Data Sufficiency

if x and y are integers and x<y, what is the value of x+y?

1. x^y=4
2. x absolute = y absolute

it seems weird as obviously the only y that there is not Y which is less than X that satisfies either/both 1 and 2.....


what is your advise?
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my answer is D
(1) the only pair of x,y such that y>x and x^y=4, is x=-2, y=2, -2+2=0 suff
(2)|x|=|y|
if x>0 and y>0 then x=y but according to the problem y>x not possible
if x<0 and y>0 then -x=y and we can find the sum x+(-x)=0
if x>0 and y<0 then x>y not possible
if x<0 and y<0 then -x=-y x=y again not possible
so st2 seems suff

(-2)^2 =4

so, 1 is sufficient .

now

|x| = |y|

and x < y

so, 2 is sufficient would mean x+y =0

The solution is D

clock60 wrote:my answer is D
(1) the only pair of x,y such that y>x and x^y=4, is x=-2, y=2, -2+2=0 suff
(2)|x|=|y|
if x>0 and y>0 then x=y but according to the problem y>x not possible
if x<0 and y>0 then -x=y and we can find the sum x+(-x)=0
if x>0 and y<0 then x>y not possible
if x<0 and y<0 then -x=-y x=y again not possible
so st2 seems suff

But, x absolute could equal y absolute with any integer (one is obviously negative), say 3 and -3, 4 and -4. From (2) we can not infer the answer.

Now X^Y=4 (I hope you understood that ^ means degree, sorry I don't know how to put symbols in messages) it is not clear , because we know that x<y. So, it can not be 2. If we put both statements together, it seems like the answer is 2 and -2, but again, then the condition 1 will not hold, because if we put x into degree of -2, the answer is not 4.

What do you think, maybe the question itself is not correctly stipulated and there is no solution for this problem?

Anurag@Gurome wrote:

But, x absolute could equal y absolute with any integer (one is obviously negative), say 3 and -3, 4 and -4. From (2) we can not infer the answer. (Look at your numbers! In each case they add up to zero.)

Now X^Y=4 (I hope you understood that ^ means degree, sorry I don't know how to put symbols in messages) it is not clear , because we know that x<y. So, it can not be 2. If we put both statements together, it seems like the answer is 2 and -2, but again, then the condition 1 will not hold, because if we put x into degree of -2, the answer is not 4.

(As I explained, there is one and only possible set of values for x and y, which is : x = -2 and y = 2)

What do you think, maybe the question itself is not correctly stipulated and there is no solution for this problem?

Thanks a lot. Now this question seems to obvious..sad part is that questions solved by others always look simple post-factum ((( Hope that soon I could master these concepts myself - I should say recall them from my school's years...thanks, great work by Experts and others! Great site!

both alone are sufficient

(D) is the answr

narrowly missed .. Did not work on option B

Good question

gr8 pvt tutor , nice throw , u caught me this time ...

what is the best way to do this?

table format?

B

|-2|=|2|

D, 2^2 , -2^2 and 4^1

If x and y are integers and x < y, what is the value of x + y?

1. x^y = 4
2. |x| = |y|

Question Stem: y>x and x and y integers.

1)x^y = 4
=> (-2)^2 = 4 (bcz. y>x)
So, x+y = -2+2 = 0 Sufficient
2)|x| = |y|
if x = -2, then y = 2 (bcz. y>x)
if x = -3, then y = 3 (bcz. y>x)
So, x+y = -2+2 = 0
or -3+3 = 0 Sufficient
IMO: D