Does x = y?

(1) 4x - 2y = 80

(2) x = (40 + y)/2

The OA is the option E.

Using both equations, cannot find the correct answer? Experts, I would be thankful for your explanation.

## Does x = y?

##### This topic has expert replies

- DavidG@VeritasPrep
- Legendary Member
**Posts:**2666**Joined:**14 Jan 2015**Location:**Boston, MA**Thanked**: 1153 times**Followed by:**125 members**GMAT Score:**770

The key is to recognize that the statements are identical:Vincen wrote:Does x = y?

(1) 4x - 2y = 80

(2) x = (40 + y)/2

The OA is the option E.

Using both equations, cannot find the correct answer? Experts, I would be thankful for your explanation.

Statement 2: x = (40 + y)/2

Multiply both sides by 4:

4x = 2(40 + y)

4x = 80 + 2y

4x - 2y = 80

Clearly, neither statement alone is sufficient, so if the statements are identical, the answer must be E

(If it doesn't feel intuitive that neither statement alone is sufficient, consider cases, If x = y, then we'd have 4x -2x =80 --> 2x = 80 --> x =. 40. So it could be the case that x = 40 and y = 40, giving us a YES. But it could also be the case that x = 20 and y = 0, giving us a NO.)

### GMAT/MBA Expert

- Scott@TargetTestPrep
- GMAT Instructor
**Posts:**4190**Joined:**25 Apr 2015**Location:**Los Angeles, CA**Thanked**: 43 times**Followed by:**21 members

We need to determine whether x = y.Vincen wrote:Does x = y?

(1) 4x - 2y = 80

(2) x = (40 + y)/2

Statement One Alone:

4x - 2y = 80

Simplifying the equation we have, 2x - y = 40; however, we cannot determine whether x = y. If we let x = 0 and y = -40, then we see that x is not equal to y. However, if we let x = 40/3 and y = 40/3, then x = y.

Statement Two Alone:

x = (40 + y)/2

Simplifying the equation, we have:

2x = 40 + y

2x - y = 40

Again, we cannot determine whether x = y.

Statements One and Two Together:

Using both statements together, we see that they produce the identical equations of 2x - y = 40; thus, we cannot determine whether x = y.

Answer: E

**Scott Woodbury-Stewart**

Founder and CEO

scott@targettestprep.com

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews