Arithmetical Reasoning Questions and Answers

Q: A waiter's income consists of his salary and tips. During one week his tips were 5/4 of his salary. What fraction of his income came from tips ?

Correct answer: 5/9Take the salary as 4 units, so the tips are 5 and the income is 9. The tips are therefore \[ \frac{5}{9} \] of the income. The trap is 5/4, which is the ratio of tips to salary as given rather than to income - the denominator must be the whole, not the other part.

Q: If 100 cats kill 100 mice in 100 days, then 4 cats would kill 4 mice in how many days ?

Correct answer: 100 daysDivide the whole statement through by 100: if 100 cats kill 100 mice in 100 days, then one cat kills one mouse in 100 days. Multiplying back up, 4 cats kill 4 mice in the same 100 days, because the cats and the mice scale together and the time is unchanged. The expected answer of 4 days comes from scaling only one of the two.

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31.

Mac has £ 3 more than Ken, but then Ken wins on the horses and trebles his money, so that he now has £ 2 more than the original amount of money that the two boys had between them. How much money did Mac and Ken have between them before Ken's win ?

A.£ 9
B.£ 11
C.£ 13
D.£ 15

Answer: C

Let money with Ken = x. Then, money with Mac = x + £ 3.

Now, 3x = (x + x + £ 3) + £ 2

\(\Rightarrow x = £ 5.\)

Therefore Total money with Mac and Ken = 2x + £ 3 = £ 13

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32.

In a class, there are 18 boys who are over 160 cm tall. If these constitute three-fourths of the boys and the total number of boys is two-thirds of the total number of students in the class, what is the number of girls in the class ?

A.6
B.12
C.18
D.24

Answer: B

Let the number of boys be x. Then, (3/4)x = 18 or x = 18 x(4/3) = 24.

If total number of students is y, then (2/3) y = 24 or y = 24 x (3/2) = 36.

Therefore Number of girls in the class = (36 - 24) = 12

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33.

A father is now three times as old as his son. Five years back, he was four times as old as his son. The age of the son (in years) is

A.12
B.15
C.18
D.20

Answer: B

Let son's age be x years. Then, father's age = (3x) years.

Five years ago, father's age = (3x - 5) years and son's age = (x - 5) years.

So, 3x - 5 = 4 (x - 5)

\(\Rightarrow 3x - 5 = 4x - 20\)

\(\Rightarrow x = 15\)

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34.

A waiter's income consists of his salary and tips. During one week his tips were 5/4 of his salary. What fraction of his income came from tips ?

A.4/9
B.5/4
C.5/8
D.5/9

Answer: D

Correct answer: 5/9

Take the salary as 4 units, so the tips are 5 and the income is 9. The tips are therefore \[ \frac{5}{9} \] of the income. The trap is 5/4, which is the ratio of tips to salary as given rather than to income - the denominator must be the whole, not the other part.

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35.

If you write down all the numbers from 1 to 100, then how many times do you write 3 ?

A.11
B.18
C.20
D.21

Answer: C

Clearly, from 1 to 100, there are ten numbers with 3 as the unit's digit- 3, 13, 23, 33, 43, 53, 63, 73, 83, 93; and ten numbers with 3 as the ten's digit - 30, 31, 32, 33, 34, 35, 36, 37, 38, 39.

So, required number = 10 + 10 = 20

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36.

If 100 cats kill 100 mice in 100 days, then 4 cats would kill 4 mice in how many days ?

A.1 day
B.4 days
C.40 days
D.100 days

Answer: D

Correct answer: 100 days

Divide the whole statement through by 100: if 100 cats kill 100 mice in 100 days, then one cat kills one mouse in 100 days. Multiplying back up, 4 cats kill 4 mice in the same 100 days, because the cats and the mice scale together and the time is unchanged. The expected answer of 4 days comes from scaling only one of the two.

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