题目信息
n = 24 ⋅ 32 ⋅ 52 and positive integer d is a divisor of n. Is d >
?
?
A:Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B:Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C:BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D:EACH statement ALONE is sufficient.
E:Statements (1) and (2) TOGETHER are NOT sufficient.
参考答案及共享解析
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已选答案：
正确答案：
C:BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
Arithmetic Properties of integers
Given n = 24 ⋅ 32 ⋅ 52, then
= (22)(3)(5) = 60. If d is a divisor of n, determine whether d > 60 is true.
It is given that d is divisible by 10. If d = 10, then d is divisible by 10 and d is a divisor of n since n = (10)(23 ⋅ 32 ⋅ 5), but d > 60 is not true. However, if d = 80, then d is divisible by 10, d is a divisor of n since n = (80)(32 ⋅ 5), and d > 60 is true; NOT sufficient. It is given that d is divisible by 36. If d = 36, then d is divisible by 36 and d is a divisor of n since n = (36)(22 ⋅ 52), but d > 60 is not true. However, if d = 72, then d is divisible by 36, d is a divisor of n since n = (72)(2 ⋅ 52), and d > 80 is true; NOT sufficient.
Taking (1) and (2) together, it follows that d is divisible by 22 ⋅ 32 ⋅ 5 = 180 and every multiple of 180 is greater than 60.
The correct answer is C;both statements together are sufficient.
Given n = 24 ⋅ 32 ⋅ 52, then
= (22)(3)(5) = 60. If d is a divisor of n, determine whether d > 60 is true.It is given that d is divisible by 10. If d = 10, then d is divisible by 10 and d is a divisor of n since n = (10)(23 ⋅ 32 ⋅ 5), but d > 60 is not true. However, if d = 80, then d is divisible by 10, d is a divisor of n since n = (80)(32 ⋅ 5), and d > 60 is true; NOT sufficient. It is given that d is divisible by 36. If d = 36, then d is divisible by 36 and d is a divisor of n since n = (36)(22 ⋅ 52), but d > 60 is not true. However, if d = 72, then d is divisible by 36, d is a divisor of n since n = (72)(2 ⋅ 52), and d > 80 is true; NOT sufficient.
Taking (1) and (2) together, it follows that d is divisible by 22 ⋅ 32 ⋅ 5 = 180 and every multiple of 180 is greater than 60.
The correct answer is C;both statements together are sufficient.
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