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# If x is an integer greater than 1, is y divisible by x ?

Author Message
Manager
Joined: 29 Nov 2018
Posts: 52
Location: India
Concentration: Entrepreneurship, General Management
GPA: 3.99
WE: Engineering (Computer Hardware)
If x is an integer greater than 1, is y divisible by x ?  [#permalink]

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18 Dec 2018, 20:25
1
00:00

Difficulty:

55% (hard)

Question Stats:

60% (02:13) correct 40% (03:19) wrong based on 5 sessions

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If x is an integer greater than 1, is y divisible by x?

(1) y is divisible by x−1
(2) y=x!+x−1

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed
Manager
Joined: 29 Nov 2018
Posts: 52
Location: India
Concentration: Entrepreneurship, General Management
GPA: 3.99
WE: Engineering (Computer Hardware)
Re: If x is an integer greater than 1, is y divisible by x ?  [#permalink]

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18 Dec 2018, 20:33
OA from Veritas:

This problem rewards students who remember that all multiples of the integer x will be x units apart. Statement (1) gives that y is divisible by x−1. This can be proven insufficient with a quick number picking thought experiment. If x=4 is it possible to have a number that is divisible by both x=4 and x−1=3? If you multiply 3 and 4 together to get 12, the answer is yes, there are an infinite number of ways to have a value of y that is divisible by both x and x−1.

Conversely, there are also an infinite number of integers that are divisible by x−1 that aren't divisible by x. In the case of x−1=3, 6, 9, and 21 are all divisible by 3 but aren't divisible by 4. Since this means you can get both a "yes" and a "no" based on the information given in statement (1), statement (1) is insufficient. Eliminate (A) and (D).

Statement (2) gives that y=x!+x−1. This may seem to give information similar to what is given in statement (1), but it is much more sufficient.

Remember that x! can be written as "(x)(x−1)(x−2)(x−3).....(2)(1)".

This means that for any given value for x where x is an integer greater than 1, that x! must be divisible by x−1 as well as x.

If you add x−1 to x!, you get a number that is divisible by x−1 but that cannot be divisible by x. To understand this, it helps to pick numbers.

If x=4, then x!=(4)(3)(2)=24. If you add x−1=3 to that, you get 27, which is still divisible by 3 but that isn't divisible by 4.

This is because multiples of the same number are evenly spaced - all multiples of 4 will be 4 apart, all multiples of 3 will be 3 apart, etc. So for whatever number you pick for x, if you add x−1 you will always get a number that is 1 less than a multiple of x, which means that y can never be divisible by x.

This means that statement (2) gives you a consistent "no" and is sufficient. Answer choice (B) is correct.
Math Expert
Joined: 02 Sep 2009
Posts: 52285
Re: If x is an integer greater than 1, is y divisible by x ?  [#permalink]

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18 Dec 2018, 21:02
ruchik wrote:
If x is an integer greater than 1, is y divisible by x?

(1) y is divisible by x−1
(2) y=x!+x−1

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed

Discussed here: https://gmatclub.com/forum/if-x-is-an-i ... 72152.html

THE TOPIC IS LOCKED AND ARCHIVED.
_________________
Re: If x is an integer greater than 1, is y divisible by x ? &nbs [#permalink] 18 Dec 2018, 21:02
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