If x and y are positive integers, is x% of y > y?

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:

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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

The question in algebra would be "is \(x\%*y > y\)?" Since we know y is positive we can chop off y on both sides and change the question to "is \(x\% > 1\)?", and multiply both sides by 100 to change the question to " is x > 100?"

Statement 1:

x must be at least 100, if x = 100 then x is not greater than 100. If x > 100 then x is greater than 100. Insufficient.

Statement 2:

x must be at most 100. If x = 100 then x is not greater than 100. If x < 100 then x is still not greater than 100. Therefore this is sufficient.

Ans: B
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