This problem was way over my head. Manhattan simplifies and then says "Therefore, the answer to the prompt question is affirmative if either x2 + 100x - 10,000 = 0 or y = 0"

I do not see the connection. Also, Manhattan says that statement 1 can rearrange to give 0, but didn't give the details, of how/why.

Thanks!

x% of y is (x/100)(y), since, for example, 40% of 10 = 40/100 * 10 = 4.
x% of [x% of y] is (x/100)[(x/100)(y)]

x% less than y is [y - (x/100)(y)], since, for example, 10% less than 100 is [100 - (10/100)(100)] = 90

(x/100)[(x/100)(y)] = y - (x/100)(y)?
(x/100)[(x/100)(y)] + (x/100)(y) = y?
(x/100)(y)[(x/100) + 1] = y?
(x/100)[(x/100) + 1] = 1? (we have to keep in mind we are assuming that y does not equal 0 in this step)
x(x/100 + 1) = 100?
x(x + 100) = 10000?

Statement 1) Sufficient.
Statement 2) This says that y is not equal to 0, otherwise the product y(y + 1) would be 0. This alone does not give any extra information. Insufficient.

A

Buix0065 wrote:Is x% of x% of y equal to x% less than y ?

(1) x(x + 100) = 10,000
(2) y(y + 1) = 1


OA: A

The question is asking whether a certain percentage of y is equal to another percentage of y.
If y=0, then the answer is a definite YES.
If y≠0, then the value of y is irrelevant. All that matters is the value of x.

Let y = 100.

Plugging y=100 into the question stem, we get:

x% of x% of 100 = 100 - x% of 100

x/100 * x/100 * 100 = 100 - (x/100)100

x²/100 = 100 - x

x² = 10,000 - 100x

x² + 100x = 10,000.

Question rephrased: Does y=0 or does x² + 100x = 10,000?

Statement 1: x(x + 100) = 10,000
x² + 100x = 10,000.
Sufficient.

Statement 2: y(y + 1) = 1
Thus, y≠0.
No information about x.
Insufficient.

The correct answer is A.

Hi Mitch

Thank you for your fine explanation on this question. But there is something i dun understand; maybe i have not understood fully certain basic - why did you say Y is not equal to 0...

... since Y(y+1) = 1;

therefore Y = 1 OR Y+1=1 => Y=1-1=0

Doesn't the above suggest that Y=1 or Y=0, so we dun know which is true?

vanquish wrote:Hi Mitch

Thank you for your fine explanation on this question. But there is something i dun understand; maybe i have not understood fully certain basic - why did you say Y is not equal to 0...

... since Y(y+1) = 1;

therefore Y = 1 OR Y+1=1 => Y=1-1=0

Doesn't the above suggest that Y=1 or Y=0, so we dun know which is true?

If we plug y=1 into y(y+1) = 1, we get:
1(1+1) = 1
2 = 1.
Doesn't work.

If we plug y=0 into y(y+1) = 1, we get:
0(0+1) = 1
0 = 1.
Doesn't work.

Neither y=1 nor y=0 is a valid value.
To determine the solutions to the equation, we first have to set the equation equal to 0.
y(y+1) - 1 = 0.
y² + y - 1 = 0.
From here, we would have to apply the quadratic formula.

I got this thing. The inequation or the inequality was really easy to solve but the main part in this question was the original DS part itself...

What GmatGuru said is actually correct. Let me explain this question using an example...

Let us say that you solved a quadratic equation and you get two solutions as: x = 5 or x = -7
These two solutions are present in stimulus or the question given...

And let us say that the two statements given are as follows:

1] x = 5

2] x = -7

Now what should be the answer... then the OA would be D as each statement tells the answer...

Like if x = 5 or x = -7 and in fact there is one thing to consider here,

The C option cannot be the answer choice at all.

The E option Cannot be the answer choice also

It is only D as Each statement that is possible to get the answer choice..

In the same way the current stimulus gives the following equation:

Either x^2 + 100x - 10000 = 0 OR y = 0

These are the two possibilities where, the above equation can be equal...

Statement 1 says that the quadratic eqation (x^2 + 100x - 10000) = 0

Hence statement 1 solely is the answer is correct.

Statement 2: It says y not equal to 0.

Hence the option B alone is not sufficient.

Therefore A is the correct answer choice....

A...

Hope this post helps u really:

Here the answer is in the question itself.
The question stem converted to mathematical notations is

yx^2/10^4 = y(1-x/100)

y is not = 0

x^2/10^4 = 1-x/100

x^2 = 10^4-100x

x^2+100x = 10000

x(x+100) = 10000

Which is statement 1.

(A) is sufficient.