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by fskilnik@GMATH » Wed Mar 13, 2019 4:12 am
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GMATH practice exercise (Quant Class 6)

The number of candidates rejected in a certain admission process was four times greater than the number of candidates accepted. Which of the following could be the total number of candidates that applied for this admission process?

(A) 726
(B) 727
(C) 728
(D) 729
(E) 730

Answer: [spoiler]_____(A)__[/spoiler]
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by Brent@GMATPrepNow » Wed Mar 13, 2019 5:20 am
fskilnik@GMATH wrote:GMATH practice exercise (Quant Class 6)

The number of candidates rejected in a certain admission process was four times greater than the number of candidates accepted. Which of the following could be the total number of candidates that applied for this admission process?

(A) 726
(B) 727
(C) 728
(D) 729
(E) 730

Answer: [spoiler]_____(A)__[/spoiler]

The number of candidates rejected in a certain admission process was four times GREATER than the number of candidates accepted.
Let x = the number of candidates accepted
So, x + 4x = the number of candidates rejected
In other words, 5x = the number of candidates rejected

So, 6x = TOTAL number of candidates (since x + 5x = 6x)

Which of the following could be the total number of candidates that applied for this admission process?
Since 6x = TOTAL number of candidates, we can see that the TOTAL number of candidates must be divisible by 6
Check the answer choices.....only answer choice A is divisible by 6

Answer: A

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Brent
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by fskilnik@GMATH » Wed Mar 13, 2019 9:56 am
fskilnik@GMATH wrote:GMATH practice exercise (Quant Class 6)

The number of candidates rejected in a certain admission process was four times greater than the number of candidates accepted. Which of the following could be the total number of candidates that applied for this admission process?

(A) 726
(B) 727
(C) 728
(D) 729
(E) 730
$$?\,\,\,:\,\,\,{\rm{total}}\,\,{\rm{\# }}\,\,\,\left( {{\rm{possible}}\,\,{\rm{value}}} \right)$$
$$\left\{ \matrix{
\,{\rm{accepted}} = k \hfill \cr
\,{\rm{rejected}} = 5k \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = 6k\,\,\,\,\,\,\left( {k \ge 1\,\,{\mathop{\rm int}} } \right)$$
$$\left( A \right)\,\,\,726\,\,\,\,\left\{ \matrix{
\,{\rm{even}} \hfill \cr
\,{\rm{multiple}}\,\,{\rm{of}}\,\,3\,\,\,\,\left( {7 + 2 + 6 = 15} \right) \hfill \cr} \right.\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{done}}!$$

The correct answer is (A).

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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