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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Does x = y?
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DavidG@VeritasPrep
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The key is to recognize that the statements are identical: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.
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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Scott@TargetTestPrep
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We need to determine whether x = y.Vincen wrote:Does x = y?
(1) 4x - 2y = 80
(2) x = (40 + y)/2
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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