Arithmetical Reasoning Questions and Answers

Q: In a garden, there are 10 rows and 12 columns of mango trees. The distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden. The length of the garden is

Correct answer: 24 mThe length runs along the 12 columns, so there are 11 gaps of 2 metres between the outer trees, plus 1 metre of margin at each end: \[ 11\times2 + 1 + 1 = 24\ \mathrm{m}. \] The step to be careful with is that 12 trees make 11 gaps, not 12 - using 12 gives 26, which is offered here.

Q: A number of friends decided to go on a picnic and planned to spend Rs. 96 on eatables. Four of them, however, did not turn up. As a consequence, the remaining ones had to contribute Rs. 4 each extra. The number of those who attended the picnic was

Correct answer: 8Let \( n \) be the original number. Each was to pay \( 96/n \) and each of the \( n-4 \) who came paid 4 more: \[ \frac{96}{n-4} - \frac{96}{n} = 4 \;\Rightarrow\; 384 = 4n(n-4) \;\Rightarrow\; n^2 - 4n - 96 = 0, \] giving \( n = 12 \). The question asks how many attended, which is \( 12-4 = 8 \) - and answering 12 is the trap the wording sets.

Q: A motorist knows four different routes from Bristol to Birmingham. From Birmingham to Sheffield he knows three different routes and from Sheffield to Carlisle he knows two different routes. How many routes does he know from Bristol to Carlisle ?

Correct answer: 24The three legs are chosen independently, so the routes multiply: \[ 4 \times 3 \times 2 = 24. \] Adding them gives 9 and is the standard error. Multiplication is right because every one of the four first legs can be followed by any of the three second legs, and each of those twelve combinations by either of the two third legs.

Q: A man wears socks of two colours - Black and brown. He has altogether 20 black socks and 20 brown socks in a drawer. Supposing he has to take out the socks in the dark, how many must he take out to be sure that he has a matching pair ?

Correct answer: 3There are only two colours, so among any three socks two must match - the pigeonhole principle. Two is not enough, since they could be one of each. The count of 20 in each colour is irrelevant to the answer, and it is put there to tempt the solver towards 20 or 21.

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21.

In a garden, there are 10 rows and 12 columns of mango trees. The distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden. The length of the garden is

A.20 m
B.22 m
C.24 m
D.26 m

Answer: C

Correct answer: 24 m

The length runs along the 12 columns, so there are 11 gaps of 2 metres between the outer trees, plus 1 metre of margin at each end: \[ 11\times2 + 1 + 1 = 24\ \mathrm{m}. \] The step to be careful with is that 12 trees make 11 gaps, not 12 - using 12 gives 26, which is offered here.

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22.

A number of friends decided to go on a picnic and planned to spend Rs. 96 on eatables. Four of them, however, did not turn up. As a consequence, the remaining ones had to contribute Rs. 4 each extra. The number of those who attended the picnic was

A.8
B.12
C.16
D.24

Answer: A

Correct answer: 8

Let \( n \) be the original number. Each was to pay \( 96/n \) and each of the \( n-4 \) who came paid 4 more: \[ \frac{96}{n-4} - \frac{96}{n} = 4 \;\Rightarrow\; 384 = 4n(n-4) \;\Rightarrow\; n^2 - 4n - 96 = 0, \] giving \( n = 12 \). The question asks how many attended, which is \( 12-4 = 8 \) - and answering 12 is the trap the wording sets.

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23.

A motorist knows four different routes from Bristol to Birmingham. From Birmingham to Sheffield he knows three different routes and from Sheffield to Carlisle he knows two different routes. How many routes does he know from Bristol to Carlisle ?

A.4
B.8
C.12
D.24

Answer: D

Correct answer: 24

The three legs are chosen independently, so the routes multiply: \[ 4 \times 3 \times 2 = 24. \] Adding them gives 9 and is the standard error. Multiplication is right because every one of the four first legs can be followed by any of the three second legs, and each of those twelve combinations by either of the two third legs.

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24.

A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?

A.45
B.60
C.75
D.90

Answer: D

Let number of notes of each denomination be x.

Then, x + 5x + 10x = 480

\(\Rightarrow 16x = 480\)

\(\Rightarrow x = 30.\)

Hence, total number of notes = 3x = 90

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25.

A man wears socks of two colours - Black and brown. He has altogether 20 black socks and 20 brown socks in a drawer. Supposing he has to take out the socks in the dark, how many must he take out to be sure that he has a matching pair ?

A.3
B.20
C.39
D.None of these

Answer: A

Correct answer: 3

There are only two colours, so among any three socks two must match - the pigeonhole principle. Two is not enough, since they could be one of each. The count of 20 in each colour is irrelevant to the answer, and it is put there to tempt the solver towards 20 or 21.

Discuss in Forum

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