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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7372
GMAT 1: 760 Q51 V42 GPA: 3.82
M60-16  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 50% (01:33) correct 50% (01:58) wrong based on 6 sessions

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Is $$n < 0$$?

1) $$n - 1 < 0$$

2) $$|3 - n| > |n + 5|$$

_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7372
GMAT 1: 760 Q51 V42 GPA: 3.82
Re M60-16  [#permalink]

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Official Solution:

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) :

$$|3-n| > |n+5|$$

⇔ $$|3-n|^2 > |n+5|^2$$

⇔ $$(3-n)^2 > (n+5)^2$$

⇔ $$n^2 -6n + 9 > n^2+10n + 25$$

⇔ $$-16 > 16n$$

⇔ $$n < -1$$

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
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Intern  B
Joined: 08 Jul 2018
Posts: 3
Re: M60-16  [#permalink]

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In this question and the next, why is it that similar method or solving is giving contradictory results for statement 1?
Manager  B
Joined: 07 Apr 2018
Posts: 104
Location: United States
Concentration: General Management, Marketing
GPA: 3.8
M60-16  [#permalink]

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MathRevolution wrote:
Official Solution:

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) :

$$|3-n| > |n+5|$$

⇔ $$|3-n|^2 > |n+5|^2$$

⇔ $$(3-n)^2 > (n+5)^2$$

⇔ $$n^2 -6n + 9 > n^2+10n + 25$$

⇔ $$-16 > 16n$$

⇔ $$n < -1$$

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

should we always take the square of the mod on both side of an inequality? if the value of the mod is less than 1 and greater than 0 M60-16   [#permalink] 26 Mar 2019, 18:00
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