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# If y ≠ 0, what is the value of (5x/y)^2?

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Math Expert
Joined: 02 Sep 2009
Posts: 50044
If y ≠ 0, what is the value of (5x/y)^2?  [#permalink]

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21 Sep 2018, 01:38
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Difficulty:

15% (low)

Question Stats:

81% (00:31) correct 19% (00:31) wrong based on 43 sessions

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If y ≠ 0, what is the value of $$(\frac{5x}{y})^2$$?

(1) x = 3
(2) 5x − 2y = 0

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Joined: 31 Oct 2013
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Re: If y ≠ 0, what is the value of (5x/y)^2?  [#permalink]

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21 Sep 2018, 01:52
Bunuel wrote:
If y ≠ 0, what is the value of $$(\frac{5x}{y})^2$$?

(1) x = 3
(2) 5x − 2y = 0

Statement 1: x =3. No information about y. NOT sufficient.

Statement 2:

5x - 2y = 0

5x = 2y

x / y = 2/5.

Question :$$(5x /y)^2 = (5*x/y)^2 = (5*2/5)^2 = 4.$$

Sufficient .

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Joined: 04 Jan 2015
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Re: If y ≠ 0, what is the value of (5x/y)^2?  [#permalink]

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22 Sep 2018, 03:33

Solution

Given:
• The value of y ≠ 0

To find:
• Value of the expression $$(\frac{5x}{y})^2$$

Analysing Statement 1
From the information given in statement 1, x = 3.
• From this statement, we don’t have any information about the value of y.

Hence, statement 1 is not sufficient.

Analysing Statement 2
From the information given in statement 2, 5x – 2y = 0
• Or, 5x = 2y
• Or, $$\frac{5x}{y}$$ = 2

Therefore, we can find the value of $$(\frac{5x}{y})^2$$.

Hence, statement 2 is sufficient.

The correct answer is option B.

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Re: If y ≠ 0, what is the value of (5x/y)^2?  [#permalink]

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22 Sep 2018, 10:04
Top Contributor
Bunuel wrote:
If y ≠ 0, what is the value of $$(\frac{5x}{y})^2$$?

(1) x = 3
(2) 5x − 2y = 0

Target question: What is the value of (5x/y)²

Statement 1: x = 3
Since we have no information about the value of y, statement 1 is not sufficient.

If we're not convinced, we can some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 3 and y = 1. In this case, the answer to the target question is (5x/y)² = (15/1)² = 225
Case b: x = 3 and y = 5. In this case, the answer to the target question is (5x/y)² = (15/5)² = 9
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 5x − 2y = 0
Add 2y to both sides to get: 5x = 2y
Divide both sides by y to get: 5x/y = 2
Square both sides to get: (5x/y)² = 2² = 4
So, the answer to the target question is (5x/y)² = 4
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent
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Re: If y ≠ 0, what is the value of (5x/y)^2? &nbs [#permalink] 22 Sep 2018, 10:04
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