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ruchik
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18 Dec 2018, 21:25
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
50% (02:13) correct
50%
(02:51)
wrong
based on 6
sessions
History
Date
Time
Result
Not Attempted Yet
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
EACH statement ALONE is sufficient to answer the question asked
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed
(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
EACH statement ALONE is sufficient to answer the question asked
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed
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ruchik
Joined: 29 Nov 2018
Last visit: 09 Feb 2026
Posts: 91
Own Kudos:
Given Kudos: 57
Location: India
Concentration: Entrepreneurship, General Management
Schools: Sloan Fellows '22 IMD '22 (D)
GMAT 1: 730 Q50 V40
GPA: 3.99
WE:Engineering (Computer Hardware)
18 Dec 2018, 21:33
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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.
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.
18 Dec 2018, 22:02
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ruchik
Discussed here: if-x-is-an-integer-greater-than-1-is-y-divisible-by-x-272152.html
THE TOPIC IS LOCKED AND ARCHIVED.
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
