# Aptitude practice questions (Group 4)

> This page has practice questions on Aptitude for the Group 4 / VAO (Combined Civil Services Examination-IV) exam, 20 in all: new questions our editors prepared and the founder approved, not previous-year questions. Tap “Answer and explanation” under each question for the correct answer and a short, sourced explanation. For previous-year papers and official answer keys, see tnpsc.gov.in.

Last updated: 2026-10-27 · By TNPSC Guide editorial team
URL: https://www.tnpscguide.com/exams/group-4/questions/aptitude

### Question 1

Consider the following statements on perfect squares.
1. A perfect square that ends in zero ends in an odd number of zeros.
2. A perfect square divided by 3 never leaves remainder 2.
3. A perfect square divided by 4 leaves remainder 0 or 1.
Which of these are correct?

- A. 2 only
- B. 1 and 2 only
- C. 2 and 3 only
- D. 1, 2 and 3

Correct answer: C. 2 and 3 only

A square ending in zero ends in an even number of zeros (2500, 10000); a perfect square leaves 0 or 1 on division by 3 and 0 or 1 on division by 4; so 2 and 3 are correct and 1 is wrong.

Source: கணக்கு, எட்டாம் வகுப்பு, தமிழ் வழி (Mathematics, Standard VIII, Tamil medium; Samacheer Kalvi) (இயல் 1 எண்கள், p. 28 (PDF p. 34))

### Question 2

Assertion [A]: 10 − 2 + 3 = 11.
Reason [R]: Although A (addition) is written before S (subtraction) in BIDMAS, addition and subtraction are done from left to right.

- A. Both [A] and [R] are true and [R] is the correct explanation of [A]
- B. Both [A] and [R] are true but [R] is not the correct explanation of [A]
- C. [A] is true but [R] is false
- D. [A] is false but [R] is true

Correct answer: A. Both [A] and [R] are true and [R] is the correct explanation of [A]

BIDMAS is worked from left to right: 10 − 2 + 3 = 8 + 3 = 11; doing 10 − 5 = 5 is wrong; so both are true and [R] explains [A].

Source: கணக்கு, ஆறாம் வகுப்பு, முதல் பருவம், தொகுதி 2, தமிழ் வழி (Mathematics, Standard VI, Term I, Volume 2, Tamil medium; Samacheer Kalvi) (இயல் 1 எண்கள் (1.7 செயலிகளின் வரிசை), p. 17 (PDF p. 21))

### Question 3

What is the difference between the values of 5 × (6 + 2) and (5 × 6) + 2?

- A. 0
- B. 8
- C. 2
- D. 10

Correct answer: B. 8

5 × (6 + 2) = 5 × 8 = 40 and (5 × 6) + 2 = 30 + 2 = 32; the difference is 40 − 32 = 8; putting brackets in the right place avoids confusion.

Source: கணக்கு, ஆறாம் வகுப்பு, முதல் பருவம், தொகுதி 2, தமிழ் வழி (Mathematics, Standard VI, Term I, Volume 2, Tamil medium; Samacheer Kalvi) (இயல் 1 எண்கள் (1.7 செயலிகளின் வரிசை), pp. 16-17 (PDF pp. 20-21))

### Question 4

Consider the following statements on successive percentage changes.
1. Increasing a number by 25% and then decreasing it by 20% leaves it unchanged.
2. An income that rises by 10% and then falls by 10% is unchanged.
3. If P's income is 50% more than Q's, then Q's income is 33⅓% less than P's.
Which of these are correct?

- A. 1 only
- B. 1 and 2 only
- C. 1 and 3 only
- D. 1, 2 and 3

Correct answer: C. 1 and 3 only

25 − 20 − 25 × 20/100 = 0, so 1 is correct; 10 − 10 − 10 × 10/100 = −1, a 1% decrease, so 2 is wrong; with Q = 100, P = 150 and 50/150 × 100 = 33⅓%, so 3 is correct.

Source: கணக்கு, எட்டாம் வகுப்பு, தமிழ் வழி (Mathematics, Standard VIII, Tamil medium; Samacheer Kalvi) (விடைகள் (பயிற்சி 4.1, 4.2, 4.5), p. 286 (PDF p. 292))

### Question 5

Write 45% as a fraction in its lowest form.

- A. 9/20
- B. 45/10
- C. 4/5
- D. 9/2

Correct answer: A. 9/20

Per cent means per hundred; x% = x/100: 45% = 45/100 = 9/20.

Source: கணக்கு, எட்டாம் வகுப்பு, தமிழ் வழி (Mathematics, Standard VIII, Tamil medium; Samacheer Kalvi) (இயல் 4 வாழ்வியல் கணிதம், p. 128 (PDF p. 134))

### Question 6

In one class 32 of 40 pupils took part in a contest, and in another class 42 of 50. Consider the following statements.
1. The first class took part at 80% and the second at 84%.
2. The second class is ahead by 4 percentage points.
3. A rise from 80 to 84 is a 4% rise on 80.
Which of these are correct?

- A. 1 only
- B. 1 and 3 only
- C. 1, 2 and 3
- D. 1 and 2 only

Correct answer: D. 1 and 2 only

32/40 × 100 = 80% and 42/50 × 100 = 84%; the gap is 4 percentage points (the book, p. 127, calls it "4% more"); but a rise from 80 to 84 is 4/80 × 100 = 5%, not 4%; so 1 and 2 are correct and 3 is wrong.

Source: கணக்கு, எட்டாம் வகுப்பு, தமிழ் வழி (Mathematics, Standard VIII, Tamil medium; Samacheer Kalvi) (இயல் 4 வாழ்வியல் கணிதம், p. 127 (PDF p. 133))

### Question 7

Find the HCF of 396, 504 and 636.

- A. 36
- B. 6
- C. 24
- D. 12

Correct answer: D. 12

First the HCF of two: 504 = 396 × 1 + 108, 396 = 108 × 3 + 72, 108 = 72 × 1 + 36, 72 = 36 × 2 + 0, so (396, 504) = 36; then 636 = 36 × 17 + 24, 36 = 24 × 1 + 12, 24 = 12 × 2 + 0, so the HCF is 12.

Source: கணிதம், பத்தாம் வகுப்பு, தமிழ் வழி (Mathematics, Standard X, Tamil medium; Samacheer Kalvi) (இயல் 2 எண்களும் தொடர்வரிசைகளும், pp. 42-43 (PDF pp. 48-49))

### Question 8

By what other name is the highest common factor (HCF) known?

- A. Greatest common divisor
- B. Least common multiple
- C. Prime factor
- D. Co-prime number

Correct answer: A. Greatest common divisor

The largest number that divides the given numbers exactly is the HCF; it is also called the greatest common divisor (GCD).

Source: கணக்கு, எட்டாம் வகுப்பு, தமிழ் வழி (Mathematics, Standard VIII, Tamil medium; Samacheer Kalvi) (இயல் 7 தகவல் செயலாக்கம் (7.6 மீப்பெரு பொதுக் காரணி), p. 259 (PDF p. 265))

### Question 9

Which of the following ratios is the greatest?

- A. 2 : 3
- B. 5 : 8
- C. 3 : 4
- D. 7 : 12

Correct answer: C. 3 : 4

Write the ratios as fractions over the common denominator 24: 2/3 = 16/24, 3/4 = 18/24, 5/8 = 15/24, 7/12 = 14/24; so 3 : 4 is the greatest.

Source: கணக்கு, ஆறாம் வகுப்பு, முதல் பருவம், தொகுதி 2, தமிழ் வழி (Mathematics, Standard VI, Term I, Volume 2, Tamil medium; Samacheer Kalvi) (இயல் 3 விகிதம் மற்றும் விகித சமம், pp. 54-55 (PDF pp. 58-59))

### Question 10

A ratio compares two quantities of what kind?

- A. Quantities of the same kind
- B. Quantities of different kinds
- C. Lengths only
- D. Fractions only

Correct answer: A. Quantities of the same kind

A ratio compares two quantities of the same kind by saying how many times one is of the other; comparing quantities of different kinds is meaningless.

Source: கணக்கு, ஆறாம் வகுப்பு, முதல் பருவம், தொகுதி 2, தமிழ் வழி (Mathematics, Standard VI, Term I, Volume 2, Tamil medium; Samacheer Kalvi) (இயல் 3 விகிதம் மற்றும் விகித சமம், p. 48 (PDF p. 52))

### Question 11

The difference between the compound and simple interest on a sum at 2% a year for 2 years is ₹1. What is the principal?

- A. ₹50
- B. ₹250
- C. ₹5000
- D. ₹2500

Correct answer: D. ₹2500

For two years C.I − S.I = P(r/100)²: P × (2/100)² = 1, so P × 0.0004 = 1 and P = ₹2500.

Source: கணக்கு, எட்டாம் வகுப்பு, தமிழ் வழி (Mathematics, Standard VIII, Tamil medium; Samacheer Kalvi) (விடைகள் (பயிற்சி 4.3), p. 286 (PDF p. 292))

### Question 12

What is the formula for simple interest I? (P principal, N years, R annual rate)

- A. I = PNR
- B. I = PNR/100
- C. I = P(1 + R/100)ᴺ
- D. I = 100PN/R

Correct answer: B. I = PNR/100

Simple interest I = PNR/100, where P is the principal, N the number of years and R the annual rate.

Source: கணக்கு, எட்டாம் வகுப்பு, தமிழ் வழி (Mathematics, Standard VIII, Tamil medium; Samacheer Kalvi) (இயல் 4 வாழ்வியல் கணிதம் (4.4 கூட்டுவட்டி), p. 139 (PDF p. 145))

### Question 13

What is the compound interest on ₹10000 at 8% compounded annually for the fractional period of 2¾ years?

- A. ₹2200
- B. ₹2363.84
- C. ₹12363.84
- D. ₹1664

Correct answer: B. ₹2363.84

For a fractional period A = P(1 + r/100)ᵃ × (1 + (b/c) × r/100) = 10000 × (27/25)² × 53/50 = ₹12363.84; C.I = ₹2363.84.

Source: கணக்கு, எட்டாம் வகுப்பு, தமிழ் வழி (Mathematics, Standard VIII, Tamil medium; Samacheer Kalvi) (இயல் 4 வாழ்வியல் கணிதம் (4.4 கூட்டுவட்டி), p. 142 (PDF p. 148))

### Question 14

Under compound interest, what happens to the interest earned in one period?

- A. It is subtracted from the principal
- B. It is worked out again on the first principal only
- C. It lowers the next year's rate of interest
- D. It is added to the principal, which becomes the principal for the next period

Correct answer: D. It is added to the principal, which becomes the principal for the next period

In post offices and banks the interest of the first period is added to the principal, and that sum is the principal for the next period; this is compound interest.

Source: கணக்கு, எட்டாம் வகுப்பு, தமிழ் வழி (Mathematics, Standard VIII, Tamil medium; Samacheer Kalvi) (இயல் 4 வாழ்வியல் கணிதம் (4.4 கூட்டுவட்டி), p. 139 (PDF p. 145))

### Question 15

Polishing costs ₹45 per sq m. What does it cost to polish 200 rhombus tiles with diagonals 40 cm and 25 cm?

- A. ₹450
- B. ₹45,00,000
- C. ₹45000
- D. ₹4500

Correct answer: A. ₹450

One tile is ½ × 40 × 25 = 500 sq cm; 200 tiles make 100000 sq cm = 10 sq m (1 sq m = 10000 sq cm); the cost is 10 × 45 = ₹450.

Source: கணக்கு, ஏழாம் வகுப்பு, முதல் பருவம், தொகுதி 2, தமிழ் வழி (Mathematics, Standard VII, Term I, Volume 2, Tamil medium; Samacheer Kalvi) (இயல் 2 அளவைகள், p. 44 (PDF p. 48))

### Question 16

What is the perimeter of a square of side a?

- A. a²
- B. 2a
- C. 4a
- D. 4a²

Correct answer: C. 4a

A rectangle has perimeter 2(l + b) and area l × b; a square has perimeter 4a and area a × a.

Source: கணக்கு, ஏழாம் வகுப்பு, முதல் பருவம், தொகுதி 2, தமிழ் வழி (Mathematics, Standard VII, Term I, Volume 2, Tamil medium; Samacheer Kalvi) (இயல் 2 அளவைகள், p. 34 (PDF p. 38))

### Question 17

Consider the following statements on packing boxes in a carton.
1. Large volume ÷ small volume is the upper limit on the number of boxes that can be packed.
2. If the three sides of the carton are divisible by the three sides of the box in some order, each by a different side, that number is packed exactly.
3. In the 1 m × 88 cm × 63 cm carton, one of 22, 18 and 10 cm divides 63 cm exactly.
Which of these are correct?

- A. 1 only
- B. 1 and 2 only
- C. 2 and 3 only
- D. 1, 2 and 3

Correct answer: B. 1 and 2 only

The quotient of the volumes is an upper limit; if the sides divide one to one, that number is packed exactly; but none of 22, 18 and 10 divides 63 (63 = 22 × 2 + 19 = 18 × 3 + 9 = 10 × 6 + 3); so 1 and 2 are correct and 3 is wrong.

Source: கணக்கு, ஒன்பதாம் வகுப்பு, தமிழ் வழி (Mathematics, Standard IX, Tamil medium; Samacheer Kalvi) (இயல் 7 அளவியல் (7.5 கனச்செவ்வகம், கனச்சதுரத்தின் கனஅளவு), p. 275 (PDF p. 281))

### Question 18

How many edges does a cube have?

- A. 6
- B. 8
- C. 24
- D. 12

Correct answer: D. 12

A cube has 6 faces, 12 edges and 8 vertices.

Source: கணக்கு, எட்டாம் வகுப்பு, தமிழ் வழி (Mathematics, Standard VIII, Tamil medium; Samacheer Kalvi) (இயல் 2 அளவைகள் (2.4 முப்பரிமாண வடிவங்கள்), p. 69 (PDF p. 75))

### Question 19

Consider the following statements on the multiplicative factor method.
1. The ratio of each column is written as first-row value : second-row value.
2. For a quantity in direct proportion with the unknown, the inverse of that ratio is the multiplying factor.
3. For a quantity in inverse proportion with the unknown, the inverse of the ratio is also the multiplying factor.
Which of these are correct?

- A. 1 only
- B. 2 and 3 only
- C. 1 and 2 only
- D. 1, 2 and 3

Correct answer: C. 1 and 2 only

Ratio = first row : second row; for direct proportion take its inverse (20 days → 12 days: factor 12/20), for inverse proportion keep it (15 women → 32 women: factor 15/32); so 1 and 2 are correct and 3 is wrong.

Source: கணக்கு, எட்டாம் வகுப்பு, தமிழ் வழி (Mathematics, Standard VIII, Tamil medium; Samacheer Kalvi) (இயல் 4 வாழ்வியல் கணிதம் (4.5 கலப்பு மாறல்), p. 148 (PDF p. 154))

### Question 20

Which of these pairs is in inverse variation?

- A. Workers and the time to finish the work
- B. Distance and time at a constant speed
- C. Things bought and the money spent
- D. Working hours and earnings

Correct answer: A. Workers and the time to finish the work

Two quantities are in inverse variation when their product is constant (xy = k): for the same work, workers × time stays the same, so more workers need less time; distance and time at a constant speed, purchase and spending, and working hours and earnings vary directly (y/x = k).

Source: கணக்கு, எட்டாம் வகுப்பு, தமிழ் வழி (Mathematics, Standard VIII, Tamil medium; Samacheer Kalvi) (இயல் 4 வாழ்வியல் கணிதம் (4.5 கலப்பு மாறல்), p. 147 (PDF p. 153))

## Sources

- [Official syllabus page](https://www.tnpsc.gov.in/english/syllabus.html)
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