Q1
What is the unit digit of 7^95?
- (1)7
- (2)9
- (3)3✓ Correct answer
- (4)1
Answer: (3) 3
Explanation
Unit digits of powers of 7 repeat as 7, 9, 3, 1; 95 leaves remainder 3 when divided by 4, so the digit is 3.
Number system & simplification MCQ with Answers
15 questionswith explanationsfor RAS, Patwari, VDO and other Rajasthan exams
Questions
Q2
What is the remainder when 2^100 is divided by 7?
- (1)1
- (2)5
- (3)2✓ Correct answer
- (4)6
Answer: (3) 2
Explanation
2^3 = 8 leaves remainder 1 on division by 7; 2^100 = (2^3)^33 × 2, so the remainder is 2.
Q3
The HCF of two numbers is 12 and their LCM is 360. If one of the numbers is 72, what is the other number?
- (1)60✓ Correct answer
- (2)30
- (3)48
- (4)120
Answer: (1) 60
Explanation
Product of the numbers = HCF × LCM, so the other number = 12 × 360/72 = 60.
Q4
What is the smallest number which, when divided by 12, 15, 20 and 27, leaves a remainder of 5 in each case?
- (1)540
- (2)535
- (3)1085
- (4)545✓ Correct answer
Answer: (4) 545
Explanation
LCM of 12, 15, 20 and 27 = 540; required number = 540 + 5 = 545.
Q5
What is the largest four-digit number exactly divisible by 88?
- (1)9988
- (2)9944✓ Correct answer
- (3)9966
- (4)9900
Answer: (2) 9944
Explanation
9999 ÷ 88 leaves remainder 55; 9999 − 55 = 9944 (= 88 × 113).
Q6
If the six-digit number 437x92 is divisible by 11, where x is a digit, what is the value of x?
- (1)5
- (2)8
- (3)0
- (4)4✓ Correct answer
Answer: (4) 4
Explanation
(2 + x + 3) − (9 + 7 + 4) = x − 15 must be a multiple of 11, so x = 4.
Q7
Simplify: 48 ÷ 6 × 4 − 3 + 18 ÷ 3 × 2
- (1)17
- (2)32
- (3)41✓ Correct answer
- (4)29
Answer: (3) 41
Explanation
Division and multiplication from left to right: 8 × 4 = 32 and 6 × 2 = 12; then 32 − 3 + 12 = 41.
Q8
Simplify: (3/4 + 5/6) ÷ (7/12 − 1/3)
- (1)19/3✓ Correct answer
- (2)3/19
- (3)19/4
- (4)19/36
Answer: (1) 19/3
Explanation
3/4 + 5/6 = 19/12 and 7/12 − 1/3 = 3/12; (19/12) ÷ (3/12) = 19/3.
Q9
Express 0.2363636… (where 36 repeats) as a fraction in its lowest terms.
- (1)118/495
- (2)13/55✓ Correct answer
- (3)59/250
- (4)26/99
Answer: (2) 13/55
Explanation
0.2363636… = (236 − 2)/990 = 234/990 = 13/55.
Q10
What is the value of √1.69 + √0.0169 + √0.000169?
- (1)1.56
- (2)1.443✓ Correct answer
- (3)1.4313
- (4)1.3143
Answer: (2) 1.443
Explanation
√1.69 = 1.3, √0.0169 = 0.13 and √0.000169 = 0.013; the sum is 1.443.
Q11
What is the smallest number by which 2400 must be multiplied to make it a perfect cube?
- (1)45
- (2)30
- (3)15
- (4)90✓ Correct answer
Answer: (4) 90
Explanation
2400 = 2^5 × 3 × 5^2; multiplying by 2 × 3^2 × 5 = 90 gives 2^6 × 3^3 × 5^3 = 60^3.
Q12
Which of the following is the largest?
- (1)∜10✓ Correct answer
- (2)√3
- (3)∛5
- (4)⁶√30
Answer: (1) ∜10
Explanation
Raise all to the 12th power: √3 → 729, ∛5 → 625, ∜10 → 1000, ⁶√30 → 900; so ∜10 is the largest.
Q13
Arrange the fractions 2/3, 3/5, 5/8 and 7/11 in ascending order.
- (1)3/5 < 7/11 < 5/8 < 2/3
- (2)5/8 < 3/5 < 7/11 < 2/3
- (3)3/5 < 5/8 < 7/11 < 2/3✓ Correct answer
- (4)3/5 < 5/8 < 2/3 < 7/11
Answer: (3) 3/5 < 5/8 < 7/11 < 2/3
Explanation
In decimals: 3/5 = 0.600, 5/8 = 0.625, 7/11 ≈ 0.636, 2/3 ≈ 0.667.
Q14
How many positive factors (divisors) does 360 have?
- (1)20
- (2)18
- (3)22
- (4)24✓ Correct answer
Answer: (4) 24
Explanation
360 = 2^3 × 3^2 × 5, so the number of factors = (3+1)(2+1)(1+1) = 24.
Q15
Consider the following statements: 1. The product of any three consecutive natural numbers is divisible by 6. 2. 91 is a prime number. 3. The square of every odd natural number leaves a remainder of 1 when divided by 8. Which of the statements given above is/are correct?
- (1)1 and 2 only
- (2)1 and 3 only✓ Correct answer
- (3)2 and 3 only
- (4)1, 2 and 3
Answer: (2) 1 and 3 only
Explanation
Statements 1 and 3 are true; 91 = 7 × 13, so it is not prime.