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

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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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

Answer: A

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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Similar questions to practice:
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is-x-0-1-x-3-4x-3-2-x-1-2x-1-can-100357.html
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Please format your reply properly.

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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Perfect ...........Thanks a lot......

[quote="ArunpriyanJ"]

Hi arun..
Refer your PM ..
I hope the query is clear now..
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Thanks Bunuel. It really helped

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?


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No, that's not acceptable. I explained this here: https://gmatclub.com/forum/is-x-216394.html#p2093126
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Is x > 0 ?
(1) |x–5|=7x+2
(2) |x–3|=|15x–3|

anyone help me in solving this!

Posted from my mobile device

I re-posted this question here: https://gmatclub.com/forum/is-x-0-1-x-5 ... l#p2759851 You can also find there a solution to it. Hope it helps.
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Statement 1

x-5 = 7x+2 or -(x-5) = 7x+2

on solving
x = -7/6 or x = 3/8

Always substitute the values (specifically while solving modulus)
x = -7/6 ; 37/8 =-37/8
x = 3/8 ; 23/6 = 23/6

Therefore, x = 3/8
Clearly answers x < 0?
Which is NO


Statement 2

Square on both sides.
x^2 + 10x + 25 = 16x^2 + 40x + 25......................[(a+b)^2 = a^2 + b^2 + 2ab]

on solving
x = 0 or x = -2

substitute the values
Both the values satisfy the equation. i.e. x = 0 or x = -2
Therefore, we can not clearly decipher if x < 0
As it can be a Yes or No.


Answer: A