Arithmetical Reasoning Questions and Answers

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: 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

Correct answer: Data inadequate

The fractions apply to two different groups, so the combined fraction depends on how many girls and boys there are. With equal numbers it would be \[ \tfrac{1}{2}\left(\tfrac{1}{5}+\tfrac{1}{8}\right) = \tfrac{13}{80}, \] but with twice as many girls as boys it is different again, and nothing in the question fixes the ratio. Adding the fractions or their numerators and denominators has no justification at all.

Answer: B

Let Rs. x be the fare of city B from city A and Rs. y be the fare of city C from city A.

Then, 2x + 3y = 77 ...(i) and

3x + 2y = 73 ...(ii)

Multiplying (i) by 3 and (ii) by 2 and subtracting, we get: 5y = 85 or y = 17.

Putting y = 17 in (i), we get: x = 13

Answer: C

Let x and y be the ten's and unit's digits respectively of the numeral denoting the woman's age.

Then, woman's age = (10X + y) years; husband's age = (10y + x) years.

Therefore \((10y + x)- (10X + y) = (1/11) (10y + x + 10x + y)\)

\(\Rightarrow\) (9y-9x) = (1/11)(11y + 11x) = (x + y)

 \(\Rightarrow\) \(10x = 8y\)

 \(\Rightarrow\) \( x = (4/5)y\)

Clearly, y should be a single-digit multiple of 5, which is 5.

So, x = 4, y = 5.

Hence, woman's age = 10x + y = 45 years

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: 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

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: 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: 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.