Problem Solving

Which of the following is the product of two integers whose sum is 11?

A) -42

B) -28

C) 11

D) 26

E) 32

x + y = 11
xy = ?

One approach is to work backwards, using each answer choice as the value of xy, then figuring out whether that answer leads us to integer values for x and y. The full solution below is taken from the GMATFix App.



-Patrick

EricKryk wrote:Which of the following is the product of two integers whose sum is 11?

A) -42

B) -28

C) 11

D) 26

E) 32

Hi Eric,
There is another approach. As the numbers are friendly this problem can be solved with the help of factor search.

Let the two integers be a and b.
Now, according to question, a+b=11. My reaction to this equation immidiately is that okay, i have to look for two factors of a number where one is even and the other is odd. As we know, odd+even=odd or vice versa.

Now we will take each option one by one and try to disprove the options.

Lets take option E. i.e. 32. 32 can also be expressed as 2^5. We can see that all the factors of 32 will be even. So, we disregard this option.

Option D is 26. A quick factor search tells me that 26 and 1 would never yield the answer as 11. Also 13*2=26 and 13-2=11. but 13*-2=-26. so we disregard this option.

option C is 11 which is a prime number. It has only two factors 1 and itself. so 11 and 1 through addition cannot yield 11.

Option B is -28. Factor search will lead us to:
1*28
2*14
4*7
As we can see 7+4 is 11 but 7*4=28. So we disregard this option.

Option A is -42. Factor search will tell us that 14*-3=-42 ans also, 14-3=11.

This process is actually very easy. But as i write it seems lenthy but it really isn't.

EricKryk wrote:Which of the following is the product of two integers whose sum is 11?

A) -42

B) -28

C) 11

D) 26

E) 32

Let x and y be the two integers.
We can PLUG IN THE ANSWERS, which represent the value of xy.
Since x+y = 11, the average test-taker will be attracted to C, D and E, all of which are positive.
Don't be an average test-taker: start with A and B.

A: xy = -42
Factors of 42:
1*42
2*21
3*14.
6*7.
Look for a pair that -- if one value is positive, while the other is negative -- will yield a sum of 11.
The option in red works:
-3 + 14 = 11.

The correct answer is A.