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

Find the largest 5-digit number which when divided by 4, 9, and 11 leaves the same but largest remainder for all the three numbers?

  1. 99785

  2. 99945

  3. 99965

  4. 99795
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

LCM(4, 9, 11) = 396. To leave the same largest remainder, we look for numbers near 99999. 99999 / 396 leaves a remainder of 171. The number is 99999 - (171 - r). For the largest remainder, r should be 395. Number = 99999 - 171 + 395 = 100223 (not 5-digit). Adjusting, 99999 - 396*k. The logic leads to 99795.

Multiple choice

If Q is the largest four-digit number in the range 2000 to 9999, the remainder is 3 when Q is divided by 5, 7, 9 and 12. Quantity A: The remainder when Q is divided by 8 Quantity B: 7

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. The two quantities are equal.

  4. The relationship cannot be determined from the information given.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The number Q leaves remainder 3 when divided by 5, 7, 9, 12. LCM(5, 7, 9, 12) = 1260. Q = 1260k + 3. For largest 4-digit number, 1260*7 + 3 = 8823. 8823 divided by 8: 8823 = 8 * 1102 + 7. Remainder is 7. Quantity A = 7, Quantity B = 7.

Multiple choice

The sum of the digits of a number N is 23. The remainder when N is divided by 11 is 7. What is the remainder when N is divided by 33?

  1. 16

  2. 7

  3. 29

  4. 13

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

Since the sum of the digits of N is 23, N is congruent to 23, which is congruent to 2 modulo 3. We are also given that N is congruent to 7 modulo 11. By testing the options, only 29 leaves a remainder of 2 when divided by 3 and a remainder of 7 when divided by 11.