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OG What is the value of (2t + t - x)/(t - x)

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Source: — Data Sufficiency |
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by GMATGuruNY » Mon Aug 21, 2017 7:54 pm
What is the value of (2t+t-x)/(t-x)?

(1) (2t)/(t-x) = 3
(2) t-x = 5
One approach is to simplify the statements 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.

Statement 2: t-x = 5
t = x+5.
If x=1 and t=6, then (2t+t-x)/(t-x) = (2*6 + 6 - 1)/(6-1) = 17/5.
If x=2 and t=7, then (2t+t-x)/(t-x) = (2*7 + 7 - 2)/(7-2) = 19/5.
Since (2t+t-x)/(t-x) can be equal to different values, INSUFFICIENT.

The correct answer is A.
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by GMATGuruNY » Mon Aug 21, 2017 8:25 pm
AbeNeedsAnswers wrote:What is the value of (2t + t - x)/(t - x)?

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

(2) t - x = 5
An algebraic approach:
(2t + t - x)/(t - x)

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

= 2t/(t-x) + 1.

To determine the value of the expression in blue, we need to know the value of 2t/(t-x).
Question stem, rephrased:
What is the value of 2t/(t-x)?

Statement 1: 2t/(t-x) = 3
SUFFICIENT.

Statement 2: t-x = 5
Thus:
2t/(t-x) = 2t/5.
Since the value of t is unknown, we cannot proceed any further.
INSUFFICIENT.

The correct answer is A.
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Re: OG What is the value of (2t + t - x)/(t - x)

by Scott@TargetTestPrep » Mon May 31, 2021 12:55 pm
AbeNeedsAnswers wrote: ↑
Mon Aug 21, 2017 7:44 pm
 What is the value of (2t + t - x)/(t - x)?

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

(2) t - x = 5

A
Solution:

We need to determine the value of (2t + t - x) / (t - x).

Statement One Alone:

Knowing 2t / (t - x) = 3 is sufficient since (2t + t - x) / (t - x) = 2t / (t - x) + (t - x) / (t - x) = 2t / (t - x) + 1 = 3 + 1 = 4.

Statement Two Alone:

Knowing t - x = 5 is not sufficient. Notice that (2t + t - x) / (t - x) = (2t + 5) / 5. Without knowing the value of t, we can’t determine the value of (2t + 5) / 5.

Answer: A

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