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DS (Inequality)

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DS (Inequality)

by rintoo22 » Sat Mar 23, 2013 7:30 am
Q If |n + 5| = 5, what is the value of n?
(1) n^2 is not equal to 0.
(2) n^2 + 10n = 0

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.


To simplify the main equation
n+5 = 5 => n=0 ---- 1
-n-5 = 5 => -n=10 => n=-10 ------ 2

According to Statement 1, it satifies the 2. So it should be sufficient
According to statement 2, it satisfies both 1 and 2. So it should be sufficient.

Therefore in my opinion answer should be D. However answer is A. Kindly guide....
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by Brent@GMATPrepNow » Sat Mar 23, 2013 7:38 am
rintoo22 wrote:Q If |n + 5| = 5, what is the value of n?
(1) n^2 is not equal to 0.
(2) n^2 + 10n = 0
Target question: What is the value of n?

Given: |n + 5| = 5
This tells us that n = 0, or n = -10
Great, now we're looking for information that helps us determine whether n = 0 or -10

Statement 1: n^2 is not equal to 0.
This means that does not equal 0
Since n = either 0 or -10, we can now be certain that n = -10
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: n^2 + 10n = 0
Factor to get: n(n+10) = 0
This means that n = 0, or n = -10
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

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by Anju@Gurome » Sat Mar 23, 2013 7:58 am
rintoo22 wrote:According to statement 2, it satisfies both 1 and 2. So it should be sufficient.
When a data sufficiency problem asks for a value of a variable, we need to look for a definite value; one single value.

In this case, as per statement 2, there are two possible values of n.
Hence, statement 2 is not sufficient.
rintoo22 wrote:Q If |n + 5| = 5, what is the value of n?
(1) n² is not equal to 0.
(2) n² + 10n = 0
|n + 5| = 5
Hence, distance of n from -5 on the number line is 5.
So, n must be equal to either -10 or 0.

Statement 1: This means n is not equal to 0.
Hence, n must be equal to -10.

Sufficient

Statement 2: n² + 10n = n(n + 10) = 0
So, either n = 0 or (n + 10) = 0
--> either n = 0 or n = -10

Not sufficient

The correct answer is A.
Anju Agarwal
Quant Expert, Gurome

Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.

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