tonebeeze wrote:
If n is positive, is \(\sqrt {n} > 100\)?
(1) \(\sqrt {n-1} > 99\)
(2) \(\sqrt {n+1} > 101\)
Target question: Is √n > 100?This is a good candidate for
REPHRASING the target question.
Take
√n > 100 and square both sides to get
n > 10,000So, we get:
REPHRASED target question: Is n > 10,000? Statement 1: √(n - 1) > 99 Square both sides to get n - 1 > 99²
Evaluate: n - 1 > 9801
Add 1 to both sides to get: n > 9802
So, x COULD equal 9803, in which case
n < 10,000Conversely, x COULD equal 10,001, in which case
n > 10,000Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: √(n + 1) > 101 Square both sides to get n + 1 > 101²
Evaluate: n + 1 > 10,201
Subtract 1 from both sides to get: n > 10,200
If x is greater than 10,200, then we can be certain that
x > 10,000Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer =
RELATED VIDEO
_________________
Brent Hanneson – Creator of gmatprepnow.com
I’ve spent the last 20 years helping students overcome their difficulties with GMAT math, and the biggest thing I’ve learned is…
Many students fail to maximize their quant score NOT because they lack the skills to solve certain questions but because they don’t understand what the GMAT is truly testing -
Learn more