Mathematical Reasoning and Aptitude Questions and Answers

Answer: D

DEFG is coded as IMPR.

Compare JKLM with OSVX letter by letter: J + 5 = O, K + 8 = S, L + 10 = V, M + 11 = X.

Apply the same shifts to DEFG: D + 5 = I, E + 8 = M, F + 10 = P, G + 11 = R, giving IMPR. ILNQ, JLNP and KMOR use other shifts that do not reproduce OSVX from JKLM.

Answer: A

FEG is coded as 879.

Each letter becomes its alphabet position plus 2: D = 4 gives 6, A = 1 gives 3, C = 3 gives 5, which is 635.

For FEG: F = 6 gives 8, E = 5 gives 7, G = 7 gives 9, so the code is 879. The other options rearrange the same digits in the wrong order.

Answer: B

He is facing West, 25 meters from the start.

Trace the walk from (0, 0).

• Facing south, 15 m: (0, -15).
• Right turn from south is west; 10 m: (-10, -15).
• Right turn from west is north; 15 m: (-10, 0).
• Left turn from north is west; 15 m: (-25, 0).

He ends facing west, 25 m due west of the starting point. 15 m is only the last leg, and the other directions come from turning the wrong way at one step.

Answer: B

Kanta's profit is Rs. 1,85,185.

The ratio 3 : 5 : 1 has \(3 + 5 + 1 = 9\) parts, and Kanta has 5 of them.

\[ \begin{aligned} \text{one part} &= 333333 \div 9 = 37037 \\ \text{Kanta} &= 5 \times 37037 = 185185 \end{aligned} \]

Check: Shanta gets 111,111 and Bhranta 37,037, and \(111111 + 185185 + 37037 = 333333\). The option 1,11,111 is Shanta's share, not Kanta's.

Answer: D

The watch will show Friday, 6 pm.

Split 101 hours into whole days and the remainder:

\[ 101 = 4 \times 24 + 5 \]

Four days after Monday 1 pm is Friday 1 pm, and 5 more hours make Friday 6 pm. The option Thursday, 5 pm is only 76 hours after the starting time, and the Monday and Tuesday options are fewer still.

Answer: A

The most beneficial is 10% per annum compounded yearly.

Compare the effective annual rate of each offer, \((1 + \frac{r}{n})^{n} - 1\):

• 10% yearly: 10.00%
• 9% six-monthly: \(1.045^{2} - 1 = 9.20\%\)
• 8% quarterly: \(1.02^{4} - 1 \approx 8.24\%\)
• 7% monthly: \((1 + \frac{0.07}{12})^{12} - 1 \approx 7.23\%\)

More frequent compounding adds only a fraction of a percentage point, far too little to make up the gap in the nominal rates, so the 10% yearly offer earns the most.

Answer: A

The largest ratio is \(\frac{H}{T}\).

In a right-angled triangle the hypotenuse is the longest side, so \(H \gt T\) and \(H \gt B\).

• \(\frac{H}{T} \gt 1\), since the hypotenuse is longer than the height.
• \(\frac{T}{H} \lt 1\) and \(\frac{B}{H} \lt 1\), since each divides a leg by the hypotenuse.
• \(\frac{B}{T}\) has the same denominator as \(\frac{H}{T}\) but a smaller numerator, because \(B \lt H\), so \(\frac{B}{T} \lt \frac{H}{T}\).

So \(\frac{H}{T}\) is larger than every other option, whatever the shape of the triangle.

Answer: D

Third from the top is Shyam.

Build the order from the clues:

• Vishal is below Shyam and above Vijay: Shyam, Vishal, Vijay.
• Mohan is above Shyam but below Rohan: Rohan, Mohan, Shyam.
• Vijay is between Vishal and Ashok, so Ashok comes after Vijay.

The full ranking is Rohan, Mohan, Shyam, Vishal, Vijay, Ashok. The third from the top is Shyam. Mohan is second and Vishal fourth.

Answer: C

SANGLI is coded as RBMHKJ.

In MUMBAI to LVLCZJ, the letters are shifted alternately back and forward by one place: M-1 = L, U+1 = V, M-1 = L, B+1 = C, A-1 = Z, I+1 = J.

Apply the same pattern to SANGLI: S-1 = R, A+1 = B, N-1 = M, G+1 = H, L-1 = K, I+1 = J, giving RBMHKJ.

RZMFKJ shifts the second and fourth letters the wrong way, TZMHKJ the first and second, and RZOFMJ gets most of the shifts reversed.

Answer: A

She has walked 37 meter, and is facing North-East.

The question asks how much distance she has walked, which is the total length of her path: 10 + 12 + 15 = 37 meter.

For the direction: she starts facing East; turning left makes her face North; turning 45° to her right from North makes her face North-East, and she keeps that direction while walking the last 15 meter.

The options with 37 meter and East get the final turn wrong, and 27 or 22 meter do not match the distances given.