M60-16

Question

Is  n < 0 ?

1)  n - 1 < 0

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

MathRevolution · Answer

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

Ruminate · Answer

In this question and the next, why is it that similar method or solving is giving contradictory results for statement 1?

HAPPYatHARVARD · Answer

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

gracelfs · Answer

I think this is a  poor-quality  question and I don't agree with the explanation. the question is 'is n<0?'
in the 1st statement we found that n<1, hence the answer to the question would be no No, but the statement give us data that support the answer to the question, so why it is insufficient? isn't the answer D since both statement provide answer to the question?

ArindamLucky · Answer

When we derive that n<1 and in the question it is asked if n<0 
We can't say because n can be -1 ,-2 and n can also be 0.1,0.2 both satisfy n<1 but not n<0

Posted from my mobile device

jscaf · Answer

I think this is a  high-quality  question and the explanation isn't clear enough, please elaborate. Hello, Can you please elaborate on why we square stmt 2? My approach was to break stmt 2 into two (a: when the absolute value is positive for both....3 - n > n + 5 = n < -1 and b: when the absolute value is negative on both sides.....-3 + n > -n - 5 = n > -1). So I selected answer E. Can you please clarify why my approach to stmt 2 is incorrect? Thanks, Jason

amit bawa · Answer

in st-2 only 1 of the absolute term can be negative but not both. try by adding value for n. for example: n=-5.1

anish823 · Answer

I did the same thing and get lost in the process. Would be beautiful if anyone explains the solution proposed

BottomJee · Answer

I think this is a  high-quality  question and I agree with explanation.

M60-16

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