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Is x>16? 1) x/4>4 2) 4/x<1/4

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by Max@Math Revolution » Thu Mar 24, 2016 3:59 pm
Is x>16?

1) x/4>4
2) 4/x<1/4


* A solution will be posted in two days.
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by ratanvk » Thu Mar 24, 2016 9:56 pm
Max@Math Revolution wrote:Is x>16?

1) x/4>4
2) 4/x<1/4


* A solution will be posted in two days.

ANS A
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by Brent@GMATPrepNow » Fri Mar 25, 2016 6:56 am
Max@Math Revolution wrote:Is x > 16?

1) x/4 > 4
2) 4/x < 1/4
Target question: Is x > 16?

Statement 1: x/4 > 4
Multiply both sides by POSITIVE 4 to get: x > 16
Perfect!!
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: 4/x < 1/4
Multiply both sides by POSITIVE 4 to get: 16/x < 1
NOTE: we must avoid the temptation to multiply both sides by x to get: 16 < x. Doing so would be incorrect since we don't know whether x is POSITIVE or NEGATIVE.

Aside: for more on this, see our free video here: https://www.gmatprepnow.com/module/gmat ... /video/979

There are several values of x that satisfy statement the fact that 16/x < 1. Here are two:
Case a: x = 20, in which case x > 16
Case b: x = -1, in which case x < 16
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

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Brent
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by Max@Math Revolution » Mon Mar 28, 2016 3:49 am
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Is x>16?

1) x/4>4
2) 4/x<1/4


In the original condition, there is 1 variable(x), which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), x>16 -> yes and sufficient.
For 2), multiply 4x^2 to the both equations. Since the square is a positive integer, the direction of inequality doesn't change.
16x<x^2, x(x-16)>0, x<10 or 16<x -> no and yes, which is not sufficient. Thus, A is the answer.
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