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

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

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

(1) xy is the square of an integer.

(2) 600 percent of x equals 200 percent of y.

OA E

Source: Magoosh

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BTGmoderatorDC wrote:
If x and y are positive, what is the value of y ?

(1) xy is the square of an integer.

(2) 600 percent of x equals 200 percent of y.

Source: Magoosh
\[x,y\,\, > 0\,\,\]
\[? = y\]

Let´s go straight to (1+2). Our BIFURCATION will guarantee that the correct answer is (E) immediately!

$$\left( {1 + 2} \right)\,\,\,\,\left\{ \matrix{
\,xy = {M^2}\,,\,\,M\,\,{\mathop{\rm int}} \hfill \cr
\,6x = 2y\,\,\, \Rightarrow \,\,\,y = 3x \hfill \cr} \right.\,\,\,\,\,\left( * \right)\,\,\,\,\,\,\,\,\,\left[ {\, \Rightarrow \,\,\,\,\,\,3{x^2} = {M^2}\,\,,\,\,\,M\,\,{\mathop{\rm int}} \,} \right]$$
$$\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {\sqrt 3 ,3\sqrt 3 } \right)\,\,\,\, \Rightarrow \,\,\,\,\,\left( * \right)\,\,\,{\rm{ok}}\,\,\,\, \Rightarrow \,\,\,\,\,y = 3\sqrt 3 \,\,\, \hfill \cr
\,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {2\sqrt 3 ,6\sqrt 3 } \right)\,\,\,\, \Rightarrow \,\,\,\,\,\left( * \right)\,\,\,{\rm{ok}}\,\,\,\, \Rightarrow \,\,\,\,\,y = 6\sqrt 3 \,\, \hfill \cr} \right.$$

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

Regards,
Fabio.

_________________
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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What is the value of y?
Statement 1
xy is the square of an integer.
xy gives a perfect square if x and y are two integers it could be any positive number $$1,2,3,4,5$$ e.t.c
if x and y are integers it will $$\ 1,4,9,16,25$$ $$\ 1,4,9,16,25$$ e.t.c . However, this doesn't mean that x=y
$$\sin ce\ 4\cdot1=4,\ 2\cdot8=16\ e.t.c$$
$$hence\ Statement\ 1\ is\ INSUFFICIENT$$

Statement 2
$$600\%\ of\ \ x=200\%\ of\ y$$
$$\frac{600}{100}\cdot x=\frac{200}{100}\cdot y$$
$$y=3x$$ , This leaves with an unknown variable, hence $$statement\ 2\ is\ INSUFFICIENT$$

Statement 1 and 2 together
if x and y are non integers then it could be any pair of number leaving us with many solutions. since the
value of y is not definite.
$$statement\ 1\ and\ \ 2 together\ are\ INSUFFICIENT$$
$$answer\ is\ option\ E$$

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BTGmoderatorDC wrote:
If x and y are positive, what is the value of y ?

(1) xy is the square of an integer.
(2) 600 percent of x equals 200 percent of y.
Target question: What is the value of y?

Given: x and y are positive

Statement 1: xy is the square of an integer.
There are several values of x and y that satisfy this condition. Here are two:
Case a: x = 1 and y = 1. Here xy = (1)(1) = 1, which is the square of an integer. In this case y = 1
Case b: x = 2 and y = 2. Here xy = (2)(2) = 4, which is the square of an integer. In this case y = 2
Since we cannot answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: 600 percent of x equals 200 percent of y.
So, 6x = 2y
Divide both sides by 2 to get: 3x = y
There are several values of x and y that satisfy this condition. Here are two:
Case a: x = 1 and y = 3. In this case y = 3
Case a: x = 2 and y = 6. In this case y = 6
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that xy is the square of an integer.
Statement 2 tells us that 3x = y
Take statement 1 and replace y with 3x to get: x(3x) is the square of an integer.
In other words, 3x² is the square of an integer.
There are several values of x that satisfy this condition. Here are two:
Case a: x = √3. This means 3x² = 3(√3)² = 9, and 9 is the square of an integer. From statement 2, if x = √3, then y = 3√3.
Case b: x = 4√3. This means 3x² = 3(4√3)² = 36, and 36 is the square of an integer. From statement 2, if x = 4√3, then y = 12√3.
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent

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Brent Hanneson – Creator of GMATPrepNow.com
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