important Number System Questions with answers and detailed solutions. Ideal for SSC CGL, CHSL, MTS, and other government job exams.
Q1) What is the smallest number which when divided by 12, 15 and 18 leaves remainder 2 in each case?
A) 182
B) 272
C) 362
D) 542
Correct Option is: A) 182
Explanation:
LCM of 12, 15, 18 = 180
Required number = 180 + 2 = 182
Q2) The HCF and LCM of two numbers are 8 and 96 respectively. If one of the numbers is 32, then the other number is:
A) 24
B) 28
C) 30
D) 48
Correct Option is: A) 24
Explanation:
Product of two numbers = HCF × LCM
= 8 × 96
= 768
Other number = 768 ÷ 32 = 24
Q3) Find the unit digit of 7¹⁰³
A) 3
B) 7
C) 9
D) 1
Correct Option is: A) 3
Explanation:
Unit digit cycle of powers of 7: 7, 9, 3, 1 (repeats every 4)
103 ÷ 4 → remainder = 3
3rd in cycle = 3
Q4) A number when divided by 5, 6 and 7 leaves remainder 1 in each case. What is the least such number?
A) 211
B) 301
C) 421
D) 511
Correct Option is: A) 211
Explanation:
LCM of 5, 6, 7 = 210
Required number = 210 + 1 = 211
Q5) If a number gives remainder 7 when divided by 13, what will be the remainder when its square is divided by 13?
A) 10
B) 9
C) 11
D) 8
Correct Option is: A) 10
Explanation:
Let number = 13k + 7
Then square = (13k + 7)²
→ remainder of 7² mod 13 = 49 ÷ 13
= remainder 10
Q6) What is the sum of first 50 natural numbers?
A) 1275
B) 1225
C) 1325
D) 1375
Correct Option is: A) 1275
Explanation:
Sum = n(n + 1)/2
= 50 × 51 ÷ 2
= 1275
Q7) How many numbers between 1 and 100 are divisible by both 3 and 4?
A) 6
B) 8
C) 12
D) 9
Correct Option is: B) 8
Explanation:
LCM of 3 and 4 = 12
Count of multiples of 12 in 1–100
= 100 ÷ 12
= 8
Q8) If the product of two numbers is 120 and their HCF is 4, what is their LCM?
A) 30
B) 60
C) 120
D) 150
Correct Option is: A) 30
Explanation:
HCF × LCM = Product of numbers
4 × LCM = 120
→ LCM = 30
Q9) A number is divisible by 9 and 12. Which of the following numbers is definitely divisible by it?
A) 36
B) 72
C) 108
D) 144
Correct Option is: A) 36
Explanation:
LCM of 9 and 12 = 36
So the number must be divisible by 36
All options are divisible, but smallest is 36
Q10) What is the greatest 4-digit number exactly divisible by 88?
A) 9999
B) 9944
C) 9976
D) 9988
Correct Option is: B) 9944
Explanation:
9999 ÷ 88 = 113.63
So 88 × 113 = 9944
✍️ Final Words
Practicing these Number System Questions helps in building strong fundamentals and speed during exams. These types of questions are repeatedly asked in SSC exams like CGL, CHSL, MTS, etc.
Make sure to revise LCM, HCF, unit digits, remainders, and divisibility rules to score full marks in the number system section.
📌 Stay tuned for Practice Set 02!
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