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

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MathRevolution
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Is x > 16? (1) x/4 > 4 (2) 4/x < 1/4 [#permalink] Is x > 16? (1) x/4 > 4 (2) 4/x < 1/4   24 Mar 2016, 16:58
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Is x > 16?

(1) x/4 > 4
(2) 4/x < 1/4
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A
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BrentGMATPrepNow
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Re: Is x > 16? (1) x/4 > 4 (2) 4/x < 1/4 [#permalink] Is x > 16? (1) x/4 > 4 (2) 4/x < 1/4   25 Mar 2016, 08:00
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MathRevolution 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
Cheers,
Brent
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Re: Is x > 16? (1) x/4 > 4 (2) 4/x < 1/4 [#permalink] Is x > 16? (1) x/4 > 4 (2) 4/x < 1/4   24 Mar 2016, 20:48
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MathRevolution wrote:
Is x>16?

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


* A solution will be posted in two days.


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
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Re: Is x > 16? (1) x/4 > 4 (2) 4/x < 1/4 [#permalink] Is x > 16? (1) x/4 > 4 (2) 4/x < 1/4   Updated on: 28 Apr 2016, 06:48
MathRevolution wrote:
Is x>16?

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


* A solution will be posted in two days.


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

Originally posted by deabas on 24 Mar 2016, 20:59.
Last edited by deabas on 28 Apr 2016, 06:48, edited 1 time in total.
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Re: Is x > 16? (1) x/4 > 4 (2) 4/x < 1/4 [#permalink] Is x > 16? (1) x/4 > 4 (2) 4/x < 1/4   26 Mar 2016, 00:44
GMATPrepNow wrote:
MathRevolution 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
Cheers,
Brent



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
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Re: Is x > 16? (1) x/4 > 4 (2) 4/x < 1/4 [#permalink] Is x > 16? (1) x/4 > 4 (2) 4/x < 1/4   26 Mar 2016, 00:53
Expert Reply
Mo2men wrote:
GMATPrepNow wrote:
MathRevolution 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
Cheers,
Brent



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


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..
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Re: Is x > 16? (1) x/4 > 4 (2) 4/x < 1/4 [#permalink] Is x > 16? (1) x/4 > 4 (2) 4/x < 1/4   26 Mar 2016, 01:00
chetan2u wrote:


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..


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
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Re: Is x > 16? (1) x/4 > 4 (2) 4/x < 1/4 [#permalink] Is x > 16? (1) x/4 > 4 (2) 4/x < 1/4   26 Mar 2016, 01:06
Expert Reply
Mo2men wrote:
chetan2u wrote:


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..


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


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
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Re: Is x > 16? (1) x/4 > 4 (2) 4/x < 1/4 [#permalink] Is x > 16? (1) x/4 > 4 (2) 4/x < 1/4   28 Mar 2016, 04:49
Expert Reply
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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