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04 Nov 2016, 09:35
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
71% (01:26) correct
29%
(01:31)
wrong
based on 285
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Consider an integer x=251n9 where n represents the tens digit of x, what is the value of x?
(1) x is a multiple of 3
(2) x is a multiple of 9
(1) x is a multiple of 3
(2) x is a multiple of 9
Updated on: 20 Feb 2020, 17:37
Originally posted by BrentGMATPrepNow on 04 Nov 2016, 11:26.
Last edited by BrentGMATPrepNow on 20 Feb 2020, 17:37, edited 1 time in total.
Last edited by BrentGMATPrepNow on 20 Feb 2020, 17:37, edited 1 time in total.
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stonecold
Nice question, stonecold
This question tests two divisibility rules:
1) If an integer is divisible by 3 (i.e., a multiple of 3), the sum of its digits must be divisible by 3.
2) If an integer is divisible by 9 (i.e., a multiple of 9), the sum of its digits must be divisible by 9.
Target question: What is the value of x?
Given: x = 251n9 where n represents the tens digit of x
Statement 1: x is a multiple of 3
This means the sum of the digits of x must be divisible by 3
In other words, the sum 2+5+1+n+9 must be divisible by 3
Simplify: 17+n must be divisible by 3
This means there are several possible cases:
Case a: n = 1, so that 17+n = 17+1 = 18, which is divisible by 3. In this case, x = 25119
Case b: n = 4, so that 17+n = 17+4 = 21, which is divisible by 3. In this case, x = 25149
Case c: n = 7, so that 17+n = 17+7 = 24, which is divisible by 3. In this case, x = 25179
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x is a multiple of 9
This means the sum of the digits of x must be divisible by 9
In other words, the sum 2+5+1+n+9 must be divisible by 9
Simplify: 17+n must be divisible by 9
This means there is only one possible case: n = 1, so that 17+n = 17+1 = 18, which is divisible by 9.
Since no other single-digit value of n will be such that 17+n is divisible by 9, we can conclude that x = 25119
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
General Discussion
16 Aug 2019, 00:38
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In ref to the solution posted by Brent.
It just says that x is a multiple of 3 or 9. It doesn’t say that the entire number should be divisible by 3 or 9. Please correct me if I am wrong. Would be awesome if someone could help me with this query.
Posted from my mobile device
It just says that x is a multiple of 3 or 9. It doesn’t say that the entire number should be divisible by 3 or 9. Please correct me if I am wrong. Would be awesome if someone could help me with this query.
Posted from my mobile device
