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
Percent problem
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We can plug in the answers.GmatKiss 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
Answer choice C: 200
y = 50% of 50% of x = (1/2)(1/2)200 = 50.
y% of x = 50% of 200 = 100.
Success!
The correct answer is C.
Algebraically:
y = 50% of 50% of x = (1/2)(1/2)x = x/4.
Since y% of x = 100:
(x/4)/100 * x = 100
x² = 100*100*4
x = 10*10*2 = 200.
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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
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
GMAT/MBA Expert
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We can create the following equation:GmatKiss 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
y = (0.5)(0.5)x
y = 0.25x
Expressing y percent as y/100, we obtain the second equation:
(y/100)x = 100
Substituting 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
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