Numerical: Number System MCQ — 14 Practice Questions with Answers

Explanation

Check each statement by its divisibility rule. For 438, the number is even and 4 + 3 + 8 = 15 is divisible by 3, so it is divisible by 6. For 725, the last two digits are 25, so it is divisible by 25. For 1128, the alternating sum for 11 is (1 + 2) − (1 + 8) = 3 − 9 = -6, not a multiple of 11, so it is not divisible by 11. For 504, 504 ÷ 8 = 63. Only 1 statement is incorrect.

Explanation

Find the three values one by one. The factors of 24 include 1, 2, 3, 4, 6, 8, 12 and 24; the factors of 36 include 1, 2, 3, 4, 6, 9, 12, 18 and 36, so the HCF is 12. For 12 and 18, prime factors are 12 = 2^2 × 3 and 18 = 2 × 3^2, so the LCM is 2^2 × 3^2 = 36. In 4072, 7 is in the tens place, so its place value is 70. The order is 12, 36, 70.

Explanation

A number is divisible by 15 only when it is divisible by both 3 and 5. The number 47x5 already ends in 5, so it is divisible by 5 for every digit x. For divisibility by 3, the digit sum must be a multiple of 3: 4 + 7 + x + 5 = 16 + x. If x = 2, 16 + 2 = 18; if x = 5, 21; if x = 8, 24. All three are divisible by 3, so all three statements are correct.

Explanation

A rational number has a terminating decimal expansion when, after reducing the fraction to lowest terms, the denominator has only the prime factors 2 and 5. For 3/40, the fraction is already in lowest terms and 40 = 2^3 × 5. Hence its decimal expansion terminates. For 7/30, 11/45 and 13/63, the denominators contain prime factors such as 3 or 7, so they do not give terminating decimals.

Explanation

Find the nearest multiple of 11 for each number. For 283, 11 × 25 = 275, so the remainder is 283 − 275 = 8. For 517, 11 × 47 = 517, so the remainder is 0. For 945, 11 × 85 = 935, so the remainder is 945 − 935 = 10. Therefore, the correct matching is P-8, Q-0, R-10.