Is m^2n + mn^2 = 0 ? : Data Sufficiency (DS)

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14 Jul 2015, 12:57

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Bunuel

Is m^2n + mn^2 = 0 ?

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

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One suggestion for the format:

m^2n for me is something different than m^2 * n

Bunuel

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15 Jul 2015, 00:38

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LaxAvenger

Bunuel

Is m^2n + mn^2 = 0 ?

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

Kudos for a correct solution.

One suggestion for the format:

m^2n for me is something different than m^2 * n

m^2n can only mean m^2 * n. \(m^{2n}\) is written as m^(2n).

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15 Jul 2015, 11:14

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is m^2*n+mn^2=0? this can be simplified to is mn(m+n)=0? This will be the case either m+n=0=>m=-n or either of m and n are 0.

Moving to options:
(1) m+n = 1 =>m is not equal to -n . ALso no information can be deduced for m*n. hence Not Sufficicent
(2) mn =1=> m,n are not equal to 0 and m+n also not equal to 0. Hence m^2*n+mn^2 is not 0 Sufficient

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15 Jul 2015, 21:06

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Bunuel

Is m^2n + mn^2 = 0 ?

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

Kudos for a correct solution.

This is a yes/no data sufficiency problem.

m^2n + mn^2 = 0 can be factored into mn(m+n)=0

1) If m+n=1, it does not prove that the equation is 0. For example, m can be 0 and n can be 1, or vice versa, and the equation is correct. However, 3/4 + 1/4 also fits, and that does not equal 0. Insufficient.

2) If mn=1, then m or n is not 0. Therefore, the equation cannot be 0. Sufficient.

B

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15 Jul 2015, 21:37

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m^2n +mn^2= mn(m+n)
now the questions changes to is mn(m+n)=0

1. m+n =1
so mn(1) can be 0 or can not be 0. Not sufficient

2. mn=1
1(m+n) can not be 0 certainly. Definite No
Sufficient.

SO, B

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1) m+n = 1, taking m= 0, n = 1 => m^2n + mn^2 = 0^2 + 0^2 = 0 Sufficient
2) mn =1 , mn^2 =1, m^2n will never be -ve so m^2n in no case will be -1 so not equal to 0, Sufficient

So the answer is D, EACH statement ALONE is sufficient

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18 Jul 2015, 00:35

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Bunuel

Is m^2n + mn^2 = 0 ?

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

Kudos for a correct solution.

m^2*n + m*n^2 can be written as mn(m+n).
If mn(m+n) should be 0, then mn should be 0 or m+n should be 0.

St 1: given m+n = 1. If m+n != 0 then mn should be equal to 0.
Here there are two cases, m=0, n=1 or m=1/2, n=1/2.

If m=0, n=1, then mn = 0, but if m=1/2, n=1/2, then mn != 0.
Hence Not sufficient.

St 2: given mn =1, Hence neither m nor n is equal to 0.
So, m+n cannot be equal to 0.

Hence the equation, mn(m+n) is not equal to zero.

Sufficient.
Option B

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18 Jul 2015, 06:49

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Bunuel

Is m^2n + mn^2 = 0 ?

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

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Statement 1: m+n=1. Different combinations can exist. 2,1 or 0,1 etc. Insufficient
Statement 2: mn=1. This shows that neither of m or n is 0. Sufficient.
Answer B

Bunuel

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19 Jul 2015, 13:54

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Bunuel

Is m^2n + mn^2 = 0 ?

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

Kudos for a correct solution.

800score Official Solution:

m^2n + mn^2 = mn(m + n)
The formula equals 0 when mn = 0 or m + n = 0.
The statement (1) tells us that m + n = 1. It is not sufficient. If n = 0, m = 1, the equality is TRUE. But if n = 0.5, m = 0.5, it is NOT.

The statement (2) tells us that mn = 1. Therefore the first factor in the formula is not 0. Suppose the second one is. Then m + n = 0
m = -n
mn = -n^2, which is impossible because mn = 1 > 0. Therefore the second factor can NOT equal 0 and the equality is NEVER true. So the statement (2) is sufficient alone to answer the question.

The correct answer is (B).

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19 Jul 2015, 20:22

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mn^2 +m^2n = mn (m+n) = 0
so,
Either m=0. n=0 or m=-n

Stmnt 1) m+n = 1 (Clearly not sufficient)

Stmnt 2) mn = 1 (m or n not equal to 0, m = -n is also not possible)

hence B (Stmnt 2 is sufficient to say mn^2 +m^2n = 0 IS NOT POSSIBLE

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20 Jul 2015, 08:48

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Answer is B as id mn=1, m+1/n is not equal to zero.
As the equation is not equal to 0, B is sufficient

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Reduce given to mn(m+n)

(1) m + n = 1; mn(1) = m*n. m = 1-n
n(1-n) = ?
Insufficient.

(2) m(n) = 1
mn(m+n) = 1 (m+n) = m + n
m = 1/n; n = 1/m: m and n are reciprocals of one another
If you multiply them, they will always equal one. They are also both negative or both positive, since they multiply to a positive 1. We also know that m and n each do not equal 0, otherwise m*n = 0. Adding non-0 reciprocal values will never equal 0. Therefore, m + n does not equal 0. Sufficient.

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14 Mar 2017, 08:46

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Bunuel

Is m^2n + mn^2 = 0 ?

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

Kudos for a correct solution.

This a yes/No question.
If m=0 the statement will be proved.because anything multiplied by zero is zero.
statement 1..m could be 0 or n insufficient.
statement 2 ensures that neither is zero...then it gives direct answer..
B sufficient.

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15 Mar 2017, 04:01

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m^2 n + mn^2 = mn(m+n)

St 1: m+n =1 choose (m,n) = (1,0) and (0.5,0.5) you will get 0 and 0.25 respectively. INSUFFICIENT

St 2: mn=1, or m=1/n. put this in the above expression, we get n +1/n or (n^2 +1)/n. it will either more than 2 or less than -2. but cannot be zero. ANSWER

Option B

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29 May 2017, 20:34

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Bunuel

Is m^2n + mn^2 = 0 ?

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

Kudos for a correct solution.

One concise approach to this problem is to use number properties

Statement 1

M + N = 1

m and n could be 0 and 1 , or 1 and 0 - so an so forth

Insufficient

Statement 2

mn= 1

m^2n + mn^2
m^2n + 1 ....

Now, if m and n are reciprocals of each other, either negative or positive, or even or odd the results will always be a positive number. The trick is to analyze the 2 in 2n- because 2 is even it doesn't matter whether n is even or odd because any even number times another even number or odd number will always be even. If the exponent is negative and even the answer will still be positive because any negative number to an even exponent is always positive.

Hence

"B" is sufficient

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