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 number lying between 900 and 1000 which when divided by 38 and 57 leaves in each case the remainder 23 is
  1. $954$
  2. $945$
  3. $953$
  4. $935$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A number N that leaves remainder 23 when divided by both 38 and 57 must satisfy N - 23 being divisible by LCM(38,57). Since 38 = 2×19 and 57 = 3×19, LCM = 2×3×19 = 114. So N - 23 = 114k, meaning N = 114k + 23. For k = 8, N = 912 + 23 = 935, which lies between 900 and 1000. Checking: 935 ÷ 38 = 24 remainder 23, and 935 ÷ 57 = 16 remainder 23.

Multiple choice

Find the least possible number when successively divided by 2, 5, 4 and 3 gives remainders 1, 1, 3 and 1 respectively.

  1. 60

  2. 72

  3. 73

  4. 75
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Work backwards from the last division. After dividing by 3, remainder 1, so N = 3a + 1. Before this, after dividing by 4, remainder 3, so 3a + 1 = 4b + 3, giving 3a = 4b + 2. Smallest solution: a = 2, b = 1. Tracing back: N = 7. After division by 5, remainder 1, so 7 = 5c + 1 gives c = 1. After division by 2, remainder 1, so 7 = 2d + 1 gives d = 3. The least number satisfying all conditions is 73.

Multiple choice

Find the greatest number that will divide 400, 435 and 541 leaving 9, 10 and 14 as remainders respectively. सबसे बड़ी संख्या ज्ञात कीजिये जो कि 400, 435 और 541 को विभाजित करने पर क्रमशः में 9, 10 और 14 शेष के रूप में छोड़ेगी । That number can be possible:- यह संभव संख्या हो सकती है:- A. 19 B. 17 C. 13 D. 9

  1. All A, B, C and D सभी A, B, C तथा D

  2. Only B and C केवल B तथा C

  3. Only D and B केवल D तथा B

  4. Only A केवल A

  5. Only B केवल B
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

If a number N divides 400, 435, 541 leaving remainders 9, 10, 14 respectively, then N divides (400-9)=391, (435-10)=425, and (541-14)=527 exactly. We need HCF(391, 425, 527). 391 = 17 × 23, 425 = 5² × 17, and 527 = 17 × 31. The HCF is 17. The claimed answer is correct.

Multiple choice

Let x be the greatest number which divides 955, 1027, 1075, the remainder in each case is the same. Which of the following is not a factor if x?

  1. 4

  2. 6

  3. 16

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

The number that divides all three with the same remainder is the HCF of the differences between the numbers. Differences: 1027 - 955 = 72, 1075 - 1027 = 48, 1075 - 955 = 120. HCF of 72, 48, 120 = 24. So x = 24. Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. Among the options, 16 is NOT a factor of 24. This question tests the concept of common remainder.

Multiple choice

What is the least number of 4 digits which when divided by 5 , 8 , 10 and 15 leaves 2 as remainder in each case?

  1. 1076

  2. 1084

  3. 1080

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

Find LCM of 5, 8, 10, 15: LCM = 120. We need the smallest 4-digit number that when divided by each divisor leaves remainder 2. This means the number is 2 more than a common multiple of 120. Smallest 4-digit number is 1000. 1000 ÷ 120 = 8 remainder 40, so 9 × 120 = 1080 is the smallest 4-digit multiple of 120. Required number = 1080 + 2 = 1082. Checking: 1082 ÷ 5 = 216 remainder 2, 1082 ÷ 8 = 135 remainder 2, 1082 ÷ 10 = 108 remainder 2, 1082 ÷ 15 = 72 remainder 2. Since 1082 is not among options A, B, or C, the correct answer is D: None of these.

Multiple choice

If a number is divisible by 624, the remainder will be 53, If the same number is divisible by 16, then the remainder will be:

  1. 6

  2. 5

  3. 4

  4. 7
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

When a number N leaves remainder 53 when divided by 624, we can write N = 624k + 53. To find the remainder when N is divided by 16, we need to compute (624k + 53) mod 16. Since 624 = 16 × 39, 624 is perfectly divisible by 16, so 624k mod 16 = 0. Therefore, N mod 16 = 53 mod 16 = 53 - 16×3 = 5. The key insight is that 624 is a multiple of 16, so only the remainder 53 matters.