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). ---------- 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??

Users browsing this forum: No registered users and 2 guests

You cannot post new topics in this forum You cannot reply to topics in this forum You cannot edit your posts in this forum You cannot delete your posts in this forum You cannot post attachments in this forum

GMAT(TM) and GMAT CAT (TM) are registered trademarks of the Graduate Management Admission Council(TM). The Graduate Management Admission Council(TM) does not endorse, nor is affiliated in any way with the owner or any content of this site.