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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8563
GMAT 1: 760 Q51 V42
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Is x>16? 1) x/4>4 2) 4/x<1/4  [#permalink]

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24 Mar 2016, 15:58
2
10
00:00

Difficulty:

55% (hard)

Question Stats:

51% (01:22) correct 49% (01:09) wrong based on 178 sessions

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Is x>16?

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

* A solution will be posted in two days.

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" ##### Most Helpful Expert Reply GMAT Club Legend Joined: 11 Sep 2015 Posts: 4320 Location: Canada Re: Is x>16? 1) x/4>4 2) 4/x<1/4 [#permalink] ### Show Tags 25 Mar 2016, 07:00 3 3 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 _________________ Test confidently with gmatprepnow.com ##### General Discussion Math Expert Joined: 02 Aug 2009 Posts: 8268 Re: Is x>16? 1) x/4>4 2) 4/x<1/4 [#permalink] ### Show Tags 24 Mar 2016, 19:48 2 1 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 _________________ Manager Joined: 18 Feb 2016 Posts: 95 Is x>16? 1) x/4>4 2) 4/x<1/4 [#permalink] ### Show Tags Updated on: 28 Apr 2016, 05:48 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, 19:59. Last edited by deabas on 28 Apr 2016, 05:48, edited 1 time in total. SVP Joined: 26 Mar 2013 Posts: 2347 Concentration: Operations, Strategy Schools: Erasmus '21 (M$)
Re: Is x>16? 1) x/4>4 2) 4/x<1/4  [#permalink]

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25 Mar 2016, 23:44
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

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
Math Expert
Joined: 02 Aug 2009
Posts: 8268
Re: Is x>16? 1) x/4>4 2) 4/x<1/4  [#permalink]

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25 Mar 2016, 23:53
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

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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Joined: 26 Mar 2013
Posts: 2347
Concentration: Operations, Strategy
Schools: Erasmus '21 (M$) Re: Is x>16? 1) x/4>4 2) 4/x<1/4 [#permalink] ### Show Tags 26 Mar 2016, 00:00 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 Math Expert Joined: 02 Aug 2009 Posts: 8268 Re: Is x>16? 1) x/4>4 2) 4/x<1/4 [#permalink] ### Show Tags 26 Mar 2016, 00:06 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 _________________ Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8563 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Is x>16? 1) x/4>4 2) 4/x<1/4 [#permalink] ### Show Tags 28 Mar 2016, 03:49 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. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Re: Is x>16? 1) x/4>4 2) 4/x<1/4  [#permalink]

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21 Sep 2019, 08:30
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Re: Is x>16? 1) x/4>4 2) 4/x<1/4   [#permalink] 21 Sep 2019, 08:30
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