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NLP Centre, Faculty of Informatics, Masaryk University 14

aqua_rat__T5reIiuKC2kS7iSh

In eight years, David will be four times as old as Aaron. Twenty years ago, David was twice as old as Ellen. If David is seven years older than Ellen, how old is Aaron? Choose one. A) 1–5 B) 1.5–5 C) 11–15 D) 16–20 E) 21–25

Let David's present age be 'd', Aaron's present age be 'a' and Ellen's present age be 'e' In ten years, David will be four times as old as Aaron --&gt; d+8 = 4(a+8) Twenty years ago, David was twice as old as Ellen --&gt; d-16 = 2(e-16) David is seven years older than Ellen --&gt; d = e + 7 e+7-16 = 2e-32 e-9= 2e-32 e = 23 d = 30 38 = 4a + 32 a = 1.5 Answer: 1.5–5 <result>B</result>

B

In eight years, David will be four times as old as Aaron. Twenty years ago, David was twice as old as Ellen. If David is seven years older than Ellen, how old is Aaron?

aqua_rat__Tp0IgtrZydlsQOPG

If x+y=2z, then which of the following represents the average (arithmetic mean) of x, y, and z, in terms of z? Choose the correct choice from the following answers. A) 2z+1 B) 3z C) 5z D) z E) 3z/2

Pick any number like X=12, Y=10 and Z= 11 so that X+Y=2Z, now then the arithmetic mean will be (12+10+11)/3= <gadget id="calculator"> (12+10+11)/3</gadget> <output>11</output> 11. Now, just look at the answers and put the value of Z there. (A) 2.11+1=23, no. (B) 3.11=33,no (C) 5.11=55, no (z) 11, it can be the answer, lets check us the other options (E) (3.2)/2=3, no so the answer will be z.. <result>D</result>

D

If x+y=2z, then which of the following represents the average (arithmetic mean) of x, y, and z, in terms of z?

aqua_rat__MEzvlYbwDRilIhKS

If the radius of a cylinder is made 3 times and height is doubled, what is the new volume of the cylinder divided by the old one? Pick. A) 18. B) 2. C) 6. D) 4. E) 10.

let v and v' be the original and the changed volume now v=pir^2h v'=pi(3r)^2(2h) v'=18v 18.) 18 <result>A</result>

A

If the radius of a cylinder is made 3 times and height is doubled, what is the new volume of the cylinder divided by the old one?

aqua_rat__uzPhV5dsB0d0so0b

In a college, the ratio of the number of boys to girls is 8 : 5. If there are 200 girls, the total number of students in the college is Choose one: A) 420 B) 520 C) 620 D) 720 E) 820

Explanation: Let the boy are 8x and Girls are 5x =&gt; 5x = 200 =&gt; x = 40 Total students = 8x+5x = 13x 8 +5= <gadget id="calculator">8 +5</gadget> <output>13</output> 13x= 13(40) = 520 Option 520 <result>B</result>

B

In a college, the ratio of the number of boys to girls is 8 : 5. If there are 200 girls, the total number of students in the college is

aqua_rat__cK2zsVZH89pSVPkL

In an election, candidate Smith won 52% of the total vote in Counties A and S. He won 61% of the vote in County A. If the ratio of people who voted in County A to County S is 3:1, what percent of the vote did candidate Smith win in County S ? Choose the most appropriate option: A) A.25% B) B.27% C) C.34% D) D.43% E) E.49%

(61%)*3x + (y%)*x = (52%)*4x y = 25% of County S hence answer is A.25%. <result>A</result>

A

In an election, candidate Smith won 52% of the total vote in Counties A and S. He won 61% of the vote in County A. If the ratio of people who voted in County A to County S is 3:1, what percent of the vote did candidate Smith win in County S ?

aqua_rat__5u0F5IqMXL8ZiaUk

The marks obtained by Polly and Sandy are in the ratio 3:5 and those obtained by Sandy and Willy are in the ratio of 3:2. The marks obtained by Polly and Willy are in the ratio of...? Choose the correct choice A) 3:4 B) 5:6 C) 7:8 D) 9:10 E) 11:12

Polly : Sandy = 3:5 = 9:15 Sandy : Willy = 3:2 = 15:10 Polly : Sandy : Willy = 9:15:10 Polly : Willy = 9:10 The answer is 9:10. <result>D</result>

D

The marks obtained by Polly and Sandy are in the ratio 3:5 and those obtained by Sandy and Willy are in the ratio of 3:2. The marks obtained by Polly and Willy are in the ratio of...?

aqua_rat__smB5yqTn7LDHScqX

A certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint. If 2 gallons of the mixture is needed and the individual colors can be purchased only in one gallon or half gallon cans, what is the least amount of paint W, in gallons, that must be purchased in order to measure out the portions needed for the mixture? Choose the correct choice from the following. A) 2 B) 2 1/2 C) 3 D) 3 1/2 E) 4

Given W:B = 3:5 That means say 3 gallons of white paint + 5 gallons of black paint = 8 gallons of paint mixture. But we want least amount of whiteblack paints for minimum of 2 gallons of mixture, so lets reduce keeping same ratio, 1.5 : 2.5 gives 1.5 + 2.5= <gadget id="calculator"> 1.5 + 2.5</gadget> <output>4</output> 4 gallons of mixture, but we want only 2 gallons, lets further reduce 0.75: 1.25 gives 1+1.5= <gadget id="calculator"> 1+1.5</gadget> <output>2.5</output> 2.5 gallons of mixture. This looks ok, but lets reduce further just to be sure 0.375: 0.625 gives 0.5 + 1= <gadget id="calculator"> 0.5 + 1</gadget> <output>1.5</output> 1.5 gallons of mixture, thats less than 2 gallons of mixture, so not acceptable. So correct ans is 2.5 gallons. 2 1/2 <result>B</result>

B

A certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint. If 2 gallons of the mixture is needed and the individual colors can be purchased only in one gallon or half gallon cans, what is the least amount of paint W, in gallons, that must be purchased in order to measure out the portions needed for the mixture?

aqua_rat__VvimLqai3wjMXOZj

If x^2 = 231, which of the following is closest to a potential value of x? Choose the most appropriate option: A) -127 B) -11 C) 12 D) 13 E) 15

Here the thing we must not forget is that X^even has two potential solutions =&gt; x =+- √231 =&gt; +- 15 (approx) this value is closer to 15 Hence 15 is correct. <result>E</result>

E

If x^2 = 231, which of the following is closest to a potential value of x?

aqua_rat__BRuh5T5mBVLpVLIw

A fair 2 sided coin is flipped 6 times. What is the probability that tails will be the result at least twice, but not more than 5 times? Choose the correct choice from the following options. A) 5/8 B) 3/4 C) 7/8 D) 57/64 E) 15/16

It would be easier to calculate the probability of opposite event and subtract it from 1. Opposite event: 0 tail, 1 tail, 6 tails. Probability of getting no tails: 1/2^6=1/64 Probability of getting 1 tail: 67/81∗1/2^6=6/64, we must multiply by 67/81 or by 6 as tail can occur for any flip from 6, hence in 6 ways; Probability of getting 6 tails: 1/2^6=1/6^4 P=1−(1/64+6/64+1/64)=56/64=7/8 Answer: 7/8. <result>C</result>

C

A fair 2 sided coin is flipped 6 times. What is the probability that tails will be the result at least twice, but not more than 5 times?

aqua_rat__n750tsQ52W2O4rac

Each shelf of a bookcase contains 24 books. If the librarian took out 34 books and rearranged the remaining books so that all shelves but the last one contained 16 books and the last shelf contained 22 books, how many shelves does the bookcase have? Choose one. A) A)4 B) B)5 C) C)6 D) D)8 E) E)9

Denoting x the number of the shelves, we can build an equation: 24x=16(x−1)+22+34 Solving the equation, we get x=5 Answer: 5 <result>B</result>

B

Each shelf of a bookcase contains 24 books. If the librarian took out 34 books and rearranged the remaining books so that all shelves but the last one contained 16 books and the last shelf contained 22 books, how many shelves does the bookcase have?

aqua_rat__BcrCxubl0CFXwOCZ

A 420 meter long train crosses a platform in 60 seconds while it crosses a signal pole in 30 seconds. What is the length of the platform? Pick: A) 120 B) 840 C) 350 D) 420 E) 210

Speed = [420 / 30] m/sec =14 m/sec. Let the length of the platform be x meters. Then, x + 420/ 60 = 14 x + 420 = 840 è x = 420m. Answer: 420 <result>D</result>

D

A 420 meter long train crosses a platform in 60 seconds while it crosses a signal pole in 30 seconds. What is the length of the platform?

aqua_rat__60EqgVQDfF2omrTh

The cost price of 13 articles is equal to the selling price of 11 articles. Find the profit percent? Choose the correct choice from the following answers. A) 18 2/81% B) 18 2/11% C) 18 3/11% D) 18 1/11% E) 18 2/15%

13 CP = 11 SP 11 --- 2 CP 100 --- ? =&gt;18 2/11% Answer: 18 2/11% <result>B</result>

B

The cost price of 13 articles is equal to the selling price of 11 articles. Find the profit percent?

aqua_rat__WmljxYATuxG7EFQk

"I am five times as old as you were, when I was as old as you are", said a man to his son. Find out their present ages, if the sum of their ages is 64 years. Choose the correct option: A) 47 years and 28 years. B) 40 years and 24 years. C) 48 years and 27 years. D) 46 years and 26 years. E) none of these

Let the present age of the man be ’a’ and son be ’b’, Given, a + b = 64 or b = (64 - a) Now the man says "I am five times as old as you were, when I was as old as you are", So, a = 5[b - (a - b)] We get 6a = 10b, Substitute value for b, 6a = 10(64 - a), Therefore a = 40, b = 24. ANSWER:40 years and 24 years. <result>B</result>

B

"I am five times as old as you were, when I was as old as you are", said a man to his son. Find out their present ages, if the sum of their ages is 64 years.

aqua_rat__wx0Vdm2EPUUdEDFh

If 12% of x is equal to 6% of y, then 18% of x will be equal to how much % of y ? Options: A) 7% B) 9% C) 11% D) 12% E) none of these

We have , 12% of X = 6% of Y =&gt; 2% of X = 1% of Y =&gt;(2 x 9)% of X = ( 1 x 9)% of Y Thus, 18% of X = 9% of Y. ANSWER:9% <result>B</result>

B

If 12% of x is equal to 6% of y, then 18% of x will be equal to how much % of y ?

aqua_rat__xlv9cJj52VpNVSmB

Train G and H, 455 miles apart, are traveling toward each other at constant rates and in the same time zone. If train G left at 4 pm traveling at a speed of 60 miles per hour, and train H left at 5:45 pm and traveling at 45 miles per hour, then at what time would they pass each other? Choose the most appropriate option A) 9.05Am B) 9.11pm C) 8.05pm D) 7.05pm E) 9.05pm

First, since G has a headstart then in that 1hr45min or 1.75hrs he travels 105 miles Then remaining distance to be traveled will be 455 - 105= <gadget id="calculator"> 455 - 105</gadget> <output>350</output> 350 miles Now, using relative rates (105)(t)= 350 This gives 10/3 hours Now 5.45pm + 10/3 hours gives us 9.05pm Hence answer is 7.05pm <result>D</result>

D

Train G and H, 455 miles apart, are traveling toward each other at constant rates and in the same time zone. If train G left at 4 pm traveling at a speed of 60 miles per hour, and train H left at 5:45 pm and traveling at 45 miles per hour, then at what time would they pass each other?

aqua_rat__MJhFag7ykGauDB7Y

a milkman makes a profit of 20% on the sale of milk. If he were to add 10% water to the milk, by what % would his profit increase? Pick one: A) 50 % B) 60 % C) 70 % D) 80 % E) 40 %

let he sells 100 lit of milk @ 120 rs. means his cost price must b 100 to gain 20% profit. Nw he adds 10% milk ie total milk z 110 lit. Now he will get 132 rs. by selling 110 lit f milk (120*110/100) total profit = 32 rs increased profit =12 rs %age increase= 12/20= 60 % ANSWER:60 % <result>B</result>

B

a milkman makes a profit of 20% on the sale of milk. If he were to add 10% water to the milk, by what % would his profit increase?

aqua_rat__JTFQrnczpRw8mK4i

If n is a positive integer and the greatest common divisor of n and 16 is 4, and the greatest common divisor of n and 15 is 3, which of the following is the greatest common divisor of n and 48? Choose the correct option: A) 12 B) 18 C) 24 D) 30 E) 36

The greatest common divisor of n and 16 is 4 --&gt; n is a multiple of 4 but not a multiple of 8. The greatest common divisor of n and 15 is 3 --&gt; n is a multiple of 3 but not a multiple of 5. 48=2*3*8 is divisible by 12. therefore the greatest common divisor is 12 12 <result>A</result>

A

If n is a positive integer and the greatest common divisor of n and 16 is 4, and the greatest common divisor of n and 15 is 3, which of the following is the greatest common divisor of n and 48?

aqua_rat__toRXUXCd7t3eD5Gp

Out of three numbers, the first is twice the second and is half of the third. If the average of the three numbers is 70, the three numbers in order are? Choose the correct answer: A) 60, 120, and 30 B) 60, 30, and 120 C) 30, 60, and 120 D) 30, 120, and 60 E) 120, 30, and 60

Let the numbers be 2x, x and 4x (2x + x + 4x)/3 = 70 7x/3 = 70 x = 30 The numbers in order are 60, 30, and 120 The answer is 60, 30, and 120. <result>B</result>

B

Out of three numbers, the first is twice the second and is half of the third. If the average of the three numbers is 70, the three numbers in order are?

aqua_rat__Z9VUsctxDY8Ocreu

Three machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 40 hours. If one additional machine were used under the same operating conditions, in how manyfewerhours of simultaneous operation could the production order be fulfilled? Pick A) 6 B) 9 C) 10 D) 27 E) 48

If 3 Machines can do the work in 40 hr then 4 Machines can do the work in 3/4*40= <gadget id="calculator"> 3/4*40</gadget> <output>30</output> 30 Hrs. hence time saved will be 10hr option 10 is the correct answer <result>C</result>

C

Three machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 40 hours. If one additional machine were used under the same operating conditions, in how manyfewerhours of simultaneous operation could the production order be fulfilled?

aqua_rat__Ege6o9EIIUBhcqdu

X and Y started a business by investing Rs.5000/- and Rs.15000/- respectively. Find the X’s share out of a total profit of Rs.1600: Options: A) 200 B) 250 C) 300 D) 350 E) 400

X = Rs.5000/- Y = Rs.15000/- X share 1 part &amp; Y share 3 parts Total 4 parts -----&gt; Rs.1600/- ----&gt; 1 part -------&gt; Rs.400/- X share = 1 part -----&gt; Rs.400/- 400 <result>E</result>

E

X and Y started a business by investing Rs.5000/- and Rs.15000/- respectively. Find the X’s share out of a total profit of Rs.1600:

aqua_rat__81jj5y4kEL7CF0pP

In how many ways letters of the word RSCUPERATE be arranged? Choose the correct choice from the following: A) 357687 B) 247886 C) 284757 D) 456788 E) 302400

RESUPERATE has 10 letters, out of which E repeated 3 times, R repeated 2 times. Hence total ways = 10! / (3!*2!) = 302400 ways 302400 <result>E</result>

E

In how many ways letters of the word RSCUPERATE be arranged?

aqua_rat__dQF5wXzuogSi9NGC

A and B complete a work in 16 days. A alone can do it in 40 days. If both together can do the work in how many days? Choose the correct choice from the following options. A) 1.0875 days B) 0.1875 days C) 0.0675 days D) 0.0875 days E) 0.0775 days

1/16 + 1/40= <gadget id="calculator">1/16 + 1/40</gadget> <output>7/80 = around 0.0875</output> 0.0875 days ANSWER:0.0875 days <result>D</result>

D

A and B complete a work in 16 days. A alone can do it in 40 days. If both together can do the work in how many days?

aqua_rat__w2ARig2Txz7CxM9J

A researcher computed the mean, the median, and the standard deviation for a set of performance scores. If25 were to be added to each score, which of these three statistics would change? Select the correct option. A) The mean only B) The mean and the median C) The standard deviation only D) The median only E) The mean and the standard deviation

The correct answer is The mean and the median. <result>B</result>

B

A researcher computed the mean, the median, and the standard deviation for a set of performance scores. If25 were to be added to each score, which of these three statistics would change?

aqua_rat__iQ7zE6zbas0lM6qo

In how many ways can 5 boys and 2 ladiesbe arranged at a table if 2 ladies are never together? Options. A) 245 B) 278 C) 390 D) 420 E) 480

Total ways of arranging 7 person in a circle = 6! = 720 ways If we consider two women as one, then we have 5+1= <gadget id="calculator"> 5+1</gadget> <output>6</output> 6 persons. Arranging these six persons in circle will take= 5! = 120 ways And two women can arrange themselves in 2! ways Total ways in which two women sit together in circle = 5!*2! = 240 ways Total ways in which two women doesn’t sit together in circle = 6! - 5!*2! = 720 - 240= <gadget id="calculator">720 - 240</gadget> <output>480</output> 480 ways 480 <result>E</result>

E

In how many ways can 5 boys and 2 ladiesbe arranged at a table if 2 ladies are never together?

aqua_rat__rCGp9tR3WRi7CR52

A farm has chickens, cows and sheep. There are five times the number of chickens and cows than sheep. If there are more cows than chickens or sheep, and together, cows and chickens have a total of 100 feet and heads, how many sheep live at the farm? Answers: A) 5 B) 8 C) 10 D) 4 E) 17

Chicken - ch Cows - C Sheep -S ch+C=6S C&gt; ch and c&gt;s Each cow has 4 legs and 1 head Each chicken has 2 legs and 1 head So 5c+3ch=100 (sum of legs and head) There are 2 possible solutions to this equation c=11 and ch=9 or c=14 and ch=10 Since from first equation where ch+c=5s The sum of ch and c should be divisbile by 5. 24 is not so the only possible solution is c=11 and ch=9. So s=4 Answer : 4 <result>D</result>

D

A farm has chickens, cows and sheep. There are five times the number of chickens and cows than sheep. If there are more cows than chickens or sheep, and together, cows and chickens have a total of 100 feet and heads, how many sheep live at the farm?

aqua_rat__g0xvKjZDuYMRODPl

If m is an integer, what is the greatest possible value for m that would still make the following statement true: 11*10^m < 1/10 ? Choose the correct choice from the following answers: A) –4 B) –3 C) –2 D) –1 E) 0

Just putting values, the LHS becomes m =0 --&gt; 11 m =-1 --&gt; 11/10 m =-2 --&gt; 11/100 m =-3 --&gt; 11/1000 Anything lower will be smaller than 11/1000. m =-2, equality doesn't hold but it does for m =-3. Answer is –3. <result>B</result>

B

If m is an integer, what is the greatest possible value for m that would still make the following statement true: 11*10^m < 1/10 ?

aqua_rat__6zYSOMeFN9UQpobO

Two men A and B start from place X walking at 4 1/2 kmph and 5 1/2 kmph respectively. How many km apart they are at the end of 3 1/2 hours if they are walking in the same direction? Choose the correct choice from the following answers. A) 4 3/9 B) 4 3/5 C) 4 3/8 D) 4 3/2 E) 4 3/1

RS = 5 3/2 - 4 1/2 = 1 1/4 T = 3 1/2 h. D = 5/4 * 7/2 = 35/8 = 4 3/8 km Answer: 4 3/8 <result>C</result>

C

Two men A and B start from place X walking at 4 1/2 kmph and 5 1/2 kmph respectively. How many km apart they are at the end of 3 1/2 hours if they are walking in the same direction?

aqua_rat__mbyE0k4gbNPPm9a5

A shopkeeper mixed 7kg of salt worth Rs.6 per kg, 5kg of salt worth Rs.4 per kg and 6 kg of salt worth Rs.5 per kg. For what amount of money should he sell 4 kg of the mixed variety of salt in order to make a profit of 12½%? Choose the correct choice from the following answers A) 22.95 B) 23.95 C) 24.95 D) 25.95 E) 26.95

7kg*Rs6---- Rs 42 5 kg*Rs4---- Rs 20 6kg*Rs5---- Rs 30 18kg for Rs--92 cost price of 1 kg=92/18=&gt;Rs5.11111 cost of 4 kg ---- 4*5.11111=Rs 20.4444 Profit=12.5% SP={(100+Gain%)/100}*CP ={(100+25/2)/100}*20.444 =22.95 22.95NSWER:22.95 <result>A</result>

A

A shopkeeper mixed 7kg of salt worth Rs.6 per kg, 5kg of salt worth Rs.4 per kg and 6 kg of salt worth Rs.5 per kg. For what amount of money should he sell 4 kg of the mixed variety of salt in order to make a profit of 12½%?

aqua_rat__J9Jz6biXAg7t99vy

If 28a+30b+31c=427. then a+b+c=?.a,b,c are natural numbers Select. A) 6 B) 14 C) 12 D) 45 E) 28

have a look on your calender since,we all knw a year consist of 365 days february is d only month which has 28 days 4 months in a year has 30 days and,rest 7 months has 31 days.. so,following d given eq. we can write 28*1 + 30*4 + 31*9.. hence values of a,b and c are 1, 4 and 9 respectively.. a+b+c=14 ANSWER:14 <result>B</result>

B

If 28a+30b+31c=427. then a+b+c=?.a,b,c are natural numbers

aqua_rat__AmIDe9ITh1j7LiRs

Find the odd one out: 125, 106, 83, 76, 65, 58, 53 Pick one. A) 33 B) 83 C) 26 D) 18 E) 222

Explanation: This sequence represents a series in which from the reverse order a prime number is added: 53+5= <gadget id="calculator">53+5</gadget> <output>58</output> 58 58+7= <gadget id="calculator">58+7</gadget> <output>65</output> 65 65+11= <gadget id="calculator">65+11</gadget> <output>76</output> 76 76+13= <gadget id="calculator">76+13</gadget> <output>89</output> 89 89+17= <gadget id="calculator">89+17</gadget> <output>106</output> 106 106+19= <gadget id="calculator">106+19</gadget> <output>125</output> 125 Hence 83 is the answer. ANSWER: 83 <result>B</result>

B

Find the odd one out: 125, 106, 83, 76, 65, 58, 53

aqua_rat__KgKtQKVP6AbZfDsY

P can complete a piece of work in 18 days & B can do the same piece of work in 15 days. They started working together but after 3 days P left & Q alone completed the remaining work. The whole work was completed in how many days? Select. A) 12 days B) 12.5 days C) 13 days D) 14.5 days E) 15.5 days

Both together worked for 3 days. In 3 days , P can do = 3 x 1 18 = 1 6 th work In 3 days, Q can do = 3 x 1 15 = 1 5 th work In 3 days , work finished = 1 6 + 1 5 = 11 30 12.5 daysalance work = 19 30 12.5 daysalance work finished by Q =&gt; Time taken by Q to finish the balance work = 19 30 x 15 = 9.5 days The whole work was completed in 9.5 + 3= <gadget id="calculator"> 9.5 + 3</gadget> <output>12.5</output> 12.5 days 12.5 days <result>B</result>

B

P can complete a piece of work in 18 days & B can do the same piece of work in 15 days. They started working together but after 3 days P left & Q alone completed the remaining work. The whole work was completed in how many days?

aqua_rat__0v0UIvL8VTj6TAJ0

If 4^x = 8^y, then the value of (x/y)-1 is equal to : Choose the most appropriate option: A) 1/2 B) 0 C) 1/4 D) 3/4 E) 2/3

4^x = 8^y, 2^2x= 2^3y so 2x=3y x/y = 3/2 (x/y)-1 = (3/2)-1= 1/2 1/2NSWER:1/2 <result>A</result>

A

If 4^x = 8^y, then the value of (x/y)-1 is equal to :

aqua_rat__PDOwvyrViZJwhqoQ

complete the numerical series with the correct number 5+3+2=151022 9+2+4=183652 8+6+3=482466 5+4+5=202541 9+5+5= ? Choices A) 468645 B) 454586 C) 454585 D) 454386 E) 444586

454585orrect Answer : 454585 number is formed as 5+3+2 5*3 3*2 2*5 = 151022 similarly, 9*5 9*5 (9*5+9*5-5)= 454585 <result>C</result>

C

complete the numerical series with the correct number 5+3+2=151022 9+2+4=183652 8+6+3=482466 5+4+5=202541 9+5+5= ?

aqua_rat__PxQOKdmCkM1fkic6

A man can do a job in 15 days. His father takes 20 days and his son finishes it in 25 days. How long will they take to complete the job if they all work together? Pick. A) 6.4 days B) 4.4 days C) 5.4 days D) 8.4 days E) 2.4 days

6.4 days 6.4 days 1 day work of the three persons = (1/15 + 1/20 + 1/25) = 47/300 So, all three together will complete the work in 300/47 = 6.4 days.- <result>A</result>

A

A man can do a job in 15 days. His father takes 20 days and his son finishes it in 25 days. How long will they take to complete the job if they all work together?

aqua_rat__gTdHbv0YRUwYjEeT

The edges of three iron cubes are 6cm; 8cm; 10cm respectively. A new cube was made by melting them. Find the edge of the new cube? Choose the correct choice from the following choices A) 17 B) 19 C) 16 D) 12 E) 14

63 + 83 + 103 = a3 =&gt; a = 12 Answer:12 <result>D</result>

D

The edges of three iron cubes are 6cm; 8cm; 10cm respectively. A new cube was made by melting them. Find the edge of the new cube?

aqua_rat__hIViyfPVDnBLXMHv

The average age of a husband and his wife was 26 years at the time of their marriage. After five years they have a one-year old child. The average age of the family now is : Choose one: A) 11 B) 18 C) 21 D) 287 E) 27

Explanation: Sum of the present ages of husband, wife and child = (26 * 2 + 5 * 2) + 1= <gadget id="calculator">(26 * 2 + 5 * 2) + 1</gadget> <output>63</output> 63 years. Required average= (63/3)= <gadget id="calculator">(63/3)</gadget> <output>21</output> 21 years. Answer: 21) 21 <result>C</result>

C

The average age of a husband and his wife was 26 years at the time of their marriage. After five years they have a one-year old child. The average age of the family now is :

aqua_rat__iB4UW4K2LjHkkYtq

A dealer purchases 15 articles for Rs. 25 and sells 12 articles for Rs. 33. Find the profit percentage? Select the correct option A) 65% B) 50% C) 59% D) 40% E) 53%

L.C.M of 15 and 12 = 60 CP of 60 articles = Rs. 100 (25 * 4) SP of 60 articles = Rs. 165 (33 * 5) Profit percentage = (165 - 100)/100 * 100= <gadget id="calculator">(165 - 100)/100 * 100</gadget> <output>65</output> 65% 65%nswer: 65% <result>A</result>

A

A dealer purchases 15 articles for Rs. 25 and sells 12 articles for Rs. 33. Find the profit percentage?

aqua_rat__C9b3nwE4RkHSb9Z0

A soccer team played 158 games and won 40 percent of them. How many games did it win? Choose the correct choice from the following answers: A) 84 B) 63.2 C) 104 D) 50.8 E) 15.8

40% of 158=x 0.40*158= <gadget id="calculator">0.40*158</gadget> <output>63.2</output> x 63.2=x answer :63.2 <result>B</result>

B

A soccer team played 158 games and won 40 percent of them. How many games did it win?

aqua_rat__KpGgAvljOZFAqppa

Given a bag with 2 red balls and 3 yellow balls, you randomly select one of them, in order. If the second ball you take is yellow, what is the probability that the first one was also yellow? Answers: A) 1/2 B) 1/5 C) 3/4 D) 1/3 E) 3/5

This is a conditional probability question. Basically we are told that out of 2 balls picked one is yellow and are asked to find the probability of the other one also to be yellow. So, possible options for this other ball would be: W, W, B, B (as one yellow is already picked) So the probability for that ball to be yellow too is 2/4=1/2. Option 1/2 <result>A</result>

A

Given a bag with 2 red balls and 3 yellow balls, you randomly select one of them, in order. If the second ball you take is yellow, what is the probability that the first one was also yellow?

aqua_rat__UOE0CGfVt0d2jv6P

If the difference between the length and breadth of a rectangle is 23 m and its perimeter is 186 m, what is its area? Choose the correct choice. A) 2510 B) 2535 C) 2530 D) 2030 E) 2520

length = breadth +23. Therefore, 4× breadth +2×23=186 m ⇒ breadth =35 m length =35+23= <gadget id="calculator">35+23</gadget> <output>58</output> 58 m Area=58×35=2030 m2 Answer is 2030. <result>D</result>

D

If the difference between the length and breadth of a rectangle is 23 m and its perimeter is 186 m, what is its area?

aqua_rat__GYLjD0I4BfonqaKE

Sequence P is defined by pn=pn−1+3, p1=11, sequence Q is defined as qn=qn−1–4, q3=103. If pk>qk+2, what is the smallest value k can take? Select the correct option. A) 6 B) 9 C) 11 D) 14 E) 15

Set P = {11, 14, 17,.....} Set Q = {110, 107, 103,....} For Arithmetic progression a(n)=a(1)+(n−1)d Started with C) 11 does not satisfy pk &gt; qk+2 and D) 14, pk = qk+2 So Answer is 15 <result>E</result>

E

Sequence P is defined by pn=pn−1+3, p1=11, sequence Q is defined as qn=qn−1–4, q3=103. If pk>qk+2, what is the smallest value k can take?

aqua_rat__cC0aWRzRbS07qx4i

Out of seven given numbers, the average of the first four numbers is 4 and that of the last four numbers is also 4. If the average of all the seven numbers is 3, fourth number is Choose the most appropriate option: A) 3 B) 4 C) 7 D) 11 E) 12

(a+b+c+d)/4=4 =&gt;(a+b+c+d)=16...........(1) (d+e+f+g)/4=4 =&gt;(d+e+f+g)=16 =&gt;(e+f+g)=16-d...........(2) Also, (a+b+c+d+e+f+g)/7=3 (Given) using (1) and (2) equations 16+16-d=21 =&gt; d=11 ANSWER:11 <result>D</result>

D

Out of seven given numbers, the average of the first four numbers is 4 and that of the last four numbers is also 4. If the average of all the seven numbers is 3, fourth number is

aqua_rat__fNIZrwkgRZX5Hdze

Tough and Tricky questions: Percents. Over the course of a year, a certain microbrewery increased its beer output by 80 percent. At the same time, it decreased its total working hours by 10 percent. By what percent did this factory increase its output per hour? Pick: A) 100 B) 200 C) 300 D) 400 E) 500

Lets assume the initial production was 100 litres of beer for 100 hr. With the 80% increase the total amount of beer production will be 180 litres and with 10 % decrease in total hours will be reduced to 90 hr. 100hr ----&gt; 100 lts 1hr -----&gt; 1 lts 90hr -----&gt; 180 lts 1hr -----&gt; 2 lts Total Increase in production for 1 hr = 200% Answer 200 <result>B</result>

B

Tough and Tricky questions: Percents. Over the course of a year, a certain microbrewery increased its beer output by 80 percent. At the same time, it decreased its total working hours by 10 percent. By what percent did this factory increase its output per hour?

aqua_rat__rhGWBwgS11rcp60c

A man can swim in still water at 3 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is? Select the correct option: A) 1.7 B) 1.4 C) 1.1 D) 1.5 E) 1

M = 3 S = x DS = 3 + x US = 3 + x 3 + x = (3 - x)2 3 + x = 6 -2x 3x = 3 x = 1 Answer:1 <result>E</result>

E

A man can swim in still water at 3 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?

aqua_rat__LoCtK38zSxtPbeKg

On Monday morning, Chris receives tickets to a baseball game that will be played at 7pm on the next evening that it does not rain. However, Chris is only in town until Wednesday morning, at which point he must fly to another city. If there is a 40% chance of rain each of the next two evenings, what is the probability that Chris will be able to attend the game? Choose the correct option: A) 36% B) 60% C) 66% D) 80% E) 84%

Chris won't be able to attend the game if it be raining on Monday evening and Tuesday evening. The probability of that is 0.4*0.4 = 0.16. So, the probability that he will be able to attend is 1 - 0.16 = 0.84. Answer: 84%. <result>E</result>

E

On Monday morning, Chris receives tickets to a baseball game that will be played at 7pm on the next evening that it does not rain. However, Chris is only in town until Wednesday morning, at which point he must fly to another city. If there is a 40% chance of rain each of the next two evenings, what is the probability that Chris will be able to attend the game?

aqua_rat__MNsMwhyIjNVLWdeE

Each night before he goes to bed, Jordan likes to pick out an outfit to wear the next day. He has 12 different shirts, 10 different pairs of jeans, and 7 pairs of sneakers. If an outfit consists of 1 shirt, 1 pair of jeans, and 1 pair of sneakers, how many different outfits does Jordan have? Select the correct option. A) 30 B) 840 C) 240 D) 480 E) 960

Total # of outfits = 12 * 10 * 7= <gadget id="calculator">12 * 10 * 7</gadget> <output>840</output> 840 Answer - 840 <result>B</result>

B

Each night before he goes to bed, Jordan likes to pick out an outfit to wear the next day. He has 12 different shirts, 10 different pairs of jeans, and 7 pairs of sneakers. If an outfit consists of 1 shirt, 1 pair of jeans, and 1 pair of sneakers, how many different outfits does Jordan have?

aqua_rat__FdwlGkjKSwFK2mNk

There are 36 students in a certain geometry class. If one third of the students are boys and one fourth of the boys are under six feet tall, how many boys in the class are under six feet tall? Options. A) 3 B) 12 C) 18 D) 24 E) 27

Total Students = 36 One third of the students are boys = 1/3*36= <gadget id="calculator">1/3*36</gadget> <output>12</output> 12 One fourth of the boys are under six feet tall= 1/4*12= <gadget id="calculator">1/4*12</gadget> <output>3</output> 3 ... Therefore Number of boys in the class under six feet tall= 3 ... Answer A.... Alternatively... Number of boys in the class under six feet tall = 1/4 of 1/3 of Total Students = 1/4*1/3*36 = 3... 3nswer 3 <result>A</result>

A

There are 36 students in a certain geometry class. If one third of the students are boys and one fourth of the boys are under six feet tall, how many boys in the class are under six feet tall?

aqua_rat__43OKRcjpjPfyh6xB

John and Jacob set out together on bicycle traveling at 15 and 9 miles per hour, respectively. After 40 minutes, John stops to fix a flat tire. If it takes John one hour to fix the flat tire and Jacob continues to ride during this time, how many hours will it take John to catch up to Jacob assuming he resumes his ride at 15 miles per hour? (consider John's deceleration/acceleration before/after the flat to be negligible) Options: A) 3 B) 3 1/3 C) 3 1/2 D) 4 E) 1 1/4

John's speed - 15 miles/hr Jacob's speed - 9 miles/hr After 40min (i.e 2/3hr), distance covered by John = 15x2/3 = 10 miles. Jacob continues to ride for a total of 1hour and 40min (until John's bike is repaired). Distance covered in 1 hour 40min (i.e 5/3hr) = 9x5/3 = 15 miles. Now, when John starts riding back, the distance between them is 7.5 miles. Jacob and John are moving in the same direction.For John to catch Jacob, the effective relative speed will be 15-9= <gadget id="calculator"> 15-9</gadget> <output>6</output> 6 miles/hr. Thus, to cover 7.5 miles at 6 miles/hr, John will take 7.5/6= <gadget id="calculator"> 7.5/6</gadget> <output>1.25</output> 1.25 hours Answer 1 1/4 <result>E</result>

E

John and Jacob set out together on bicycle traveling at 15 and 9 miles per hour, respectively. After 40 minutes, John stops to fix a flat tire. If it takes John one hour to fix the flat tire and Jacob continues to ride during this time, how many hours will it take John to catch up to Jacob assuming he resumes his ride at 15 miles per hour? (consider John's deceleration/acceleration before/after the flat to be negligible)

aqua_rat__0B3k9XWEfS5ns1iV

Five marbles are randomly selected, one at a time (without return), from a bowl of 100 marbles (20 green, 30 blue, 10 yellow, and 40 black). What is the probability that all five marbles are black? (Answer in lowest terms). Choose the correct choice from the following: A) 201/125 B) 9139/1045660 C) 11350/146790 D) 21/75 E) 2/5

Let K = black. The bowl has 40 black marbles (we don't care what color the other marbles are because success is black only), so the probability of getting black is P(K) = 40/100 on the first selected marble. Because selection is (without return), the P(K) has changed for following selections. Now, there are 99 marbles and black is dependent upon whether first marble was black, or not... and so on.... Therefore, conditional probability! The probability that event B occurs, given that event A has already occurred is: Formula = P(A\B) = P(A and B)/P(B). P(A\9139/1045660) = (40/100)(39/99)(38/98)(37/97)(36/96) = 78960960/9034502400 = 9139/1045660 Answer: 9139/1045660 <result>B</result>

B

Five marbles are randomly selected, one at a time (without return), from a bowl of 100 marbles (20 green, 30 blue, 10 yellow, and 40 black). What is the probability that all five marbles are black? (Answer in lowest terms).

aqua_rat__ysmIzycxb5of6ULJ

If the largest three digit number is subtracted from the smallest five digit number, then the remainder is Select the correct option. A) 1 B) 9000 C) 9001 D) 90001 E) None

Solution Required remainder = (10000 - 999)= <gadget id="calculator">(10000 - 999)</gadget> <output>9_001</output> 9001 Answer 9001 <result>C</result>

C

If the largest three digit number is subtracted from the smallest five digit number, then the remainder is

aqua_rat__KlfX7Ou2F4awiI8C

Look at this series: 15, __, 27, 27, 39, 39, ... What number should fill the blank? Choose the most appropriate option: A) 51 B) 39 C) 23 D) 15 E) None

Explanation: In this simple addition with repetition series, each number in the series repeats itself, and then increases by 12 to arrive at the next number. Answer: Option 15 <result>D</result>

D

Look at this series: 15, __, 27, 27, 39, 39, ... What number should fill the blank?

aqua_rat__0zJsMuZ0VXIi4u8a

What is the present worth of Rs. 132 due in 2 years at 5% simple interest per annum Choose the correct choice from the following answers. A) 110 B) 120 C) 130 D) 140 E) None of these

Explanation: Let the present worth be Rs.x Then,S.I.= Rs.(132 - x) =� (x*5*2/100) = 132 - x =� 10x = 13200 - 100x =� 110x = 13200 x= 120 Answer: 120 <result>B</result>

B

What is the present worth of Rs. 132 due in 2 years at 5% simple interest per annum

aqua_rat__qeXsqR6GENkUnJi6

With what number must 0.580 be multiplied in order to obtain the number 580? Answers: A) 100 B) 1,000 C) 10,000 D) 100,000 E) None of these

Explanation: The decimal must be moved three places to the right. To do this, we must multiply by a number with three zeroes. The correct answer is 1000.The decimal must be moved three places to the right. To do this, we must multiply by a number with three zeroes. The correct answer is 1000. Answer : (1,000) <result>B</result>

B

With what number must 0.580 be multiplied in order to obtain the number 580?

aqua_rat__2pUC9SCuvaUyX0SW

10 men and 15 women together can complete a work in 6 days. It takes 100 days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work? Pick one: A) 127 days B) 667 days C) 177 days D) 187 days E) 225 days

1 man's 1 day work = 1/100 (10 men + 15 women)'s 1 day work = 1/6 15 women's 1 day work = (1/6 - 10/100) = 1/15 1 woman's 1 day work = 1/225 1 woman alone can complete the work in 225 days. Answer:225 days <result>E</result>

E

10 men and 15 women together can complete a work in 6 days. It takes 100 days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work?

aqua_rat__8P4OxHn3oZW4zijK

A School Bus is used to transport students from home to college. There are total of 20 students who want to take the bus. There are 10 seats in the bus. 2 in the front row, 4 in the middle row and 4 in the last row. Bus driver has to make sure that front 2 seats are for nausea students. 4 students have nausea and can only sit in the front 2 seats. How many ways can the students sit in the bus. Choose the correct choice from the following answers: A) 100068 B) 24443 C) 2392329 D) 445678 E) 5405400

4C2 Select 2 students from 4 who have nausea and can sit in front seats only. 16C4 Select 4 students from 16 who have to sit in middle row. (As 4 students who have nausea cannot sit anywhere else/ 20-4 = 16) 12C4 Select 4 students who will sit in the last row. (As 4 students who have nausea cannot sit anywhere else. 4 are sitting in the middle row. 20-4-4 = 12) Total Number of selection = 4C2 * 16C4 * 12C4 = 5405400 Ans = 5405400 <result>E</result>

E

A School Bus is used to transport students from home to college. There are total of 20 students who want to take the bus. There are 10 seats in the bus. 2 in the front row, 4 in the middle row and 4 in the last row. Bus driver has to make sure that front 2 seats are for nausea students. 4 students have nausea and can only sit in the front 2 seats. How many ways can the students sit in the bus.

aqua_rat__1dtHcfzefiKdI5EZ

Percentage of profit earned by selling a book e for $1920 is equal to the percentage loss incurred by selling the same book for $1280. What price should the book be sold to make 25% profit? Choose the correct choice from the following answers: A) $500 B) $1000 C) $1500 D) $1700 E) $2000

Let C.P. be Rs. x. Then, 1920 - x x 100 = x - 1280 x 100 x x 1920 - x = x - 1280 2x = 3200 x = 1600 Required S.P. = 125% of Rs. 1600 = Rs. 125 x 1600 = $2000 100 $2000 <result>E</result>

E

Percentage of profit earned by selling a book e for $1920 is equal to the percentage loss incurred by selling the same book for $1280. What price should the book be sold to make 25% profit?

aqua_rat__ZaBa6Iuj5RXckwUQ

For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum of all the integers between 100 and 200? Choose the correct choice from the following: A) 4545 B) 5050 C) 6525 D) 4352 E) 4652

sum = 100*101/2 = 50*101= <gadget id="calculator">50*101</gadget> <output>5_050</output> 5050 Answer is 5050 <result>B</result>

B

For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum of all the integers between 100 and 200?

aqua_rat__e2WoOAPkd6Em5kgY

In the reading room of a library, there are 25 reading spots. Each reading spot consists of a round table with 9 chairs placed around it. There are some readers such that in each occupied reading spot there are different numbers of readers. If in all there are 36 readers, how many reading spots do not have even a single reader? Select A) 17 B) 16 C) 15 D) 14 E) 9

1+2+3+4+5+6+7+8= <gadget id="calculator">1+2+3+4+5+6+7+8</gadget> <output>36</output> 36 so, 8 spots are occupied by users 25-8= <gadget id="calculator"> 25-8</gadget> <output>17</output> 17, 17NSWER:17 <result>A</result>

A

In the reading room of a library, there are 25 reading spots. Each reading spot consists of a round table with 9 chairs placed around it. There are some readers such that in each occupied reading spot there are different numbers of readers. If in all there are 36 readers, how many reading spots do not have even a single reader?

aqua_rat__EWYDYgw9KIJhlQJ5

Whats the next number in this number series ? 18, 46, 94, 63, 52, ? Select the correct option. A) 23 B) 12 C) 34 D) 61 E) 55

61 61 Reversed digits of squares of number in descending order. <result>D</result>

D

Whats the next number in this number series ? 18, 46, 94, 63, 52, ?

aqua_rat__r7gF3JN8eVvEjIGc

Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour? Choices: A) 9 B) 10 C) 12 D) 20 E) 22

Due to stoppages, it covers 9 km less. Time taken to cover 9 km = (9/54 x 60) min = 10 min. Answer:10 <result>B</result>

B

Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?

aqua_rat__0LM9YkETM1x56vDj

How many different possible permutations can be made from the word ‘VULLAT’ such thatthe vowels are never together? Select the correct option: A) 120 B) 200 C) 240 D) 260 E) 270

The word ‘BULLAT’ contains 6 letters of which 1 letter occurs twice = 6! / 2! = 360 No. of permutations possible with vowels always together = 5! * 2! / 2! = 120 No. of permutations possible with vowels never together = 360-120= <gadget id="calculator">360-120</gadget> <output>240</output> 240. 240 <result>C</result>

C

How many different possible permutations can be made from the word ‘VULLAT’ such thatthe vowels are never together?

aqua_rat__3S9v5pzl3WkSEENg

Consider a set S given as {11,22,33,44,55,66,77,88,99} . If each element of the data set is multiplied by -6 then by what factors will the Mean,Variance and Standard Deviation respectively change ? Choose the correct answer A) -6,-6,-6 B) -6,6,6 C) 1,1,1 D) -6,36,6 E) 6,6,36

Mean: If all values are multiplied by -6 then their sum will also be multiplied by -6 so Mean will also get -6 Variance: Variance is equal to (Sum of (Square of (the difference between mean and individual values))/Total number of values When we multiply all the values by -6 then the difference between the mean and the individual values also gets multiplied by -6 and the square of that difference becomes 36. So, the variance gets multiplied by a factor of 36 SD: Standard Deviation is the square root of variance so sqrt(36)=6. So SD gets multiplied by a factor of 6. So, answer will be -6,36,6. <result>D</result>

D

Consider a set S given as {11,22,33,44,55,66,77,88,99} . If each element of the data set is multiplied by -6 then by what factors will the Mean,Variance and Standard Deviation respectively change ?

aqua_rat__huAXOkuvCNqRlAU5

A committee has 4 men and 6 women. What are the number of ways of selecting 2 men and 4 women from the given committee? Choose one: A) 75 B) 90 C) 105 D) 120 E) 135

The number of ways to select two men and four women = 4C2 * 6C4 = 6 * 15= <gadget id="calculator">6 * 15</gadget> <output>90</output> 90 The answer is 90. <result>B</result>

B

A committee has 4 men and 6 women. What are the number of ways of selecting 2 men and 4 women from the given committee?

aqua_rat__0LuRIemph8Tp4HRd

Two men are walking towards each other alongside a railway track. A freight train overtakes one of them in 20 seconds and exactly 10 minutes later meets the other man coming from the opposite direction. The train passes this man is 18 seconds. Assume the velocities are constant throughout. How long after the train has passed the second man will the two men meet? Pick: A) 89.7 minutes B) 90 minutes C) 90.3 seconds D) 91 seconds E) None of these

Explanation : Let ‘L’ be the length of train, ‘x’ be the speed of the first man, ‘y’ be the speed of the second man and ‘z’ be the speed of the train. =&gt;20=1/(z−x) and =&gt;18=1/(z+x) =&gt;z=10x+9y. Distance between the two men =600(z+y). Time = (600(z+y)-600(x+y))/(x+y). =&gt;600(9x+9y)/(x+y). =&gt; 90 minutes. Answer : 90 minutes <result>B</result>

B

Two men are walking towards each other alongside a railway track. A freight train overtakes one of them in 20 seconds and exactly 10 minutes later meets the other man coming from the opposite direction. The train passes this man is 18 seconds. Assume the velocities are constant throughout. How long after the train has passed the second man will the two men meet?

aqua_rat__k5nSUmqDhdjaQQsK

A cube of side 3 meter length is cut into small cubes of side 15 cm each. How many such small cubes can be obtained? Choose one: A) 8078 B) 1040 C) 1058 D) 1021 E) 8000

Along one edge, the number of small cubes that can be cut = 300/15= <gadget id="calculator">300/15</gadget> <output>20</output> 20 Along each edge 20 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut= 20 * 20 * 20= <gadget id="calculator">20 * 20 * 20</gadget> <output>8_000</output> 8000 Answer:8000 <result>E</result>

E

A cube of side 3 meter length is cut into small cubes of side 15 cm each. How many such small cubes can be obtained?

aqua_rat__npGkBY8qImdjW5dt

x = 13.165 y = 7.686 z = 11.545 The number A is obtained by first rounding the values of x, y, and z to the hundredths place and then adding the resulting values. The number B is obtained by first adding the values of x, y, and z and then rounding the sum to the hundredths place. What is the value of A – B? Select the correct option: A) 0.01 B) 0.02 C) 0.03 D) 0.1 E) 0.2

Rounding off the values: x = 13.17 y = 7.69 z = 11.55 A = 13.17 + 7.69 + 11.55= <gadget id="calculator">13.17 + 7.69 + 11.55</gadget> <output>32.41</output> 32.41 x + y + z= 13.165 + 7.686 + 11.545 = 32.206 B = 32.21 A - B = 0.2 Option 0.2 <result>E</result>

E

x = 13.165 y = 7.686 z = 11.545 The number A is obtained by first rounding the values of x, y, and z to the hundredths place and then adding the resulting values. The number B is obtained by first adding the values of x, y, and z and then rounding the sum to the hundredths place. What is the value of A – B?

aqua_rat__A1tuM9QjWh22fL2m

A boat travels 32 km downstream in 8 hours and 24 km upstream in 12 hours. Find the speed of the boat in still water and the speed of the water current. Select: A) 3 km/hr, 1 km/hr B) 5 km/hr, 4 km/hr C) 1 km/hr, 6 km/hr D) 2 km/hr, 1 km/hr E) 4 km/hr, 1 km/hr

Downstream speed=32km/8hrs =4kmph upstream speed32 /8= <gadget id="calculator">32 /8</gadget> <output>4</output> 4kmph upstream speed=24km/12hrs =2kmph speed of boat24 /12= <gadget id="calculator">24 /12</gadget> <output>2</output> 2kmph speed of boat=avg of downstream and upstream speeds speed of boat=(4+2)/2= <gadget id="calculator">(4+2)/2</gadget> <output>3</output> 3kmph. current speed=half of the difference of downstream and upstream speeds currend speed=(4-2)/2= <gadget id="calculator">(4-2)/2</gadget> <output>1</output> 1kmph ans is 3km/hr,1km/hr 3 km/hr, 1 km/hrNSWER:3 km/hr, 1 km/hr <result>A</result>

A

A boat travels 32 km downstream in 8 hours and 24 km upstream in 12 hours. Find the speed of the boat in still water and the speed of the water current.

aqua_rat__CA78mecTLsB6ltN6

Population of a colony of ants is increasing by 20% per day. If the population on Monday was 3000, on which day of that week the population would be 5184 ? Choose one A) Wednesday B) Thursday C) Monday D) sunday E) tuesday

Monday - 3000, Tuesday = 3000+(3000*.20)= <gadget id="calculator">3000+(3000*.20)</gadget> <output>3_600</output> 3600 wednesday= 3600+(3600*.20)= <gadget id="calculator">3600+(3600*.20)</gadget> <output>4_320</output> 4320 Thursday= 4320+(4320*.20)= <gadget id="calculator">4320+(4320*.20)</gadget> <output>5_184</output> 5184 ANSWER:Thursday <result>B</result>

B

Population of a colony of ants is increasing by 20% per day. If the population on Monday was 3000, on which day of that week the population would be 5184 ?

aqua_rat__oTiGXYoErtrX28LF

A bag contains 10 red and 6 white balls. One ball is drawn at random. What is the probability that the ball drawn is white? Choose the correct option. A) 4/7 B) 2/3 C) 5/8 D) 1/4 E) 5/7

Total number of balls = 10+6= <gadget id="calculator">10+6</gadget> <output>16</output> 16 number of white balls= 10 Probability = 10/16 = 5/8 Answer is 5/8 <result>C</result>

C

A bag contains 10 red and 6 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?

aqua_rat__XzKoMXHooXJ7qwLG

A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits $ 1600 each in 1st month and 7th month of a year. At the end of the year, the amount he would have gained by way of interest is? Choose one: A) 121 B) 50 C) 100 D) 160 E) 80

Amount = (1600)* (1 + (5/2*100))^2 Amount = 1600 * (41/40) * (41/40)= <gadget id="calculator">1600 * (41/40) * (41/40)</gadget> <output>1_681</output> 1681 ------(for investment in 1st month) Amount= 1600 * (41/40)= <gadget id="calculator">1600 * (41/40)</gadget> <output>1_640</output> 1640 -----(for investment in 7th month) Total Amount= 1681 + 1640= <gadget id="calculator">1681 + 1640</gadget> <output>3_321</output> 3321 Interest= 3321-3200 = 121.............. 121ns -121 <result>A</result>

A

A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits $ 1600 each in 1st month and 7th month of a year. At the end of the year, the amount he would have gained by way of interest is?

aqua_rat__JEpakVsYYEdmOjLZ

If q and r are both odd numbers B, which of the following must also be odd? Pick: A) q – r B) (q + r)^2 C) q(q + r) D) (qr)^2 E) q/r

We're told that q and r are both ODD numbers B. We're asked which of the following must also be odd. IF... q = 1 r = 3 Answer A) q – r = 1-3 = -2 NOT odd Answer B) (q + r)^2 = (1+3)^2 = 16 NOT odd Answer C) q(q + r) = (1)(4) = 4 NOT odd Answer (qr)^2) (qr)^2 = (3)^2 = 9 This IS O(qr)^2(qr)^2 Answer E) q/r = 1/3 NOT odd Final Answer: (qr)^2 <result>D</result>

D

If q and r are both odd numbers B, which of the following must also be odd?

aqua_rat__U6XlurkhfCrWGZOL

A, Band C can do a piece of work in 35 days, 20 days and 55 days respectively, working alone. How soon can the work be done if A is assisted by Band C on alternate days? Choose one: A) 7 days B) 8 days C) 9 days D) 10 days E) 16 days

(A+B)'s 1 day's work = 1/35+1/20 = 11/140 (A+C)'s 1 day's work = 1/35+1/55 = 18/385 work done in 2 day's = 11/140+18/385 = 48/383 48/383th work done in 2 days work done= 383/48*2 = 16 days (approx) ANSW16 daysR:16 days <result>E</result>

E

A, Band C can do a piece of work in 35 days, 20 days and 55 days respectively, working alone. How soon can the work be done if A is assisted by Band C on alternate days?

aqua_rat__eQ38TiZNIrzpE4Au

The words mentioned below have been arranged in a particular order. SHOP, FEAR, BALL, DEAD Can you find the logic behind the order? Choices: A) 58 > 30 > 27 > 14 B) 58 > 30 > 27 > 15 C) 58 > 30 > 27 > 16 D) 58 > 30 > 27 > 17 E) None

Solution: Here, the alphabets can be re-written to their corresponding numbers: A = 1, B = 2, C = 3... and so on SHOP = 19 + 8 + 15 + 16= <gadget id="calculator">19 + 8 + 15 + 16</gadget> <output>58</output> 58 FEAR= 6 + 5 + 1 + 18= <gadget id="calculator">6 + 5 + 1 + 18</gadget> <output>30</output> 30 BALL= 2 + 1 + 12 + 12= <gadget id="calculator">2 + 1 + 12 + 12</gadget> <output>27</output> 27 DEAD= 4 + 5 + 1 + 4= <gadget id="calculator">4 + 5 + 1 + 4</gadget> <output>14</output> 14 Now, clearly 58 &gt; 30 &gt; 27 &gt; 14 Thus, the order. 58 &gt; 30 &gt; 27 &gt; 14nswer 58 &gt; 30 &gt; 27 &gt; 14 <result>A</result>

A

The words mentioned below have been arranged in a particular order. SHOP, FEAR, BALL, DEAD Can you find the logic behind the order?

aqua_rat__lTpjTepseZUHmeNl

2 no.'s, when divided by 17, leave remainders 13 and 11 respectively. If the sum of those 2 no.'s is divided by 17, the remainder will be Answers: A) 5 B) 6 C) 7 D) 8 E) 9

(7) Required remainder = remainder by (13 +11)/17 = 7 <result>C</result>

C

2 no.'s, when divided by 17, leave remainders 13 and 11 respectively. If the sum of those 2 no.'s is divided by 17, the remainder will be

aqua_rat__gXjdeTrAgMGc2RlH

If the price of a TV is first decreased by 20% and then increased by 55%, then the net change in the price will be : Choose the correct choice from the following choices: A) 4% increase B) 24% increase C) 10% decrease D) 6% increase E) None of these

Explanation : Solution: let the original price be Rs. 100. New final price = 155% of(80% of 100) =Rs. 155/100 * 80/100 * 100 = Rs. 124. .'. Increase = 24% Answer : 24% increase <result>B</result>

B

If the price of a TV is first decreased by 20% and then increased by 55%, then the net change in the price will be :

aqua_rat__u9MKqUiqKpKkG88b

Ben and Andrew are partners in a business. Ben is a working partner while Andrew is a sleeping partner. Ben gets 8% of the profit for managing the business, and the rest is divided in proportion to their capitals. If Ben invested 25000 and Andrew invested 38000, what is Ben's share in profit of 3500? Choose the correct choice from the following choices A) 1557.8 B) 1157.8 C) 1540.8 D) 3557.8 E) 2557.8

The amount Ben gets for managing = 8% of Rs. 3500 = 280 Remaining profit = 3500 – 280 = 3220 This is to be divided in the ratio 25000 : 38000=25: 38. Share of Ben = 25/63 of 3220 = 1277.8 ⇒ Total share of Ben = 280 + 1277.8 = 1557.8. 1557.8nswer 1557.8 <result>A</result>

A

Ben and Andrew are partners in a business. Ben is a working partner while Andrew is a sleeping partner. Ben gets 8% of the profit for managing the business, and the rest is divided in proportion to their capitals. If Ben invested 25000 and Andrew invested 38000, what is Ben's share in profit of 3500?

aqua_rat__z20uQCGxFNT9DO4S

The cost of 20 articles is equal to selling price of 10. Find the gain or loss percent? Choose the correct choice from the following options A) 50% B) 100% C) 25% D) 15% E) 60%

C.P. of each article be $1 C.P. of 10 articles = 10 gain% = 10/10*100= <gadget id="calculator">10/10*100</gadget> <output>100</output> 100% Answer is 100% <result>B</result>

B

The cost of 20 articles is equal to selling price of 10. Find the gain or loss percent?

aqua_rat__ENWqQeEZs8XWlhdw

The area of a triangle is with base 18m and height 6m? Choices: A) 88 m2 B) 10 m2 C) 66 m2 D) 54 m2 E) 31 m2

1/2 * 18 * 6= <gadget id="calculator">1/2 * 18 * 6</gadget> <output>54</output> 54 m2 Answer: 54 m2 <result>D</result>

D

The area of a triangle is with base 18m and height 6m?

aqua_rat__p4DzqAeOmFSRWpGx

A person purchased a TV set for Rs. 2000 and a DVD player for Rs. 1000. He sold both the items together for Rs. 6000. What percentage of profit did he make? Answers: A) 80% B) 89% C) 100% D) 48% E) 10%

The total CP = Rs. 2000 + Rs. 1000 = Rs. 3000 and SP = Rs. 6000 Profit(%) = (6000 - 3000)/3000 * 100= <gadget id="calculator">(6000 - 3000)/3000 * 100</gadget> <output>100</output> 100% Answer: 100% <result>C</result>

C

A person purchased a TV set for Rs. 2000 and a DVD player for Rs. 1000. He sold both the items together for Rs. 6000. What percentage of profit did he make?

aqua_rat__JaWOPQxAuJkOb1dc

R and S together can plough a field in 10 hours but by himself R requires 15 hours. How long would S take to plough the same field? Choose the most appropriate option: A) 24hours B) 5 hours C) 10hours D) 15hours E) 20hours

f R and S together can do a piece of work in x days and R alone can do the same work in y days, then S alone can do the same work in x y/ y – x days. the No. of hours required by S= 10 × 20/ 20 – 10 = 200/10= <gadget id="calculator">200/10</gadget> <output>20</output> 20 hours 20hours <result>E</result>

E

R and S together can plough a field in 10 hours but by himself R requires 15 hours. How long would S take to plough the same field?

aqua_rat__LDQu4MAeOB5dufK9

In a restaurant, the profit is 130% of the cost. If the cost increases by 12% but the selling price remains constant, approximately what percentage of the selling price is the profit? Choose the correct choice from the following choices. A) 30% B) 51% C) 90% D) 100% E) None of these

Explanation : Let C.P.= Rs. 100. Then, Profit = Rs. 130, S.P. = Rs. 230. New C.P. = 112% of Rs. 100 = Rs. 112 New S.P. = Rs. 230. Profit = Rs. (230 - 112) = Rs. 118. Required percentage = (118 /230 *100) % = 51 % appox Answer : 51% <result>B</result>

B

In a restaurant, the profit is 130% of the cost. If the cost increases by 12% but the selling price remains constant, approximately what percentage of the selling price is the profit?

aqua_rat__egzwcVZMAvhEYezQ

A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B's share? Select the correct option: A) 4000 B) 5000 C) 2000 D) 1000 E) 6000

Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively. Then, 4x - 3x = 1000 x = 1000. B's share = Rs. 2x = Rs. (2 x 1000) = Rs. 2000. Answer is 2000. <result>C</result>

C

A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B's share?

aqua_rat__it3LW116B61evWqP

If k, (k+200), (k+350), and 15*K are all multiples of S then S could equal which of the following ? Choose the correct choice from the following answers A) 20 B) S=25 C) 75 D) 100 E) 150

{Multiple of S} - {Multiple of S} = {Multiple of S}. (K+200) - k = 200 = {Multiple of S}. (K+350) - k = 350 = {Multiple of S}. Both 200 and 350 are multiples of only option B. Answer: S=25. <result>B</result>

B

If k, (k+200), (k+350), and 15*K are all multiples of S then S could equal which of the following ?

aqua_rat__kfWWevL4iOEXYMro

The sum of three consecutive even numbers is 366. Find the middle number of the three? Answers: A) 111 B) 123 C) 122 D) 152 E) 142

Middle number =366/3= <gadget id="calculator">366/3</gadget> <output>122</output> 122 Ans 122 <result>C</result>

C

The sum of three consecutive even numbers is 366. Find the middle number of the three?

aqua_rat__vvVILJOwCoqXUYTa

90 students represent x percent of the boys at Jones Elementary School. If the boys at Jones Elementary make up 30% of the total school population of x students, what is x? Choose one: A) 125 B) 173 C) 225 D) 250 E) 500

90=x/100*30/100*x=&gt;x^2 = 9*10000/3 = &gt; x = 173 173 <result>B</result>

B

90 students represent x percent of the boys at Jones Elementary School. If the boys at Jones Elementary make up 30% of the total school population of x students, what is x?

aqua_rat__RRVHupoJqHKkFSVE

A farm used two harvesting machines, H and K, to harvest 100 acres of wheat. Harvesting machine H, working alone at its constant rate, harvested 30 acres of wheat in 8 hours. Then harvesting machine K was brought in, and harvesting machines H and K, working together at their respective constant rates, harvested the remaining acres of wheat in 7 hours. Harvesting machine K harvested how many acres of wheat per hour? Choose the correct choice from the following options: A) 7 B) 8 C) 12 D) 3 E) 15

Rate of H = 7 acres/hr Remaining land to be harvested = 100 - 30= <gadget id="calculator">100 - 30</gadget> <output>70</output> 70 Rate of H and K= 70/7= <gadget id="calculator">70/7</gadget> <output>10</output> 10 acres/hr Rate of K= 10 - 7= <gadget id="calculator">10 - 7</gadget> <output>3</output> 3 Answer: 3 <result>D</result>

D

A farm used two harvesting machines, H and K, to harvest 100 acres of wheat. Harvesting machine H, working alone at its constant rate, harvested 30 acres of wheat in 8 hours. Then harvesting machine K was brought in, and harvesting machines H and K, working together at their respective constant rates, harvested the remaining acres of wheat in 7 hours. Harvesting machine K harvested how many acres of wheat per hour?

aqua_rat__AeGoXtCMfblcR1UU

A train crosses a platform of200 m in 15 sec, same train crosses another platform of length 300 m in 20 sec. then find the length of the train? Options A) 100m B) 180m C) 159m D) 250m E) 152m

Length of the train be ‘X’ X + 200/15 = X +300/20 4X + 800 = 3X + 900 X = 100m 100mnswer:100m <result>A</result>

A

A train crosses a platform of200 m in 15 sec, same train crosses another platform of length 300 m in 20 sec. then find the length of the train?

aqua_rat__eVAXEti5nsu8omPj

Four boys picked up 30 mangoes .In how many ways can they divide them if all mangoes be identical? Select. A) 4^30 B) 2^30 C) 1^30 D) 3^30 E) 6^30

Each Mango can be given to any one of the four people or in other words..1 mango can be divided into 4 ways...so all 30 can be divided in 4^30 ways 4^30NS:4^30 <result>A</result>

A

Four boys picked up 30 mangoes .In how many ways can they divide them if all mangoes be identical?

aqua_rat__j91FQZmt3JE8cM0s

John has 6 friends who want to ride in his new car that can accommodate only 5 people at a time (John plus 4 passengers). How many different combinations of 4 passengers can be formed from John's 6 friends? Select the correct option A) 3 B) 8 C) 10 D) 15 E) 20

6C4 = 15 The answer is 15. <result>D</result>

D

John has 6 friends who want to ride in his new car that can accommodate only 5 people at a time (John plus 4 passengers). How many different combinations of 4 passengers can be formed from John's 6 friends?

aqua_rat__Ew6rQcU0UhHgPHPK

The cost price of a radio is Rs.3300 and it was sold for Rs.1230, find the loss %? Choose the correct choice from the following choices. A) 62.7% B) 65% C) 88% D) 65% E) 62%

3300 ---- 2070 100 ---- ? =&gt; 62.7% 62.7%nswer:62.7% <result>A</result>

A

The cost price of a radio is Rs.3300 and it was sold for Rs.1230, find the loss %?

aqua_rat__aVhluBRqZQpT1qKX

The greatest number of four digits which is divisible by 10, 16, 24 and 80 is: Choose the correct choice from the following answers A) 9000 B) 9420 C) 9660 D) 9840 E) 9900

Greatest number of 4-digits is 9999. L.C.M. of 10,16, 24 and 80 is 240. On dividing 9999 by 240, the remainder is 159. Required number (9999 - 159)= <gadget id="calculator"> (9999 - 159)</gadget> <output>9_840</output> 9840. Answer: Option 9840 <result>D</result>

D

The greatest number of four digits which is divisible by 10, 16, 24 and 80 is:

aqua_rat__Y2mUTvyWloOX1s4D

Missing number in the series 4 9 20 43 90 ? Choices. A) 175 B) 185 C) 190 D) 195 E) 180

4*2+1= <gadget id="calculator">4*2+1</gadget> <output>9</output> 9 9*2+2= <gadget id="calculator">9*2+2</gadget> <output>20</output> 20 20*2+3= <gadget id="calculator">20*2+3</gadget> <output>43</output> 43 43*2+4= <gadget id="calculator">43*2+4</gadget> <output>90</output> 90 so 90*2+5= <gadget id="calculator">90*2+5</gadget> <output>185</output> 185 ANSWER:185 <result>B</result>

B

Missing number in the series 4 9 20 43 90 ?

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There are 4 sections with 7 questions each. If three questions are selected from each section, the chance of getting different questions is________ Choose the correct choice: A) 23456 B) 45678 C) 42875 D) 40000 E) 16000

we have to select three questions from each section so the chances are 7C4. 7428754.7428754=42875 ANSWER:42875 <result>C</result>

C

There are 4 sections with 7 questions each. If three questions are selected from each section, the chance of getting different questions is________

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A trader bought a car at 20% discount on its original price. He sold it at a 70% increase on the price he bought it. What percent of profit did he make on the original price? Choose the correct choice from the following choices. A) 17% B) 72% C) 12% D) 82% E) 36%

Original price = 100 CP = 80 S = 80*(170/100)= <gadget id="calculator">80*(170/100)</gadget> <output>136</output> 136 100 - 136= 36% Answer:36% <result>E</result>

E

A trader bought a car at 20% discount on its original price. He sold it at a 70% increase on the price he bought it. What percent of profit did he make on the original price?

aqua_rat__KPNMPVyXJeFg4BZg

If a boat is rowed downstream for 50 km in 5 hours and upstream for 24 km in 6 hours, what is the speed of the boat and the river? Choose the most appropriate option. A) (7 , 3) km/hr B) (7 , 9) km/hr C) (3 , 3) km/hr D) (7 , 5) km/hr E) (7 , 7) km/hr

Explanation: If x: speed of boats man in still water y: speed of the river Downstream speed (Ds) = x + y Upstream speed (Us) = x – y x = (Ds + Us) / 2 y = (Ds – Us) / 2 In the above problem Ds = 10 ; Us = 4 x = (10 + 4) / 2 = 14/2= <gadget id="calculator">14/2</gadget> <output>7</output> 7 km/hr y= (10 - 4)/2 = 6/2= <gadget id="calculator">6/2</gadget> <output>3</output> 3 km/hr (7 , 3) km/hrNSWER: (7 , 3) km/hr <result>A</result>

A

If a boat is rowed downstream for 50 km in 5 hours and upstream for 24 km in 6 hours, what is the speed of the boat and the river?

aqua_rat__wb7T19EWSrBQyOOw

Arithmetic mean and standard deviation of a certain normal distribution are 11.5 and 1.5. What value is exactly 2 standard deviations less than the mean? Choices: A) 10.5 B) 11 C) 11.5 D) 12 E) 8.5

The value which is exactly two SD below the mean is: mean-2*SD=11.5-2*1.5=8.5. Answer: 8.5. <result>E</result>

E

Arithmetic mean and standard deviation of a certain normal distribution are 11.5 and 1.5. What value is exactly 2 standard deviations less than the mean?

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If x, y, and z are positive integers and 3x = 5y = 8z, then the least possible value of x + y + z is Choose the correct choice. A) 45 B) 79 C) 50 D) 55 E) 60

given 3x=5y=8z x+y+z in terms of x = x+(3x/5)+(3x/8) = 79x/40 now checking with each of the answers and see which value gives a minimum integer value. A x = 40/79*45 , not an integer C,D,E can be ruled out similarly. 79 is minimum value as x = 79*40/79 = 79 Answer is 79 <result>B</result>

B

If x, y, and z are positive integers and 3x = 5y = 8z, then the least possible value of x + y + z is

aqua_rat__JOx8iElBpFgqDPKj

The sum of three numbers is 98. The ratio of the first to the second is 2/3, and the ratio of the second to the third is 5/8. The second number is Choose the correct answer A) 15 B) 20 C) 25 D) 30 E) 32

Solution: Let the three numbers be x, y and z. Sum of the numbers is 98. x + y + z = 98………………(i) The ratio of the first to the second is 2/3. x/y = 2/3. x = 2/3 × y. x = 2y/3. The ratio of the second to the third is 5/8. y/z = 5/8. z/y = 8/5. z = 8/5 × y. z = 8y/5. Put the value of x = 2y/3 and z = 8y/5 in (i). 2y/3 + y + 8y/5 = 98 49y/15 = 98. 49y = 98 × 15. 49y = 1470. y = 1470/49.= <gadget id="calculator">1470/49.</gadget> <output>30</output> 30 . Therefore, the second number is 30. ANSWER:30 <result>D</result>

D

The sum of three numbers is 98. The ratio of the first to the second is 2/3, and the ratio of the second to the third is 5/8. The second number is

aqua_rat__YdyG2eNkzQ4kHgeO

If there are 200 questions in a 3 hr examination. Among these questions are 100 type A problems, which requires twice as much as time be spent than the rest of the type B problems. How many minutes should be spent on type A problems? Choices A) 72 min B) 62 min C) 70 min D) 74 min E) 120 min

x=time for type B prolems 2x=time for type A problem total time=3hrs=180min 100x+100*2x=180 x=180/300= <gadget id="calculator">180/300</gadget> <output>3/5 = around 0.6</output> 0.6 time taken for type A problem=100*2*0.6= <gadget id="calculator">100*2*0.6</gadget> <output>120</output> 120min ANSW120 minR:120 min <result>E</result>

E

If there are 200 questions in a 3 hr examination. Among these questions are 100 type A problems, which requires twice as much as time be spent than the rest of the type B problems. How many minutes should be spent on type A problems?

aqua_rat__lqZy9w9SqDTnRTQd

Two trains, each 160 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is? Choose the correct choice from the following: A) 26 km/hr B) 17 km/hr C) 60 km/hr D) 77 km/hr E) 96 km/hr

Let the speed of the slower train be x m/sec. Then, speed of the train = 2x m/sec. Relative speed = ( x + 2x) = 3x m/sec. (160 + 160)/8 = 3x =&gt; x = 40/3. So, speed of the faster train = 80/3 = 80/3 * 18/5= <gadget id="calculator">80/3 * 18/5</gadget> <output>96</output> 96 km/hr. Answer:96 km/hr <result>E</result>

E

Two trains, each 160 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is?