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

100 and 80 leave the same remainder when divided by a divisor d (where d ϵ N). How many values can d take?

  1. 1

  2. 3

  3. 6

  4. 20
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If 100 and 80 leave the same remainder when divided by d, then d must be a divisor of (100-80) = 20. The divisors of 20 are 1, 2, 4, 5, 10, 20. Since the remainder must be less than the divisor, for d=1, remainder is 0. For d=2, remainder is 0. For d=4, remainder is 0. For d=5, remainder is 0. For d=10, remainder is 0. For d=20, remainder is 0. All 6 divisors work.

Multiple choice

A and B are natural numbers which when divided by a divisor d leave remainders of 23 and 13 respectively. When A+B is divided by d, the remainder is 3. What is the value of d?

  1. 10

  2. 33

  3. 36

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

A = q1*d + 23, B = q2*d + 13. A+B = (q1+q2)d + 36. Given A+B = q3*d + 3, so 36 = q4*d + 3, which means q4*d = 33. The divisor d must be a factor of 33 and greater than the remainders (23 and 13). The only factor of 33 greater than 23 is 33.

Multiple choice

Find the remainder when the number 12121212… (100 digits) is divided by 1001

  1. 211

  2. 212

  3. 455

  4. 666
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The number is (12 * 10^98) + (12 * 10^96) + ... + 12. This is a geometric series. 1001 = 7 * 11 * 13. Using modular arithmetic, 10^3 = -1 mod 1001. The pattern repeats every 6 digits (121212). 100 digits / 6 = 16 groups of 121212 plus 4 digits (1212). 1212 mod 1001 = 211. This is not the standard approach, but calculation confirms 666.

Multiple choice

When 125 is divided by a divisor d (where d ϵ N), the remainder is 5. How many values can d take?

  1. 1

  2. 11

  3. 16

  4. 120
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

If 125 divided by d leaves a remainder of 5, then d must be a divisor of (125 - 5) = 120, and d must be greater than the remainder 5. The divisors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120. Divisors greater than 5 are 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120, which are 11 values.

Multiple choice

A student types a number using the first 100 natural numbers from left to right as 1234567891011121314…99100. Find the remainder when this number is divided by 9.

  1. 0

  2. 1

  3. 2

  4. 8
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A number is divisible by 9 if the sum of its digits is divisible by 9. The number is formed by concatenating 1 to 100. The sum of digits of numbers 1-99 can be found by pairing (0,99), (1,98)...(49,50), each pair summing to 18, plus the digits of 100. The total sum of digits is 901. 901 mod 9 = 1.