Problem Solving

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

(1) w(x^2) = 16

(2) y = 4

The correct answer is (a). I believe you supposed to manipulate the first statement, but I am not exactly sure.

Thanks!

thedude232 wrote:If wx=y, what is the value of xy?

(1) w(x^2) = 16

(2) y = 4

The correct answer is (a). I believe you supposed to manipulate the first statement, but I am not exactly sure.

Thanks!

wx = y ; xy = ?

Statement 1:
w(x^2) = wx*x = y*x = xy = 16 -> Sufficient

Statement 2:
y=4 -> Not sufficient

So, answer is A.

w(x^2) = 16


or

w*x*x = 16

or w*x = 16/x

w*x = y

So, 16/x = y

so xy = x * 16/x = 16

Hence A.

Statement B is not sufficient.

thedude232 wrote:If wx=y, what is the value of xy?

(1) w(x^2) = 16

(2) y = 4

The correct answer is (a). I believe you supposed to manipulate the first statement, but I am not exactly sure.

Thanks!

thedude232 wrote:If wx=y, what is the value of xy?

(1) w(x^2) = 16

(2) y = 4

The correct answer is (a). I believe you supposed to manipulate the first statement, but I am not exactly sure.

Thanks!

An efficient approach -- one that doesn't require any algebraic insight -- would be to plug in two sets of values that satisfy the conditions given. If the value of xy stays the same, then the statement is sufficient. If the value of xy changes, then the statement is insufficient.

Statement 1: w(x^2) = 16
Let w=4, x=2, so that 4*(2^2) = 16.
Then y = wx = 4*2 = 8.
xy = 2*8 = 16.

Let w=16, x=1, so that 16*(1^2) = 16.
Then y = wx = 16*1 = 16.
xy = 1*16 = 16.

Since the value of xy stays the same, sufficient.

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

The correct answer is A.

GMATGuruNY wrote: An efficient approach -- one that doesn't require any algebraic insight -- would be to plug in two sets of values that satisfy the conditions given. If the value of xy stays the same, then the statement is sufficient. If the value of xy changes, then the statement is insufficient.

Since the value of xy stays the same, sufficient.
.

GMATGuruNY, would you be able to give me an example of an equation in which the value of xy changes? Also how do we determine when it is suffice to stop looking for values of XY if we keep getting the same values after plugging in for XY? Thanks a lot in advance!

chendawg wrote:

GMATGuruNY wrote: An efficient approach -- one that doesn't require any algebraic insight -- would be to plug in two sets of values that satisfy the conditions given. If the value of xy stays the same, then the statement is sufficient. If the value of xy changes, then the statement is insufficient.

Since the value of xy stays the same, sufficient.
.

GMATGuruNY, would you be able to give me an example of an equation in which the value of xy changes? Also how do we determine when it is suffice to stop looking for values of XY if we keep getting the same values after plugging in for XY? Thanks a lot in advance!

What is the value of xy?

Statement 1: x = y+2
y=1, x=3, xy = 3*1 = 3.
y=2, x=4, xy = 4*2 = 8.
Since the value of xy changes, insufficient.

Statement 2: x = 3y-1
y=1, x=2, xy = 2*1 = 2.
y=2, x=5, xy = 5*2 = 10.
Since the value of xy changes, insufficient.

Statements 1 and 2 together:
2 variables, 2 linear equations, sufficient.

The correct answer is C.

Ahh, thanks for the simple example. I think I was looking for an unicorn there!

thedude232 wrote:If wx=y, what is the value of xy?

(1) w(x^2) = 16

(2) y = 4

The correct answer is (a). I believe you supposed to manipulate the first statement, but I am not exactly sure.

Thanks!

IMO A.

Approach is as follows

QUESTION REPHRASE
What is xy? Question stem gives us wx = y, multiply both sides by x to get xy.
This gives us w(x^2) = xy.
Therefore, a stmt will be sufficient if it tells us either xy explicitly OR w(x^2)

STMT 1
Sufficient. This gives us w(x^2) = 16 = xy
(See the rephrasing above came in handy!)

STMT 2
Insufficient.

given wx= y
so w(x^2) = xy

Statement 1

w(x^2) = 4
so xy = 4
sufficent

Statement 2

y = 4
wx = y = 4 but we neither know w nor x so not sufficient.

wx = y ....(1)
wx^2 = 16 ....(2)
Dividing (1) by (2)
xy = 16
assuming w =/ 0
(A) is answer as statement 2 does not give value of w and makes the eqn not unsolvable.

statement1) w(x^2) = 16
w*x*x =16
wx=y
so, yx=16
sufficient Ans -A
In statement 2 no information of X so insufficient..

wx = y...i)

Multiply both sides by x, we get
wx^2 = xy , but wx^2 = 16 (already given)....A), therefore xy = 16.

On the other hand B) i.e. y = 4 tells us that wx = 4, but doesn't tell us the value of xy.

Therefore A) is the correct answer.

IMO A

Simple one, but teaches a lot !

A in Answer.

What if w = 4 and x = -2?
The question did not mention w and x must be positive or negative integers.