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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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83% (02:06) correct
17%
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wrong
based on 140
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Find all solutions of \(|||Q|–7|+Q|=Q\) ?
15 Nov 2010, 02:35
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krishnasty
I've never seen real GMAT question involving triple modulus. Though the above question is not very hard.
\(|||q|-7|+q|=q\)
Now, absolute value is always non-negative \(|some \ expression|\geq{0}\), so as LHS (left hand side) above is an absolute value it must be non-negative then RHS must also be non-negative --> \(q\geq{0}\), so \(|q|=q\), so \(|||q|-7|+q|=q\) becomes: \(||q-7|+q|=q\).
\(||q-7|+q|=q\):
If \(q\leq{7}\) then \(|q-7|\) becomes \(-(q-7)\) so \(|-q+7+q|=q\) --> \(q=|7|=7\);
If \(q>{7}\) then \(|q-7|\) becomes \(q-7\) so \(|q-7+q|=q\) --> \(|2q-7|=q\) --> as \(q>{7}\) then \(|2q-7|=2q-7\) so \(2q-7=q\) --> \(q=7\).
So, only one solution \(q=7\).
General Discussion
15 Nov 2010, 02:03
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hey guys....
can somebody tell me how to solve such kind of questions ? i am getting confused ..
can somebody tell me how to solve such kind of questions ? i am getting confused ..
