2. 外语
  3. n = 24 × 32 × 52 and positive integer d is a divisor of n. Is d>? (1) d is divisible by 10. (2) d is divisible by 36.

n = 24 × 32 × 52 and positive integer d is a divisor of n. Is d>? (1) d is divisible by 10. (2) d is divisible by 36.

admin2022-10-18  13
问题 n = 24 × 32 × 52 and positive integer d is a divisor of n. Is d>?
(1) d is divisible by 10.
(2) d is divisible by 36.
选项 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.
答案C
解析 Given n = 24 × 32 × 52, then = (22)(3)(5) = 60. If d is a divisor of n, determine whether d > 60 is true.
(1)     It is given that d is divisible by 10. If d = 10, then dis 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.
(2)     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 lot 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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