few princeton review DS questions from 2nd ed math workout

[coachy]

On Page 222 they have thus DS question
Is it true that X < Y?
1 5x < 5y
2 zx < zy

I thought the answer should be D. They say it is A.
Explaination is that in second statement Z could be +ve or -ve.

I chose D because we are already given zx < zy. Isn't it true that we have to assume that statement 2 is true.


Similarly on page 223

the question is
If X and Y are integers, does x = y?
1) xy = y2 (2 here is square)
2) x2 = y2 (2 here is square)

I thought the answer should be again D but the book says it is C.

[jayhawk2001]

[quote="coachy"]On Page 222 they have thus DS question
Is it true that X < Y?
1 5x < 5y
2 zx < zy

I thought the answer should be D. They say it is A.
Explaination is that in second statement Z could be +ve or -ve.

I chose D because we are already given zx < zy. Isn't it true that we have to assume that statement 2 is true.


[/quote]

[size=18]x < y holds true from 5x < 5y for all values of x and y. So, (1) is
sufficient.

zx < zy does not necessarily mean x < y, as we don't know whether
z is positive or negative. So, (2) is insufficient.

Hence A.

[/size]

[quote="coachy"]
Similarly on page 223

the question is
If X and Y are integers, does x = y?
1) xy = y2 (2 here is square)
2) x2 = y2 (2 here is square)

I thought the answer should be again D but the book says it is C.[/quote]

Can you please explain why this should be D ?

(1) is sufficient as you can safely cancel out y from both sides
leading to x = y

I'd say (2) is insufficient as x^2 = y^2 can be expressed as
(x+y)(x-y)=0 which means x = y or x=-y.

[kandelaki]

Is it true that X < Y?
1 5x < 5y
2 zx < zy


well if we assume that z=0 then x is not < than y , they both will be 0
that is why only first choice gives sufficient explanation.......

[coachy]

if we assume z = 0 even the 2nd statement would not be true...

zx < zy

tells us that z cannot be 0.

[kandelaki]

you're right.
I guess it just about z being positve or negative, nothing to do with 0.
thanks