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16 Jun 2021, 06:48
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
49% (01:03) correct
51%
(01:09)
wrong
based on 234
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If x and y are positive integers, is x% of y > y?
(1) x > 99
(2) x < 101
(1) x > 99
(2) x < 101
Solving this question helps.
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16 Jun 2021, 15:42
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BrentGMATPrepNow
It has been 9 hours and no responses, so......
Target question: Is x% of y > y?
This is a good candidate for rephrasing the target question.
Take: Is x% of y > y?
Rewrite as: Is (\(\frac{x}{100})(y) > y\) ?
Since we're told y is POSITIVE, we can safely divide both sides of the inequality by y to get: Is \(\frac{x}{100} > 1\) ?
Multiply both sides of the inequality by 100 to get: Is \(x > 100\) ?
REPHRASED target question: Is x > 100?
Aside: the video below has tips on rephrasing the target question
Statement 1: x > 99
There are several values of x that satisfy statement 1. Here are two:
Case a: If x = 100, the answer to the REPHRASED target question is NO, x is not greater than 100
Case b: If x = 101, the answer to the REPHRASED target question is YES, x is greater than 100
Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x < 101
This means x could equal 100 or 99 or 98 or 97 or ....
For every possible value of x, the answer to the REPHRASED target question is always the same: NO, x is not greater than 100
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT
Answer: B
VIDEO ON REPHRASING THE TARGET QUESTION:
17 Jun 2021, 02:52
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If the question did not mention that x and y were positive integers, this question would have been a bit more challenging than it is.
Breaking down the question stem, is x% of y > y, by taking y on to the LHS and maintaining the RHS as 0, we have,
Is x% of y – y > 0?
Factoring out y,
Is y(\(\frac{x}{100}\) – 1) > 0?
Since y is a positive integer (and hence already more than 0), the only way in which the above product can be greater than 0 is by having (\(\frac{x}{100}\) – 1) > 0.
Therefore, we can rephrase the question stem as,
Is \(\frac{x}{100}\) – 1 > 0??
Which can be simplified to,
Is\( \frac{x}{100}\) > 1?
And further to
Is x > 100?
Now, this is the question we are trying to answer.
From statement I alone, x > 99.
This means x is definitely not more than 100 because x could be equal to 100.
Statement I alone is insufficient. Answer options A and D can be eliminated. Possible answer options are B, C or E.
From statement II alone, x <101.
Since x is an integer, this means that x can be 100 or lesser; which then means that x is never greater than 100.
IS x > 100? NO, it is not.
Statement II alone is sufficient to answer the question with a NO. Answer options C and E can be eliminated.
The correct answer option is B.
Hope that helps!
Aravind B T
Breaking down the question stem, is x% of y > y, by taking y on to the LHS and maintaining the RHS as 0, we have,
Is x% of y – y > 0?
Factoring out y,
Is y(\(\frac{x}{100}\) – 1) > 0?
Since y is a positive integer (and hence already more than 0), the only way in which the above product can be greater than 0 is by having (\(\frac{x}{100}\) – 1) > 0.
Therefore, we can rephrase the question stem as,
Is \(\frac{x}{100}\) – 1 > 0??
Which can be simplified to,
Is\( \frac{x}{100}\) > 1?
And further to
Is x > 100?
Now, this is the question we are trying to answer.
From statement I alone, x > 99.
This means x is definitely not more than 100 because x could be equal to 100.
Statement I alone is insufficient. Answer options A and D can be eliminated. Possible answer options are B, C or E.
From statement II alone, x <101.
Since x is an integer, this means that x can be 100 or lesser; which then means that x is never greater than 100.
IS x > 100? NO, it is not.
Statement II alone is sufficient to answer the question with a NO. Answer options C and E can be eliminated.
The correct answer option is B.
Hope that helps!
Aravind B T
