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 Post subject: GMAT Algebra
PostPosted: Mon Oct 21, 2013 12:27 pm 
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Joined: Tue Apr 13, 2010 8:48 am
Posts: 478
If 15x + 4y = 10 and 3x + 2y = 20, then which of the following is the largest?
A. 9x + 6y
B. 18x + 6y
C. 30x + 8y
D. 60x + 16y
E. 30


(A) The fastest way to solve this question is to see that the expressions in the answer choices A – D can be made of the expressions in the question statement. So we don’t need to find the actual values of x and y in this case.
(A) 9x + 6y = 3 × (3x + 2y) = 3 × 20 = 60
(B) 18x + 6y = (15x + 4y) + (3x + 2y) = 10 + 20 = 30
(C) 30x + 8y = 2 × (15x + 4y) = 2 × 10 = 20
(D) 60x + 16y = 4 × (15x + 4y) = 4 × 10 = 40
(E) 30
The correct answer is A.

Solving the original system of equations to find x and y is also an option.
Multiplying second equation by 5 we get 10y + 15x = 100. Subtracting first equation we get:
10y – 4y + 15x – 15x = 100 – 10
6y = 90
y = 15
Substituting y into second equation we can find x:
2 × 15 + 3x = 20
3x = -10
x = -10/3
Now we can calculate all of the answer choices:
(A) 9x + 6y = 6 × 15 + 9 × (-10/3) = 90 – 30 = 60
(B) 18x + 6y = 6 × 15 + 18 × (-10/3) = 90 – 60 = 30
(C) 30x + 8y= 8 × 15 + 30 × (-10/3) = 120 – 100 = 20
(D) 60x + 16y= 16 × 15 + 60 × (-10/3) = 240 – 200 = 40
(E) 30
60 is the largest. The answer is (A).
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I got this problem wrong and I don't know why, can you please help me understand. Following are the steps taken by me.

Consider the first equation as is. Multiply 2nd equation by 2. We get
15x + 4y = 10
6x + 4y =40

Subtracting we get => 9x = -30
And x is negative. What is it that I am doing wrong here??


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 Post subject: Re: GMAT Algebra
PostPosted: Mon Oct 21, 2013 12:30 pm 
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Joined: Fri Apr 09, 2010 2:11 pm
Posts: 454
Quote:
Subtracting we get => 9x = -30
And x is negative. What is it that I am doing wrong here??
You did nothing wrong. The variable x can be negative (there is noting in the question statement that restricts it from being so).

x = -30/9 = -10/3 is the correct solution, together with y = 15 .


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