Problem Solving

Positive integer y is 50% of 50% 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

This question is from the the OG12 Diagnostic test, # 12. The OA is C. Two detailed solutions and take-aways lessons are attached. People who cannot see attachments click here.

-Patrick

y is 50% of 50% of positive integer x = y is 1/2 of 1/2 of x => y = 1/4(x) ------(1)
y percent of x equals 100 = y/100 * x = 100 => xy = 1000 ------(2)
from equation 1 and 2
x*(1/4x) = 1000
x^2 = 4*1000
X^2 = 4000
X = square root of 4000
x = 200
so the answer is C

If x = 100a
then y = 25a ( y 1/2 of 1/2 of x or 1/4 of x)
25a % of x i.e (25a/100) * 100a = 100

25a² = 100

a = + - 2

since x is + so IMO C

y=(1/2)*(1/2)*x - 1
(y/100)*x=100 - 2

sub value of y from eq1 in eq2
x=200

BlueDragon2010 wrote:Positive integer y is 50% of 50% 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

The Jock wrote:y is 50% of 50% of positive integer x = y is 1/2 of 1/2 of x => y = 1/4(x) ------(1)
y percent of x equals 100 = y/100 * x = 100 => xy = 1000 ------(2)
from equation 1 and 2
x*(1/4x) = 1000
x^2 = 4*1000
X^2 = 4000
X = square root of 4000
x = 200
so the answer is C

Jock...there is a correction/ typo in your working, though your answer is correct.

xy= 10,000 (y/100*x=100), {also 100* 100=10000}....(1)

x*(1/4x) = 10000
x^2 = 4*10000
X^2 = 40000
X = square root of 40000
x = 200

Thanks, Preet.

If you struggle with percentages -- and even if you don't -- you might find it easier simply to try out the answers in order to determine which is correct.

Here's why trying out the answers will work. The question asks for a specific amount: the value of x. We know that the value of x has to be one of the answer choices. So we can just try them all out until we find the one that works. Some words of wisdom:

Whenever a PS question asks for a specific amount, consider trying out the answers in order to determine which is correct.

When you're trying out the answer choices, start with the one right in the middle (normally answer choice C).

If the answer right in the middle works, then it's the correct answer.
If the answer right in the middle is too big, you can eliminate both it and the answers that are even larger, and try those that are smaller.
If the answer right in the middle is too small, you can eliminate both it and the answers that are even smaller, and try those that are larger.

Starting with the middle answer choice can help you to eliminate three answer choices at once. Remember this rule:

Start with C and cancel three.

So let's start with answer choice C:

If x = 200, then y = (50/100)(50/100)(200) = 50.
Does y percent of x equal 100?
Yes, because 50 percent of 200 equals 100.
So answer choice C works!

See how easy?

GMATGuruNY wrote:If you struggle with percentages -- and even if you don't -- you might find it easier simply to try out the answers in order to determine which is correct.

Here's why trying out the answers will work. The question asks for a specific amount: the value of x. We know that the value of x has to be one of the answer choices. So we can just try them all out until we find the one that works. Some words of wisdom:

Whenever a PS question asks for a specific amount, consider trying out the answers in order to determine which is correct.

When you're trying out the answer choices, start with the one right in the middle (normally answer choice C).

If the answer right in the middle works, then it's the correct answer.
If the answer right in the middle is too big, you can eliminate both it and the answers that are even larger, and try those that are smaller.
If the answer right in the middle is too small, you can eliminate both it and the answers that are even smaller, and try those that are larger.

Starting with the middle answer choice can help you to eliminate three answer choices at once. Remember this rule:

Start with C and cancel three.

So let's start with answer choice C:

If x = 200, then y = (50/100)(50/100)(200) = 50.
Does y percent of x equal 100?
Yes, because 50 percent of 200 equals 100.
So answer choice C works!

See how easy?

Hi,
So here's how I approached the question. I think there is something I am missing, can you help please?

For percentage questions, I usually take 100 as starting number because it solved many problems easily.

So here I took, x = 100, so, y = 50% of 50% of 100 = 25....(equation 1).
and since y% of x = 100 as per second information, so if I put the data from 1st equation,
I get 25% of 100 = 100, which is incorrect;
So to make left hand as 100 somehow (remember, I assumed X) I'll multiply X by 4,
so when now X = 400, its 50% * 50% = 100 = Y, and 100% of X = 100, which still is incorrect.

There has to be another way than the way mentioned, I mean try and not use pen and understand and solve mentally?