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Difficulty:
65%
(hard)
Question Stats:
42% (01:00) correct
58%
(00:52)
wrong
based on 863
sessions
History
Date
Time
Result
Not Attempted Yet
Is \(m \lt 0\)?
(1) \(-m = |-m|\)
(2) \(m^2 = 9\)
(1) \(-m = |-m|\)
(2) \(m^2 = 9\)
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Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
https://gmatclub.com/forum/data-sufficiency-ds-141/
https://gmatclub.com/forum/data-sufficiency-ds-141/
Official Solution:
Is \(m \lt 0\)?
(1) \(-m=|-m|\).
Firstly, \(|-m|=|m|\), (for example: \(|-3|=|3|=3\)), so we can rewrite the statement as \(-m=|m|\). Since \(|x| = -x\) when \(x \leq 0\), then \(-m=|m|\) implies \(m \leq 0\). Therefore, \(m\) could be either negative, giving a YES answer to the question, or zero, giving a NO answer to the question. This statement is not sufficient.
(2) \(m^2=9\).
The above implies that either \(m=3\) (positive) or \(m=-3\) (negative). This information alone is not sufficient to answer the question.
(1)+(2) We know from (1) that \(m \leq 0\), and from (2) we have two possibilities: \(m=3\) or \(m=-3\). Since \(m \leq 0\), we can eliminate \(m=3\), leaving us with \(m=-3\), which is negative. Thus, the answer to the question "is \(m \lt 0\)" is YES. Sufficient.
Answer: C.
Hope it's clear.
_________________
Is \(m \lt 0\)?
(1) \(-m=|-m|\).
Firstly, \(|-m|=|m|\), (for example: \(|-3|=|3|=3\)), so we can rewrite the statement as \(-m=|m|\). Since \(|x| = -x\) when \(x \leq 0\), then \(-m=|m|\) implies \(m \leq 0\). Therefore, \(m\) could be either negative, giving a YES answer to the question, or zero, giving a NO answer to the question. This statement is not sufficient.
(2) \(m^2=9\).
The above implies that either \(m=3\) (positive) or \(m=-3\) (negative). This information alone is not sufficient to answer the question.
(1)+(2) We know from (1) that \(m \leq 0\), and from (2) we have two possibilities: \(m=3\) or \(m=-3\). Since \(m \leq 0\), we can eliminate \(m=3\), leaving us with \(m=-3\), which is negative. Thus, the answer to the question "is \(m \lt 0\)" is YES. Sufficient.
Answer: C.
Hope it's clear.
_________________
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Thanks so much Bunuel.
Posts: 1
Bunuel ,i love youuuuuuuuuuuuuuuuuuuu!!!!!!!
gurpreetsingh
Joined: 12 Oct 2009
Last visit: 15 Jun 2019
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Products:
very nicely explained by Bunnel.
The tricky part here was the consideration of zero.
While dealing with these type of DS questions always consider scenario of -ve, 0 ,and +ve numbers.
The tricky part here was the consideration of zero.
While dealing with these type of DS questions always consider scenario of -ve, 0 ,and +ve numbers.
amlandutta007
It is not an uncommon reply to Bunuels posts
You can kindly give Bunuel Kudos (there is a button for that)
P.S. You can also "Follow" bunuel (you will get daily summaries of his posts) so you don't miss any wisdom. There is a follow button next to his name.
_________________
Good work Bunuel. I missed the zero consideration too!
Posts: 164
The answer is C but I also missed the Zero part.
As Bunuel says ZIP code
As Bunuel says ZIP code
samramandy
Bunuel,
Bestow your legendary wisdom upon this mortal, so that he too can know what ZIP code is.
P.S. M assuming Z - zero...whats the rest
eaakbari
ZIP - Zero, Integers, Positive numbers.
GMAT likes to act in -1<=x<=1 range. So:
Don't assume, with no ground for it, that variable cannot be Zero. Check 0!
Don't assume, with no ground for it, that variable is an Integer. Check fractions!
Don't assume, with no ground for it, that variable is Positive. Check negative values!
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pra1785
-0 = 0 and |-0| = |0| = 0, so if M = 0, then -M = 0 = |-M|.
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