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# If m ≠ 0 and n ≠ 0, is mn > 0?

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Math Expert
Joined: 02 Sep 2009
Posts: 54375
If m ≠ 0 and n ≠ 0, is mn > 0?  [#permalink]

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29 Apr 2016, 03:56
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Question Stats:

68% (01:09) correct 32% (01:30) wrong based on 163 sessions

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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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Math Expert
Joined: 02 Aug 2009
Posts: 7563
Re: If m ≠ 0 and n ≠ 0, is mn > 0?  [#permalink]

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29 Apr 2016, 04:08
1
1
Bunuel wrote:
If m ≠ 0 and n ≠ 0, is mn > 0?

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

WHAT does the Q asks us? -- is mn>0?
mn will be >0 ONLY if both m and n are of SAME sign- both positive or both negative.

lets check the statements-

(1) |m + n| = k
We cannot say anything except that k is NOT negative
Insuff

(2) |m| + |n| = k
same as statement I
Insuff

combined
we can say |m+n|=|m|+|n|..
this is possible ONLY if both m and n are of SAME sign..

|m|+|n| will always be SUM of numeric value of m and n..
But |m+n|will depend on the numeric value as also the sign..
If both are different signs, it will become a lesser numeric value..

say m= 4 and n=-5..
|m|+|n| = 4+5=9.. BUT |m+n|=|4-5|=1..
so both m and n are of same sign and hence mn>0..
Suff
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Re: If m ≠ 0 and n ≠ 0, is mn > 0?  [#permalink]

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29 Apr 2016, 05:36
|m+n| = |m| + |n| if and only if both m and n are positive numbers
--> E
Math Expert
Joined: 02 Aug 2009
Posts: 7563
Re: If m ≠ 0 and n ≠ 0, is mn > 0?  [#permalink]

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29 Apr 2016, 05:41
deabas wrote:
|m+n| = |m| + |n| if and only if both m and n are positive numbers
--> E

Hi,

|m+n| = |m| + |n| even if both m and n are NEGATIVE numbers..
example let m =-4 and n = -7...
|m+n| = |-4-7| = |-11| =11..
|m|+|n| = |-4|+|-7| = 4+7 = 11..
so |m+n| = |m| + |n|
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Re: If m ≠ 0 and n ≠ 0, is mn > 0?  [#permalink]

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29 Apr 2016, 06:03
chetan2u wrote:
deabas wrote:
|m+n| = |m| + |n| if and only if both m and n are positive numbers
--> E

Hi,

|m+n| = |m| + |n| even if both m and n are NEGATIVE numbers..
example let m =-4 and n = -7...
|m+n| = |-4-7| = |-11| =11..
|m|+|n| = |-4|+|-7| = 4+7 = 11..
so |m+n| = |m| + |n|

You are right chetan2u.. it was a silly mistake made by me... thank you for the correction.
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Re: If m ≠ 0 and n ≠ 0, is mn > 0?  [#permalink]

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03 Aug 2017, 08:12
1
Bunuel wrote:
If m ≠ 0 and n ≠ 0, is mn > 0?

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

Given : m ≠ 0 and n ≠ 0
DS : mn > 0 which means wither m>0 and n>0 OR m<0 and n<0

Statement 1: |m + n| = k
We can't say anything about m and n . m>0 or m<0 AND n>0 or n<0
NOT SUFFICIENT

Statement 2: |m| + |n| = k
We can't say anything about m and n . m>0 or m<0 AND n>0 or n<0
NOT SUFFICIENT

Combined : Both |m + n| = k & |m| + |n| = k
So, either both m>0 and n>0 OR m<0 and n<0.

SUFFICIENT

Answer C
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Re: If m ≠ 0 and n ≠ 0, is mn > 0?  [#permalink]

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13 Aug 2017, 20:28
chetan2u wrote:
Bunuel wrote:
If m ≠ 0 and n ≠ 0, is mn > 0?

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

WHAT does the Q asks us? -- is mn>0?
mn will be >0 ONLY if both m and n are of SAME sign- both positive or both negative.

lets check the statements-

(1) |m + n| = k
We cannot say anything except that k is NOT negative
Insuff

(2) |m| + |n| = k
same as statement I
Insuff

combined
we can say |m+n|=|m|+|n|..
this is possible ONLY if both m and n are of SAME sign..

|m|+|n| will always be SUM of numeric value of m and n..
But |m+n|will depend on the numeric value as also the sign..
If both are different signs, it will become a lesser numeric value..

say m= 4 and n=-5..
|m|+|n| = 4+5=9.. BUT |m+n|=|4-5|=1..
so both m and n are of same sign and hence mn>0..
Suff

Hi chetan2u,
C was apparent but I fell in the trap that Bunuel won't give such a straight forward Q. Can you pls guide me where is the mistake in B.

|m|+|n|=K
Sq both sides & expanding we get 2|m||n|=K^2-(m^2-n^2)
or |m||n|>=0, hence both m & n should be of the same sign????!!!

Thanks
Re: If m ≠ 0 and n ≠ 0, is mn > 0?   [#permalink] 13 Aug 2017, 20:28
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# If m ≠ 0 and n ≠ 0, is mn > 0?

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