How many factors does 48 have?
Solution
48 = 2^4 × 3.
Number of factors = product of (power + 1) = 5 × 2 = 10.
Answer: (A) 10
Quantitative Aptitude · Numbers
Number System: MAH CET, NMAT and SNAP practice questions
20 questions in the pattern of MAH MBA CET, NMAT and SNAP. Each question is marked with the exams it suits. Answer it, then open the step-by-step solution.
Exam:
What is the unit digit of 23^367?
Solution
Unit digits of powers of 23 repeat every 4: 3, 9, 7, 1.
367 = 4 × 91 + 3, so the unit digit matches 23^3: 7.
Answer: (A) 7
What is the unit digit of 4^48 × 9^97 × 3^40?
Solution
Unit digits: 4^48 → 6, 9^97 → 9, 3^40 → 1 (using cycles of 4).
6 × 9 × 1 ends in 4.
Answer: (B) 4
What is the 39th term of the series 7, 17, 27, …?
Solution
First term 7, common difference 10.
T39 = 7 + (39 − 1) × 10 = 387.
Answer: (D) 387
Simplify: 200 ÷ 8 × 5 − 20 + 60 ÷ 5
Solution
Using BODMAS, do ÷ and × from left to right first: 200 ÷ 8 = 25; 25 × 5 = 125; 60 ÷ 5 = 12.
Then 125 − 20 + 12 = 117.
Answer: (A) 117
The sum of the digits of a two-digit number is 13. When the digits are reversed, the number decreases by 9. What is the number?
Solution
Let the number be 10a + b with a + b = 13.
Reversing changes it by 9|a − b| = 9, so |a − b| = 1.
Since it decreases, the tens digit is larger: a = 7, b = 6. Number = 76.
Answer: (C) 76
How many numbers from 19 to 847 (both included) are divisible by 3 or 8?
Solution
Divisible by 3: 276. By 8: 103. By both (by 24): 35.
Answer = 276 + 103 − 35 = 344.
Answer: (C) 344
What is the remainder when 5^288 is divided by 7?
Solution
5^6 leaves remainder 1 when divided by 7, so powers repeat every 6.
288 = 6 × 48 + 0, so the remainder equals that of 5^0 = 1, which is 1.
Answer: (B) 1
How many zeros are there at the end of 323! ?
Solution
Each trailing zero needs a factor 10 = 2 × 5, and 5s are fewer than 2s.
Number of 5s = 64 + 12 + 2 = 78.
Answer: (C) 78
How many factors does 120 have?
Solution
120 = 2^3 × 3 × 5.
Number of factors = product of (power + 1) = 4 × 2 × 2 = 16.
Answer: (D) 16
Which of the following numbers between 88 and 128 is a prime number?
Solution
101 has no factor other than 1 and itself (check primes up to √101 ≈ 10).
121 = 11 × 11.
119 = 7 × 17.
123 = 3 × 41.
Answer: (D) 101
What is the largest 4-digit number exactly divisible by 24?
Solution
The largest 4-digit number is 9999. 9999 ÷ 24 leaves remainder 15.
9999 − 15 = 9984.
Answer: (D) 9984
What is the remainder when 3^330 is divided by 7?
Solution
3^6 leaves remainder 1 when divided by 7, so powers repeat every 6.
330 = 6 × 55 + 0, so the remainder equals that of 3^0 = 1, which is 1.
Answer: (B) 1
The sum of 3 consecutive even numbers is 114. What is the largest of them?
Solution
Let the smallest be x: x + (x + 2) + (x + 4) = 114.
3x + 6 = 114, so x = 36.
Largest = 40.
Answer: (A) 40
A number when divided by 144 leaves a remainder of 68. What will be the remainder when the same number is divided by 12?
Solution
The number = 144k + 68. Since 144 = 12 × 12, 144k is divisible by 12.
So the remainder is 68 mod 12 = 8.
Answer: (C) 8
What is the unit digit of 7^25 × 4^37 × 9^70?
Solution
Unit digits: 7^25 → 7, 4^37 → 4, 9^70 → 1 (using cycles of 4).
7 × 4 × 1 ends in 8.
Answer: (A) 8
What is the difference between the place value and the face value of 2 in 429215?
Solution
Face value of 2 = 2. Place value = 2 × 10000 = 20000.
Difference = 20000 − 2 = 19998.
Answer: (A) 19,998
A number when divided by 144 leaves a remainder of 27. What will be the remainder when the same number is divided by 12?
Solution
The number = 144k + 27. Since 144 = 12 × 12, 144k is divisible by 12.
So the remainder is 27 mod 12 = 3.
Answer: (D) 3
How many zeros are there at the end of 63! ?
Solution
Each trailing zero needs a factor 10 = 2 × 5, and 5s are fewer than 2s.
Number of 5s = 12 + 2 = 14.
Answer: (C) 14
What is the unit digit of 47^473?
Solution
Unit digits of powers of 47 repeat every 4: 7, 9, 3, 1.
473 = 4 × 118 + 1, so the unit digit matches 47^1: 7.
Answer: (A) 7
These are original practice questions written by Target Campus in the pattern and difficulty of MAH MBA CET, NMAT, SNAP and other MBA entrance tests. They are not previous-year papers.
Preparing for MAH CET, SNAP or NMAT? Courses, live classes and mocks by Dr. Kiran Derle at Target Campus.
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