HSPT Question of the Day

1. 56 (correct answer)
2. 84
3. 108
4. 126

Explanation: This question tests your understanding of multiples and how to check divisibility by composite numbers. When determining if a number is a multiple of another number, you need to check if the division results in a whole number with no remainder. Let's check each option systematically. For a number to be a multiple of 14, it must be divisible by 14. For it to NOT be a multiple of 6, division by 6 must leave a remainder. Choice A: $56 ÷ 14 = 4$ (exact), so 56 is a multiple of 14. $56 ÷ 6 = 9.33...$ (not exact), so 56 is NOT a multiple of 6. This satisfies both conditions. Choice B: $84 ÷ 14 = 6$ (exact), so 84 is a multiple of 14. However, $84 ÷ 6 = 14$ (exact), so 84 IS also a multiple of 6. This fails the "not a multiple of 6" requirement. Choice C: $108 ÷ 14 = 7.71...$ (not exact), so 108 is NOT a multiple of 14. This immediately eliminates this choice since it fails the first condition. Choice D: $126 ÷ 14 = 9$ (exact), so 126 is a multiple of 14. However, $126 ÷ 6 = 21$ (exact), so 126 IS also a multiple of 6. Like choice B, this fails the second condition. Only choice A meets both criteria: it's a multiple of 14 but not a multiple of 6. Strategy tip: For "multiple but not multiple" questions, always check both conditions systematically. Many wrong answers will satisfy one condition but not both, making this a good way to eliminate choices quickly.