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(2t + t - x)/(t - x)?

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by Vincen » Tue Oct 03, 2017 5:32 pm
What is the value of (2t + t - x)/(t - x)?

(1) 2t/(t - x) = 3

(2) t - x = 5

The OA is A.

I already know that statement (2) alone is not sufficient because at the end we get 2t. But, how can I know the value of (2t + t - x)/(t - x) using statement (1)?
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by Jay@ManhattanReview » Tue Oct 03, 2017 11:18 pm
Vincen wrote:What is the value of (2t + t - x)/(t - x)?

(1) 2t/(t - x) = 3

(2) t - x = 5

The OA is A.

I already know that statement (2) alone is not sufficient because at the end we get 2t. But, how can I know the value of (2t + t - x)/(t - x) using statement (1)?
Hi Vincen,

We wish to know the value of (2t + t - x)/(t - x) using Statement 1 alone.

(2t + t - x)/(t - x) = [2t + (t - x)] / (t - x) = [2t/(t - x)[ + [(t - x)/(t - x)[ = [2t/(t - x)] + 1

So, the question is: what's the value of 2t/(t - x)?

Statement 1 provides that.

Hope this helps!

-Jay

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by GMATGuruNY » Wed Oct 04, 2017 4:09 am
Vincen wrote:What is the value of (2t + t - x)/(t - x)?

(1) 2t/(t - x) = 3

(2) t - x = 5
But, how can I know the value of (2t + t - x)/(t - x) using statement (1)?
One approach is to simplify the statement and TEST TWO CASES.

Statement 1: (2t)/(t-x) = 3
2t = 3t - 3x
3x = t.
If x=1 and t=3, then (2t+t-x)/(t-x) = (2*3 + 3 - 1)/(3-1) = 8/2 = 4.
If x=2 and t=6, then (2t+t-x)/(t-x) = (2*6 + 6 - 2)/(6-2) = 16/4 = 4.
Since (2t+t-x)/(t-x) = 4 in each case, SUFFICIENT.
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by Brent@GMATPrepNow » Wed Oct 04, 2017 8:23 am
Vincen wrote:What is the value of (2t + t - x)/(t - x)?

(1) 2t/(t - x) = 3
(2) t - x = 5
Target question: What is the value of (2t + t - x)/(t - x)?
This is a good candidate for REPHRASING the target questions.
We'll use the fact that (a + b)/c = a/c + b/c
Likewise, (2t + t - x)/(t - x) = 2t/(t - x) + (t - x)/(t - x)
= 2t/(t - x) + 1
At this point, we can see that we really just need to find the value of 2t/(t - x)
REPHRASED target question: What is the value of 2t/(t - x)?

Statement 1: 2t/(t - x) = 3
Perfect! This is EXACTLY the information we need!
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: t - x = 5
There are several values of t and x that satisfy statement 2. Here are two:
Case a: t = 5 and x= 0, in which case 2t/(t - x) = 5
Case b: t = 6 and x= 1, in which case 2t/(t - x) = 12/5
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent
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