Positive integer y is 50 percent of 50 percent of positive

 

The first information can be rewritten as \(y=0.5*0.5x=0.25x=\frac{x}{4}\), while the second information can be translated into \(\frac{y}{100}x=100\).
If we substitute y from the first equation into the second one, we get \(\frac{x}{400}x=100\), from which \(x^2=400*100\), or \(x=\sqr{400*100}=\sqr{400}*\sqr{100}=20*10=200\).

Answer: C­

I need help understanding a pretty basic bit of substitution in the first explanation (I'm tired!). How do you jump from xy = 100 x 100 to x^2 = 4 x 100 x 100?

Thanks

\(xy=100*100\) and \(y=0.25x=\frac{x}{4}\);

\(x*\frac{x}{4}=100*100\);

\(x^2=4*100*100\).

Hope it's clear.

Bunuel

Ah, of course, I must be having one of those days! thanks

Given:
x >0 and y > 0
y = \(\frac{50}{100}\)(\(\frac{50}{100}\)*x) = 0.25x - (i)
\(\frac{y}{100}\)*x = 100. Hence xy = 10000 - (ii)

Required: Value of x
Substituting the value of y in (ii)

x*0.25x = 10000
\(x^2\) = 100*100*100/25 = 4*100*100
x = 200 and - 200
We will consider only the positive value as we are told that x > 0

x = 200
Option C

y = 50% of 50% of x = (1/2)*(1/2)*x = x/4

(y/100)x=100
x^2/400 = 100
x = 200

IMO - C­

Hi All,

This question can be solved by TESTing THE ANSWERS.

We're told that:
1) Positive integer Y is 50 percent of 50 percent of positive integer X
2) Y percent of X equals 100

We're asked for the value of X.

Let's TEST Answer B: 100

IF....
X = 100
Y = (.5)(.5)(100) = 25
25% of 100 = 25 (but it's supposed to be 100). This answer is TOO SMALL.

Let's TEST Answer D: 1000

IF....
X = 1000
Y = (.5)(.5)(1000) = 250
250% of 1000 = 2500 (but it's supposed to be 100). This answer is TOO BIG.

The likely correct answer is C, but we can TEST it rather easily...

IF....
X = 200
Y = (.5)(.5)(200) = 50
50% of 200 = 100. This is an exact MATCH for what we were told, so this MUST be the answer.

Final Answer:

GMAT assassins aren't born, they're made,
Rich

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 ?

\(y = \frac{50}{100} * \frac{50}{100} * x\)

\(y Percent * x = 100\)

\(\frac{y}{100} * x = 100\)

\(x = \frac{(100 * 100)}{y}\)

\(x = \frac{(100 * 100)}{(50/100) * (50/100) * x}\)

\(x^2 =\frac{(100 * 100 * 100 * 100)}{(50 * 50)}\)

\(x^2 = 40000\)

\(x = 200\)

(We are not taking other value of -200 as it is given that x is positive number)

Hence, Answer is C

We can create the following equations:

y = (0.5)(0.5)x

y = 0.25x

and

(y/100)x = 100

Substitute y = 0.25x into the above equation:

(0.25x/100)x = 100

0.25x^2 = 10,000

x^2 = 40,000

x = 200

Answer: C

 

Hello everyone happy to see you all

i think this problem can be solved logically


if if y is 50 percent of 50 percent of positive integer x which implies that X is twice bigger number than y and if y percent of x equals 100 --- this means that 50 percent of 50 percent of positive integer x = 100 ( hence y = 100 and x = 200) y = .50 (200) = 100

it means that answer must be 200

options D and E are eliminated stright away because x can not be bigger number. likewise A and B are out cant be equal or smaller than 50% of x

YAY ­

is there a way to arrive to the solution by plugging numbers??? anyone suggests tips to dissect quickly whether algebra or plugging is the best strategy given the problem? sometimes you have time only to choose one of the two strategies... I started by plugging numbers but clearly I was lost for some reason... went to doing the algebra and got the right answer... but I lost a minute or so....

Clearly, I can't do math.

Why doesn't doing this yield the same solution?

y = x/4
xy = 10^4

y = 10^4/x = x/4 = 40000

40000x = 10^4
x = 10000 / 40000 = 0.25

Just a terrible day overall.

Positive integer y is 50 percent of 50 percent of positive integer x
We can write: y = (50/100)(50/100)(x)
Simplify: y = (1/2)(1/2)(x)
Simplify: y = x/4

y percent of x equals 100.
We can write: (y/100)(x) = 100
Simplify: xy/100 = 100
Multiply both sides of the equation by 100 to get: xy = 10,000

What is the value of x?
Take: xy = 10,000
Replace y with x/4 to get: x(x/4) = 10,000
Simplify: x²/4 = 10,000
Multiply both sides by 4 to get: x² = 40,000
Solve: x = 200 or x = -200
Since we're told x is positive, we can be certain that x = 200 \

Answer: C­

Let's break down the problem step by step:

Positive integer y is 50 percent of 50 percent of positive integer x:
This can be expressed as: y = 0.5 * 0.5 * x = 0.25x

Now, we are given that y percent of x equals 100:
This can be expressed as: (y/100) * x = 100

Substituting the value of y from the first equation:
(0.25x/100) * x = 100

Simplifying the equation:
0.25x^2 = 100 * 100 = 10000

Dividing both sides of the equation by 0.25:
x^2 = 10000 / 0.25 = 40000

Taking the square root of both sides:
x = √40000 = 200

Therefore, the value of x is 200, which corresponds to option (C) in the given choices.

hi
I solved this question from the options themselves by taking the value of x from the option and then performing the calculation written in the question so I was able to get the answer in 1min 30 sec so is my approach correct?

Why does the tag say 500-600 difficulty level? But the question says 650 difficulty level.
Is the tag talking about Focus edition difficulty?

­Ignore the difficulties that were in the original post. They were just preliminary difficulties, which were then updated automatically in tags after user attempts.