Arithmetical Reasoning Questions and Answers

Answer: D

Correct answer: None of these

A telephone dial carries the digits 0 to 9, and any product containing a zero is zero. So the answer is 0, which is not among the first three options. The item works by inviting the solver to start multiplying 1 through 9 and never notice the zero - and the three plausible-looking six-figure numbers are there to encourage exactly that.

Answer: C

Since B and D are twins, so B = D.

Now, A = B + 3 and A = C - 3.

Thus, B + 3 = C - 3 

\(\Rightarrow  D + 3 = C-3\) 

\(\Rightarrow  C - D = 6.\)

Answer: B

Correct answer: 29

Every match eliminates exactly one player, and 29 of the 30 must be eliminated to leave one winner, so 29 matches are needed - no more and no fewer. The argument holds whatever the draw looks like and whoever wins, which is why byes and uneven brackets make no difference to the total.

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.

Answer: B

Manick's present age = 12 years, Rahul's present age = 4 years.

Let Manick be twice as old as Rahul after x years from now.

Then, 12 + x = 2 (4 + x) 

\(\Rightarrow  12 + x = 8 + 2x\) 

\(\Rightarrow  x = 4.\)

Hence, Manick's required age = 12 + x = 16 years

Answer: D

Correct answer: 120 rolls

Cutting a roll into 10 pieces takes 9 cuts, not 10. In 24 minutes he makes \[ 45\times24 = 1080\ \mathrm{cuts}, \qquad \frac{1080}{9} = 120\ \mathrm{rolls}. \] Dividing by 10 instead gives 108, which is offered as a distractor - the same fencepost point as the garden question above.

Answer: C

Let the number of boys and girls participating in sports be 3x and 2x respectively.

Then, 3x = 15 or x = 5.

So, number of girls participating in sports = 2x = 10.

Number of students not participating in sports = 60 - (15 + 10) = 35.

Let number of boys not participating in sports be y.

Then, number of girls not participating in sports = (35 -y).

Therefore (35 - y) = y + 5 

\(\Rightarrow  2y = 30\) 

\(\Rightarrow  y = 15.\)

So, number of girls not participating in sports = (35 - 15) = 20.

Hence, total number of girls in the class = (10 + 20) = 30

Answer: D

Correct answer: 60

With \( d \) deer at four legs and \( p \) peacocks at two: \[ d + p = 80, \qquad 4d + 2p = 200. \] Halving the second gives \( 2d + p = 100 \), and subtracting the first gives \( d = 20 \), so \( p = 60 \). Check: 80 heads and \( 80 + 120 = 200 \) legs.

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.

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.