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# What is the value of x?

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Manager
Joined: 08 Dec 2012
Posts: 64
Location: United Kingdom
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What is the value of x? [#permalink]

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06 Oct 2013, 10:01
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Difficulty:

55% (hard)

Question Stats:

47% (00:53) correct 53% (00:42) wrong based on 348 sessions

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What is the value of x?

(1) 4 < x < 6

(2) |x| = 4x − 15
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 44412
Re: What is the value of x? (1) 4 < x < 6 (2) |x|=4x−15 [#permalink]

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06 Oct 2013, 10:05
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What is the value of x?

(1) 4 < x < 6. Clearly insufficient, x can be any number from 4 to 6, not inclusive.

(2) |x| = 4x − 15. LHS is an absolute value, which is always non negative, hence RHS must also be non-negative: $$4x-15\geq{0}$$ --> $$x\geq{\frac{15}{4}}$$ --> $$x$$ is positive, thus $$|x|=x$$ --> $$x=4x-15$$ --> $$x=5$$. Sufficient

Hope it's clear.
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Posts: 44412
Re: What is the value of x? (1) 4 < x < 6 (2) |x|=4x−15 [#permalink]

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06 Oct 2013, 10:06
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Bunuel wrote:
What is the value of x?

(1) 4 < x < 6. Clearly insufficient, x can be any number from 4 to 6, not inclusive.

(2) |x| = 4x − 15. LHS is an absolute value, which is always non negative, hence RHS must also be non-negative: $$4x-15\geq{0}$$ --> $$x\geq{\frac{15}{4}}$$ --> $$x$$ is positive, thus $$|x|=x$$ --> $$x=4x-15$$ --> $$x=5$$. Sufficient

Hope it's clear.

Similar questions to practice: what-is-x-126874.html
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Joined: 12 May 2013
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Re: What is the value of x? (1) 4 < x < 6 (2) |x|=4x−15 [#permalink]

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06 Oct 2013, 12:32
bunuel , m still confused that why B
i got the point rhs and lhs being positive , but why 5 , there can be other possibilities as well such as 4(6)-15=9
so won't the ans be "c" ??? plz correct me ,where i m wrong
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Re: What is the value of x? (1) 4 < x < 6 (2) |x|=4x−15 [#permalink]

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06 Oct 2013, 12:35
bunuel , m still confused that why B
i got the point rhs and lhs being positive , but why 5 , there can be other possibilities as well such as 4(6)-15=9
so won't the ans be "c" ??? plz correct me ,where i m wrong

Does x=6 satisfy |x| = 4x − 15?
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Re: What is the value of x? (1) 4 < x < 6 (2) |x|=4x−15 [#permalink]

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06 Oct 2013, 12:43
thankz , bunuel it was a silly mistake
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22 Mar 2014, 10:45
According to me there are 2 solutions for x for option 2 and multiple solutions for option 1 as well (as x can be a non-integer ex. 4.5 or 5 or 5.5) So i think it should be E.
But its not. Can someone please explain why?

Source: Babson Practise Test

Data Sufficiency -

What is the value of x?

(1) 4 < x < 6

(2) |x|=4x−15

A statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;

B statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;

C BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked;

E statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
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22 Mar 2014, 12:47

Regarding to option 2, how x can be 4.5 or 5.5 ? try to let x=4.5 or 5.5, do you think the equation will be correct?
no i do not think so, the only answer is x=5
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GMAT 2: 770 Q50 V47
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22 Mar 2014, 14:48
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derek123 wrote:
According to me there are 2 solutions for x for option 2 and multiple solutions for option 1 as well (as x can be a non-integer ex. 4.5 or 5 or 5.5) So i think it should be E.
But its not. Can someone please explain why?

Source: Babson Practise Test

Data Sufficiency -

What is the value of x?

(1) 4 < x < 6

(2) |x|=4x−15

A statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;

B statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;

C BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked;

E statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

you are confused for option 2:

|x|=4x−15

X can be +ve / -ve.
for X = +ve

x = 4x - 15 , hence x = 5

For X = -ve

-x =4x - 15, hence x=3 , however this contradicts your assumption that x is -ve. So this solution is ruled out, leaving x=5 as unique solution.
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Manager
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Location: India
Concentration: Technology, Marketing
What is the value of x? [#permalink]

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18 Sep 2014, 12:41
Bunuel wrote:
Bunuel wrote:
What is the value of x?

(1) 4 < x < 6. Clearly insufficient, x can be any number from 4 to 6, not inclusive.

(2) |x| = 4x − 15. LHS is an absolute value, which is always non negative, hence RHS must also be non-negative: $$4x-15\geq{0}$$ --> $$x\geq{\frac{15}{4}}$$ --> $$x$$ is positive, thus $$|x|=x$$ --> $$x=4x-15$$ --> $$x=5$$. Sufficient

Hope it's clear.

Similar questions to practice: what-is-x-126874.html

Hello Bunuel,
I am confused that why B is answer. I still don't understand that why in this case we did not taken two cases for mod.

I solved by taking two condition for LHS, one is positive and one is negative.
|x|=4x−15

X can be +ve / -ve.
for X = +ve
x = 4x - 15 , hence x = 5

For X = -ve
-x =4x - 15, hence x=3

Why we rejected answer choice with -ve X. Also can u please help me understand that in which cases we should take both +ve and -ve values for MOD and in which cases should not. Absolute Value is a weak pint for me in DS

Thanks
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Re: What is the value of x? [#permalink]

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18 Sep 2014, 13:18
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Expert's post
him1985 wrote:
Bunuel wrote:
Bunuel wrote:
What is the value of x?

(1) 4 < x < 6. Clearly insufficient, x can be any number from 4 to 6, not inclusive.

(2) |x| = 4x − 15. LHS is an absolute value, which is always non negative, hence RHS must also be non-negative: $$4x-15\geq{0}$$ --> $$x\geq{\frac{15}{4}}$$ --> $$x$$ is positive, thus $$|x|=x$$ --> $$x=4x-15$$ --> $$x=5$$. Sufficient

Hope it's clear.

Similar questions to practice: what-is-x-126874.html

Hello Bunuel,
I am confused that why B is answer. I still don't understand that why in this case we did not taken two cases for mod.

I solved by taking two condition for LHS, one is positive and one is negative.
|x|=4x−15

X can be +ve / -ve.
for X = +ve
x = 4x - 15 , hence x = 5

For X = -ve
-x =4x - 15, hence x=3

Why we rejected answer choice with -ve X. Also can u please help me understand that in which cases we should take both +ve and -ve values for MOD and in which cases should not. Absolute Value is a weak pint for me in DS

Thanks

When you consider the case when x is negative and get x = 3 = positive, you should reject it, as x is not negative. Also, plug x = 3 into the equation, does it hold true?

Theory on Abolute Values: math-absolute-value-modulus-86462.html
Absolute value tips: absolute-value-tips-and-hints-175002.html
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Re: What is the value of x? [#permalink]

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10 Oct 2017, 09:12
Expert's post
Top Contributor
nave wrote:
What is the value of x?

(1) 4 < x < 6

(2) |x| = 4x − 15

Target question: What is the value of x?

Statement 1: 4 < x < 6
ASIDE: Some students will assume that x is an integer and incorrectly conclude that x must equal 5. This is a common mistake on the GMAT.
The truth of the matter is that there are infinitely many values of x that satisfy statement 1.
For example x could equal 4.1, or x could equal 4.132 or 4.54 or 5 or 5.4211 etc
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: |x| = 4x − 15
There are 3 steps to solving equations involving ABSOLUTE VALUE:
1. Apply the rule that says: If |x| = k, then x = k and/or x = -k
2. Solve the resulting equations
3. Plug solutions into original equation to check for extraneous roots

Given: |x| = 4x − 15
So, there are two possible cases to examine:
Case a: x = 4x − 15. When we solve this equation, we get: x = 5
Case b: x = -(4x − 15). When we solve this equation, we get: x = 3
At this point, it LOOKS LIKE there are two possible values of x. However, we haven't performed step 3 yet: Plug solutions into original equation to check for extraneous roots

Let's do that.
Case a: Plug x = 5 into original equation to get: |5| = 4(5) − 15
Simplify right side of equation to get: |5| = 5
This works, so x = 5 IS a possible value of x

Case b: Plug x = 3 into original equation to get: |3| = 4(3) − 15
Simplify right side of equation to get: |3| = -3
This DOES NOT work, so x = 3 is NOT a possible value of x

Since there is only ONE possible value of x (x = 5), statement 2 is SUFFICIENT

[Reveal] Spoiler:
B

Cheers,
Brent
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Re: What is the value of x? [#permalink]

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06 Dec 2017, 06:15
Hi Bunuel,

I don't understand why ans should B?

Question does not say anything about 'X'. Therefore X can be integer or non-integer number.
So if X =3.75 then |X|= 4X-15 satisfies the condition.
Further if I combine Condition 2 (i.e |X|= 4X-15) with Condition 1 (i.e. 4<x<6) then also we will not get the exact value of X.

According to me Ans. should be E.
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Joined: 02 Sep 2009
Posts: 44412
Re: What is the value of x? [#permalink]

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06 Dec 2017, 06:23
TarunKB wrote:
Hi Bunuel,

I don't understand why ans should B?

Question does not say anything about 'X'. Therefore X can be integer or non-integer number.
So if X =3.75 then |X|= 4X-15 satisfies the condition.
Further if I combine Condition 2 (i.e |X|= 4X-15) with Condition 1 (i.e. 4<x<6) then also we will not get the exact value of X.

According to me Ans. should be E.

x = 3.75 does not satisfy |x| = 4x − 15. If x = 3.75, then 4*3.75 − 15 = 0, not 3.75.

Finally, before attempting questions one should go through the basics:

10. Absolute Value

For more check Ultimate GMAT Quantitative Megathread

Hope it helps.
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Re: What is the value of x? [#permalink]

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06 Dec 2017, 06:29
Yup Bunnel,
You are right. Made the same mistake as done by Derek123.
Thank you
Re: What is the value of x?   [#permalink] 06 Dec 2017, 06:29
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