Product of 2 ints whose sum is 11

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EricKryk: Senior | Next Rank: 100 Posts; Posts: 83; Joined: Tue Mar 31, 2009 11:03 am; Thanked: 3 times

by EricKryk » Tue Feb 11, 2014 6:04 am

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

A) -42

B) -28

C) 11

D) 26

E) 32

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Source: Beat The GMAT — Problem Solving | Tue Feb 11, 2014 6:04 am

Patrick_GMATFix: GMAT Instructor; Posts: 1052; Joined: Fri May 21, 2010 1:30 amFollowed by: 98 members; Thanked: 335 times

by Patrick_GMATFix » Tue Feb 11, 2014 6:16 am

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.

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parveen110: Senior | Next Rank: 100 Posts; Posts: 91; Joined: Fri Jan 17, 2014 7:34 am; Thanked: 7 times

by parveen110 » Tue Feb 11, 2014 6:51 am

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.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Tue Feb 11, 2014 7:15 am

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

I should point out that the question SHOULD read, "Which of the following COULD BE the product of two integers whose sum is 11"

I'd start testing PAIRS of values for x and y that add to 11.

Note: I see that some answers are positive and some are negative. This tells me that I need to consider PAIRS in which the 2 values are positive, and I need to consider PAIRS in which 1 value is positive and 1 is negative.

Let's begin with POSITIVE pairs.
1 + 10 = 11 and (1)(11) = 11 (not on list)
2 + 9 = 11 and (2)(9) = 18 (not on list)
3 + 8 = 11 and (3)(8) = 24 (not on list)
4 + 7 = 11 and (4)(7) = 28 (not on list)
5 + 6 = 11 and (5)(6) = 30 (not on list)

Now that we've considered all possible pairs of POSITIVE values, we'll need to try PAIRS in which 1 value is positive and 1 is negative:
(-1) + 12 = 11 and (-1)(12) = -12 (not on list)
(-2) + 13 = 11 and (-2)(13) = -26 (not on list)
(-3) + 14 = 11 and (-3)(14) = -42 ON THE LIST

Answer: A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Feb 11, 2014 1:31 pm

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.

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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Tue Feb 11, 2014 2:08 pm

Hi EricKryk,

Each of the posts in this thread provides a suitable approach to solving this problem. On Test Day, you have two goals when attempting to answer a question:

1) Come up with the correct answer
2) Do so in the fastest way possible

Sometimes the "best" way to go about solving a Quant question is with "brute force" - instead of high-concept, elegant math solutions, just try pounding on the question until you find the answer that matches. Here, we know that we're dealing with two integers that add up to 11; the answers are also relatively simple, so the possibilities are rather limited.

Brent's approach provides a great example of brute force. In a relatively short amount of time, you'll have the answer. Don't be shy about working a few Quant questions in this way during a CAT and/or on Test Day.

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

Contact Rich at [email protected]

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