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Re: Which of the following is the product of two integers whose [#permalink]

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29 Mar 2008, 07:43

1

This post received KUDOS

Yeah, there doesn't seem to be an easy way to just plug stuff in and solve algebraically. My method may shed some light though:

let the two numbers be x and y, and N be the answer

With the given information, I know that xy=N and that x+y = 11

which gives: x(11-x)=N 11x-x^2=N 0 = x^2 - 11x + N 0=(x ?)(x ?)

At this point, I had the following thoughts:

(A) -42 : to get -42, it must be (x + ?)(x - ?) so how can a positive and negative number add to -11 and yet still multiply together for -42? (B) -28 : similar thought process to (A) if you didn't start by evaluating A first (C) 12: (x + ?)(x + ?) or (x - ?)(x - ?) (D) 26 (E) 32

Truthfully, this is one of those questions where going through the entire calculation may not be necessary and just trying out numbers would be quicker.

Re: Which of the following is the product of two integers whose [#permalink]

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22 Aug 2014, 10:09

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Re: Which of the following is the product of two integers whose [#permalink]

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30 Dec 2015, 19:38

A+B=11 A=1 B=10 -> AB=10 no A=2 B=9 -> 18 no A=3 B=8 - no A=4 B=7 - NO A=5 B=6 - NO A=7 B=4 - NO A=8 B=3 - NO A=9 B=2 - NO A=10 B=1 - N0 A=11 B=0 - NO A=12 B=-1 - NO A=13 B=-2 - NO A=14 B=-3 -> AB=-42. WE HAVE SUCH AN ANSWER, THUS A IS THE CORRECT ONE.

-1 is NOT a prime factor. Prime factors as per the definition are positive integers. You were lucky with your approach.

The simplest way is to realize that x+y=11 for which xy = options given. When you see option (A), it should trigger the observation that you can even use negative integers.

Factors of 42 : 1,2,3,6,7,14,21,42 (and their negative counterparts). Now see that -3 and 14 are in this group and 14+(-3)=11 (14*-3=-42). Thus A is the correct answer.

Re: Which of the following is the product of two integers whose [#permalink]

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12 Mar 2016, 03:40

lumone wrote:

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

(A) -42 (B) -28 (C) 12 (D) 26 (E) 32

I solved this Question like this,

Let the two integers are x,y x+y=11 (Given) xy=? (Needed)

instead of solving this algebraically, Test the Answer choices

A. -42 Do the factorization : (-1,42)----> There sum is not 11--eliminate (-2,21)---->There sum is not 11--eliminate (-3,14)-----> there sum is 11 Bingo!!!!

So, my answer is A...

As the answer is in A, it took me very less time to answer the question. but i think this method is be simple and efficient.

Re: Which of the following is the product of two integers whose [#permalink]

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13 Mar 2016, 05:54

lumone wrote:

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

(A) -42 (B) -28 (C) 12 (D) 26 (E) 32

I just plugged in the values. If both the integers are positive, then their product will be positive. With positive options, we cannot plug in any values. Therefore, one integer is positive and another is negative. (12,1) or (13,2) or (14,3) and so on. (14, -3) fits the answer.

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