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Bunuel
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What is the value of |x + 4| + x? (1) x ≤ −4 (2) |x + 4| = 0 10 Feb 2021, 01:15
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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75% (hard)

Question Stats:

46% (01:29) correct 54% (01:26) wrong based on 204 sessions

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What is the value of \(|x+4|+x\)?

(1) \(x ≤ −4\)

(2) \(|x+4| = 0\)


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D
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What is the value of |x + 4| + x? (1) x ≤ −4 (2) |x + 4| = 0 11 Feb 2021, 01:30
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Bunuel
What is the value of \(|x+4|+x\)?

(1) \(x ≤ −4\)

(2) \(|x+4| = 0\)


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What is the value of |x+4|+x?

(1) x ≤ −4 --> x + 4 ≤ 0, thus |x + 4| = -(x + 4). Therefore |x + 4| + x = -(x + 4) + x = -4. Sufficient.

(2) |x+4| = 0 --> x = -4 --> |x + 4| + x = 0 - 4 = -4. Sufficient.

Answer: D.
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What is the value of |x + 4| + x? (1) x ≤ −4 (2) |x + 4| = 0 Updated on: 11 Feb 2021, 07:01
Originally posted by TarunKumar1234 on 10 Feb 2021, 11:58.
Last edited by TarunKumar1234 on 11 Feb 2021, 07:01, edited 1 time in total.
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What is the value of |x+4|+x?

Stat1: x≤−4; then, |x+4| ≤0, so, expression: -x-4+x= -4 Sufficient.

Stat2: |x+4|=0; x= -4, then |x+4|+x can be calculated. Sufficient.

So, It is D. :)
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What is the value of |x + 4| + x? (1) x ≤ −4 (2) |x + 4| = 0 10 Feb 2021, 18:29
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Statement1-

x+4 is non-positive; Hence, |x+4| = -(4+x)

\(|x+4|+x\) = -(4+x)+x = -4-x+x = -4

Sufficient

Statement 2-

x=-4

\(|x+4|+x\) = -4+4-4 = -4

Sufficient



Bunuel
What is the value of \(|x+4|+x\)?

(1) \(x ≤ −4\)

(2) \(|x+4| = 0\)


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What is the value of |x + 4| + x? (1) x ≤ −4 (2) |x + 4| = 0 10 Feb 2021, 20:43
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What is the value of |x+4|+x?

(1) x≤−4
x = -5
|-5+4| + (-5)
= -4

x = -8
|-8+4| + (-8)
= -4
Sufficient

(2) |x+4|=0
x = -4
|x+4|+x
= 0 - 4
= -4

Sufficient

Option D

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What is the value of |x + 4| + x? (1) x ≤ −4 (2) |x + 4| = 0 11 Feb 2021, 01:10
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What is the value of \(|x+4|+x\)?

Statement 1

\(x≤−4\)

The value of X can be anything like -5, -6 etc
So the value of |x+4|+x will keep on fluctuating.

Not Sufficient.

Statement 2

\(|x+4|=0\)

\(x=-4.\\
\)

Sufficient.

On substituting the value of x in the equation |x+4|+x, we will get the value of the equation.

The OA is B.
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What is the value of |x + 4| + x? (1) x ≤ −4 (2) |x + 4| = 0 11 Feb 2021, 02:24
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a) If x > -4

Value of expression = 2x + 4

b) If x < -4

Value of expression = -(x + 4) + x = -4

(1) is sufficient because since x =< -4, we know that value of expression = -4

(2) is suffficient because it says that x = -4. Here also, value of expression = -4

So, D.
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What is the value of |x + 4| + x? (1) x ≤ −4 (2) |x + 4| = 0 27 Nov 2023, 09:32
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Bunuel
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What is the value of \(|x+4|+x\)?

(1) \(x ≤ −4\)

(2) \(|x+4| = 0\)


Project DS Butler Data Sufficiency (DS3)


For DS butler Questions Click Here

What is the value of |x+4|+x?

(1) x ≤ −4 --> x + 4 ≤ 0, thus |x + 4| = -(x + 4). Therefore |x + 4| + x = -(x + 4) + x = -4. Sufficient.

(2) |x+4| = 0 --> x = -4 --> |x + 4| + x = 0 - 4 = -4. Sufficient.

Answer: D.
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Hi,

here we are not given if X is an integer and the answer when using a fraction is not -4, then how can we say that 1 is sufficient? Am I missing/miscalculating something?
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Bunuel
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What is the value of |x + 4| + x? (1) x ≤ −4 (2) |x + 4| = 0 27 Nov 2023, 09:44
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kapoor6295
Bunuel
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What is the value of \(|x+4|+x\)?

(1) \(x ≤ −4\)

(2) \(|x+4| = 0\)


Project DS Butler Data Sufficiency (DS3)


For DS butler Questions Click Here

What is the value of |x+4|+x?

(1) x ≤ −4 --> x + 4 ≤ 0, thus |x + 4| = -(x + 4). Therefore |x + 4| + x = -(x + 4) + x = -4. Sufficient.

(2) |x+4| = 0 --> x = -4 --> |x + 4| + x = 0 - 4 = -4. Sufficient.

Answer: D.

Hi,

here we are not given if X is an integer and the answer when using a fraction is not -4, then how can we say that 1 is sufficient? Am I missing/miscalculating something?
Show more

Your concern about x needing to be an integer is not necessary for this problem. The solution works for any real value of x, including fractions. This is because the solution's validity is based on the handling of the absolute value function and the inequality, rather than on x being an integer or a fraction. Moreover, the solution doesn't specifically assume or mention that x should be an integer; it uses a general approach applicable to all real numbers. To see this in practice, you can try the solution with fractional values like -4.5 or -7.2, or any non-integer value of x less than -4. In each case, you'll find that |x + 4| + x still equals -4.
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