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Is m > 0? (1) mn = 15 (2) m + n = 8

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Is m > 0? (1) mn = 15 (2) m + n = 8  [#permalink]

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New post 01 Feb 2020, 18:46
1
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A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

83% (01:07) correct 17% (00:40) wrong based on 23 sessions

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Re: Is m > 0? (1) mn = 15 (2) m + n = 8  [#permalink]

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New post 01 Feb 2020, 18:49
(1) mn= 15 or any positive number
it shows either both m and n are positive or both m and n are negative
NOT Sufficient
(2) m + n= 8 or any positive number
It shows at least one of m and n is positive
NOT Sufficient

Combining Statements 1 & 2, we get both m and n are positive, hence SUFFICIENT

Answer C
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Re: Is m > 0? (1) mn = 15 (2) m + n = 8  [#permalink]

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New post 01 Feb 2020, 19:10
1) If m=-3 and n=-5, then m=-3<0. However, if m=3 and n=5, then m=3>0. Therefore, this statement is clearly insufficient.
2) If m=-4 and n=12, then m=-4<0. However, if m=4 and n=4, then m=4>0. Therefore, this statement is clearly insufficient.
1)+2)
from 2): n=8-m. Plugging this equation into 1)
m(8-m)=15
m^2-8m+15=0
(m-3)(m-5)=0
here m=3 or m=5. In either case m>0. Sufficient.
Answer: C
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Re: Is m > 0? (1) mn = 15 (2) m + n = 8  [#permalink]

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New post 01 Feb 2020, 19:32
is m > 0?

(1) mn= 15
(2) m + n= 8

(1) mn = 15

When m=5 , n=3 , then m*n = 15 and m>0
when m=-5, n=-3 , then m*n = 15 and m<0

Option A not sufficient.

(2) m+n = 8
when m=4,n=4 , then m+n = 8 and m >0
when m = -1 , n = 9, then m+n=8 and m<0

Option B is not sufficient

Consider (1) + (2)
m*n = 15 and m+n = 8

Only possible option to satisfy both condition is M=5,N=3 or M=3,N=5 and in both the case m > 0

Option (C) is the answer

Ans C
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Re: Is m > 0? (1) mn = 15 (2) m + n = 8  [#permalink]

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New post 01 Feb 2020, 20:18
Qs: is m > 0?

(1) mn= 15

no information on sign of m & n, both can be negative or positive.
m=3, n= 5 then mn= 15, so m is positive , hence m>0
if m =-3, n=-5, then mn= 15 but m is negative hence m<0
not sufficient to answer the question.

(2) m + n= 8

this state that at-least one of the variable is positive but which one is not clear. or m can be zero also.
if m = 2, n=6 then m+n= 8 and m is positive
m =-2, n= 10, then m+n= 8 and m is negative. not sufficient to answer the question.

combining, we know from statement -2 that at-least one will be positive and from statement -1, that both should be of same sign. therefore both the variable are positive in sign.

therefore m>0 is possible to determine.

Answer is C.
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Re: Is m > 0? (1) mn = 15 (2) m + n = 8  [#permalink]

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New post 01 Feb 2020, 20:20
Is m > 0?

(1) mn= 15
(2) m + n= 8

1) m can be any negative number and in that case if n is also is a negative number, mn can still be equal to an positive number. not sufficient.

2) same as 1, for any negative value of m, n can still cover so that their sum equals to 8. not sufficient.

together, the negative number can be either m or n, which cannot be determined from the information given. not sufficient.

E is the answer.
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Re: Is m > 0? (1) mn = 15 (2) m + n = 8  [#permalink]

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New post 01 Feb 2020, 21:47
m>0?

Type : Y/N

Statement 1: mn=15
m=3 n=5 gives us Y
m=-3 n=-5 gives us N.

Statement 2: m+n=8
m=3 n=5 gives us Y
m=-5 n=13 gives us N.

Combined:
mn=15
m+n=8 Therefore n=8-m

Substituting n=8-m in mn=15

m(8-m)=15
Gives us a quadratic equation which gives us 2 values of m as 3 and 5. Both are greater than 0.

Answer C
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Re: Is m > 0? (1) mn = 15 (2) m + n = 8  [#permalink]

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New post 01 Feb 2020, 22:08
Statement 1: mn=15

m=-3, n=-5 or m=3,n=5 so in any of the cases we cannot say for sure if m>0, it could be -1,1 -3,3,-5,5,15,-15.

Not Sufficient.

Statement 2: m+n = 8

Here again, since sum is even, so both m and n are either odd or both are even, so some of the possible combinations could be:

-2+10 = 8,
3+5 = 8
and etc.
So we cannot say for sure, if m > 0. So

Insufficient.

If we combine the 2, we get 2 values of n = 3 and 5, in both cases m will be >0. So,

Answer will be C.
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Re: Is m > 0? (1) mn = 15 (2) m + n = 8  [#permalink]

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New post 01 Feb 2020, 22:34
(1) or (2) alone is clearly insufficient.

Both together though are sufficient:
(1) mn=15: m and n must have same sign (positive or negative)
(2) m+n=8: can the sum of two negative (says -3 and -5) be postive?
Nah, therefore m>0 always
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Re: Is m > 0? (1) mn = 15 (2) m + n = 8  [#permalink]

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New post 02 Feb 2020, 01:15
is m > 0?

(1) mn= 15
(2) m + n= 8
#1
mn= ( 3,5) ( -3,-5) ( 15,1) ( 45,1/3) insufficient
#2
m+n = 8
( 8,0) ( 7,1) ( 3,5) .. insufficient
from 1 &2
m,n = 3,5 sufficient
IMO C
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Re: Is m > 0? (1) mn = 15 (2) m + n = 8   [#permalink] 02 Feb 2020, 01:15

Is m > 0? (1) mn = 15 (2) m + n = 8

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