Is x 16? (1) x/4 4 (2) 4/x

Question

Is x > 16?

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

BrentGMATPrepNow · Accepted Answer

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 Cheers, Brent

chetan2u · Answer

Hi, never X multiply when a variable is there in denominator.. lets see the statements-- 1) x/4>4 x>16 straightway SUFF 2) \frac{4}{x}<\frac{1}{4} here too it is easy to x-multiply and feel th estatement to be suff, ut we have th evariable in denominator.. \frac{4}{x}<\frac{1}{4} .. \frac{4}{x}-\frac{1}{4}<0 .. \frac{{(16-x)}}{{4x}}<0 so we have three cases -- 1) x=0, undefined 2) x<0.. Numerator should be +ive as denominator is -ive.. hence 16-x>0 or x<16 ans is NO 3) x>0.. denominator is +ive so Num should be -ive.. hence 16-x<0 or x>16 ans is YES two different answers.. Insuff ans A

deabas · Answer

1) Multiply both sides by 4 -> x>16 > Sufficient 2) Multiply both sides by 1/4 -> 1/4 < 1/16 If x<0 -> Answer No If x>0 -> It depends on the value of x -> Not Sufficient Answer: A

Mo2men · Answer

Hi Brent,

Can you tell me where I went wrong for statement 2:

4/x < 1/4 .... I can flip the fraction and change '> 'sign so x/4>1/4...........hence x>16 ........(B) is sufficient.

Thanks

chetan2u · Answer

Hi 
you flip the sign by multiplying both sides by '-' sign, but can't flip the sign by taking reciprocals..
you are not aware of the SIGN of x, so we do not x-multiply the two sides DIRECTLY but take both terms on one side and then solve..

Mo2men · Answer

Thanks a lot chetan2u

But when you say 'can't flip the sign by taking reciprocals' do you as general rule?

When I say 1/2>1/3.....this means 2<3 when i take reciprocals

chetan2u · Answer

yes, you never FLIP or X-multiply when there is a VARIABLE in the denominator since we are not aware whether it is POSITIVE or NEGATIVE

MathRevolution · Answer

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.

bumpbot · Answer

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

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