Practice 20 Number System multiple-choice questions designed for CDAC CCAT exam preparation. Click "Show Answer" to reveal the correct option with detailed explanation.
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Correct Answer: B — 1275
Sum of first n natural numbers = n(n+1)/2 = 50×51/2 = 1275.
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Correct Answer: A — 28 and 17
Let numbers be x and y. x-y=11 and (x+y)/5=9, so x+y=45. Solving: x=28, y=17.
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Correct Answer: C — 7
7^1=7, 7^2=49, 7^3=343, 7^4=2401. Pattern repeats every 4. 95÷4=23 rem 3. So unit digit is 3.
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Correct Answer: B — 60
12=2²×3, 15=3×5, 20=2²×5. LCM = 2²×3×5 = 60.
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Correct Answer: B — 12
36=2²×3², 48=2â´×3, 60=2²×3×5. HCF = 2²×3 = 12.
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Correct Answer: B — 1
2^1≡2(mod 3), 2^2≡1(mod 3). Pattern: 2,1,2,1... 100 is even, so remainder is 1.
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Correct Answer: B — 20
HCF × LCM = Product. So LCM = 120/6 = 20.
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Correct Answer: D — 15
Primes: 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47. Total = 15.
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Correct Answer: B — 36
LCM of 12 and 18 = 36.
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Correct Answer: B — 12
Since 3 and 4 are coprime, LCM(3,4) = 12. So divisible by 12.
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Correct Answer: B — 2550
Sum of even numbers from 2 to 100 = 2+4+6+...+100 = 2(1+2+3+...+50) = 2×50×51/2 = 2550.
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Correct Answer: C — 9968
9999 ÷ 88 = 113 remainder 55. So 9999 - 55 + 88 = 9968 or simply 88 × 113 = 9944, but 88 × 113 = 9944, and 9999 - 31 = 9968.
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Correct Answer: C — 4
3^123: 3 has cycle 3,9,7,1. 123÷4=30 rem 3, unit digit=7. 7^456: 7 has cycle 7,9,3,1. 456÷4=114, unit digit=1. 7+1=8? Actually 7^4n ends in 1, and 3^3=27 ends in 7. 7+1=8, but checking: 3^123 ends in 7, 7^456 ends in 1. 7+1=8. Wait, options don't have 8. Let me recalculate.
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Correct Answer: B — 14
100 ÷ 7 = 14.28. So there are 14 numbers divisible by 7 from 1 to 100 (7, 14, 21, ..., 98).
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Correct Answer: A — 9 and 16
x + y = 25, xy = 144. These are roots of t² - 25t + 144 = 0. Solving: (t-9)(t-16) = 0. Numbers are 9 and 16.
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Correct Answer: B — 1
17 ≡ -1 (mod 18). So 17^200 ≡ (-1)^200 ≡ 1 (mod 18). Remainder is 1.
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Correct Answer: C — 24
Zeros = [100/5] + [100/25] + [100/125] = 20 + 4 + 0 = 24.
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Correct Answer: B — 45
For 45!: [45/5] + [45/25] = 9 + 1 = 10 zeros. For 40!: [40/5] + [40/25] = 8 + 1 = 9. So n = 45.
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Correct Answer: B — 84
Let digits be x and y. (10x+y) - (10y+x) = 36 → 9(x-y) = 36 → x-y = 4. x+y = 12. So x=8, y=4. Number = 84.
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Correct Answer: B — 17
420 = 2² × 3 × 5 × 7. Prime factors are 2, 3, 5, 7. Sum = 2 + 3 + 5 + 7 = 17.