zisis 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
x2y = 10,000y – 100xy [multiplying by the common denominator 10,000]
x2y + 100xy – 10,000y = 0 [everything to one side, because it’s quadratic]
y(x2 + 100x – 10,000) = 0 [factoring]
Therefore, the answer to the prompt question is affirmative if either x2 + 100x – 10,000 = 0 or y = 0.
(1) SUFFICIENT: This statement rearranges to give = 0.
(2) INSUFFICIENT: y cannot be 0, but no information is provided about x, making it impossible to determine whether x2 + 100x – 10,000 = 0.
The correct answer is A.
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But, I believe D:
A sufficient
B: y=1 or y+1=1 therefore y=0 therefore B sufficient...
what am i missing? please help
Question: is \(\frac{x}{100}*\frac{x}{100}*y=y(1-\frac{x}{100})\)? --> is \(x^2y=100y(100-x)\)? --> is \(x^2y=y(10,000-100x)\) --> is \(y(x^2+100x-10,000)=0\)?
Basically question is does \(y=0\) or/and \(x^2+100x-10,000=0\)?
(1) \(x(x + 100)=10,000\) --> \(x^2+100x-10,000=0\). Directly gives the answer. Sufficient.
(2) \(y(y+1)=1\). Here it's clear that \(y\neq{0}\), (substitute \(y=0\) in this equation: \(0(0+1)=0\neq{1}\)). So we know that \(y\neq{0}\), but don't know whether \(x^2+100x-10,000=0\)? Not sufficient.
To elaborate more: the problem with your solution is that you solved incorrectly \(y(y+1)=1\).
\(y(y+1)=1\) --> \(y^2+y-1=0\) --> solving for \(y\): \(y=\frac{-1-\sqrt{5}}{2}\) or \(y=\frac{-1+\sqrt{5}}{2}\), so \(y\neq{0}\).
Answer: A.
Hope it's clear.