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If x and y are integers, is |x| > |y|? 1) |x| = |y+1| 2) [#permalink]
 05 May 2010, 07:28
Question Stats:
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93% (01:25) wrong based on 16 sessions
If x and y are integers, is |x| > |y|?
1) |x| = |y+1|
2) x^y = x! + |y|
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Re: Ineq + absolute values [#permalink]
11 May 2010, 23:21
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Re: Ineq + absolute values [#permalink]
12 May 2010, 07:33
1) this is not enough ....lets look at two possibilities
x = 0 y = -1
in this case |x| > |y|
x = 3 y = 2
in this case |x| < |y|
So insufficient
2) x! is always positive so adding this to |y| will increase y thus x > y
so |x| > |y|
Sufficient
So IMO answer should be B
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Re: Ineq + absolute values [#permalink]
14 May 2010, 22:40
Quote: 2) x! is always positive [highlight]so adding this to |y| will increase y thus x > y
so |x| > |y|[/highlight]
Sufficient
So IMO answer should be B I'm curious how you can say which one of x or y is greater. Does this statement not just say that x,y>0. So should the answer not be (C). Please correct me if/where i'm wrong.
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Re: Ineq + absolute values [#permalink]
14 May 2010, 23:44
Sorry I don't understand why the 2nd stmt is sufficient...
If we consider x^y=x! + |y| and we plug in y=0, we get two solutions:
x=0 (since 0^0=1 and 0!=1)
x=1 (since 1^0=1 and 1!=1)
So we have y=0, x=0 >>>> |x|=|y|
but we also have y=0, x=1 >>>> |x|>|y|
(if you try with y=2, you will get x=2, so y=x again)
So stmt 2 should be insufficient...
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Re: Ineq + absolute values [#permalink]
15 May 2010, 07:14
It would be great if either of Bunnel or Fig clarify on this point.
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Re: Ineq + absolute values [#permalink]
15 May 2010, 08:00
hey anybody could explain this? Bunnel?
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Re: Ineq + absolute values [#permalink]
15 May 2010, 09:33
Just to give it a try, while waiting for Bunuel...  stmt 1 If x=0, y=-1, stmt 1 is satisfied, and |x|<|y| If x=1, y=0, stmt 1 is satisfied, and |x|>|y| not sufficient stmt 2 If we consider x^y=x! + |y| and we plug in y=0, we get two solutions: x=0 (since 0^0=1 and 0!=1) x=1 (since 1^0=1 and 1!=1) So we have y=0, x=0 >>>> |x|=|y| but we also have y=0, x=1 >>>> |x|>|y| (if you try with y=2, you will get x=2, so |x|=|y| again) not sufficient stmt 1 + stmt 2 The only acceptable solution that satisfies both stmt 1 and 2 is y=0, x=1 If you try to plug in stmt 2 other values for x and y that satisfy stmt 1 (eg, x=2, y=1; x=3, y=2; x=5, y=4), you'll see that there are no other acceptable solutions. So, if y=0 and x=1, |x|>|y| Answer C (I hope so!) Any opinions?
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Re: Ineq + absolute values [#permalink]
15 May 2010, 11:38
Simple correction! 0 raised to the 0 power is undefined. U cant say 0^0 = 1.
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Re: Ineq + absolute values [#permalink]
15 May 2010, 19:20
it looks like 0^0=1, at least according to most of the sources... Have a look here: gmatclub dot com/forum/0-raised-to-9060 dot html (sorry I'm a new member and I can't post links yet!) but it also says we shouldn't need 0^0 for the GMAT 
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Re: Ineq + absolute values [#permalink]
30 Jun 2010, 23:54
ii. x^y = x! + |y|
x! and |y| are both integers, so x! + |y| is also integer, therefore x^y must be integer, which means y must be greater or equal zero so as not to make x^y a fraction. Now knowing that x,y are integers greater than or equal zero, we need to find the value of x,y for which the equation is true. I can only find x=2 y=2 that satisfy the equation, which gives me a B
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Re: Ineq + absolute values [#permalink]
27 Jul 2010, 06:11
My answer is E. Statement1: First, recall that |a+b|<=|a|+|b|, therefore |x|=|y+1|<=|y|+1 meaning that |x| is either equal to |y|+1 or inferior to |y|+1 then NOT SUFFICIENT Statement 2: as x! is used, hence x>=0 if x=0, then y=0, since 0^0 is not accepted, then x>0 if y=0, then x^0=x!+0, or x=1, therefore |x|>|y| if y=1, then x^1=x!+1, there is no solution of x if y=2, then x^2=x!+2, or x=2, therefore |x|=|y| then NOT SUFFICIENT
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Re: Ineq + absolute values [#permalink]
27 Jul 2010, 07:59
I'll go with C. 1 is clearly insufficient... 2: Try substituting values of x =0 and y =1 and vice versa. 0 = 1 1 = 1. Not sufficient. Together: The only acceptable solution that satisfies both stmt 1 and 2 is y=0, x=1 C
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Re: Ineq + absolute values [#permalink]
28 Jul 2010, 09:52
I think it is C.
(1) If Y is negative, X<Y. If Y is positive or zero, X>Y. (but at least we know they're both integers)
(2) We know X! is always positive and b/c both X&Y are both integers, Y cannot be negative (since anything raised to a negative power, besides 1 or zero, is a non-integer. We can also know that X,Y cannot be 0,1 (b/c you get 0 on the left and 1 on the right), X,Y cannot be 1,1. X,Y CAN be 1,0. We found out that Y & X must both be positive or X,Y is 1,0.
We can't say for sure which is larger. NOT SUFFICIENT
Using both we see that b/c Y is positive or zero, X>Y. So I choose C. Let me know if someone catches something I missed - first post.
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Re: Ineq + absolute values [#permalink]
28 Jul 2010, 19:15
I will go with C. As per (1) |x|=|y+1|. If y is positive or zero then |x|>|y| If y is negative then |x|<|y|. So not sufficient. As per 2 x! is used so x>=0 x!+|y|>=0 and is an integer.So x^y can't be a fraction which means y>=0 But x=1 y=0 and x=2 y=2 produces different results. So not sufficient Combining 1 and 2 As per 2, x and y both have to be positive So 1 can be re-written as x= y+1 Which means x > y and |x|>|y| as both are positive. So sufficient
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Re: Ineq + absolute values [#permalink]
07 Aug 2010, 09:16
Bunuel, Can you please settle the issue? Thanks. PS what is 0^0?
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Re: Ineq + absolute values [#permalink]
08 Aug 2010, 21:51
I was surprises when I read 0 ^ 0 = 1. So I went and check with my best Friend Google. Typed 0 ^ 0 and google returned 1. So I think 0 ^ 0 = 1.
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Re: Ineq + absolute values [#permalink]
09 Aug 2010, 03:04
I was reluctant to reply to this question for a long time because I don't like it all. First of all: 0^0, in some sources equals to 1, some mathematicians say it's undefined. Anyway you won't need this for GMAT as the case of 0^0 is not tested on the GMAT. Second: GMAT would give some constraints for unknowns in the stem (or at leas in second statement), for example: As there is x! in statement (2) then in the stem (or at leas in second statement) GMAT most likely would specify that x\geq{0} as factorial of negative number is undefined; Also as there is x^y in statement (2) then in the stem (or at leas in second statement) GMAT most likely would also specify that x and y can not be zero simultaneously as 0^0 is not tested on the GMAT. So either we would have A. x\geq{0} and y\neq{0} OR B. x>0. If we place these constraint in the stem the question will be completely changed (no need for |x| in the stem and statement 1.) so we should place either of them them in statement 2. So the question could be for example: If x and y are integers, is |x|>|y|? (1) |x| = |y+1|. Clearly insufficient. (2) x>{0} and x^y = x! + |y| --> if x=2 and y=2 then answer is NO but if x=1 and y=0 then answer is YES. Not sufficient. (1)+(2) Only one solution x=1 and y=0. Sufficient. Answer: C.
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If x and y are integers, is |x| > |y|?
(1) |x| = |y + 1|
(2) x^y = x! + |y|
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Re: Algebra - Tough! [#permalink]
26 Aug 2011, 12:32
DeeptiM wrote: If x and y are integers, is |x| > |y|?
(1) |x| = |y + 1|
(2) x^y = x! + |y| St 1 : case 1 X= -9 , y = -10 ( where |X| < |Y|) |-9| = |-10 +1| ----> 9 = 9 case 2: where |X| > |Y| X = -3 , Y = 2 Insufficient. St 2 : X = 2, Y = 2 & X = 1, Y = 0 Inconsistent results. Insufficient. Combining st 1 & st 2; use X = 1, Y = 0 ( using both the statements together) we see |X| > |Y|. Pick C.
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Re: Algebra - Tough!
[#permalink]
26 Aug 2011, 12:32
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