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# What is the value of x? (1) |y| ≤ −3x (2) |5x − 1| = x + 7

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Joined: 02 Sep 2009
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What is the value of x? (1) |y| ≤ −3x (2) |5x − 1| = x + 7  [#permalink]

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24 Jul 2017, 23:22
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55% (hard)

Question Stats:

40% (01:49) correct 60% (01:36) wrong based on 112 sessions

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What is the value of x?

(1) | y| ≤ −3x
(2) |5x − 1| = x + 7

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Re: What is the value of x? (1) |y| ≤ −3x (2) |5x − 1| = x + 7  [#permalink]

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25 Jul 2017, 01:09
Bunuel wrote:
What is the value of x?

(1) y ≤ −3x
(2) |5x − 1| = x + 7

(1) y ≤ −3x no information about y ...Not sufficient

(2) if (5x-1)<0 => x<1/5
then
5x-1 = -x-7
x=-1 and here x<1/5 so x=-1
Also if (5x-1)>0 =>x>1/5
then
5x-1 = x+7
x=2 and here x>1/5 so x=2
Hence Not Sufficient
E
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Re: What is the value of x? (1) |y| ≤ −3x (2) |5x − 1| = x + 7  [#permalink]

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26 Jul 2017, 11:58
Bunuel wrote:
What is the value of x?

(1) y ≤ −3x
(2) |5x − 1| = x + 7

Statement 1 itself doesn't give any values of either Y or X.

Solving statement 2, we get 2 values of x, x =2 and x = -1.

Putting back both the values of x in statement two, both the values fit in the equation. therefore, we get 2 values of x. Not sufficient.

Combining statement 1 & 2, we still get 2 values of x. Hence (E).
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Re: What is the value of x? (1) |y| ≤ −3x (2) |5x − 1| = x + 7  [#permalink]

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27 Jul 2017, 09:26
Bunuel wrote:
What is the value of x?

(1) y ≤ −3x
(2) |5x − 1| = x + 7

Statement 1 alone is insufficient as value of Y is unknown.

From statement 2 we have two values for x; 0 and 3.5 so statement 2 alone insufficient

combining 1 & 2, still not sufficient to give the unique value of x

So answer is E
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Posts: 7580
Re: What is the value of x? (1) |y| ≤ −3x (2) |5x − 1| = x + 7  [#permalink]

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27 Jul 2017, 09:35
1
Bunuel wrote:
What is the value of x?

(1) y ≤ −3x
(2) |5x − 1| = x + 7

Hi Bunuel,

I believe there is a TYPO in statement 1 otherwise it would not be 600-700 level and would be way too easy to eliminate a statement..
statement II gives 2 values of x, one positive and one negative.
I am sure the statement I would tell us some thing about x as + or -..
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Re: What is the value of x? (1) |y| ≤ −3x (2) |5x − 1| = x + 7  [#permalink]

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27 Jul 2017, 09:41
chetan2u wrote:
Bunuel wrote:
What is the value of x?

(1) y ≤ −3x
(2) |5x − 1| = x + 7

Hi Bunuel,

I believe there is a TYPO in statement 1 otherwise it would not be 600-700 level and would be way too easy to eliminate a statement..
statement II gives 2 values of x, one positive and one negative.
I am sure the statement I would tell us some thing about x as + or -..

You are absolutely correct.

Sorry guys. The first statement reads (1) | y| ≤ −3x not (1) y ≤ −3x. Edited.
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Re: What is the value of x? (1) |y| ≤ −3x (2) |5x − 1| = x + 7  [#permalink]

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27 Jul 2017, 09:48
1
1
Bunuel wrote:
What is the value of x?

(1) | y| ≤ −3x
(2) |5x − 1| = x + 7

Hi..

(1) | y| ≤ −3x
Can be eliminated straightway BUT lets find the info it gives..
|y| will ATLEAST be 0, so -3x>0 or x<0
insuff

(2) |5x − 1| = x + 7
Square both sides..
$$|5x-1|^2=(x+7)^2.......25x^2-10x+1=x^2+14x+49......24x^2-24x-48=0$$....
$$x^2-x-2=0..... (x-2)(x+1)=0$$
so x can be 2 or -1
insuff

Combined
x can be 2 or -1..
x<0..

ONLY value that fits in is x=-1
suff

C
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Re: What is the value of x? (1) |y| ≤ −3x (2) |5x − 1| = x + 7  [#permalink]

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27 Jul 2017, 20:04
1. No information on x. Insufficient.
2. x=2 or x=-1. Insufficient

Combined: 2 cannot be an option when combined with a negative since the absolute value of y, which has to be positive, is less than -3x.

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Re: What is the value of x? (1) |y| ≤ −3x (2) |5x − 1| = x + 7  [#permalink]

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28 Jul 2017, 12:56
value of x?
1) |y| <= -3x
not clue about x. Not suff

2) solving equation with abs value; we get two values of x = 2 and -3/2
1) + 2) we have no singular value
so E.
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Re: What is the value of x? (1) |y| ≤ −3x (2) |5x − 1| = x + 7  [#permalink]

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29 Jul 2017, 07:13
value of x?
1) |y| <= -3x
not clue about x. Not suff

2) solving equation with abs value; we get two values of x = 2 and -3/2
1) + 2) we have no singular value
so E.

Hey Madhavi1990 Statement 1 tells us that x <= - |y|/3
This means that x can only be negative - As |y|/3 can only be positive and thus x MUST be negative.
When statement 2 gives us two values - -ive and +ive we can eliminate the +ive value.

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Re: What is the value of x? (1) |y| ≤ −3x (2) |5x − 1| = x + 7   [#permalink] 29 Jul 2017, 07:13
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# What is the value of x? (1) |y| ≤ −3x (2) |5x − 1| = x + 7

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