Question 1

Which digit should replace * in 5*3 to make it divisible by 3?

Accepted Answer

Step 1: A number is divisible by 3 if the sum of its digits is divisible by 3. Step 2: Sum of known digits = 5 + 3 = 8. Step 3: We need 8 + * to be divisible by 3. Step 4: If * = 1, sum = 9, which is divisible by 3. Therefore, * = 1.

Question 2

Convert 0.625 to a fraction in simplest form.

Accepted Answer

Step 1: Write 0.625 as 625/1000. Step 2: Find GCD(625, 1000). 625 = 5⁴ and 1000 = 2³ × 5³, so GCD = 5³ = 125. Step 3: Divide both numerator and denominator by 125: 625÷125 = 5 and 1000÷125 = 8. Step 4: Answer is 5/8.

Question 3

Simplify: 48 ÷ 6 + 12 × 2 − 5

Accepted Answer

Step 1: Apply BODMAS — Division and Multiplication first (left to right). 48 ÷ 6 = 8 and 12 × 2 = 24. Step 2: Now we have 8 + 24 − 5. Step 3: Addition and Subtraction (left to right): 8 + 24 = 32, then 32 − 5 = 27.

Question 4

Simplify: 2 + 8 × 3 − 10 ÷ 2

Accepted Answer

Step 1: Apply BODMAS — Multiplication and Division first (left to right). 8 × 3 = 24 and 10 ÷ 2 = 5. Step 2: Expression becomes 2 + 24 − 5. Step 3: Addition and Subtraction (left to right): 2 + 24 = 26, then 26 − 5 = 21.

Question 5

Calculate: 36 ÷ 3 × 2 + 4 − 1

Accepted Answer

Step 1: Apply BODMAS — Division and Multiplication first (left to right). 36 ÷ 3 = 12, then 12 × 2 = 24. Step 2: Expression becomes 24 + 4 − 1. Step 3: Addition and Subtraction (left to right): 24 + 4 = 28, then 28 − 1 = 27.

Question 6

Solve: 50 − 15 + 20 ÷ 4 × 2

Accepted Answer

Step 1: Apply BODMAS — Division and Multiplication first (left to right). 20 ÷ 4 = 5, then 5 × 2 = 10. Step 2: Expression becomes 50 − 15 + 10. Step 3: Subtraction and Addition (left to right): 50 − 15 = 35, then 35 + 10 = 45.

Question 7

Evaluate: 72 ÷ 8 + 6 × 3 − 2

Accepted Answer

Step 1: Apply BODMAS — Division and Multiplication first. 72 ÷ 8 = 9 and 6 × 3 = 18. Step 2: Expression becomes 9 + 18 − 2. Step 3: Addition and Subtraction (left to right): 9 + 18 = 27, then 27 − 2 = 25.

Question 8

Which of the following numbers is divisible by both 4 and 6?

Accepted Answer

Step 1: A number divisible by both 4 and 6 must be divisible by their LCM. Step 2: LCM(4, 6) = 12. Step 3: Check 144: 144 ÷ 12 = 12 (exactly divisible). Therefore, 144 is the answer.

Question 9

A number when divided by 9 leaves remainder 0. Which of the following is definitely true about this number?

Accepted Answer

Step 1: If a number is divisible by 9 (remainder 0), then by the divisibility rule of 9, the sum of its digits must be divisible by 9. Step 2: A number divisible by 9 is also divisible by 3 (since 9 = 3²). Step 3: Therefore, the number must be divisible by 3. The answer is that the number is divisible by 3.

Question 10

A number is divisible by 11 if the difference between the sum of digits at odd positions and the sum of digits at even positions is divisible by 11. Using this rule, which number is divisible by 11?

Accepted Answer

Step 1: For divisibility by 11, calculate (sum of odd-position digits) − (sum of even-position digits). Step 2: Test 4587: Odd positions (1st, 3rd) = 4 + 8 = 12. Even positions (2nd, 4th) = 5 + 7 = 12. Difference = 12 − 12 = 0. Step 3: 0 is divisible by 11. Therefore, 4587 is divisible by 11.

Question 11

Which of the following numbers is NOT divisible by 8?

Accepted Answer

Step 1: A number is divisible by 8 if its last three digits form a number divisible by 8. Step 2: Test 2456: Last three digits = 456. 456 ÷ 8 = 57 (exactly divisible). Step 3: Test 3264: Last three digits = 264. 264 ÷ 8 = 33 (exactly divisible). Step 4: Test 5432: Last three digits = 432. 432 ÷ 8 = 54 (exactly divisible). Step 5: Test 6218: Last three digits = 218. 218 ÷ 8 = 27.25 (NOT exactly divisible). Therefore, 6218 is NOT divisible by 8.

Question 12

A number is divisible by 6 if it is divisible by both 2 and 3. Which of the following is divisible by 6?

Accepted Answer

Step 1: For divisibility by 6, the number must be even (divisible by 2) AND the sum of digits must be divisible by 3. Step 2: Test 318: It is even (ends in 8). Sum of digits = 3 + 1 + 8 = 12, which is divisible by 3. Step 3: Since 318 is divisible by both 2 and 3, it is divisible by 6. Therefore, 318 is the answer.

Question 13

If 2/5 of a number is 24, what is the number?

Accepted Answer

Step 1: Let the number be x. Step 2: Set up equation: (2/5) × x = 24. Step 3: Multiply both sides by 5/2: x = 24 × (5/2) = (24 × 5)/2 = 120/2 = 60. Step 4: Verify: (2/5) × 60 = 24 ✓

Question 14

Evaluate: 100 − 20 ÷ 4 + 3 × 5

Accepted Answer

Step 1: Apply BODMAS — Division and Multiplication first. 20 ÷ 4 = 5 and 3 × 5 = 15. Step 2: Expression becomes 100 − 5 + 15. Step 3: Subtraction and Addition (left to right): 100 − 5 = 95, then 95 + 15 = 110.

Question 15

Which of the following numbers is divisible by 11?

Accepted Answer

Step 1: Apply divisibility rule for 11: alternating sum of digits (from right to left) must be divisible by 11. Step 2: Test 121: (1-2+1) = 0, divisible by 11✓. Test 1234: (4-3+2-1) = 2, not divisible by 11. Test 5678: (8-7+6-5) = 2, not divisible by 11. Test 9876: (6-8+7-9) = -4, not divisible by 11. Therefore, 121 is divisible by 11.

Question 16

A number is divisible by 6. Which statement must be true?

Accepted Answer

Step 1: A number is divisible by 6 if and only if it is divisible by both 2 and 3 (since 6 = 2×3 and gcd(2,3)=1). Step 2: Divisibility by 2 requires the number to be even. Step 3: Divisibility by 3 requires the sum of digits to be divisible by 3. Step 4: Therefore, the number must be even AND have digit sum divisible by 3. The correct statement is: 'It is divisible by both 2 and 3.'

Question 17

The ratio of two numbers is 7:5. If their difference is 24, what is the smaller number?

Accepted Answer

Step 1: Let the numbers be 7x and 5x. Step 2: Their difference = 7x - 5x = 2x = 24. Step 3: Solve for x: x = 12. Step 4: Smaller number = 5x = 5 × 12 = 60.

Question 18

If 0.6 of a quantity equals 120, what is 0.35 of that quantity?

Accepted Answer

Step 1: Let quantity = x. Then 0.6x = 120. Step 2: Solve for x: x = 120/0.6 = 200. Step 3: Find 0.35 of 200: 0.35 × 200 = 70.

Question 19

A number is divisible by both 4 and 9. Which of the following must also divide this number?

Accepted Answer

Step 1: A number divisible by both 4 and 9 must be divisible by their LCM. Step 2: Since gcd(4,9) = 1, LCM(4,9) = 4 × 9 = 36. Step 3: Therefore, the number must be divisible by 36.

Question 20

Simplify: 144 ÷ 12 + 8 × 3 − 5 + 2

Accepted Answer

Step 1: Apply BODMAS — Division and Multiplication first (left to right). 144 ÷ 12 = 12 and 8 × 3 = 24. Step 2: Rewrite as 12 + 24 − 5 + 2. Step 3: Addition and Subtraction (left to right): 12 + 24 = 36, 36 − 5 = 31, 31 + 2 = 33. Therefore, answer is 33.

SSC GD Constable Number System Questions

SSC GD Constable Number System — Past Exam Questions

Study by Subtopic — Number System

Study Next — Quantitative Aptitude Topics