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# Is x < 0 ? (1) |x - 5| = 7x + 2 (2) |x + 5| = |4x + 5|

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Is x < 0 ? (1) |x - 5| = 7x + 2 (2) |x + 5| = |4x + 5|  [#permalink]

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Updated on: 07 Feb 2019, 08:12
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Difficulty:

95% (hard)

Question Stats:

39% (02:25) correct 61% (02:18) wrong based on 158 sessions

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Is x < 0 ?

(1) |x - 5| = 7x + 2
(2) |x + 5| = |4x + 5|

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Originally posted by stonecold on 09 Apr 2016, 23:13.
Last edited by Bunuel on 07 Feb 2019, 08:12, edited 2 times in total.
Edited the question.
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Joined: 02 Aug 2009
Posts: 8341
Re: Is x < 0 ? (1) |x - 5| = 7x + 2 (2) |x + 5| = |4x + 5|  [#permalink]

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10 Apr 2016, 00:35
2
3
Vyshak wrote:
St1: x - 5 = 7x + 2 or 5 - x = 7x + 2
x = -7/6 or x = 3/8
Substitute the two values back in |x - 5| = 7x + 2. Only x = 3/8 is a valid value. Is x < 0? No
Sufficient

Hi Vyshak,

another way to look at the statement after you have got your values..
Since |x-5| is greater than or equal to 0...
7x+2 will also be > or = 0..
x will be >= -2/7...
-7/6 can be eliminated as it is <-2/7
so ONLY 3/8 is left..
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Re: Is x < 0 ? (1) |x - 5| = 7x + 2 (2) |x + 5| = |4x + 5|  [#permalink]

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09 Apr 2016, 23:54
4
3
St1: x - 5 = 7x + 2 or 5 - x = 7x + 2
x = -7/6 or x = 3/8
Substitute the two values back in |x - 5| = 7x + 2. Only x = 3/8 is a valid value. Is x < 0? No
Sufficient

St2: Square on both sides --> x^2 + 10x + 25 = 16x^2 + 40x + 25
15x^2 + 30x = 0
x = 0 or x = -2
Substitute the 2 values back in the original equation. Both the values satisfy the equation. Is x < 0? Can be yes or no.
Not Sufficient

##### General Discussion
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Re: Is x < 0 ? (1) |x - 5| = 7x + 2 (2) |x + 5| = |4x + 5|  [#permalink]

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24 Apr 2016, 08:15
2
ArunpriyanJ wrote:
Vyshak wrote:
St1: x - 5 = 7x + 2 or 5 - x = 7x + 2
x = -7/6 or x = 3/8
Substitute the two values back in |x - 5| = 7x + 2. Only x = 3/8 is a valid value. Is x < 0? No
Sufficient

I am struggling to understand this step.....When i put -7/6 in Equn i am getting -37=-37...

Pls help

St2: Square on both sides --> x^2 + 10x + 25 = 16x^2 + 40x + 25
15x^2 + 30x = 0
x = 0 or x = -2
Substitute the 2 values back in the original equation. Both the values satisfy the equation. Is x < 0? Can be yes or no.
Not Sufficient

Vyshak has used the value of 3/8 as the value of -7/6 is not a valid option.

When you put -7/6 into the given equation |x-5| = 7x+2 ---> you get 37/6 on the LHS and you get -37/6 on the RHS. Thus this value of x=-7/6 is not a valid one.

Do note here that LHS has |x-5| and as |x|$$\geq$$0 for all x, LHS $$\neq$$ -37/6 .

Hope this helps.
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Joined: 02 Aug 2009
Posts: 8341
Re: Is x < 0 ? (1) |x - 5| = 7x + 2 (2) |x + 5| = |4x + 5|  [#permalink]

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24 Apr 2016, 11:01
1
[quote="ArunpriyanJ"]

Hi arun..
I hope the query is clear now..
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Re: Is x < 0 ? (1) |x - 5| = 7x + 2 (2) |x + 5| = |4x + 5|  [#permalink]

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14 Jul 2018, 10:15
1
gmatbusters wrote:
Hi Bunuel

Statement 1 is giving x = 3/8
Statement 2 is giving x = -2 or 0.

is it acceptable for Statements to contradict each other?

Bunuel wrote:
stonecold wrote:
Is x < 0 ?

(1) |x - 5| = 7x + 2
(2) |x + 5| = |4x + 5|

Similar questions to practice:
http://gmatclub.com/forum/is-x-0-1-x-3- ... 27978.html
http://gmatclub.com/forum/is-x-0-1-x-3- ... 00357.html

No, that's not acceptable. I explained this here: https://gmatclub.com/forum/is-x-216394.html#p2093126
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Re: Is x < 0 ? (1) |x - 5| = 7x + 2 (2) |x + 5| = |4x + 5|  [#permalink]

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24 Apr 2016, 07:31
1
stonecold wrote:
Is x < 0 ?

(1) |x - 5| = 7x + 2
(2) |x + 5| = |4x + 5|

Similar questions to practice:
is-x-0-1-x-3-4x-3-2-x-3-2x-127978.html
is-x-0-1-x-3-4x-3-2-x-1-2x-1-can-100357.html
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Re: Is x < 0 ? (1) |x - 5| = 7x + 2 (2) |x + 5| = |4x + 5|  [#permalink]

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24 Apr 2016, 10:31
Engr2012 wrote:
ArunpriyanJ wrote:
Vyshak wrote:
St1: x - 5 = 7x + 2 or 5 - x = 7x + 2
x = -7/6 or x = 3/8
Substitute the two values back in |x - 5| = 7x + 2. Only x = 3/8 is a valid value. Is x < 0? No
Sufficient

I am struggling to understand this step.....When i put -7/6 in Equn i am getting -37=-37...

Pls help

St2: Square on both sides --> x^2 + 10x + 25 = 16x^2 + 40x + 25
15x^2 + 30x = 0
x = 0 or x = -2
Substitute the 2 values back in the original equation. Both the values satisfy the equation. Is x < 0? Can be yes or no.
Not Sufficient

Vyshak has used the value of 3/8 as the value of -7/6 is not a valid option.

When you put -7/6 into the given equation |x-5| = 7x+2 ---> you get 37/6 on the LHS and you get -37/6 on the RHS. Thus this value of x=-7/6 is not a valid one.

Do note here that LHS has |x-5| and as |x|$$\geq$$0 for all x, LHS $$\neq$$ -37/6 .

Hope this helps.

Perfect ...........Thanks a lot......
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Posts: 60579
Re: Is x < 0 ? (1) |x - 5| = 7x + 2 (2) |x + 5| = |4x + 5|  [#permalink]

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12 Jul 2018, 03:13
Is x < 0?

(1) |x - 5| = 7x + 2

If x <= 5, then x - 5 <= 0, thus |x - 5| = -(x - 5). So, in this case we'd have -(x - 5) = 7x + 2 --> x = 3/8.

If x > 5, then x - 5 > 0, thus |x - 5| = x - 5. So, in this case we'd have x - 5 = 7x + 2 --> x = -7/6. Discard this root because it is not in the range we are considering (x > 5).

Thus, x = 3/8. Sufficient.

(2) |x + 5| = |4x + 5|.

Square (we can safely do that since both sides are non-negative): x^2 + 10x + 25 = 16x^2 + 40x + 25 --> x(x + 2) = 0 --> x = 0 or x = -2. Not sufficient.

Technically answer should be A, as statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

But even though formal answer to the question is A, this is not a realistic GMAT question, as: on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other. But the statements above contradict each other:
From (1) x = 3/8 and from (2) x = 0 or x = -2. The statements clearly contradict each other.

So, the question is flawed. You won't see such a question on the test.
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Re: Is x < 0 ? (1) |x - 5| = 7x + 2 (2) |x + 5| = |4x + 5|  [#permalink]

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12 Jul 2018, 18:43
Thanks Bunuel. It really helped
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Re: Is x < 0 ? (1) |x - 5| = 7x + 2 (2) |x + 5| = |4x + 5|  [#permalink]

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14 Jul 2018, 10:03
Hi Bunuel

Statement 1 is giving x = 3/8
Statement 2 is giving x = -2 or 0.

is it acceptable for Statements to contradict each other?

Bunuel wrote:
stonecold wrote:
Is x < 0 ?

(1) |x - 5| = 7x + 2
(2) |x + 5| = |4x + 5|

Similar questions to practice:
http://gmatclub.com/forum/is-x-0-1-x-3- ... 27978.html
http://gmatclub.com/forum/is-x-0-1-x-3- ... 00357.html

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Re: Is x < 0 ? (1) |x - 5| = 7x + 2 (2) |x + 5| = |4x + 5|   [#permalink] 14 Jul 2018, 10:03
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