Mathematical Reasoning and Aptitude Questions and Answers

Answer: D

The terms follow the pattern \(n^{3}-n\) for n = 1, 2, 3, and so on.

\[ 1^3-1=0,\quad 2^3-2=6,\quad 3^3-3=24 \]

\[ 4^3-4=60,\quad 5^3-5=120 \]

\[ 6^3-6=210,\quad 7^3-7=336 \]

The sixth term is 210, which agrees with the last given term, 336. The values 240, 220 and 280 do not fit the pattern. The answer is 210. The same pattern can be written as (n - 1) x n x (n + 1), the product of three consecutive integers, which for the sixth term is 5 x 6 x 7 = 210.

Answer: B

A group of 7 with a majority of boys must have at least 4 boys. The possible splits from 6 boys and 4 girls are 4 boys and 3 girls, 5 boys and 2 girls, and 6 boys and 1 girl.

\[ \binom{6}{4}\binom{4}{3}=15\times 4=60 \]

\[ \binom{6}{5}\binom{4}{2}=6\times 6=36 \]

\[ \binom{6}{6}\binom{4}{1}=1\times 4=4 \]

The total is 60 + 36 + 4 = 100 ways. The answer is 100.

Answer: C

The average of the whole group is the total of all the observations divided by their number. The first 10 observations total 10 x 4.5 = 45, and the other 30 total 30 x 3.5 = 105.

\[ \text{Total}=45+105=150 \]

\[ \text{Average}=\frac{150}{40}=\frac{15}{4} \]

The value 15/4 is 3.75, which lies between the two group averages, as it must. The values 4 and 6 are not equal to the weighted result, and 15/2 is double it. The answer is 15/4.

Answer: A

Compare MOHAN with KMFYL letter by letter: each letter has been moved two places back in the alphabet.

\[ M\to K,\ O\to M,\ H\to F,\ A\to Y,\ N\to L \]

Apply the same shift to COUNT: C goes to A, O to M, U to S, N to L and T to R, giving AMSLR. The other codes are rearrangements of these letters or use a different shift. The answer is AMSLR.

Answer: A

Let the present ages be A and B with A + B = 50. Five years ago the ages were A - 5 and B - 5 in the ratio 5 : 3.

\[ 3(A-5)=5(B-5) \]

\[ 3A-5B=-10 \]

Put B = 50 - A, so that 3A - 250 + 5A = -10, which gives 8A = 240 and A = 30, B = 20. Check: five years ago the ages were 25 and 15, whose ratio is 5/3. The pairs 35 and 15, 38 and 12, 40 and 10 give five-year-ago ratios of 3, 26/7 and 7 respectively, none being 5/3. The answer is 30, 20.

Answer: D

The pairs show a relation between two roles on opposite sides: the examiner examines the examinee, the pleader acts for the client. A preceptor is a teacher or instructor, and the one he teaches is a disciple. A customer is related to a shopkeeper, a path-finder to a guide, and a perceiver to the thing perceived. The answer is disciple. The same relation holds for 'pleader and client', in which one person acts for the other, and so the missing word names the person who is taught.

Answer: C

The next number is 72. The terms are products of consecutive integers: \(1\times2 = 2\), \(2\times3 = 6\), \(3\times4 = 12\), \(4\times5 = 20\), \(5\times6 = 30\), \(6\times7 = 42\) and \(7\times8 = 56\). The following term is therefore

Another way to see it is that the differences between the terms are 4, 6, 8, 10, 12, 14, which go up by 2 each time, so the next difference is 16 and \(56 + 16 = 72\). The numbers 60, 64 and 70 do not fit either pattern. The answer is 72.

Answer: B

The next letter is M. Each letter in the series is three places before the previous one in the alphabet. Giving each letter its position, Y is 25, V is 22, S is 19 and P is 16, so the numbers fall by 3 each time and the next is

and the thirteenth letter of the alphabet is M. The letters N, O and L are 14, 15 and 12, which do not follow the step of 3 from P. The answer is M.

Answer: A

The digit for 'sunny' is 3. The word sunny appears only in the third statement, '634' for 'spring is sunny', so its digit must be one that appears in that code and in no other. The digit 6 appears in 645, and the digit 4 appears in 645 and in 42, so neither of them can be reserved for sunny alone, but the digit 3 appears in no other code, so it can only stand for sunny. The code is not fully consistent for every word, but this elimination gives a single answer. The digits 2, 4 and 5 appear in the other codes and are tied to words such as warm, spring and day. The answer is 3.

Answer: C

The person between A and F is D. From the conditions, B is between F and C, so F, B and C are in a row, and A is between E and D, so E, A and D are in a row. F is to the left of D, so going round the circle in order the seating can be C, B, F, D, A, E, and then back to C. Reading it round, F is followed by D and then A, which puts D between F and A. Checking: B is between F and C, A is between D and E, and F is left of D, so all the conditions hold. The answer is D.