Number System Questions for SSC CHSL: Download Free PDF

Are you preparing for the SSC CHSL exam to secure a government job as an LDC or DEO? We know that for many students, the Quantitative Aptitude is a tough section. You might feel confident in English or GK, but when it comes to Math, you get nervous. But there is a topic which simple, easy, and scoring, which is the number system. It tests your speed and basic logic. If you master it, you automatically get better at Algebra and Arithmetic. The questions are straightforward, usually about remainders, divisibility, or unit digits. To help you practice the right questions, we have compiled the most important Number System questions for SSC CHSL into a free PDF. You can download it from this blog.

Why is the Number System Important for SSC CHSL?

In the Tier 1 exam (25 Math questions), Number System is a critical area.

• Consistent Marks: You can expect 2-3 questions in every shift. These are often the first few questions in the paper.
• Foundation for Algebra: Concepts like “Rationalization” or “Surds and Indices” learned here are directly used in Algebra.
• Option Elimination: Number System teaches you divisibility rules. You can use these rules to eliminate wrong options in topics like Mensuration and Profit & Loss without solving the whole problem.

Download Free PDF of Number System Questions for SSC CHSL

We have prepared a comprehensive PDF containing exam-level questions. We have chosen questions that match the exact difficulty level of SSC CHSL—tricky yet solvable in under 40 seconds. Download it, save it, and practice these questions to sharpen your logic.

Q1. If the 8-digit number 789x531y is divisible by 72, then the value of (5x − 3y) is:

(a) 0
(b) 1
(c) 2
(d) −1

Answer: (d) −1

Logic:
For 72 → check divisibility by 8 and 9.

Divisible by 8:
Last three digits 31y must be divisible by 8.
312 works → y = 2

Divisible by 9:
7 + 8 + 9 + x + 5 + 3 + 1 + 2 = 35 + x
Next multiple of 9 is 36 → x = 1

So,
5x − 3y = 5(1) − 3(2) = 5 − 6 = −1

Q2. What is the remainder when 67⁶⁷ + 67 is divided by 68?

(a) 1
(b) 63
(c) 66
(d) 67

Answer: (c) 66

Logic:
67 ≡ −1 (mod 68)

(−1)⁶⁷ + (−1) = −1 − 1 = −2

Remainder cannot be negative → 68 − 2 = 66

Q3. The sum of three consecutive odd natural numbers is 87. What is the smallest number?

(a) 29
(b) 27
(c) 31
(d) 25

Answer: (b) 27

Logic:
Average = middle number
87 ÷ 3 = 29

So numbers: 27, 29, 31
Smallest = 27

Q4. Find the unit digit of (4387)²⁴⁵ × (621)⁷²

(a) 1
(b) 7
(c) 9
(d) 3

Answer: (b) 7

Logic:
Last digit of 4387 → 7
Cycle of 7 repeats every 4.

245 ÷ 4 leaves remainder 1 → unit digit = 7

621 ends with 1 → always gives 1

7 × 1 = 7

Q5. Which of the following numbers is divisible by 11?

(a) 4823718
(b) 8423718
(c) 8432718
(d) 4832718

Answer: (d) 4832718

Logic:
(4 + 3 + 7 + 8) − (8 + 2 + 1) = 22 − 11 = 11

Since 11 is divisible by 11 → number is divisible.

Q6. If a positive integer n is divided by 7, the remainder is 2. Which gives remainder 0 when divided by 7?

(a) n + 2
(b) n + 1
(c) n + 5
(d) n − 5

Answer: (c) n + 5

Logic:
Take n = 9 (because 9 ÷ 7 leaves remainder 2)
9 + 5 = 14 → divisible by 7

Q7. How many numbers between 200 and 800 are divisible by both 5 and 7?

(a) 15
(b) 16
(c) 17
(d) 18

Answer: (c) 17

Logic:
LCM of 5 and 7 = 35

200 ÷ 35 ≈ 5.7 → start from 6th multiple
800 ÷ 35 ≈ 22.8 → up to 22nd multiple

22 − 5 = 17

Q8. The value of 0.4(23 repeating) is:

(a) 419/990
(b) 423/1000
(c) 423/990
(d) 419/999

Answer: (a) 419/990

Logic:
(423 − 4) / 990 = 419 / 990

Q9. If √x + 1/√x = √6, then find x² + 1/x²

(a) 18
(b) 14
(c) 16
(d) 12

Answer: (b) 14

Logic:
Square both sides:

x + 1/x + 2 = 6
x + 1/x = 4

Square again:

x² + 1/x² + 2 = 16
x² + 1/x² = 14

Q10. The HCF of two numbers is 23 and the other two factors of their LCM are 13 and 14. The larger number is:

(a) 299
(b) 322
(c) 345
(d) 325

Answer: (b) 322

Logic:
Numbers = 23 × 13 and 23 × 14
Larger = 23 × 14 = 322

5 Preparation Tips to Master the Number System

Number System is the art of playing with digits. You don’t always need long division or multiplication. You need smart methods. To help you score full marks in this section, here are 5 practical tips designed specifically for the SSC CHSL exam pattern:

1. Master Divisibility Rules (7, 11, 13, 72, 88): SSC CHSL mostly asks, “Is this number divisible by 88?” Don’t divide by 88. Check divisibility by 8 and 11. Similarly, for 72, check 8 and 9. This trick solves 50% of the questions.
2. Learn the “Cyclicity” of Unit Digits: Don’t multiply huge numbers. Learn that the unit digit of numbers ending in 2, 3, 7, 8 repeats every 4 times (Cycle 4). This helps you solve questions like 2³⁵ in seconds.
3. Use Option Elimination: If a question asks “Which number is divisible by X?”, start by eliminating options using the unit digit or digital sum. Often, you can find the answer without solving.
4. Practice Remainder Theorem: Learn the basics of positive and negative remainders. For example, 17 divided by 18 gives a remainder of -1 (which is 17). This concept is crucial for power-based questions.
5. Attempt Topic Tests: Reading formulas is passive. Applying them is active. Attempt our free Topic Tests to train your brain to spot the logic in under 30 seconds.

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