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21 May 2017, 04:36
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
67% (00:54) correct
33%
(00:54)
wrong
based on 83
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Is the sum of x, y, and z equal to 3?
(1) xyz = 1
(2) x, y, and z are each greater than zero.
(1) xyz = 1
(2) x, y, and z are each greater than zero.
21 May 2017, 04:42
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2nd statement is explicitly not sufficient and statement 1st could imply (x+y+z) >= 3 as AM >= GM and too would not make the statement sufficient. Taking these two statement together would not do any good either -> E
21 May 2017, 05:18
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Bunuel
Target question: Is the sum of x, y, and z equal to 3?
Statement 1: xyz = 1
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of x, y and z that satisfy statement 1. Here are two:
Case a: x = 1, y = 1 and z = 1, in which case x + y + z = 1 + 1 + 1 = 3
Case b: x = 1, y = 0.5 and z = 2, in which case x + y + z = 1 + 0.5 + 2 = 3.5
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, read my article: https://www.gmatprepnow.com/articles/dat ... lug-values
Statement 2: x, y, and z are each greater than zero
There are several values of x, y and z that satisfy statement 2. Here are two:
Case a: x = 1, y = 1 and z = 1, in which case x + y + z = 1 + 1 + 1 = 3
Case b: x = 1, y = 0.5 and z = 2, in which case x + y + z = 1 + 0.5 + 2 = 3.5
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
IMPORTANT: Notice that I was able to use the same counter-examples to show that each statement ALONE is not sufficient. So, the same counter-examples will satisfy the two statements COMBINED.
In other words,
Case a: x = 1, y = 1 and z = 1, in which case x + y + z = 1 + 1 + 1 = 3
Case b: x = 1, y = 0.5 and z = 2, in which case x + y + z = 1 + 0.5 + 2 = 3.5
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT
Answer:
Cheers,
Brent
