Data Sufficiency

Can anyone explain how to solve this problem? I'm totally stumped. Thank you!

Wow, Brent. First off, kudos on the immediate and thorough response. I knew this was a relatively simple DS problem, but for whatever reason I just couldn't see it. Your response was crystal clear and very helpful - thank you very much!!

If wx=y, what is the value of xy?

(1) wx² = 16

(2) y = 4

Alternate approach:

Statement 1: wx² = 16
Test TWO CASES.
If the value of xy is the SAME in each case, then the statement is SUFFICIENT.
If the value of xy CHANGES, then the statement is INSUFFICIENT.

Case 1: w=4 and x=2, so that wx² = 4*2² = 16.
Here:
y = wx = 4*2 = 8.
xy = 2*8 = 16.

Case 2: w=16 and x=1, so that wx² = 16*1² = 16.
Here:
y = wx = 16*1 = 16.
xy = 1*16 = 16.

Since the value of xy is the same in each case, SUFFICIENT.

Statement 2: y=4
No way to determine the value of x.
INSUFFICIENT.

The correct answer is A.

Thanks for that alternative approach, Mitch. I'm a big fan of plugging in numbers for variables, but in this case I was reluctant to do so because there were three variables. Happy to see it is possible and a viable alternative to the above solution.

Quick questions: When you first saw this problem, what made you go with your approach rather than the one described by Brent. My biggest issue with quant is recognizing the skill being tested on each problem, so it'd be helpful to gain a bit of insight into your thought process.

Thanks again for your time and help!

Mustbeatquant wrote:Thanks for that alternative approach, Mitch. I'm a big fan of plugging in numbers for variables, but in this case I was reluctant to do so because there were three variables. Happy to see it is possible and a viable alternative to the above solution.

Quick questions: When you first saw this problem, what made you go with your approach rather than the one described by Brent. My biggest issue with quant is recognizing the skill being tested on each problem, so it'd be helpful to gain a bit of insight into your thought process.

Thanks again for your time and help!

How many men attended the party?
What was the selling price of the dress?
What is the value of xy?
All of these questions ask for a SPECIFIC VALUE.
When a DS problem asks for a specific value, one way to evaluate the statements is to TEST CASES.
If the value stays the same in each case, the statement is SUFFICIENT.
If the value changes, the statement is INSUFFICIENT.

Many of these problems can also be solved algebraically.
The GMAT is designed to allow for different approaches.
Use whichever approach works best for you.

In the problem above, one more way to evaluate statement 1 is to divide one equation (wx² = 16) by the other (wx = y):
wx²/wx = 16/y
x = 16/y
xy = 16.

wx = y
==> wx*x = x*y
==> wx² = xy
==> 16 = xy

Hi
I got the answer as A
used the method
wx^2 = 16
wx*x = 16
xy = 16

thanks and regards

Mustbeatquant wrote:

Can anyone explain how to solve this problem? I'm totally stumped. Thank you!

If y = wx, then xy = wx^2.

(1) wx^2 = 16 means xy = 16, hence sufficient. A/D.

(2) y = 4 may have many possible values of x than one, hence [spoiler]insufficient.

Choose (A).[/spoiler]

Mustbeatquant wrote:If wx=y, what is the value of xy?

(1) wx² = 16

(2) y = 4

Given : WX=Y

Question : The value of XY = ?

Statement 1) wx² = 16
i.e. WX x X = 16
i.e. YX = 16
SUFFICIENT

Statement 2) y = 4
i,e, WX = 4
But W can't be eliminated and therefore WX can't be calculated
INSUFFICIENT

Answer: Option A