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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

Answer: B
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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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gmatbusters
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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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

B is the answer here

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