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25 Sep 2018, 08:36
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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:
15%
(low)
Question Stats:
85% (00:59) correct
15%
(01:09)
wrong
based on 82
sessions
History
Date
Time
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Not Attempted Yet
For what smallest value of x, 350*x will be square of an Integer?
A) 2
B) 5
C) 7
D) 10
E) 14
Source: www.GMATinsight.com
A) 2
B) 5
C) 7
D) 10
E) 14
Source: www.GMATinsight.com
25 Sep 2018, 08:58
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GMATinsight
\(x \geqslant 1\,\,\operatorname{int}\)
\(? = \min \,x\)
Important: any perfect square greater than 1 is characterized as the product of distinct primes, each prime with an even power.
\(\left. \begin{gathered}\\
350x = 2 \cdot {5^2} \cdot 7 \cdot x \hfill \\\\
350x\,\, = {\text{prime}}{{\text{s}}^{\,{\text{even}}}}\,\, \hfill \\ \\
\end{gathered} \right\}\,\,\,\,\, \Rightarrow \,\,\,\,? = 2 \cdot 7 = 14\)
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
P.S.: note that 350*0 = 0 is the square of an integer.
25 Sep 2018, 13:07
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GMATinsight
In order to make 350*x a perfect square we have to find out the dna of this number.
\(350x = 5*5*7*2 *x = 5^2 * 7 * 2 x.\)
Since 350x has to be perfect square we need additional one 7 and one 2. It means x has to be 14.
\(350*14 = 5^2*7^2*2^2\)
The best answer is E.
