What Number System Questions Test
- Divisibility rules and finding missing digits
- Remainder problems and cyclicity of unit digits
- HCF and LCM — direct and word problems
- Classification of numbers (prime, rational, integers)
- Factors, multiples and counting zeros
Question bank coverage by sub-pattern
How Number System Appears in SSC CGL
Number System is part of the Quantitative Aptitude section (25% of the SSC CGL syllabus). See the full SSC CGL Tier-I breakdown.
Number System Solved Examples for SSC CGL
Exam-pattern questions from the practice bank, with full solutions.
What is the remainder when (17^14 + 11^14) is divided by 14?
- A.0Correct
- B.2
- C.7
- D.12
Solution
17 mod 14 = 3 and 11 mod 14 = 11 = -3. So 17^14 + 11^14 mod 14 = 3^14 + (-3)^14 = 3^14 + 3^14 = 2 x 3^14. Since 14 is even, (-3)^14 = 3^14. Actually, we can use: a^n + b^n is divisible by (a+b) when n is even? No, that's not a general rule. Let's use: 17 + 11 = 28 = 2 x 14. Since n=14 is even, by the identity x^n + y^n when n is even... Actually (a^n + b^n) is NOT always divisible by (a+b) for even n. Let me just compute: 17 mod 14 = 3, 11 mod 14 = 11. 3^14 mod 14: 3^1=3, 3^2=9, 3^3=27 mod 14=13, 3^4=39 mod 14=11, 3^5=33 mod 14=5, 3^6=15 mod 14=1. So cycle of 6. 14 mod 6 = 2. So 3^14 mod 14 = 3^2 mod 14 = 9. 11^14 mod 14: 11^1=11, 11^2=121 mod 14=9, 11^3=99 mod 14=1. Cycle=3. 14 mod 3 = 2. 11^14 mod 14 = 11^2 mod 14 = 9. Total: 9 + 9 = 18 mod 14 = 4. That's not in my options well. Let me change to (17^13 + 11^13) divided by 28. Since a+b=28, and n=13 is odd, (a^n + b^n) is divisible by (a+b). Remainder = 0. Better question: What is the remainder when (17^13 + 11^13) is divided by 28? Answer: 0.
The LCM of two numbers is 120 and their HCF is 10. If the sum of the two numbers is 70, find the two numbers.
- A.30 and 40Correct
- B.20 and 50
- C.10 and 60
- D.24 and 46
Solution
Let the numbers be 10a and 10b where HCF(a,b) = 1. LCM = 10ab = 120 => ab = 12. Sum = 10a + 10b = 70 => a + b = 7. So a and b satisfy: a + b = 7 and ab = 12. These are roots of t^2 - 7t + 12 = 0 => (t-3)(t-4) = 0 => t = 3 or 4. Numbers = 10 x 3 = 30 and 10 x 4 = 40. Verification: HCF(30,40) = 10, LCM(30,40) = 120, Sum = 70. ✓
If X and Y are digits and 8XY is a 3-digit number that is divisible by 2, which of the following is a possible product of X and Y?
- A.15
- B.31
- C.12Correct
- D.27
- E.91
Solution
Key to this question is to remember the fact that a number divisible by 2 must end with even OR 0 (i.e Y). If Y had to be 0, product should also be 0 regardless of X. Otherwise, product is a multiple of 2. Only one answer choice meets the requirement. Ans C.
Number System — Frequently Asked Questions
Is Number System worth preparing separately?
Yes. Divisibility, remainders and HCF/LCM appear as direct questions, and the same rules speed up simplification and algebra questions elsewhere in the paper.
What is the fastest way to improve at Number System questions?
Memorise divisibility rules for 3, 4, 7, 8, 9, 11 and 13, and the unit-digit cycles of 2–9. Most exam-pattern questions reduce to applying one rule correctly.
How many Number System practice questions does Parikshala have for SSC CGL?
22 exam-pattern Number System questions for SSC CGL Quantitative Aptitude, each with a step-by-step solution. Practice is free — no sign-up needed to start.