If 6/(x(x+1))1, which of the following could the value of x?

Question

If  \frac{6}{x(x+1)}>1 , which of the following could the value of x?

A. -3.5
B. -2.5
C. 2.5
D. 3.5
E. 4.5

EMPOWERgmatRichC · Accepted Answer

Hi viktorija,

This question can be solved by TESTing THE ANSWERS. One (and only one) or those numbers could be a solution to the given inequality, so we could check them (just plug them in) until we find one that "fits" the given inequality.

There is a logical math shortcut here though that we can take advantage of:

We're told that 6/(product) > 1 so the denominator must be LESS than 6. That way 6/(less than 6) will be > 1. So we're really just looking for a product that's less than 6. Logically, we're probably looking for a value for X that's relatively close to 0, so let's check answers B and C....But don't do the math just yet...

Answer B: X = -2.5
Denominator = (-2.5)(-1.5)

Answer C: X = 2.5
Denominator = (2.5)(3.5)

Since the negative signs will cancel out in Answer B, you don't have to do the math to see that Answer B is smaller. Since there's only one answer that will "fit", it has to be B.

Final Answer:  B

GMAT assassins aren't born, they're made,
Rich

manpreetsingh86 · Answer

\frac{6}{x(x+1)} >1 let's analyze the denominator. x(x+1) = x^2+x. now x^2+x will always be positive except for numbers lying between -1 and 0. now if x lies between -1 and 0, then the fraction \frac{6}{x(x+1)} will be negative. this violates our initial given condition that \frac{6}{x(x+1)} >1 . hence the expression x^2+x will always be positive. now since expression x^2+x is positive, therefore we can cross multiply. Thus we have x^2+x<6 x^2+x-6<0 (x+3)(x-2)<0 now for all values of x which are less than -3, (x+3)(x-2) will always be positive. similarly for all values of x , which are greater than 2, (x+3)(x-2) will always be positive. hence our desired range is between -3 and 2. i.e. -3

Lucky2783 · Answer

If 6/(x(x+1))>1, which of the following could the value of x?

A.-3.5
B.-2.5
C.2.5
D.3.5
E.4.5

Given 6/(x(x+1))>1 i.e x(x+1) is +ive implies X is positive ; 
since we are dealing with all positives 
6/(x(x+1))>1 ---> (x+3)(x-2)<0
++++++(-3)----(2)++++++
so anything between -3 and 2 satisfies the inequality . 
B. -2.5

Bunuel  am i doing right ?

sytabish · Answer

Lucky2783  ,I don't think this derivation of yours is right:  x(x+1) is +ive implies X is positive . Please check!

Lucky2783 · Answer

thanks . actually we do not need know the sign of X here Given 6/(x(x+1))>1 implies (x(x+1)) is a +ive quantity so we can simply multilply both sides of inequality by (x(x+1)) 6 > (x(x+1)) 6> x^2 + x x^2+x-6 < 0 (x+3)(x-2)<0 ++++++(-3)----(2)++++++ so anything between -3 and 2 satisfies the inequality . B. -2.5

EMPOWERgmatRichC · Answer

Hi styabish,

You have to be very careful with your assumptions in the Quant section. This specific Number Property WILL show up on Test Day....

(X)(X+1) = positive

This does NOT mean that X has to be positive.

X COULD be positive....

eg 
X = 1
(1)(2) = 2

X COULD be NEGATIVE though...

eg
X = -2
(-2)(-1) = 2

GMAT assassins aren't born, they're made,
Rich

PareshGmat · Answer

\frac{6}{(x(x+1))} > 1

\frac{6}{x^2 + x} > 1

For x = -3.5

\frac{6}{12.25-3.5}  >> This would be less than 1

For x = -2.5

\frac{6}{6.25-2.5}  >> This would be greater than 1

Answer = B

aggarwalpooja · Answer

isn't this what you get after factorising
x<-3 or x<2
then how is -2.5 the answer? (since -2.5 is greater than -3)
Can someone help, please?

Bunuel · Answer

Let me ask you: what does x < -3 (x is less than -3) or x < 2 (x is less than 2) even mean? As for the solution please see above. Theory on Inequalities: Solving Quadratic Inequalities - Graphic Approach: solving-quadratic-inequalities-graphic-approach-170528.html Inequality tips: tips-and-hints-for-specific-quant-topics-with-examples-172096.html#p1379270 inequalities-trick-91482.html data-suff-inequalities-109078.html range-for-variable-x-in-a-given-inequality-109468.html everything-is-less-than-zero-108884.html graphic-approach-to-problems-with-inequalities-68037.html All DS Inequalities Problems to practice: search.php?search_id=tag&tag_id=184 All PS Inequalities Problems to practice: search.php?search_id=tag&tag_id=189 700+ Inequalities problems: inequality-and-absolute-value-questions-from-my-collection-86939.html

ENGRTOMBA2018 · Answer

The most straightforward method for this type of question will be to use the values in the options and see which one gives you >1 . Only 1 option must satisfy this requirement. Additionally, for algebraic solution, look below: Given : \frac{6}{x(x+1)} > 1 ----> \frac{6}{x(x+1)} - 1 > 0 ---> \frac{6-x^2-x}{x(x+1)} > 0 ----> \frac{-6+x^2+x}{x(x+1)} < 0 \frac{(x+3)(x-2)}{x(x+1)} < 0 ----> -3

aggarwalpooja · Answer

Let me ask you: what does x < -3 (x is less than -3) or x < 2 (x is less than 2) even mean? As for the solution please see above. This link sorted my worries! For anyone who struggled in the last bit after factorising refer this: https://www.khanacademy.org/math/algebr ... equalities Thanks Bunuel! Now I know why did you ask me what didx < -3 (x is less than -3) or x < 2 (x is less than 2) even mean?

aggarwalpooja · Answer

Thanks Engr12, plugging in the value is guess the easiest!

kanusha · Answer

\frac{6}{(x(x+1))} > 1

6 > x(x+1)
 6 > x^{2} + x 
Plug In options
B

dave13 · Answer

hello there!

How did you manage to draw the line based on this (x+3)(x-2)<0 is there rule to transform it into line ?

thank you

Probus · Answer

Hi dave13 , Let me try to respond to your query. If \frac{6}{x(x+1)} >1, which of the following could the value of x? note x and (x+1) are two consecutive numbers, then their product is always positive . Why if x is negative then (x+1) is also negative and their product is always positive if x is positive then (x+1) is also positive and their product is always positive But x cannot be -1 and 0 , because the exp will be undefined for these values. So we can write \frac{6}{x(x+1)} >1 as \frac{6}{x(x+1)} -1>0 So \frac{(6-x(x+1)}{x(x+1)} >0 \frac{(6-x^2-x)}{x(x+1)} >0 \frac{-((x+3)(x-2))}{x(x+1)} >0 When we multiply by -1 on both sides we change the sign of inequality. \frac{((x+3)(x-2))}{x(x+1)} <0 Now if you draw the number line and have positive and negative regions this is how it would look ++++++++++++(-3)---------------------(-1)++++++++++++(0)--------------------(2)++++++++++ Now the region where the inequality holds is -3

AkshdeepS · Answer

\frac{6}{ } > 1 \frac{6}{ } > 1 We know that x^2 + x can never be negative irrespective of the value of "x" , therefore 6 > x^2 + x Or x^2 + x - 6 < 0 (x + 3) (x - 2) < 0 (x - 2) < 0 or (x + 3) > 0 x < 2 or x > -3 -3 < x < 2 Answer : B = -2.5

CrackverbalGMAT · Answer

Solution:

6/x(x+1) > 1 and this is not possible for x(x+1)<0

=> x(x+1) >0 and in other words it implies x(x+1) is positive.

=>6 and 1 are positive values too and hence we can now confidently write

6/x(x+1) >1 => 6>x(x+1)

=>x(x+1)<6

=>x^2 + x <6

=>x^2 + x -6 < 0 (Add -6 on both sides)

=>x^2 +3x - 2x -6 < 0

=> x(x+3) - 2(x+3) <6

=> (x+3)(x-2) < 6

Use the wavy line approach now to reach the critical points as -3 and 2,plot them on the number line and consider the negative interval values only
=> +.................(-3)................. - ...................(2)...............+...

NEGATIVE INTERVAL To be considered AS "<" sign in inequality

=> -3<x<2 and the only option satisfying the range is -2.5 (option b)

Devmitra Sen
GMAT SME

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If 6/(x(x+1))>1, which of the following could the value of x?

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If 6/(x(x+1))>1, which of the following could the value of x?

Prep Toolkit

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