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Positive integer y is 50 percent of 50 percent of positive i

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by [email protected] » Sat Oct 01, 2016 9:57 am
Hi GMATgirl,

Did this question come from a GMAT source (I ask because it includes just 4 answers; GMAT questions have 5 answers)? If you're truly studying for the GMAT, then you should focus on GMAT-centric materials.

That having been said, there are a couple of different ways that you can approach this question. Translating prompts into 'math' is an essential skill for Test Day, so here's how you can use that work (and some algebra) to get to the correct answer.

We're told that X and Y are positive integers

50% = 1/2, so....

50% OF 50% of X = (1/2)(1/2)(X)

Y = (1/2)(1/2)(X) = (1/4)(X)
Y = X/4
4Y = X

Y PERCENT = (Y)(1/100)

Y percent of X = 100
(Y)(1/100)(X) = 100

(X)(Y)/100 = 100
(X)(Y) = 10,000

So now we know that....
4Y = X
XY = 10,000

We can substitute in 4Y for X....
(4Y)(Y) = 10,000
4Y^2 = 10,000
Y^2 = 2,500
Y = 50

Since 4Y = X, 4(50) = X and X=200

Final Answer: [spoier]C[/spoiler]

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by GMATGuruNY » Sat Oct 01, 2016 10:08 am
I posted a solution here:
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by ceilidh.erickson » Sat Oct 01, 2016 7:15 pm
This question is PS #D 12 in OG2017 (and 2016 and 2015). Please always POST YOUR SOURCE, and make sure you've transcribed the question correctly!
Positive integer y is 50 percent of 50 percent of positive integer x, and y percent of x equals 100. What is the value of x?
A. 50
B. 100
C. 200
D. 1,000
E. 2,000

We can also solve using decimals:

y = (0.5)(0.5)x --> y = 0.25x

(y/100)x = 100
yx = 10,000

Substitute:
(0.25x)x = 10,000
x^2 = (10,000)/(0.25)
shift the decimals:
x^2 = 1,000,000/25
x^2 = 40,000
x = 200
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by MBA Challengers » Mon Oct 03, 2016 6:10 pm
Hi,

You might want to try the method of elimination for this question as well. Here, y is 50% of 50% of x. Simply put,

y = 1/2 * 1/2 * x = 1/4x; Thus, y = 1/4x
Also, x% of y = 100

Now, start looking at the options for the question:
A. 50
B. 100
C. 200
D. 1000
E. 2000

While, it is a good practice to start from the middle option, in this case to illustrate the point, let's start with option D.
If x = 1000, this implies y = 1/4 * 1000 = 250. Also, y% of x means 250% of 1000 = 2500. 2500 is much greater than 100. So, try a smaller value for x.
Try Option C. x = 200. This implies y = 1/4 * 200 = 50. Also, y% of x means 50% of 200 = 100. This, fits in with the requirements of the question. So, the answer is C.
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by Scott@TargetTestPrep » Thu Oct 06, 2016 7:04 am
Gmatgirl wrote:
Positive integer y is 50 percent of 50 percent of positive integer x, and y percent of x equals 100. What is the value of x ?

A. 50
B. 100
C. 200
D. 1,000
E. 2,000

We are given that positive integer y is 50 percent of 50 percent of positive integer x. We can translate this into an equation:

y = (0.5)(0.5)(x)

y = 0.25x

We are also given that y percent of x equals 100. We can translate this into an equation:

(y/100)(x) = 100

(yx/100) = 100

yx = 10,000

Since y = 0.25x, we can substitute 0.25x for y in the equation yx = 10,000. So we have:

(0.25x)x = 10,000

0.25x^2 = 10,000

(¼)x^2 = 10,000

x^2 = 40,000

x = 200

Answer: C

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