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 7-digit number which, when divided by 5, 7, 11, and 13, respectively, leaves the same and the largest possible remainder for all four divisors.

  1. 99,99,995

  2. 99,99,994

  3. 99,99,987

  4. 99,99,986
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The LCM of 5, 7, 11, 13 is 5005. To find the largest 7-digit number with the same remainder, we find the largest multiple of 5005 less than 9,999,999, which is 9,999,995. The remainder is 4. Thus, the number is 9,999,995 - 1 = 9,999,994.

Multiple choice

What is the positive difference between the smallest and largest 5-digit numbers which, when divided by 2, 3, 5, and 7 respectively, leave the same remainder for all four divisors?

  1. 88980

  2. 89760

  3. 89880

  4. 88990

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

LCM(2,3,5,7) = 210. Numbers are of form 210k + r. Smallest 5-digit number is 10000. 10000/210 = 47.6, so 210*48 = 10080. Largest is 99999/210 = 476.19, so 210*476 = 99960. Difference = 99960 - 10080 = 89880.

Multiple choice

Directions: In the following item, Quantity I and Quantity II are given. Determine the relationship between the quantities and choose the appropriate option. If P is the smallest five-digit number in the range 10000 to 99999 that leaves a remainder of 4 when divided by 6, 8, 10, and 15 Quantity I: The remainder when P is divided by 11 Quantity II: 5

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I ≥ Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II, or No relation
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

The number n is a 2-digit number. When n is divided by 10, the remainder is 9, and when n is divided by 9, the remainder is 8. What is the value of n?

  1. 99

  2. 89

  3. 79

  4. 65
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

n = 10a + b. n mod 10 = 9 implies n ends in 9. n mod 9 = 8 implies n = 9k + 8. Testing 2-digit numbers ending in 9: 19 (19/9=2 R 1), 29 (29/9=3 R 2), 39 (39/9=4 R 3), 49 (49/9=5 R 4), 59 (59/9=6 R 5), 69 (69/9=7 R 6), 79 (79/9=8 R 7), 89 (89/9=9 R 8). 89 fits.

Multiple choice

Determine the smallest 5-digit number that, when divided by 72, 84, and 48 respectively, leaves remainders of 53, 65, and 29.

  1. 10,016

  2. 10,061

  3. 10,601

  4. 10,610

  5. 16,001
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The differences between divisors and remainders are: 72-53=19, 84-65=19, 48-29=19. Find the LCM of 72, 84, 48, which is 1008. Multiples of 1008 are 10080, 11088, etc. The smallest 5-digit number is 10080. Subtracting the common difference 19 gives 10080 - 19 = 10061.