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by Malolo355 » Wed Nov 13, 2013 9:52 am
Hi everyone!
I just saw a DS question and I thought what the answer would be if I paraphrase it.
The official is "Is (3x+8)/(x+2) an integer? (1)x is an integer , (2) x=0 " and the OA is clearly B , since we are given a value for x.
I am curious what would happen if we had as a (2) x>0 .
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Source: — Data Sufficiency |
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by theCodeToGMAT » Wed Nov 13, 2013 10:22 am
To find: (3x+8)/(x+2) is INTEGER

3x/(x+2) + 8/(x+2)

Statement 1:
X is Integer.
X = 0, result = 8/2 YES INT
X = 1, result = 11/3 NOT INT
INSUFFICIENT

Statement 2:
x=0
X = 0, result = 8/2 YES INT
SUFFICIENT

Answer [spoiler]{B}[/spoiler]
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by theCodeToGMAT » Wed Nov 13, 2013 10:27 am
I believe that the answer to your rephrased question will still be {B} because:

if Statement 2 were, x>0

To find: (3x+8)/(x+2) is INTEGER

IMP: It's not given that "x" is INTEGER

Now, lets try some Integer values for expression
(3x+8)/(x+2) = 0 ==> 3x + 8 = 0 ==> x = -8/3 .. Doesn't Satisfy condition of x >0
(3x+8)/(x+2) = 1 ==> 3x+8 = x+2 ==> x = -3 .. Doesn't Satisfy condition of x >0

Similarly, if we try for more values of expression then "X" will not satisfy the equation as LHS has "8" which becomes "-8" when moved to RHS.. So, RHS will keep on resulting in "-ve" till the time we have expression value as "4" to make "4*2" to make RHS as "0" .. but then this will impact LHS as it would inturn become "-ve" for further values after "4" ...
So, we can conclude that (3x+8)/(x+2) is Not Integer for x>0
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by Brent@GMATPrepNow » Wed Nov 13, 2013 10:31 am
Here's the answer to your NEW question
Malolo355 wrote: Is (3x+8)/(x+2) an integer?

(1)x is an integer

(2) x > 0
Target question: Is (3x+8)/(x+2) an integer?

Statement 1: x is an integer
There are several values of x satisfy this condition. Here are two:
Case a: x = 0, in which case (3x+8)/(x+2) = 8/2 = 4 an integer
Case b: x = 2, in which case (3x+8)/(x+2) = 14/4 = 3.5 not an integer
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT


Statement 2: x > 0
This statement is sufficient. Here's why.
Notice that (3x+8)/(x+2) = (3x+6 + 2)/(x+2)
= (3x+6)/(x+2) + (2)/(x+2)
= 3 + 2/(x+2)

Since 2 will always be less than x+2, we can see that 2/(x+2) will always be less than 1.
In fact, we know that 0 < 2/(x+2) < 1
In other words, 2/(x+2) can NEVER be an integer.
As such, 3 + 2/(x+2) can NEVER be an integer.
This means that (3x+8)/(x+2) is definitely not an integer.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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