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# Is (3x+8)/(x+2) an integer?

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Senior DS Moderator
Joined: 27 Oct 2017
Posts: 1195
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)

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01 Nov 2018, 07:21
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Difficulty:

5% (low)

Question Stats:

93% (00:39) correct 7% (01:38) wrong based on 43 sessions

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Is $$\frac{(3x+8)}{(x+2)}$$ an integer?

(1) x is an integer.
(2) x = 0

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Status: It always seems impossible until it's done.
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Re: Is (3x+8)/(x+2) an integer?  [#permalink]

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01 Nov 2018, 07:33
gmatbusters wrote:
Is $$\frac{(3x+8)}{(x+2)}$$an integer?
(1) x is an integer.
(2) x = 0

For the fraction to be an integer : either the denominator should be 1 or denominator should evenly divide the numerator.

(1) Not sufficient as for x = 1 the denominator does not evenly divide the numerator. 11/3. But for x = 0 it is an integer.

(2) Sufficient At x = 0, the fraction becomes 8/2 = 4. Hence always an integer.

Hence Option (B) is our choice.

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Re: Is (3x+8)/(x+2) an integer?  [#permalink]

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02 Nov 2018, 04:14
gmatbusters wrote:
Is $$\frac{(3x+8)}{(x+2)}$$ an integer?

(1) x is an integer.
(2) x = 0

1)
3x+8=x+2 => 2x = -6 => x = -3. $$\frac{-1}{-1}$$ YES.
check x=1 => $$\frac{11}{3}$$ NO.

2) clearly sufficient
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Re: Is (3x+8)/(x+2) an integer?  [#permalink]

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02 Nov 2018, 11:57
Statement 1 : Since x is an integer, it can be any number positive or negative.
If x =5, then 23/5 is not an integer
If x = 0, then 8/2 is an integer

Therefore, not sufficient

Statement 2: x = 0 which gives us 8/2 = 4 is an integer... Sufficient

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Re: Is (3x+8)/(x+2) an integer? &nbs [#permalink] 02 Nov 2018, 11:57
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