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If x and y are nonnegative integers, what is the value of y?

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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Sat Nov 24, 2018 11:00 pm
BTGmoderatorDC wrote:If x and y are nonnegative integers, what is the value of y?

(1) 3^x = 5^y
(2) |y| = −y

OA D

Source: Veritas Prep
Given x and y are nonnegative integers, we have x: {0, 1, 2, 3, ...} and y: {0, 1, 2, 3, ...}

Question: What is the value of y?

Let's take each statement one by one.

(1) 3^x = 5^y

Given x and y are integers, the only value possible for x and y for 3^x = 5^y to be true is x = y = 0.

Since 3^x = 5^y => 3^0 = 5^0 => 1 = 1. Sufficient.

(2) |y| = −y

Given that |y| is non-negative, -y must also be non-negative. The only possible value for y = 0. Sufficient.

The correct answer: D

Hope this helps!

-Jay
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If x and y are nonnegative integers, what is the value of y?

by fskilnik@GMATH » Sun Nov 25, 2018 2:52 am
BTGmoderatorDC wrote:If x and y are nonnegative integers, what is the value of y?

(1) 3^x = 5^y
(2) |y| = −y
Source: Veritas Prep
\[x,y \geqslant 0\,\,\,{\text{ints}}\,\,\,\,\left( * \right)\]
\[? = y\]
\[\left( 1 \right)\,\,\,\left\{ \begin{gathered}
\,\,{3^x}\,\left[ {{\text{and}}\,\,\left( * \right)} \right]\,\,\, = \,\,\,\underline 1 \,\,\,{\text{or}}\,\,{\text{only}}\,\,3\,\,{\text{as}}\,\,{\text{prime}}\,\,{\text{factor}} \hfill \\
\,\,{5^y}\,\left[ {{\text{and}}\,\,\left( * \right)} \right]\,\,\, = \,\,\,\underline 1 \,\,\,{\text{or}}\,\,{\text{only}}\,\,5\,\,{\text{as}}\,\,{\text{prime}}\,\,{\text{factor}} \hfill \\
\end{gathered} \right.\,\,\,\,\,\mathop \Rightarrow \limits^{\left( 1 \right)} \,\,\,\,\underline {x = y = 0} \,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{SUFF}}.\]
\[\left( 2 \right)\,\,\,\left| y \right| = - y\,\,\,\, \Leftrightarrow \,\,\,\,\,y \leqslant 0\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,y = 0\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{SUFF}}.\]

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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by Brent@GMATPrepNow » Sun Nov 25, 2018 9:10 am
BTGmoderatorDC wrote:If x and y are non-negative integers, what is the value of y?

(1) 3^x = 5^y
(2) |y| = −y

OA D

Source: Veritas Prep
The above solutions are great.
I just wanted to add that whenever you're told that a value is non-negative on the GMAT, you should be sure to consider what happens when that value equals zero
Keep in mind that, if the test-makers wanted to restrict a value to POSITIVE values only, then they'd just write "the value is positive"
So, if they use the term non-negative, then there's a good chance that something important occurs when that value equals zero.

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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