"Mathematical Reasoning and Aptitude" — Practice

Question 1

A quality-control officer inspects 500 randomly sampled bulbs from a factory's daily output and finds every one within the acceptable brightness range, then concludes that the factory's entire daily output meets the brightness standard. This conclusion is reached through:
(a) Inductive reasoning  (b) Deductive reasoning  (c) A valid syllogism  (d) Analogical coding

Accepted Answer

The officer moves from a finite set of specific observed instances (500 sampled bulbs) to a general conclusion about the entire day's output — the defining movement of inductive reasoning, where the conclusion is probable but not certain, since an unsampled bulb could still fail.

Answer: (a) Inductive reasoning. Trap (b) would require the conclusion to follow necessarily from general premises, not be built upward from a sample. Trap (c) misapplies a specific two-premise deductive structure (a syllogism) to a single statistical generalisation. Trap (d) is an invented, unrelated term combining two separate ideas from this chapter.

Question 2

Which of the following arguments is logically valid in form, regardless of whether its premises are actually true?
(a) All squares are rectangles. This shape is a rectangle. Therefore, this shape is a square.  (b) All squares are rectangles. This shape is a square. Therefore, this shape is a rectangle.  (c) No rectangles are triangles. This shape is not a triangle. Therefore, this shape is a rectangle.  (d) Some rectangles are squares. This shape is not a square. Therefore, this shape is not a rectangle.

Accepted Answer

Option (b) has the valid form 'All A are B; X is A; therefore X is B' — if every square really is a rectangle, and this particular shape really is a square, the conclusion that it is a rectangle follows necessarily.

Answer: (b). Trap (a) reverses the direction incorrectly (affirming the consequent) — being a rectangle doesn't guarantee being a square, since many rectangles aren't squares. Trap (c) commits a similar error — not being a triangle doesn't guarantee being a rectangle, since the shape could be a circle or anything else. Trap (d) is invalid because 'some rectangles are squares' leaves open that other rectangles are not squares, so a shape being 'not a square' does not rule out it still being a rectangle.

Question 3

Find the missing number in the series: 5, 8, 13, 20, 29, ?
(a) 36  (b) 38  (c) 40  (d) 42

Accepted Answer

The first differences are 3, 5, 7, 9 — consecutive odd numbers increasing by 2 each time — so the next difference is 11, giving 29 + 11 = 40.

Answer: (c) 40. Trap (a) 36 comes from wrongly continuing the difference pattern by adding 7 again instead of advancing it to 11. Trap (b) 38 comes from adding 9 again instead of advancing to 11. Trap (d) 42 comes from overshooting the pattern by adding 13 instead of 11.

Question 4

Find the next term in the letter series: B, D, G, K, ?
(a) M  (b) N  (c) O  (d) P

Accepted Answer

Converting to alphabet positions: B=2, D=4, G=7, K=11 — the differences are 2, 3, 4, so the next difference is 5, giving 11 + 5 = 16, which is P.

Answer: (d) P. Trap (a) M (position 13) comes from wrongly adding only 2 again instead of advancing the difference to 5. Trap (b) N (position 14) comes from adding 3 again. Trap (c) O (position 15) comes from adding 4 again instead of the correctly advancing difference of 5.

Question 5

In a certain code, CHAIR is written as DIBJS. Using the same coding pattern, how is TABLE written?
(a) UBCMF  (b) UBCLF  (c) SZAKD  (d) UACLF

Accepted Answer

Comparing CHAIR to DIBJS shows every letter shifted forward by exactly one alphabet position (C→D, H→I, A→B, I→J, R→S). Applying the identical shift to TABLE: T→U, A→B, B→C, L→M, E→F, giving UBCMF.

Answer: (a) UBCMF. Trap (b) UBCLF leaves the fourth letter unshifted (L instead of M), a common slip of missing one letter. Trap (c) SZAKD shifts every letter backward instead of forward, the opposite-direction error. Trap (d) UACLF shifts only some letters correctly and leaves others (A, L) unshifted, an inconsistent partial application of the rule.

Question 6

Doctor is to Hospital as Teacher is to:
(a) Blackboard  (b) School  (c) Student  (d) Textbook

Accepted Answer

The relationship in the given pair is specifically 'typical place of work' — a doctor's characteristic workplace is a hospital, just as a teacher's characteristic workplace is a school.

Answer: (b) School. Trap (a) Blackboard is a tool a teacher uses, not a place of work, mismatching the tested relationship. Trap (c) Student is a person a teacher interacts with, not a location. Trap (d) Textbook is likewise a tool or resource, not a workplace, so it fails to preserve the specific relationship being tested.

Question 7

A shopkeeper's monthly revenue rises from ₹40,000 to ₹52,000. Find the percentage increase.
(a) 20%  (b) 24%  (c) 30%  (d) 33%

Accepted Answer

The increase is ₹52,000 − ₹40,000 = ₹12,000. Percentage increase = 12,000 ÷ 40,000 × 100 = 30%, using the original ₹40,000 as the base.

Answer: (c) 30%. Trap (a) 20% and trap (b) 24% both arise from mistakenly dividing the increase by a wrong, larger base (such as 60,000 or 50,000) instead of the correct original value. Trap (d) 33% arises from a similar base-confusion error, approximating the increase against too small a base.

Question 8

An article purchased for ₹1,200 is sold at a loss of 15%. Find the selling price.
(a) ₹1,080  (b) ₹1,140  (c) ₹1,000  (d) ₹1,020

Accepted Answer

A 15% loss on a cost price of ₹1,200 is 0.15 × 1,200 = ₹180. Selling price = Cost price − Loss = 1,200 − 180 = ₹1,020.

Answer: (d) ₹1,020. Trap (a) ₹1,080 results from mistakenly using a 10% loss instead of 15%. Trap (b) ₹1,140 results from mistakenly using a 5% loss. Trap (c) ₹1,000 results from an imprecise loss estimate (treating the loss as a flat ₹200 rather than precisely 15% of ₹1,200).

Question 9

If a : b = 3 : 4 and b : c = 2 : 5, find a : b : c.
(a) 3 : 4 : 10  (b) 3 : 4 : 5  (c) 6 : 4 : 5  (d) 3 : 8 : 10

Accepted Answer

To merge the two ratios, the shared term b must match: a:b = 3:4 already has b = 4, and b:c = 2:5 needs scaling by 2 to make b = 4 as well, giving b:c = 4:10. Combined, a : b : c = 3 : 4 : 10.

Answer: (a) 3 : 4 : 10. Trap (b) 3:4:5 comes from using c's value directly from the second ratio without scaling it to match b = 4. Trap (c) 6:4:5 comes from mistakenly scaling a instead of scaling b:c to match. Trap (d) 3:8:10 comes from scaling b inconsistently while correctly scaling c, breaking the shared-term match.

Question 10

The average of 5 numbers is 24. If one of the numbers is excluded, the average of the remaining 4 numbers becomes 22. Find the excluded number.
(a) 26  (b) 32  (c) 30  (d) 28

Accepted Answer

The total of all 5 numbers is 5 × 24 = 120. The total of the remaining 4 numbers is 4 × 22 = 88. The excluded number is 120 − 88 = 32.

Answer: (b) 32. Trap (a) 26 comes from the mistaken shortcut of simply adding the difference in averages (2) to the original average (24) instead of properly weighting by the count of numbers involved. Trap (c) 30 and trap (d) 28 both arise from small arithmetic slips in computing 5 × 24 or 4 × 22 before subtracting.

Question 11

Find the compound interest on ₹10,000 for 2 years at 10% per annum, compounded annually.
(a) ₹1,000  (b) ₹2,000  (c) ₹2,100  (d) ₹2,200

Accepted Answer

Amount = 10,000 × (1.1)² = 10,000 × 1.21 = ₹12,100. Compound interest = 12,100 − 10,000 = ₹2,100, which is ₹100 more than the equivalent simple interest, because the second year's 10% is earned on ₹11,000, not the original ₹10,000.

Answer: (c) ₹2,100. Trap (a) ₹1,000 is just one year's interest at 10%, ignoring the second year entirely. Trap (b) ₹2,000 is the simple-interest answer for 2 years (10,000×10×2÷100) — the single most common error, mistaking CI for SI. Trap (d) ₹2,200 overshoots by incorrectly compounding a flat 10% of 10,000 twice as a simple addition rather than compounding on the growing amount.

Question 12

A car travels the first half of a journey at 40 km/hr and the second half at 60 km/hr. Find its average speed for the entire journey.
(a) 50 km/hr  (b) 52 km/hr  (c) 45 km/hr  (d) 48 km/hr

Accepted Answer

For two equal-distance legs at speeds x and y, average speed = 2xy ÷ (x + y) = (2 × 40 × 60) ÷ 100 = 4,800 ÷ 100 = 48 km/hr — lower than the simple average because the car spends more time at the slower speed.

Answer: (d) 48 km/hr. Trap (a) 50 km/hr is the plain arithmetic mean (40+60)/2, the single most common error in this exact question type — it ignores that more time is spent travelling at the slower speed. Traps (b) 52 km/hr and (c) 45 km/hr are plausible-looking values with no valid derivation, included to catch guessing without applying the correct formula.

Question 13

For the data set 7, 9, 7, 11, 14, 9, 9, find the mode.
(a) 7  (b) 9  (c) 11  (d) 14

Accepted Answer

Counting frequencies: 7 appears twice, 9 appears three times, 11 and 14 each appear once. The mode is the most frequently occurring value.

Answer: (b) 9. Trap (a) 7 is the second most frequent value, not the most frequent — a common miscounting error. Traps (c) 11 and (d) 14 each occur only once and would only be picked by confusing 'mode' with 'largest value' or a random single value in the set.

Practice — "Mathematical Reasoning and Aptitude"

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