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

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Math Expert
Joined: 02 Sep 2009
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Is (3x + 8)/(x + 2) an integer?  [#permalink]

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06 Mar 2017, 09:56
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15% (low)

Question Stats:

77% (00:55) correct 23% (01:21) wrong based on 60 sessions

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

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

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

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06 Mar 2017, 10:02
Bunuel wrote:
Is (3x + 8)/(x + 2) an integer?

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

2. x=0. that means 8/2 = 4 - integer. so statement 1 is sufficient. A, C, E are out right away.

now..statement 1.
x is an integer.
suppose x=1.
3+8=11.
1+2=3.
11/3 = non-integer.

suppose x=0 (satisfies the condition)
8/2 = 4. - integer

since statement 1 can yield two different outcomes, A is insufficient, and we can cross D.

the only answer left is B.
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Re: Is (3x + 8)/(x + 2) an integer?  [#permalink]

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06 Mar 2017, 19:39
B
On simplifying we get 3 + 2/(× + 2)
Statement 1
3 plus something ,and this something isn't an integer for all x
Statement 2
When x=0
3+ 2/2=4
So B

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

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07 Mar 2017, 04:07
Is (3x + 8)/(x + 2) an integer?

(1) x is an integer
Put x =0...........8/2 =4 ...........Yes

Put x=1.............11/3=non Integer..........No

Insufficient

(2) x = 0

From above example. it is Yes.

Sufficient

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

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01 Nov 2018, 08:33
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, 05:14
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, 12:57
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?   [#permalink] 02 Nov 2018, 12:57
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