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# Is n<0?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8001
GMAT 1: 760 Q51 V42
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29 Jan 2018, 04:29
00:00

Difficulty:

45% (medium)

Question Stats:

67% (01:45) correct 33% (02:12) wrong based on 76 sessions

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[GMAT math practice question]

Is $$n<0$$?

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

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Senior Manager Joined: 17 Oct 2016 Posts: 314 Location: India Concentration: Operations, Strategy GPA: 3.73 WE: Design (Real Estate) Re: Is n<0? [#permalink] ### Show Tags 29 Jan 2018, 04:37 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 _________________ Help with kudos if u found the post useful. Thanks Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8001 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Is n<0? [#permalink] ### Show Tags 31 Jan 2018, 02:49 => 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. Therefore, B is the answer. 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. Answer: B _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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31 Jan 2018, 12:46
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, 13:04
3
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, 13:04
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