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# If m ≠ 0 and n ≠ 0, is mn > 0? (1) |m + n| = k (2) |m| + |n| = k

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If m ≠ 0 and n ≠ 0, is mn > 0? (1) |m + n| = k (2) |m| + |n| = k  [#permalink]

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Updated on: 15 Mar 2019, 00:13
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If $$m \neq 0$$ and $$n \neq 0$$, is mn > 0?

(1) |m + n| = k

(2) |m| + |n| = k

Weekly Quant Quiz #7 Question No 4

_________________

Originally posted by gmatbusters on 03 Nov 2018, 10:07.
Last edited by Bunuel on 15 Mar 2019, 00:13, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If m ≠ 0 and n ≠ 0, is mn > 0? (1) |m + n| = k (2) |m| + |n| = k  [#permalink]

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03 Nov 2018, 10:26
1
If m≠0≠0and n≠0≠0, is mn > 0?
1) |m+n|=k
2) |m|+|n|=k

SInce m and does not equal to 0, we are basically asked whehter m and n have the same sign.

1.
Taking values since k can be any value.
5,3
-5,3

2.
Since k can be any value,
same examples can be applied
5,3
5,-3

Combing the statements.
We know:
|m+n|= |m|+|n|

IN this canse m and n have to have the same sign.
5.3: 8=8
5,-3: 2 does not equal to 8

Hence both of them can be either be positive or be negative.

Hence, Ans C
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Re: If m ≠ 0 and n ≠ 0, is mn > 0? (1) |m + n| = k (2) |m| + |n| = k  [#permalink]

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03 Nov 2018, 10:29
1
If m≠0. and n≠0
is mn > 0?
1) |m+n|=k
2) |m|+|n|=k

Option A: |m+n|= k
as absolute value is >0 so K>0

now m+n can either be positive or negative but absolute will always be positive , hence (m can be positive , n can be positive) or (m can be -ve and n can be +ve) or (m as -ve, n as -ve)

hence A is not sufficient

Option B:
|m|+|n| = k, again absolute is positive so K is positive
again m and n can be anything any one of the above 3 posibilities

hence B is not sufficient

Combine A and B, both are sufficient only when both are either positive or negative .

to illustrate lets say case 1(m =2 , n =3 ), case 2(m =-2 , n =-3 ), case 3(m =2 , n =-3 ), case 4(m =-2 , n =3 )
case 1, |m +n|= 5= k and |m| +|n| = 5= k so satisfies both options
case 2, |m+n|= |-5|= 5=k and |m|+|n|= |-2|+|-3|=5=k satisfies both options

case 3, |m+n| = |2-3|=1=k and |m|+|n|=|2|+|-3|= 5= k and hence k has 2 values
case 4, |m+n| = |-2+3|=1=k and |m|+|n|=|-2|+|3|= 5= k and hence k has 2 values

so only in case 1 and case 2 both options are valid and in each of the case mn>0

hence C is the answer
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Re: If m ≠ 0 and n ≠ 0, is mn > 0? (1) |m + n| = k (2) |m| + |n| = k  [#permalink]

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03 Nov 2018, 10:35
Ans is c) both Are TOgether Sufficient as given |m+n|=|m|+|n|
so either both are negative or both are positive so that when we add them their magnitude is equal
so when same sign are m,ultiplied the we get mn>0
Re: If m ≠ 0 and n ≠ 0, is mn > 0? (1) |m + n| = k (2) |m| + |n| = k   [#permalink] 03 Nov 2018, 10:35
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# If m ≠ 0 and n ≠ 0, is mn > 0? (1) |m + n| = k (2) |m| + |n| = k

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