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Which of the following is the product of two integers whose

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Which of the following is the product of two integers whose [#permalink] New post 29 Mar 2008, 07:09
00:00
A
B
C
D
E

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  25% (medium)

Question Stats:

84% (02:21) correct 16% (02:58) wrong based on 17 sessions
Which of the following is the product of two integers whose sum is 11?

(A) -42
(B) -28
(C) 12
(D) 26
(E) 32
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Re: Which of the following is the product of two integers whose [#permalink] New post 29 Mar 2008, 07:20
-42..
took some time..would love to see a short cut..

14*3=42 14-3=11
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Re: Which of the following is the product of two integers whose [#permalink] New post 29 Mar 2008, 07:36
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I have managed to solve it, but I am wondering whether there is a more efficient process.

I've done as below:

x + y = 11
x= 11-y


xy=(11-y)y=11y-y^2

Then, I plugged in with:
y=1 -> xy=11-1=10
y=2 -> xy=22-4=18
y=3 -> xy=33-9=24
y=4 -> xy=44-16=28
y=5 -> xy=55-25=30
y=6 -> xy=66-36=30
y=7 -> xy=77-49=28

Then I thought, that xy must be negative, then started to plug-in negative numbers:
y=-1 -> xy=-11-1=-12
y=-2 -> xy=-22-4=-26
y=-3 -> xy=-33-9=-42

Bingo! But this takes far too long. Can anyone help?
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Re: Which of the following is the product of two integers whose [#permalink] New post 29 Mar 2008, 07:43
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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.
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Re: Which of the following is the product of two integers whose [#permalink] New post 29 Mar 2008, 08:27
a+b=11

a*b=42

a*(11-a) = 42

a^2 - 11a + 42 = 0

(a-14)(a+3) --> a=14 is a valid solution. therefore, b=-3 .... a+b = 14-3 = 11 and a*b=(14)*(-3) = -42
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Re: Which of the following is the product of two integers whose [#permalink] New post 29 Mar 2008, 08:33
neat..same as my method but its not short enough took a valuabe 50 seconds ..cause i started with answer choice E...


pmenon wrote:
a+b=11

a*b=42

a*(11-a) = 42

a^2 - 11a + 42 = 0

(a-14)(a+3) --> a=14 is a valid solution. therefore, b=-3 .... a+b = 14-3 = 11 and a*b=(14)*(-3) = -42
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Re: Which of the following is the product of two integers whose [#permalink] New post 22 Aug 2014, 10:09
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Re: Which of the following is the product of two integers whose   [#permalink] 22 Aug 2014, 10:09
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