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20 Oct 2021, 03:30
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A
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Difficulty:
95%
(hard)
Question Stats:
47% (02:31) correct
53%
(02:37)
wrong
based on 158
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If x is a positive integer, is x divisible by 4?
(1) x^3 + x is divisible by 4.
(2) 5x + 4 is divisible by 6.
(1) x^3 + x is divisible by 4.
(2) 5x + 4 is divisible by 6.
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
20 Oct 2021, 06:54
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Bunuel
It may help to write x = 1, 2, 3 ... in your notes to remember that x is a positive integer.
Statement 1 Alone:
> \(x^3 + x = x*(x^2 + 1)\). Note the two factors have different paritys, so either x is divisible by 4, or \(x^2 + 1\) is divisible by 4.
> We can test if \(x^2 + 1\) can possibly be a multiple of 4. Set \(x = Even + 1\), as the result can only be even if x is odd.
> \(x^2 + 1 = (Even + 1)^2 + 1 = Even^2 + 2*Even + 2\). Note that \(Even^2 + 2*Even\) must be a multiple of 4, and adding 2 would force the result to NOT be a multiple of 4.
> Then from deduction, x must contain the factor of 4. Hence x is divisible by 4 and this is sufficient.
Statement 2 Alone:
> Note that \(5x\) cannot be a multiple of 6, unless \(x\) is a multiple of 6.
> This tells us the candidates for x will be increases in 6's (or \(5x + 4\) increases in 30's).
> Then x cannot always be a multiple of 4, so this is insufficient. (The actual candidates for x are 4, 10, 16 ... but we don't have to know that)
Answer: A
03 Nov 2021, 06:42
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This question is a part of Are You Up For the Challenge: 700 Level Questions collection.
