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26 Jun 2022, 15:15
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E
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Difficulty:
55%
(hard)
Question Stats:
66% (02:49) correct
34%
(02:54)
wrong
based on 172
sessions
History
Date
Time
Result
Not Attempted Yet
The mean of the set of seven positive integers 1, 2, 3, 4, 5, 6, and x is \(\frac{\sqrt{7x}}{2}\). What is the value of x?
(A) 1
(B) 7
(C) 14
(D) 21
(E) 28
(A) 1
(B) 7
(C) 14
(D) 21
(E) 28
26 Jun 2022, 15:59
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Bunuel
I'm wiling to bet that we are going to need \(\sqrt{7x}\) to be an integer. That happens when x is 7 or 7*someotherperfectsquare. Look at the answer choices. The only viable options are B and E.
Is it B? Mean would be 4. \(\frac{\sqrt{7(7)}}{2}\) = 7/2 = 3.5. Is 4 = 3.5? Nope. B is out.
Is it E? Mean would be 49/7 = 7. \(\frac{\sqrt{7(28)}}{2} = \frac{\sqrt{(7)(7)(2)(2)}}{2}\) = 14/2 = 7. Is 7=7? Yep.
Answer choice E.
26 Jun 2022, 16:53
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Back solving is an important tool to you solve GMAT questions, specially that one’s that you avoid long algebra developments.
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