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Does x = y?

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by Vincen » Tue Jan 16, 2018 9:07 am
Does x = y?

(1) 4x - 2y = 80
(2) x = (40 + y)/2

The OA is the option E.

Using both equations, cannot find the correct answer? Experts, I would be thankful for your explanation.
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Source: — Data Sufficiency |
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by DavidG@VeritasPrep » Tue Jan 16, 2018 12:07 pm
Vincen wrote:Does x = y?

(1) 4x - 2y = 80
(2) x = (40 + y)/2

The OA is the option E.

Using both equations, cannot find the correct answer? Experts, I would be thankful for your explanation.
The key is to recognize that the statements are identical:
Statement 2: x = (40 + y)/2
Multiply both sides by 4:
4x = 2(40 + y)
4x = 80 + 2y
4x - 2y = 80
Clearly, neither statement alone is sufficient, so if the statements are identical, the answer must be E

(If it doesn't feel intuitive that neither statement alone is sufficient, consider cases, If x = y, then we'd have 4x -2x =80 --> 2x = 80 --> x =. 40. So it could be the case that x = 40 and y = 40, giving us a YES. But it could also be the case that x = 20 and y = 0, giving us a NO.)
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by Scott@TargetTestPrep » Thu Jan 18, 2018 1:42 pm
Vincen wrote:Does x = y?

(1) 4x - 2y = 80
(2) x = (40 + y)/2
We need to determine whether x = y.

Statement One Alone:

4x - 2y = 80

Simplifying the equation we have, 2x - y = 40; however, we cannot determine whether x = y. If we let x = 0 and y = -40, then we see that x is not equal to y. However, if we let x = 40/3 and y = 40/3, then x = y.

Statement Two Alone:

x = (40 + y)/2

Simplifying the equation, we have:

2x = 40 + y

2x - y = 40

Again, we cannot determine whether x = y.

Statements One and Two Together:

Using both statements together, we see that they produce the identical equations of 2x - y = 40; thus, we cannot determine whether x = y.

Answer: E

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