GMATinsight wrote:

For what smallest POSITIVE INTEGER value of x will 350*x be the square of an integer?

A) 2

B) 5

C) 7

D) 10

E) 14

Source:

http://www.GMATinsight.com\(x \geqslant 1\,\,\operatorname{int}\)

\(? = \min \,x\)

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.

_________________

Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or GMATH.com.br (Portuguese version)

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