Number system
Ten quantitative aptitude questions, each marked as you answer.
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What is the HCF of 48, 36 and 120?
Answer and working
Answer C
48 = 2⁴ × 3; 36 = 2² × 3²; 120 = 2³ × 3 × 5. The factors common to all three: 2² × 3 = 12.
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What is the LCM of 12, 42 and 156?
Answer and working
Answer C
12 = 2² × 3; 42 = 2 × 3 × 7; 156 = 2² × 3 × 13. Each prime at its highest power: 2² × 3 × 7 × 13 = 1,092.
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What is the HCF of 27, 234 and 45?
Answer and working
Answer A
27 = 3³; 234 = 2 × 3² × 13; 45 = 3² × 5. The factors common to all three: 3² = 9.
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How many numbers from 200 to 800 (both included) are divisible by 13?
Answer and working
Answer A
Multiples of 13 up to 800: 61. Up to 199: 15. Difference = 46.
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What is the HCF of 165, 45 and 195?
Answer and working
Answer D
165 = 3 × 5 × 11; 45 = 3² × 5; 195 = 3 × 5 × 13. The factors common to all three: 3 × 5 = 15.
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What is the unit digit of 927?
Answer and working
Answer A
The unit digits of the powers of 9 repeat in a cycle of 2: 9, 1. 27 is position 1 in that cycle (27 ÷ 2 leaves 1), so the unit digit is 9.
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What is the smallest number which, when divided by 18, 4 or 5, leaves a remainder of 3 in each case?
Answer and working
Answer B
LCM of 18, 4, 5 = 180. Add the remainder: 180 + 3 = 183.
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The HCF and LCM of two numbers are 12 and 1,260. If one of the numbers is 84, what is the other?
Answer and working
Answer B
HCF × LCM = product of the numbers, so the other = 12 × 1,260 ÷ 84 = 180.
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What is the largest 3-digit number exactly divisible by 37?
Answer and working
Answer C
999 ÷ 37 leaves remainder 0. 999 − 0 = 999.
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What is the unit digit of 470?
Answer and working
Answer D
The unit digits of the powers of 4 repeat in a cycle of 2: 4, 6. 70 is position 2 in that cycle (70 ÷ 2 leaves 0), so the unit digit is 6.
More quantitative aptitude: Percentages, Profit, loss and discount, Simple interest, Compound interest, Ratio and proportion, Averages.