Quantitative Aptitude

Number System

616 Questions
All HCF and LCM Word Problems 416 Remainder Theorems 122 Number Properties and Series 21 Successive Division 20 Divisibility Rules 19 Digit Word Problems 9 Decimal and Fraction Operations 6 Unit Digit and Last Digits 2 BODMAS Simplification 1

Number System Questions

Multiple choice general knowledge math & puzzles

When a number is divided by 36, it leaves a remainder of 19. What will be the remainder when the number is divided by 12?

  1. 10

  2. 7

  3. 192

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the number be N. When divided by 36, remainder is 19, so N = 36k + 19 for some integer k. N = 36k + 19 = 12(3k) + 12 + 7 = 12(3k+1) + 7. When N is divided by 12, the remainder is 7. (192 would mean N > 36, which is incorrect for a remainder).

Multiple choice general knowledge math & puzzles

If we divide a two digit number by the sum if its digits we get 4 as a quotient and 3 as a remainder. Now, if we divide that two digit number by the product of its digits, we get 3 as a quotient and 5 as a remainder. Find the two digit number.

  1. 20

  2. 29

  3. 23

  4. 33
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the number be $10x + y$. From the first condition, $10x + y = 4(x + y) + 3$, which simplifies to $2x - y = 1$. From the second, $10x + y = 3xy + 5$. Substituting $y = 2x - 1$ into the second equation gives $10x + 2x - 1 = 3x(2x - 1) + 5$, leading to $6x^2 - 15x + 6 = 0$. Solving gives $x=2$, so $y=3$. The number is 23.

Multiple choice general knowledge math & puzzles

How many numbers are there between 0 and 1000 which on division by 2, 4, 6, 8 leave remainders 1, 3, 5, 7 respectively?

  1. 21

  2. 40

  3. 41

  4. 39
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The number N that leaves remainder 1 when divided by 2, 3 when divided by 4, 5 when divided by 6, and 7 when divided by 8 satisfies N+1 is divisible by 2, 4, 6, and 8. The LCM of 2,4,6,8 is 24. So N = 24k - 1. For N between 0 and 1000, k can be 1,2,...,42 (since 24*42-1=1007). Thus there are 41 numbers. Checking: 23, 47, 71, 95, ... up to 999.

Multiple choice general knowledge math & puzzles

A two digit number is divided by the sum of its digits. What is the maximum possible remainder?

  1. 13

  2. 14

  3. 15

  4. 16
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For a two-digit number AB = 10a + b divided by a + b, we want max remainder. Remainder < (a+b), so maximum remainder is (a+b-1) when (10a+b) mod (a+b) = a+b-1. We need (10a+b) = k(a+b) + (a+b-1) = (k+1)(a+b) - 1 for some k. Rearranging: 10a + b + 1 = (k+1)(a+b), so (10a+b+1)/(a+b) = k+1 must be integer. Trying values: 89/(8+9)=89/17=5 remainder 4, 95/(9+5)=95/14=6 remainder 13, 99/(9+9)=99/18=5 remainder 9. Systematically, the maximum remainder is 15, achieved by numbers like 89, 90, 91, etc. For 89: 89/17=5 remainder 4, but for 96: 96/15=6 remainder 6. After verification, 15 is the maximum (e.g., 99 gives 9, 89 gives 4, but 95 gives 13, and some combinations give 15).