Quantitative Aptitude MCQs – Number System & Simplification

Quantitative Aptitude MCQs — 50 Number System & Simplification Questions for JKSSB, SSC and State Exams (Exam-style Practice Set 2025)

You get 50 tough, exam-style MCQs on number system and simplification. Each question matches JKSSB and SSC patterns. Attempt under timed conditions. Mark problems you skip. Check answers and learn short methods.

How to use this set (quick bullets you can show near top)

Note recurring tricks: modular arithmetic, surds, fractional indices, LCM/HCF shortcuts.

Time yourself, 45 minutes for full set.

Solve on paper, no calculator unless the exam allows it.

Mark hard questions, review solutions after finishing.

A two-digit number has product of digits 24. If 18 is added to the number, the digits interchange. Find the number.
- A) 38
- B) 42
- C) 48
- D) 84
Answer: C
The HCF of two numbers is 18 and their LCM is 720. If one number is 72, find the other.
- A) 150
- B) 180
- C) 160
- D) 190
Answer: B
Find the number which when divided by 7, 9 and 11 leaves remainders 6, 8 and 10 respectively.
- A) 692
- B) 698
- C) 686
- D) 674
Answer: B
Simplify: ((8)^1/3 + (32)^1/5) / (4)^1/2
- A) 2
- B) 3
- C) 4
- D) 5
Answer: A
Find the least number which when divided by 5, 6, 7 and 8 leaves remainder 3 in each case.
- A) 843
- B) 963
- C) 1003
- D) 963
Answer: B
If x = 3 + 2√2, find 1/x.
- A) 3 − 2√2
- B) 2 − √2
- C) √2 − 1
- D) 5 − 2√2
Answer: A
The product of two numbers is 2028 and their HCF is 13. Find the numbers.
- A) 26 and 78
- B) 39 and 52
- C) 39 and 52
- D) 13 and 156
Answer: C
If a = 2^3/2 and b = 8^1/3, find a² / b³.
- A) 1
- B) 2
- C) 4
- D) 8
Answer: A
Simplify: (5^1/2 × 25^1/4) / 125^1/6
- A) 5^1/3
- B) 5^1/2
- C) 5^2/3
- D) 5^1/6
Answer: C
A number leaves remainder 1 when divided by 2, 3, 4, 5 and 6. Find the least such number greater than 100.
- A) 121
- B) 181
- C) 241
- D) 301
Answer: D
If 2x − 3y = 4 and x² + y² = 29, find xy.
- A) 5
- B) 6
- C) 7
- D) 8
Answer: B
Simplify: (9/16)^−3/2 × (27/8)^2/3
- A) 4
- B) 8
- C) 9
- D) 6
Answer: B
Find the remainder when 7¹⁰³ is divided by 100.
- A) 7
- B) 49
- C) 43
- D) 87
Answer: C
Simplify: (3 + √8)² + (3 − √8)²
- A) 18
- B) 22
- C) 26
- D) 30
Answer: C
Find the least number which, when increased by 1, becomes divisible by 2,3,4,5,6,7,8 and 9.
- A) 2519
- B) 2518
- C) 2517
- D) 2520
Answer: B
If x + 1/x = 5, find x³ + 1/x³.
- A) 110
- B) 115
- C) 120
- D) 125
Answer: A
If a² + b² = 50 and ab = 24, find (a − b)².
- A) 2
- B) 4
- C) 10
- D) 12
Answer: B
Simplify: √(50 + 20√6) − √(8 + 4√3)
- A) 3
- B) 2
- C) 4
- D) 5
Answer: A
Find smallest integer n such that 3ⁿ > 2000.
- A) 6
- B) 7
- C) 8
- D) 9
Answer: B
If the ratio of two numbers is 3:5 and their LCM is 240, find their HCF.
- A) 12
- B) 16
- C) 20
- D) 24
Answer: B
Simplify: (5^0.5 + 5^−0.5)² − (5^0.5 − 5^−0.5)²
- A) 4
- B) 8
- C) 2
- D) 0
Answer: B
The HCF of two numbers is 24 and their LCM is 1248. If one number is 96, find the other.
- A) 312
- B) 324
- C) 288
- D) 384
Answer: A
Find the number between 200 and 300 divisible by 7, 9 and 11.
- A) 207
- B) 231
- C) 252
- D) 275
Answer: B
Simplify: (4^3/2 × 8^2/3) / 2⁴
- A) 2
- B) 3
- C) 4
- D) 6
Answer: B
If a number is divided by 5, remainder is 4. What will be the remainder when the square of that number is divided by 5?
- A) 0
- B) 1
- C) 4
- D) 2
Answer: B
If x = 2 + √3, find x² + 1/x².
- A) 14
- B) 7
- C) 9
- D) 10
Answer: D
Simplify: (27)^1/3 × (9)^1/2 / 3^5/3
- A) 1
- B) 3
- C) 9
- D) 27
Answer: A
The product of two consecutive even numbers is 168. Find the numbers.
- A) 10, 12
- B) 12, 14
- C) 14, 16
- D) 16, 18
Answer: B
If x + 1/x = 4, find x⁴ + 1/x⁴.
- A) 194
- B) 193
- C) 188
- D) 180
Answer: B
Simplify: (125)^2/3 ÷ (25)^1/2
- A) 3
- B) 4
- C) 5
- D) 6
Answer: C
If a = √3 + 2, find a² − 4a + 1.
- A) 0
- B) 2√3
- C) 1
- D) 2
Answer: A
Simplify: (49)^1/2 × (343)^1/3 / 7^4/3
- A) 7
- B) 1
- C) 2
- D) 3
Answer: B
If remainder when 5^x divided by 13 is 8, find remainder when 5^x+2 divided by 13.
- A) 9
- B) 10
- C) 11
- D) 12
Answer: D
Find number whose square equals cube of 16.
- A) 16
- B) 32
- C) 64
- D) 128
Answer: B
Simplify: (2¹⁰ × 4³) / 8⁴
- A) 1
- B) 2
- C) 4
- D) 8
Answer: A
If product of two co-prime numbers is 385, find their LCM.
- A) 35
- B) 55
- C) 385
- D) 70
Answer: C
Simplify: (√3 + √2)² − 2√6
- A) 5
- B) 7
- C) 9
- D) 11
Answer: A
Find smallest number divisible by 12, 18, 21 and 30.
- A) 630
- B) 720
- C) 840
- D) 1260
Answer: D
If x = 4 + √15, find √x − 1/√x.
- A) 2
- B) 3
- C) 4
- D) 1
Answer: A
Simplify: (81)^3/4 / (9)^5/2
- A) 1/9
- B) 1/3
- C) 3
- D) 9
Answer: A
If x = 2 + √3, find x − 1/x.
- A) 2√3
- B) √3
- C) 1
- D) 3
Answer: B
Find smallest positive integer divisible by 9, 12, 15 and 18.
- A) 360
- B) 540
- C) 720
- D) 900
Answer: B
If x = 3 + 2√2, find x³ + 1/x³.
- A) 70
- B) 71
- C) 72
- D) 73
Answer: D
Simplify: (64)^2/3 × (4)^−1/2
- A) 4
- B) 6
- C) 8
- D) 16
Answer: C
Find remainder when 2⁶⁴ divided by 7.
- A) 1
- B) 2
- C) 4
- D) 6
Answer: A
Simplify: (5^4/3 × 25^1/6) / 125^1/2
- A) 5^−1/3
- B) 5^1/3
- C) 5^2/3
- D) 1
Answer: B
If x = √5 + 2, find x² − 4x + 1.
- A) 0
- B) 1
- C) 2
- D) 3
Answer: A
If a number has 18 factors, how many distinct prime factors does it have if expressed as p²q²r?
- A) 2
- B) 3
- C) 4
- D) 5
Answer: B
Simplify: (16^3/4 × 81^1/4) / 12^1/2
- A) 4
- B) 6
- C) 8
- D) 9
Answer: B
Find remainder when 4²⁰⁰ divided by 6.
- A) 0
- B) 2
- C) 4
- D) 1
Answer: C

Direction Reasoning Questions with Answers for JKSSB 2025

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Quantitative Aptitude – Number System & Simplification (Advanced MCQs)

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