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 greatest number of six digits which when divided by 24, 36, 60 and 90 leaves remainder 11 in each case. 6 अंकों की बड़ी से बड़ी संख्या ज्ञात कीजिए जो 24, 36, 60 और 90 से विभाजित करने पर प्रत्येक दशा में 11 शेषफल छोड़े।

  1. 999941

  2. 999731

  3. 999722

  4. 999631
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

We need the largest 6-digit number that leaves remainder 11 when divided by 24, 36, 60, and 90. First find LCM(24,36,60,90). 24 = 2³×3, 36 = 2²×3², 60 = 2²×3×5, 90 = 2×3²×5. LCM = 2³×3²×5 = 8×9×5 = 360. The required number is of form 360k + 11. Largest 6-digit number is 999999. 999999 ÷ 360 = 2777.77, so k = 2777. Number = 360×2777 + 11 = 999720 + 11 = 999731.

Multiple choice

The HCF of two numbers is 99 and their LCM is 2772. The numbers are -

  1. 198, 1386

  2. 396, 693

  3. 297, 924

  4. 693, 1108
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For two numbers, Product = HCF × LCM. Here, product = 99 × 2772. Option B (396, 693): HCF of 396 and 693 is 99, and LCM is 2772. Verifying: 396 = 99 × 4, 693 = 99 × 7 (4 and 7 are coprime), and LCM = 99 × 4 × 7 = 2772. Option A has LCM = 1386 (incorrect), Option C has HCF = 33 (incorrect), and Option D has HCF = 1 (incorrect).

Multiple choice

$Find the greatest number that will divide 400, 435 and 541 leaving 9, 10 and 14 as remainders respectively.$ That number can be possible:- A. 19 B. 17 C. 13 D. 9

  1. All A, B, C and D

  2. Only B and C

  3. Only D and B

  4. Only A

  5. Only 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), (435-10), (541-14) = 391, 425, 527 exactly. Find HCF of 391, 425, 527. 391 = 17 × 23, 425 = 17 × 25, 527 = 17 × 31. HCF = 17. Check: 400 ÷ 17 = 23 remainder 9 ✓, 435 ÷ 17 = 25 remainder 10 ✓, 541 ÷ 17 = 31 remainder 14 ✓. So 17 is the greatest such number. 19 and 13 don't work, and 9 is less than 17.

Multiple choice

Find the greatest number of 3 digits which is divided by both a and b. I-LCM of a and b is 60. II- Sum of a and b is 27.

  1. If statement I alone is sufficient but statement II alone is not sufficient.

  2. If statement II alone is sufficient but statement I alone is not sufficient.

  3. If each statement alone (either I or II) is sufficient.

  4. If statement I and II together are not sufficient.

  5. If both statement together are sufficient, but neither statement alone is sufficient.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

We need the largest 3-digit number (999 or below) divisible by both a and b. LCM(a,b) = 60 from statement I alone. The largest 3-digit multiple of 60 is 960 (60 × 16). Statement II (sum = 27) is not needed - the LCM alone gives us the divisibility requirement. Statement I alone is sufficient.

Multiple choice

The greatest number that will divide 729 and 901 leaving remainder 9 and 5 respectively, is सबसे बड़ी संख्या ज्ञात कीजिये जिससे 729 और 901 को भाग देने पर शेषफल 9 और 5 मिलता है ?

  1. 15

  2. 16

  3. 18

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

We need HCF of (729-9, 901-5) = HCF(720, 896). 720 = 2^4 × 3^2 × 5 and 896 = 2^7 × 7. Common factors: 2^4 = 16. Therefore HCF = 16. This is the greatest number dividing both 729 and 901 leaving remainders 9 and 5 respectively.

Multiple choice

The numbers 11284 and 7655, when divided by a certain number of three digits, leave the same remainder. Find that number of three digits.

  1. 161

  2. 171

  3. 181

  4. 191
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

If two numbers leave the same remainder when divided by N, then N must divide their difference exactly. Calculate 11284 - 7655 = 3629. Find the 3-digit factors of 3629 by prime factorization. 3629 = 19 × 191. The 3-digit divisors are 191 only (since 19 is 2-digit). Check: 11284 ÷ 191 = 59 remainder 15, and 7655 ÷ 191 = 40 remainder 15. Both leave remainder 15, confirming 191 is the answer.

Multiple choice

The largest two digit number (N), which when divided by 3, 4 and 6 leaves the remainder 1, 2 and 4 respectively. What is the remainder when (N) is divided by 5?

  1. 1

  2. 2

  3. 4

  4. 3
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

We need the largest two-digit N where N≡1 (mod 3), N≡2 (mod 4), and N≡4 (mod 6). Checking N≡4 (mod 6) means N=6k+4. For k=15, N=94: 94÷3=31R1 ✓, 94÷4=23R2 ✓, 94÷6=15R4 ✓. For k=16, N=100 (three digits). So N=98 is the largest two-digit number satisfying all conditions. When N=98 is divided by 5: 98÷5=19R3. Wait, let me verify: 98≡1 (mod 3): 98=3×32+2, remainder is 2, not 1. Checking 94: 94=3×31+1 ✓, 94=4×23+2 ✓, 94=6×15+4 ✓. For N=98: 98=3×32+2 ✗. Let me find the correct N: N≡1 (mod 3), N≡2 (mod 4), N≡4 (mod 6). From N≡4 (mod 6): N=6k+4. This gives N≡1 (mod 3) automatically since 6k is divisible by 3 and 4≡1 (mod 3). For N≡2 (mod 4): 6k+4≡2 (mod 4) → 2k≡2 (mod 4) → k=1,3,5,... For largest two-digit: k=15 gives N=94, k=16 gives N=100 (3 digits). So N=94. 94÷5=18R4. Option C is correct.

Multiple choice

A number when divided by a divisor leaves a remainder of 37. When twice the original number is divided by the same divisor, the remainder is 19. What is the value of the divisor?

  1. 53

  2. 54

  3. 55

  4. 56
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When N divided by d leaves remainder 37, N = qd + 37. When 2N is divided by d, remainder is 19, so 2N = 2qd + 74. The remainder when 74 is divided by d is 19, meaning 74 = kd + 19, so d divides (74-19) = 55. Since remainder 37 requires d > 37, and divisors of 55 are 1, 5, 11, 55, only d = 55 satisfies d > 37.

Multiple choice

The smallest number which when divided by 18, 24, 38 and 42 leaves the remainder 15, 21, 35 and 39 respectively is :-
  1. $9579$
  2. $9573$
  3. $9887$
  4. $7305$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

When a number N leaves remainder r when divided by d, we can write N = d*k + r. Here, each remainder is 3 less than the divisor (18-15=3, 24-21=3, 38-35=3, 42-39=3), so N+3 must be divisible by all four divisors. Therefore, N+3 = LCM(18,24,38,42). LCM = 2^3 × 3^2 × 7 × 19 = 9576, so N = 9576 - 3 = 9573.