GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 17 Feb 2020, 05:00

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# For x, y satisfying x-3/3= y+2/2, x and y always satisfies ax + by =

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8563
GMAT 1: 760 Q51 V42
GPA: 3.82
For x, y satisfying x-3/3= y+2/2, x and y always satisfies ax + by =  [#permalink]

### Show Tags

02 Dec 2019, 00:51
00:00

Difficulty:

55% (hard)

Question Stats:

56% (02:02) correct 44% (02:31) wrong based on 36 sessions

### HideShow timer Statistics

[GMAT math practice question]

For $$x, y$$ satisfying $$\frac{x-3}{3}= \frac{y+2}{2}$$, $$x$$ and $$y$$ always satisfies $$ax + by = 3$$. What is ($$a, b$$)?

A. $$(1, 0)$$

B. $$(2, 3)$$

C. ($$\frac{1}{2}, \frac{-3}{4}$$)

D. ($$\frac{1}{2}, \frac{-3}{2}$$)

E. ($$\frac{4}{3}, \frac{-3}{4}$$)

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Senior Manager Joined: 16 Feb 2015 Posts: 355 Location: United States Re: For x, y satisfying x-3/3= y+2/2, x and y always satisfies ax + by = [#permalink] ### Show Tags 02 Dec 2019, 02:08 MathRevolution wrote: [GMAT math practice question] For $$x, y$$ satisfying $$\frac{x-3}{3}= \frac{y+2}{2}$$, $$x$$ and $$y$$ always satisfies $$ax + by = 3$$. What is ($$a, b$$)? A. $$(1, 0)$$ B. $$(2, 3)$$ C. ($$\frac{1}{2}, \frac{-3}{4}$$) D. ($$\frac{1}{2}, \frac{-3}{2}$$) E. ($$\frac{4}{3}, \frac{-3}{4}$$) Explanation: Solving Equation: (x-3)/3 = (y+2)/2 2x-6=3y+6 2x-3y=12 Need Above Equation in form of ax + by = 3 (2/4)x + (-3/4)y = 3 (1/2,-3/4) IMO-C Please give kudos, if you find my explanation Good Enough Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8563 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: For x, y satisfying x-3/3= y+2/2, x and y always satisfies ax + by = [#permalink] ### Show Tags 04 Dec 2019, 01:17 => $$\frac{x-3}{3} = \frac{y+2}{2}$$ => $$2(x - 3) = 3(y + 2)$$ (cross multiplying) => $$2x - 6 = 3y + 6$$ (multiplying through the brackets) => $$2x - 3y = 12$$ (adding like terms) => $$(\frac{1}{2})x - (\frac{3}{4})y = 3$$ (dividing both sides by $$4$$). Then we have $$a = \frac{1}{2}$$ and $$b = \frac{-3}{4}$$. Therefore, C is the answer. Answer: C _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Re: For x, y satisfying x-3/3= y+2/2, x and y always satisfies ax + by =   [#permalink] 04 Dec 2019, 01:17
Display posts from previous: Sort by