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# Is n<0?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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29 Jan 2018, 03:29
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Difficulty:

35% (medium)

Question Stats:

67% (01:18) correct 33% (01:39) wrong based on 54 sessions

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[GMAT math practice question]

Is $$n<0$$?

$$1) n-1<0$$
$$2) |3-n| > |n+5|$$
[Reveal] Spoiler: OA

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29 Jan 2018, 03:37
B

From statement 1 we have n<1. insufficient

From statement 2 we have (3-n)^2>(n+5)^2

9+n^2-6n>n^2+25+10n
-16>16n
ie n<-1

Sufficient
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31 Jan 2018, 01:49
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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Condition 1) : $$n - 1 < 0 ⇔ n < 1$$
Since the range of the question, n < 0 does not include that of the condition 1), $$n < 1$$, the condition 1) is not sufficient.

Condition 2) :
$$|3-n| > |n+5|$$
$$⇔ |3-n|^2 > |n+5|^2$$
$$⇔ (3-n)^2 > (n+5)^2$$
$$⇔ n^2 -6n + 9 > n2 +10n + 25$$
$$⇔ -16 > 16n$$
$$⇔ n < -1$$
Since the range of the question includes that of the condition 2), the condition 2) is sufficient.

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.

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31 Jan 2018, 11:46
MathRevolution wrote:
[GMAT math practice question]

Is $$n<0$$?

$$1) n-1<0$$
$$2) |3-n| > |n+5|$$

Statement I:

Take $$n = 0, n = \frac{1}{2}$$... So, Insufficient.

Statement II:

From the equation, LHS > RHS.... This is only possible when n is -ve. So, sufficient.
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31 Jan 2018, 12:04
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Expert's post
MathRevolution wrote:
[GMAT math practice question]

Is $$n<0$$?

$$1) n-1<0$$
$$2) |3-n| > |n+5|$$

This is a different approach to statement 2:

Statement 2: |3-n| really just means 'the distance between 3 and n on a number line'.

For example, if n = 2, then |3-n| = |3-2| = |1| = 1. The distance between 3 and 2 on a number line is 1.

If n = 10, then |3-n| = |3-10| = |-7| = 7. And likewise, the distance between 3 and 10 on a number line is 7.

This is just a fact about absolute values of differences.

Similarly, |n + 5| can be read as |n - (-5)|. That makes it the absolute value of a difference. So, you can read this one as 'the distance between n and -5 on a number line'.

That means you can fully translate statement 2 like this:

The distance between n and 3 on a number line, is greater than the distance between n and -5 on a number line.

Or in other words,

n is closer to -5 than it is to 3.

What does that tell you about n? In other words, which numbers are closer to -5 than to 3? Jot down a number line on your paper and start figuring it out.

The numbers to the right of 3 will all be closer to 3, so those don't work:

Now look at the numbers in between -5 and 3:

All of the ones that are closer to -5, are negative numbers.

We can conclude that if a number is closer to -5 than it is to 3, it's definitely got to be a negative number.

That makes statement 2 sufficient.
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Re: Is n<0?   [#permalink] 31 Jan 2018, 12:04
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