If m and n are integers, what is the value of m + n ?

Question

(1) (x + m)(x + n) = x^2 + 5x + mn and x ≠ 0.
(2) mn = 4

DS53602.01

BrentGMATPrepNow · Accepted Answer

Given : m and n are integers

Target question :    What is the value of m + n ?

Statement 1 : (x + m)(x + n) = x² + 5x + mn and x ≠ 0.  
Use FOIL to expand the left side: x² + nx + mx + mn = x² + 5x + mn
Factor the two middle terms: x² + x(n + m) + mn = x² + 5x + mn
At this point, we should see that  m+n = 5 
Since we can answer the  target question  with certainty, statement 1 is SUFFICIENT

If you're not convinced, we can take a few more steps. 
Take: x² + x(n + m) + mn = x² + 5x + mn
Subtract x² from both sides: x(n + m) + mn = 5x + mn
Subtract mn from both sides: x(n + m) = 5x
Divide both sides by x to get:  n + m = 5 
Since we can answer the  target question  with certainty, statement 1 is SUFFICIENT

Statement 2 : mn = 4 
There are many values of m and n that satisfy statement 2. Here are two: 
 Case a : m = 4 and n = 1. In this case, the answer to the target question is  m + n = 4 + 1 = 5 
 Case b : m = 2 and n = 2. In this case, the answer to the target question is  m + n = 2 + 2 = 4 
Since we cannot answer the  target question  with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

Chethan92 · Answer

From S1:

(x + m)(x + n) = x^2 + 5x + mn

x^2+x(m+n)+mn = x^2+5x+mn

5x = x(m+n)

x(5-(m+n)) = 0

As x ≠ 0, m+n = 5

Sufficient.

From S2:

Clearly Insufficient.

A is the answer.

chetan2u · Answer

If m and n are integers, what is the value of m + n ?

(1) (x + m)(x + n) = x^2 + 5x + mn and x ≠ 0.
(x + m)(x + n) is a quadratic equation that has m and n as roots..
 (x + m)(x + n)=x^2+(m+n)x+mn ..
Therefore,  x^2+(m+n)x+mn=x^2 + 5x + mn 
Thus m+n is the sum of roots and is equal to 5

(2) mn = 4
Mainly for C trap.
Insuff

A

ZoltanBP · Answer

We know that  m  and  n  are integers. The original question:  m+n=?

1) We know that  (x+m)(x+n)=x^2+5x+mn  and  x
eq 0 .

x^2+mx+nx+mn=x^2+5x+mn

x(m+n)=5x

Since  x
eq 0 , we can divide both sides of the above equation by  x .

m+n=5 . Thus, the answer to the original question is a unique value.  \implies   Sufficient

2) We know that  mn=4  and can test possible cases. If  m=2  and  n=2 , then  m+n=4 . However, if  m=4  and  n=1 , then  m+n=5 . Thus, we can't get a unique value to answer the original question.  \implies   Insufficient

Answer: A

Archit3110 · Answer

#1
solve for 
(x + m)(x + n) = x^2 + 5x + mn and x ≠ 0.
we get m+n= 5
sufficeint
#2
mn=4
not sufficeint
IMO A

ScottTargetTestPrep · Answer

Statement One Alone:

(x + m)(x + n) = x^2 + 5x + mn and x ≠ 0.

Foiling we have:

x^2 + mx + nx + mn = x^2 + 5x + mn

mx + nx = 5x

x(m + n) = 5x

m + n = 5

Statement one alone is sufficient to answer the question.

Statement Two Alone:

mn = 4

Only knowing the product and m and n does not give us enough information to determine the sum of n and m. For example, if m = 1 and n = 4, then m + n = 5. However, if m = n = 2, then m + n = 4. Statement two alone is not sufficient to answer the question.

Answer: A

EMPOWERgmatRichC · Answer

Hi All,

We're told that M and N are INTEGERS. We're asked for the value of M+N. This question can be solved with a mix of Algebra and TESTing VALUES.

(1) (X + M)(X + N) = X^2 + 5X + (M)(N) and X ≠ 0.

The equation in Fact 1 should get us thinking about a Quadratic and how we can F.O.I.L. the parentheses and get the given result. Notice that the 'middle' term is "+5X"; this provides a huge clue about how M and N relate to one another. Since the SUM of M and N must be +5, you can stop right here (since the question asks for that exact value). If you didn't immediately recognize that though, you can run a few TESTs and see what happens...

IF.... 
M=1 and N=4, then (X+1)(X+4) = X^2 +5X + 4 and the answer to the question is 5. 
M=2 and N=3, then (X+2)(X+3) = X^2 +5X + 6 and the answer to the question is 5. 
M=6 and N= -1, then (X+6)(X-1) = X^2 +5X - 6 and the answer to the question is 5. 
Etc. 
The answer to the question is ALWAYS 5. 
Fact 1 is SUFFICIENT

(2) (M)(N) = 4

With the equation in Fact 2, we can come up with a couple of simple examples... 
IF.... 
M=1 and N=4, then the answer to the question is 5. 
M=2 and N=2, then the answer to the question is 4. 
Fact 2 is INSUFFICIENT

Final Answer:  A

GMAT assassins aren't born, they're made, 
Rich

TheUltimateWinner · Answer

if m=4, n=1, then m+n=5
again, if m=-4, n=-1, then m+n=-5
So, insufficient.. Cancel choice B,D

(1) (  x     +  m   )(  x     +  n   ) =   x^2   +   5  x +  mn  and x ≠ 0

we can solve this question with an easiest way..
Here, there are two sides (LHS and RHS). In the LHS (x*x) gives the value x^2 in the RHS (blue color); also the in the LHS (m*n) gives the result mn in the RHS (underlined part). If this happens in both side of the equation, you'll get m+n=5 (co-efficient of x in the middle of the LHS-in the red color). 
So, m+n=5--->sufficient.
Correct choice  A 
Hope it helps..

MHIKER · Answer

(1)  (x + m)(x + n) = x^2 + 5x + mn

⇒ x^2+nx+mx+mn=x^2+5x+mn

⇒ x(m+n)=5x

⇒ m+n=5 ; Sufficient.

(2) Insufficient.

The answer is  A

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=cG4iwhvD4i4

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If m and n are integers, what is the value of m + n ?

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