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

 It is currently 22 Jan 2020, 07:14 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # 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 V
Joined: 16 Aug 2015
Posts: 8437
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 00:00

Difficulty:   55% (hard)

Question Stats: 57% (02:02) correct 43% (02:32) wrong based on 35 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. ($$\frac{4}{3}, \frac{-3}{4}$$)

_________________
Senior Manager  G
Joined: 16 Feb 2015
Posts: 258
Location: United States
Concentration: Finance, Operations
Re: For x, y satisfying x-3/3= y+2/2, x and y always satisfies ax + by =  [#permalink]

### Show Tags

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 V
Joined: 16 Aug 2015
Posts: 8437
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

=>

$$\frac{x-3}{3} = \frac{y+2}{2}$$

=> $$2(x - 3) = 3(y + 2)$$ (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 $$b = \frac{-3}{4}$$.

_________________ Re: For x, y satisfying x-3/3= y+2/2, x and y always satisfies ax + by =   [#permalink] 04 Dec 2019, 02:17
Display posts from previous: Sort by

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