Positive integer y is 50 percent of 50 percent of positive

Question

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

PareshGmat · Accepted Answer

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

y = \frac{25x}{100}  .......... (1)

\frac{xy}{100} = 100

y = 100 * \frac{100}{x}  ..... (2)

Equating (1) & (2)

\frac{25x}{100} = 100 * \frac{100}{x}

25 x^2 = 100 * 100 * 100

x^2 = 4 * 100 * 100

x = 2 * 10 * 10 = 200

Answer = C

Bunuel · Answer

SOLUTION

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

Given:  x>0  and  y>0 .

"Positive integer y is 50 percent of 50 percent of positive integer x" implies  y=0.5*(0.5x)=0.25x ;

"y percent of x equals 100" implies  \frac{y}{100}*x=100 , which give  xy=100*100 .

Substituting  y=0.25x  yields   x(0.25x)=100*100  and finally  x^2=4*100*100 . Since  x>0 , then we get only one solution  x=200 .

Answer: C.

EvaJager · Answer

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

jackrim1 · Answer

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

Bunuel · Answer

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.

TeamGMATIFY · Answer

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

TMsport · Answer

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

EMPOWERgmatRichC · Answer

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:  C

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

ydmuley · Answer

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

ScottTargetTestPrep · Answer

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

dave13 · Answer

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

CEdward · Answer

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.

BrentGMATPrepNow · Answer

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

ArnauG · Answer

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.

Lowpoint · Answer

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

Bunuel · Answer

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

DanTheGMATMan · Answer

No sweat- write it out as they say it:

https://www.youtube.com/watch?v=qxPsMHkFhao

totaltestprepNick · Answer

C https://www.youtube.com/watch?v=rz6yOeOHDIk Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience tutoring@totaltestprep.net

Positive integer y is 50 percent of 50 percent of positive

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

GMAT Problem Solving (PS) Questions

Positive integer y is 50 percent of 50 percent of positive

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia