xy DS question

[tj123]

If x and y are greater than 0, is x= 1?

1) x/y = 1
2) xy= 1

Answer is C) Both

Please explain.

[cramya]

Stmt I

x/y = 1 (i.e x=y)

x=2 y=2
x=1 y=1

INSUFF

Stmt II

xy = 1

x=2 y=1/2
x=4y=1/4
x=1 y=1

INSUFF

Stmt I and II together
X/Y=1 I.E X=Y
XY=1

X^2 = 1
sqrt(x^2) = sqrt(1^2) (sqrt(x^2) = |x|)

|X| = 1

X=1 OR X=-1 Given x is positive so x=1

Not necessary for this problem but y=1 also
Same for y

y^2 = 1

|y| = 1

y=1 or y=-1 but since y is positive and greater than 0 y=1

SUFF

C)

[cramya]

Tj,
Thanks for posting the official answer. For the futrue problems if u could hide the OA using spoiler function then that would be much appreciated.

OA: C

This way the users will not know the answers before solving the problem as it takes the fun out of it....

Good luck!

Regards,
Cramya

[vittalgmat]

If x and y are greater than 0, is x= 1?

1) x/y = 1
2) xy= 1

Answer is C) Both

Please explain.

Stmt1: x/y = 1.
Here x and y can be any number (+ve int, frac, irrational#)
as long as x =y
OR it x and y both could be 1.
So insufficient.


stmt2: xy = 1.
Again x and y can be reciprocal of each other.
ie y = 1/x.
xy =1 => x * 1/x = 1

OR both x and y could be 1.

So insufficient.


Combining 1 and 2.

Now this will eliminate the x = y case from stmt 1 and reciprocal case from stmt2. The only remaining case is x=y =1
So answer is C

HT Helps

[ronniecoleman]

Although IMO C

but please submitter....don't post the OA with the question..


Follow the rules !