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

The numbers 1 to 29 are written side by side as follows to obtain a single number. 1 2 3 4 5 6 7 8 9 ... 27 28 29. If the number is divided by 9, then what will be the remainder?

  1. 0

  2. 1

  3. 2

  4. 3

  5. 6
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A number is divisible by 9 if the sum of its digits is divisible by 9. The sum of digits from 1 to 29: Sum of digits 1-9 = 45. Sum of digits 10-19 = (1*10) + 45 = 55. Sum of digits 20-29 = (2*10) + 45 = 65. Total sum = 45 + 55 + 65 = 165. 165 / 9 = 18 with a remainder of 3.

Multiple choice

A number x, when divided by d, leaves a remainder 10. Another number y, when divided by the same divisor, leaves 11 as remainder. If (x + y), when divided by 'd', leaves 5 as remainder, find the value of d.

  1. 16

  2. 14

  3. 12

  4. 10

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

x = q1*d + 10; y = q2*d + 11. x+y = (q1+q2)*d + 21. Dividing by d leaves remainder 5. 21 = k*d + 5. 16 = k*d. Since the remainder must be less than the divisor, d > 11. The only factor of 16 greater than 11 is 16.