Is |n| 5? (1) |n+5| = 4 (2) |n+1| 0

Question

Is |n| > 5?

(1) |n+5| = 4
(2) |n+1| > 0

Bunuel · Answer

Is |n| > 5?

(1) |n+5| = 4:

n + 5 = 4 or n + 5 = -4
n = -1 or n = -9.
If n = -1, then |n| < 5 but if n = -9, then |n| > 5.

Not sufficient.

(2) |n + 1| > 0:

Since the absolute value is always more than or equal to 0, then the above statement simply means that |n + 1| ≠ 0, so n ≠ -1. Clearly insufficient to say whether |n| > 5.

(1)+(2) From (2), we got that n ≠ -1, thus we are left only with n = -9, from (1), and thus |n| > 5. Sufficient.

Answer: C.

101Gmatguru · Answer

Bunuel  So for any inequality in the form of |n+1| > 0, it is implied that n is not equal to -1

Similarly, for |n+3| > 0, it is implied that n is not equal to -3.

Also, for |n-3| > 0, is it implied that n is not equal to 3?

av1901 · Answer

Yes, you are right in making this implication. And if you wonder how come we came to this, we can arrive using the property of modulus and inequality
Let us see how

|n+1| > 0

So entire expression of modulus is always greater than 0 but what's inside the modulus can be both greater than 0 or less than 0

If expression inside modulus is > 0, then it remains as it is, else it changes signs to negative
For eg. If x=5, |x| = x but if x=-5, |x| = -x

Similarly let us test both cases

Case 1: n+1 is positive
n + 1 > 0
n > -1

Case 2: n+1 is negative
-n - 1 > 0
n < - 1

So entire range of n is either greater than -1 or less than -1
Which implies that n is not equal to -1

Posted from my mobile device

Is |n| > 5? (1) |n+5| = 4 (2) |n+1| > 0

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions