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# If b≠0 and 7a/b is an integer with exactly two distinct factors then w

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If b≠0 and 7a/b is an integer with exactly two distinct factors then w  [#permalink]

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09 Mar 2020, 23:48
1
1
00:00

Difficulty:

65% (hard)

Question Stats:

22% (01:47) correct 78% (01:34) wrong based on 23 sessions

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If b≠0 and 7a/b is an integer with exactly two distinct factors then which of the following must be true
I) a = b
II) GCD of a and b = a
III) b = 7

A) I only
B) I and II only
C) III only
D) I, II and III all
E) None

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Re: If b≠0 and 7a/b is an integer with exactly two distinct factors then w  [#permalink]

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10 Mar 2020, 00:38
1
GMATinsight wrote:
If b≠0 and 7a/b is an integer with exactly two distinct factors then which of the following must be true
I) a = b
II) GCD of a and b = a
III) b = 7

A) I only
B) I and II only
C) III only
D) I, II and III all
E) None

Since 7a/b is an integer with exactly 2 distinct factors, it implies that 7a/b is a prime number

Since 7 itself is prime, we can have 2 scenarios:

Case 1: a = b => 7a/b = 7, which is prime

Case 2: b = 7 and a is prime => 7a/b = a
Note: Here too, we can have:

Case 2A: a = b = 7 OR
Case 2B: a = some prime other than 7 (say 3, 5, etc.) and b = 7

Let us check the statements (we need to check which statements MUST be true):

Statement 1: a = b: True in Case 1 or Case 2A; Not true in Case 2B - incorrect

Statement 2: GCD of a and b = a: True in Case 1 or Case 2A; Not true in Case 2B - incorrect

Statement 3: b = 7: True in Case 2; Not necessarily true in Case 1 - incorrect

Hence, none of the statements MUST be true

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Re: If b≠0 and 7a/b is an integer with exactly two distinct factors then w   [#permalink] 10 Mar 2020, 00:38