, the sum due is:

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From given equation find the value of x: 2x² + 9x − 5 Options: A) 1/2 B) 1 C) 3 D) 4 E) 5

That quadratic is factored as follows: 2x² + 9x − 5 = (2x − 1)(x + 5). Lesson 17. Now, it is easy to see that the second factor will be 0 when x = −5. As for the value of x that will make 2x − 1 = 0, we must solve that little equation. (Lesson 9.) We have: 2x = 1 x = 1 2 The solutions are: x = 1/2 or −5 1/2 <result>A</result>

A

From given equation find the value of x: 2x² + 9x − 5

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The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles. Choose the correct option A) 3312 B) 2888 C) 4312 D) 2881 E) 1221

Let the radii of the smaller and the larger circles be s m and l m respectively. 2∏s = 264 and 2∏l = 352 s = 264/2∏ and l = 352/2∏ Difference between the areas = ∏l2 - ∏s2 = ∏{1762/∏2 - 1322/∏2} = 1762/∏ - 1322/∏ = (176 - 132)(176 + 132)/∏ = (44)(308)/(22/7) = (2)(308)(7) = 4312 sq m Answer: 4312 <result>C</result>

C

The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles.

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An design manager has 10patterns of chairs & 6patterns of tables. In how many ways can he make a pair of table & chair? Choose the correct choice from the following answers A) 20 B) 60 C) 80 D) 90 E) 100

He has has ten patterns of chairs and eight patterns of tables Hence, A chair can be arranged in 10 ways and A table can be arranged in 6 ways Hence one chair and one table can be arranged in 10 x 6 ways = 60 ways 60 <result>B</result>

B

An design manager has 10patterns of chairs & 6patterns of tables. In how many ways can he make a pair of table & chair?

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A driver just filled the car's gas tank with 18 liters of gasohol, a mixture consisting of 5% ethanol and 95% gasoline. If the car runs best on a mixture consisting of 10% ethanol and 90% gasoline, how many liters of ethanol must be added into the gas tank for the car to achieve optimum performance? Choices. A) 1 B) 1.5 C) 1.8 D) 2.4 E) 3

Let x be the number of liters of ethanol added to the gas tank. 0.05(18) + x = 0.1(18+x) 0.9x = 1.8 - 0.9 x = 1 liter The answer is 1. <result>A</result>

A

A driver just filled the car's gas tank with 18 liters of gasohol, a mixture consisting of 5% ethanol and 95% gasoline. If the car runs best on a mixture consisting of 10% ethanol and 90% gasoline, how many liters of ethanol must be added into the gas tank for the car to achieve optimum performance?

aqua_rat__Fp1xIgKH0TlixtRH

The denominator of a fraction is 5 greater than the numerator. If the numerator and the denominator are increased by 1, the resulting fraction is equal to 7⁄12. What is the value of the original fraction? Choose the correct choice from the following answers. A) 6/11 B) 8/13 C) 11/16 D) 12/17 E) 14/19

Let the numerator be x. Then the denominator is x+5. x+1 / x+6 = 7/12. 12x+12=7x+42. 5x=30. x=6. The original fraction is 6/11. The answer is 6/11. <result>A</result>

A

The denominator of a fraction is 5 greater than the numerator. If the numerator and the denominator are increased by 1, the resulting fraction is equal to 7⁄12. What is the value of the original fraction?

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The interest on a certain deposit at 5% per annum is Rs. 101.20 in one year. How much will the additional interest in one year be on the same deposit at 6% per annum? Choose the correct choice A) Rs.20.8 B) Rs.19.74 C) Rs.20.24 D) Rs.19.5 E) Rs.19.00

Explanation : Principal, P = 100×SI/RT=100×101.20/5×1=20×101.20=Rs. 2024 Simple Interest for Rs.2024 at 6% per annum for 1 year, SI = 2024×6×1100=121.44 Additional Interest = Rs.121.44 - Rs.101.20 = Rs.20.24 Answer : Option Rs.20.24 <result>C</result>

C

The interest on a certain deposit at 5% per annum is Rs. 101.20 in one year. How much will the additional interest in one year be on the same deposit at 6% per annum?

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Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is? Choose the correct choice from the following options A) 2887 B) 444 C) 877 D) 278 E) 178

1h ----- 5 ? ------ 60 12 h RS = 16 + 21= <gadget id="calculator">16 + 21</gadget> <output>37</output> 37 T= 12 D = 37 * 12= <gadget id="calculator">37 * 12</gadget> <output>444</output> 444 Answer: 444 <result>B</result>

B

Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?

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What will be the compound interest on a sum of Rs.25,000 after 3 years at the rate of 12 p.c.p.a? Options: A) Rs.10111.00 B) Rs.10123.20 C) Rs.10123.00 D) Rs.10100.00 E) Rs.10110.00

= Rs.(25000x(1+12/100)³ = Rs.(25000x28/25x28/25x28/25) = Rs. 35123.20. C.I = Rs(35123.20 -25000) = Rs.10123.20 answer :Rs.10123.20 <result>B</result>

B

What will be the compound interest on a sum of Rs.25,000 after 3 years at the rate of 12 p.c.p.a?

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In what ratio P:Q should the Mixture P of milk and water in the ratio of 5:3 be mixed with another Mixture Q of milk and water in the ratio 1:3 so that the resultant mixture contains equal quantities of milk and water? Select the correct option. A) 5:2 B) 4:3 C) 3:2 D) 2:1 E) 4:1

(5/8)*P +(1/4)*Q = (3/8)*P+(3/4)*Q 2P=4Q P/Q = 2/1 The answer is 2:1. <result>D</result>

D

In what ratio P:Q should the Mixture P of milk and water in the ratio of 5:3 be mixed with another Mixture Q of milk and water in the ratio 1:3 so that the resultant mixture contains equal quantities of milk and water?

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The difference of two numbers is 2 and the difference of their squares is 12. The sum of the number is Choices. A) 6 B) 8 C) 10 D) 22 E) 24

Explanation: Let the numbers be a, b; ⇒ a-b=2 and a2−b2=12 a+b=a2−b2/a−b=12/2= <gadget id="calculator">12/2</gadget> <output>6</output> 6 Correct Option: 6 <result>A</result>

A

The difference of two numbers is 2 and the difference of their squares is 12. The sum of the number is

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For the positive integers x, x + 2, x + 4, x + 7, and x + 22, the mean is how much greater than the median? Choose the correct choice from the following choices: A) 0 B) 1 C) 2 D) 3 E) 7

Mean = (x + x+2 + x+4 + x+7 + x+22)/5 =(5x+35)/5 =x+7 Median = x+4 Thus Mean - Median = x+7 - (x+4) =3 Answer +7 - ( +4)= <gadget id="calculator">+7 - ( +4)</gadget> <output>3</output> 3 Answer= 3 <result>D</result>

D

For the positive integers x, x + 2, x + 4, x + 7, and x + 22, the mean is how much greater than the median?

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There are cats got together and decided to kill the mice of 999951. Each cat kills equal number of mice and each cat kills more number of mice than cats there were. Then what are the number of cats? Select: A) 941,1009 B) 993,1007 C) 991,1009 D) 791,1009 E) 931,1009

999951 can be written as 1000000 – 49 = 10002 – 72 ie of the form a2-b2=(a+b)(a-b) =(1000+7)*(1000-7) = (1007)*(993) Given that number of cats is less than number if mice. So number of cats is 993 and number of mice were 1007 Answer 993,1007 <result>B</result>

B

There are cats got together and decided to kill the mice of 999951. Each cat kills equal number of mice and each cat kills more number of mice than cats there were. Then what are the number of cats?

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A’s speed is 25/18 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that the race ends in a dead heat? Pick one: A) 1/18 B) 7/18 C) 7/25 D) 3/25 E) 1/25

We have the ratio of A’s speed and B’s speed. This means, we know how much distance A covers compared with B in the same time. This is what the beginning of the race will look like: (Start) A_________B______________________________ If A covers 25 meters, B covers 18 meters in that time. So if the race is 25 meters long, when A reaches the finish line, B would be 7 meters behind him. If we want the race to end in a dead heat, we want B to be at the finish line too at the same time. This means B should get a head start of 7 meters so that he doesn’t need to cover that. In that case, the time required by A (to cover 25 meters) would be the same as the time required by B (to cover 18 meters) to reach the finish line. So B should get a head start of 7/25th of the race. Answer (7/25) <result>C</result>

C

A’s speed is 25/18 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that the race ends in a dead heat?

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The sequence a(1), a(2), …, a(n), … is such that a(n)=4a(n–1) –3 for all integers n>1. If a(3)=x, then a(1)=? Select: A) 4x–3 B) 16x–15 C) (x+3)/4 D) (x+3)/16 E) (x+15)/16

Since we know a(3) we can find a(2), if we can find a(2) we can find a(1). a(3)=4a(2)-3 ---&gt; x=4a(2)-3 ---&gt; a(2)=(x+3)/4 a(2)=4a(1)-3 ---&gt; (x+3)/4=4a(1)-3 ---&gt; 4a(1)=(x+15)/4 ---&gt; a(1)=(x+15)/16 The answer is (x+15)/16. <result>E</result>

E

The sequence a(1), a(2), …, a(n), … is such that a(n)=4a(n–1) –3 for all integers n>1. If a(3)=x, then a(1)=?

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What is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular 11-sided polygon)? Select the correct option: A) 1/2 B) 1/3 C) 1/4 D) 1/8 E) 1/11

From any vertex, there are two vertices on sides, which do not make a diagonal but a side. So the remaining n-3 vertices make diagonals. There are 2 of these diagonals which are the shortest. The probability of choosing one of the shortest diagonals is 2/8 = 1/4. The answer is 1/4. <result>C</result>

C

What is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular 11-sided polygon)?

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The average of 11numbers is 60. Out of 11numbers the average of first 6no. is 98, and last 6numbers is 65 then find 6th number? Answers: A) A)318 B) B)65 C) C)58 D) D)62 E) E)48

6th number = sum of 1st 6no.s + sum of last 6no.s - sum of 11no.s answer = 6*98+6*65-11*60= <gadget id="calculator">6*98+6*65-11*60</gadget> <output>318</output> 318 318nswer is 318 <result>A</result>

A

The average of 11numbers is 60. Out of 11numbers the average of first 6no. is 98, and last 6numbers is 65 then find 6th number?

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Solution A is 20% sugar and Solution B is 80% sugar. If you have 30 ounces of solution A and 60 ounces of solution B, in what ratio could you mix Solution A with Solution B to produce 50 ounces of a 50% sugar solution? Answers: A) 6:4 B) 6:14 C) 4:4 D) 4:6 E) 3:7

Forget the volumes for the time being. You have to mix 20% and 80% solutions to get 50%. This is very straight forward since 50 is int he middle of 20 and 80 so we need both solutions in equal quantities. If this doesn't strike, use w1/w2 = (A2 - Aavg)/(Aavg - A1) w1/w2 = (80 - 50)/(50 - 20)= <gadget id="calculator">(80 - 50)/(50 - 20)</gadget> <output>1</output> 1/1 So the volume of the two solutions will be equal. Answer has to be 4:4=4:4 <result>C</result>

C

Solution A is 20% sugar and Solution B is 80% sugar. If you have 30 ounces of solution A and 60 ounces of solution B, in what ratio could you mix Solution A with Solution B to produce 50 ounces of a 50% sugar solution?

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In a group of 90 students, 30 are taking History, and 32 are taking Statistics. If 59 students are taking History or Statistics or both, then how many students are taking History but not Statistics? Answers: A) 9 B) 19 C) 33 D) 27 E) 31

Number of students taking history =H=30 Number of students taking statistics =S= 32 Total number of students =T= 90 Number of students taking History or Statistics or both =B= 59 Number of students taking neither history nor statistics =N= 90-59= <gadget id="calculator">90-59</gadget> <output>31</output> 31 LetXbe the number of students taking both history and statistics. Then T= H + S + N - X or 90 = 30+ 32 +31 - X or X = 3 Now, Number of students taking only history will be H-X or 36-3= <gadget id="calculator"> 36-3</gadget> <output>33</output> 33 Answer:- 33 <result>C</result>

C

In a group of 90 students, 30 are taking History, and 32 are taking Statistics. If 59 students are taking History or Statistics or both, then how many students are taking History but not Statistics?

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Two bullet train s are running in opposite directions with the same speed. If the length of each bullet train is 120 metres and they cross each other in 12 seconds, then the speed of each bullet train (in km/hr) is: Select A) 46 km/hr. B) 36 km/hr. C) 56 km/hr. D) 76 km/hr. E) 66 km/hr.

B 36 km/hr. Let the speed of each bullet train be x m/sec. Then, relative speed of the two bullet train s = 2x m/sec. So, 2x = (120 + 120)/12 --&gt; 2x = 20 --&gt; x = 10. --&gt; Speed of each bullet train = 10 m/sec = 10 x 18/5 km/hr = 36 km/hr. <result>B</result>

B

Two bullet train s are running in opposite directions with the same speed. If the length of each bullet train is 120 metres and they cross each other in 12 seconds, then the speed of each bullet train (in km/hr) is:

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A nickel is placed flat on a table. What is the maximum number of nickels that can be placed around it, flat on the table, with each one tangent to it? Choose the correct choice from the following options A) 4 B) 5 C) 6 D) 7 E) 8

Connect the midpoints of the given nickel and two others placed around it so that all three touch. This creates an equilateral triangle with 60 degree angles. Since 360=60 = 6, six nickels can be placed around the given nickel. correct answer 6 <result>C</result>

C

A nickel is placed flat on a table. What is the maximum number of nickels that can be placed around it, flat on the table, with each one tangent to it?