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Retired Moderator V
Joined: 27 Oct 2017
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WE: General Management (Education)

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Question Stats: 74% (01:09) correct 26% (01:00) wrong based on 41 sessions

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GMATBusters’ Quant Quiz Question -1

Is m-n > 0?
1) m^2 > n^2
2) n < 0

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Retired Moderator V
Joined: 27 Oct 2017
Posts: 1786
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Re: Is m-n > 0?  [#permalink]

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The official solution is as follows: Attachment: WhatsApp Image 2020-02-03 at 6.49.55 PM.jpeg [ 78.88 KiB | Viewed 272 times ]

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Re: Is m-n > 0?  [#permalink]

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1) m^2>n^2
if m=4 and n=-3, then m^2=16>n^2=9. and m-n=7>0
However, if m=-4 and n=-3, then m^2=16>n^2=9. and m-n=-1<0
Clearly, this statement is insufficient.
2) In the case above, n<0 in both cases. Therefore, it follows that this statement is also insufficient.
1)+2) Because of the explanation in 2), both statements together are insufficient as well
Senior Manager  P
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Re: Is m-n > 0?  [#permalink]

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m-n > 0 ?

1) $$M^2 > n^2$$
possible values are
1. Both positive - m=3 , n=2 , then $$m^2 > n^2$$ and this gives m-n > 0 ? as Yes
2. Both negative - m=-3 , n = -2 , this gives $$m^2 > n^2$$ and m-n < 0? as No

Two different answers, so Option 1 not sufficient.

2) N < 0
This option does not give any information about M. Hence insufficient.

Lets try (1) + (2)
Lets consider both n <0 and $$m^2 > n^2$$

Lets plug in below given values
1) m=-3 , n = -2 , this gives $$m^2 > n^2$$. M-N < 0 ? = No
2) m=-1 , n = -2 , this gives $$m^2 > n^2$$. M-N < 0 ? = Yes
Two different solution. Hence C is insufficient.

Ans: E
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Re: Is m-n > 0?  [#permalink]

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the given inequality m - n> 0 can be modified into m>n ?

st-1:m^2>n^2
this can be written as |m| > |n| which means that m & n can take multiple values (positive or negative) which will satisfy the given condition.
this not sufficient to determine which variable is greater.

st 2: n<0
there is no information about m. hence not sufficient.

combining the two statement, no concrete information can be made. the following cases are possible,
|m| > |n| & n<0
if n= -1 and m= -2 then |m| > |n| becomes |-2| > |-1| but m<n
if n=-1 and m =6 then |m| > |n| becomes |6| > |-1| but m>n
so different case are possible hence it is not possible to determine the unique case. hence insufficient.
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GMAT 1: 600 Q46 V27 Re: Is m-n > 0?  [#permalink]

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Question : m>n?

Type : Y/N

Statement 2 : n<0

Not Sufficient.

We are left with A,C and E.

Statement 1: m^2>n^2

m=2 n=-1 gives us a Yes.
m=-2 n=-1 gives us a No.
Not Sufficient.

We are left with C and E.

Combined:
m^2>n^2
n<0

n=-1 m=2 gives us Yes.
n=-2 m=-3 gives us No.

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Intern  B
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Re: Is m-n > 0?  [#permalink]

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Is m-n > 0?
1) m^2 > n^2
2) n < 0

1) This tells us that |m| is greater that |n|. So, if m>0, m-n will >0. However, that is not provided, so Not Sufficient
2) This tell us that at least one of the two numbers is less than 0, however, it says nothing about m, so Not Sufficient
1&2) statement one told us that if m>0, then m-n>0. Statement 2 told us that n<0. However, it doesn't tell us about m. so Not sufficient.

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Re: Is m-n > 0?  [#permalink]

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Is m-n > 0?
1) m^2 > n^2
2) n < 0

From 1) |m| > |n| -> m > n i.e. m-n > 0 when m>0; m < -n i.e. m+n < 0 when m<0 ---> Not sufficient

From 2) n < 0 ---> Not sufficient

Combining 1) and 2) ---> we know m-n will be possible to know only when we know sign of m, sign of n doesn't affect (m-n) or (m+n)..

we can prove by numbers m = 6, n = -5 --> n < 0, |m| > |n|, m -n = 11 > 0; m= -6, n = -5 --> |m| > |n|, m-n = -1 < 0

Hence not sufficient.
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Re: Is m-n > 0?  [#permalink]

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Is m-n > 0?
1) m^2 > n^2
2) n < 0

(1), m^2 > n^2 => m^2-n^2 >0 => (m+n) (m-n)>0
Lets put some values of m & n
m=4, n=2, 6*2>0
m=-4, n=2, -2*-6>0
m=-4,n=-2, -6*-2>0
m=4, n=-2, 2*6>0....So we really kind decide whether really m-n>0. INSUFFICIENT
(2) n<0 that means n is a negative number (may be integer or non-integer). Dont know anything else regarding m. INSUFFICIENT.

(1)+(2) in the equation, (m+n)(m-n)>0 => (m-n)(m+n)>0 (where n=-n), we dont know about m. INSUFFICIENT.

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Manager  S
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Re: Is m-n > 0?  [#permalink]

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Statement 1: m^2 > n^2
(m+n)(m-n)>0

for m-n>0 the m+n needs to be +ve, here we know nothing about m and n. Insufficient

Statement 2: n<0, insufficient, since nothing is mentioned about m, could be positive or negative.

Now, combining both the statements:
if m is +ve, n is -ve, and m>n, number wise without sign then m-n is > 0, but if n is a greater number in negative then m-n< 0.
if m is also -ve, m-n will be <0,

So without any information about m, we cannot say for sure, if m-n > 0
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Re: Is m-n > 0?  [#permalink]

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#1
m^2 > n^2
test with m=+/-2 and n = +/-1 we get yes and no insufficient
#2
n<0
m not know insufficient
from 1 &2
for n being -ve , if m is +ve then yes and if m is -ve then no
IMO E; sufficient

Is m-n > 0?
1) m^2 > n^2
2) n < 0
Senior Manager  P
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Re: Is m-n > 0?  [#permalink]

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Is m-n > 0?
rephrasing Is m>n?

1) m^2 > n^2
taking square root on both the sides
|m| > |n|
Sign of m and n is unknown
Insufficient

2) n < 0
m can be negative or positive
Insufficient

(1)+(2); Lets take cases
case1: n = -1, m =-2
case2: n = -1, m =2
Insufficient

E is correct
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Senior Manager  P
Joined: 09 Jan 2017
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Location: India
Re: Is m-n > 0?  [#permalink]

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Is m-n > 0?
1) m^2 > n^2
2) n < 0

Rewriting the question as Is m>n?

St 1 -
m^2>n^2

m=-2 n=1----m^2>n^2 -> m>n - NO
m=2 n=1--m^2>n^2 -> m>n - YES

ST 1 not sufficient

St 2
n<0
no information about m, mcould be +ve, in that case m>n - YES
m could be much negative than n, in that case m>n - NO

combiningly
m^2>n^2 & n<0
m=-2 n=-1 -> m>n - NO
m=-1 n=-0.5 m>n - YES

together not sufficient Re: Is m-n > 0?   [#permalink] 02 Feb 2020, 05:32

# Is m-n > 0?  