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If x + y >0, is x > |y|? confused...

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If x + y >0, is x > |y|? confused...

by isisalaska » Sun Jan 21, 2007 10:20 am
22. If x + y >0, is x > |y|?
(1) x > y
(2) y < 0

Is the answer a D or an E, I think is an E and here is why:

Let's say y=-5
X is > y but when Y is |5| X will NOT be > than Y
I have been trying to find examples and I still think is E. Help please?
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by MaleInNC2007 » Mon Jan 22, 2007 7:32 pm
I say the answer is D.

Looking at (1):
If x is greater than y and, (as the problem states) x + y is greater than 0 then x must always be positive.

if x is positive and is greater than y then:
4 + 3 is greater than 0 and 4 is greater than 3; if y is negative then it still must satisfy x + y is greater than 0 so the absolute | y | must be less than x; for example using the -5 you have x would need to be a positive number greater than |-5| for x + y greater than 0; i.e. 6 + (-5) is greater than 0

If you use a number less than 5 then the equation x + y is greater than 0 cannot be satisfied; i.e. 4 + (-5) = -1 and this is not greater than zero.

After doing (1) we know the answer cannot be (E) so now we go to (2) to see if the answer is possibly (D) or (A)

Looking at (2):
(2) states y is less than 0

We know from the problem that x + y is greater than 0; thus if
y is less than 0 , x must be positive which is similar to the answer
above. Consequently, | y | must be less than x, otherwise x + y
is greater than 0 cannot be satisfied.

Looking at the -5 you posted, we can insert that in the equations:

x + y is greater than 0; if y = -5 then x must be a number greater than positive 5
for the equation to be true; thus we can use 6 + (-5) is greater than 0.

Checking to see if x is greater than | y | we get 6 is greater than | -5 | or 6 is greater than 5

Just to make sure I am correct we can play with the numbers and pick a
number less than | y |, such as 4; 4 + (-5) = -1 wich does not
satisfy the equation x + y is greater than 0 so we see we cannot use a number X
that is less than the absolute value of Y.
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by isisalaska » Tue Jan 23, 2007 10:55 am
Thank you for yrou answer MaleInNC2007
However, I cannot understand the explanation due to some characters, like symbols unknow. What browser are you using?
Is tehre any way you can send me the answer again? Thansk! :)
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by beatthegmat » Tue Jan 23, 2007 11:05 am
Sorry for the messed up formatting--it will all be fixed within 24 hours, thanks!
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Re: If x + y >0, is x > |y|? confused...

by colinbendell » Tue Jan 23, 2007 9:57 pm
isisalaska wrote:22. If x + y >0, is x > |y|?
(1) x > y
(2) y < 0
I solved it another way:

From the question: x > -y (transposing from x+y > 0)

With 1) any value of x > y must also be x > -y which is the same thing as saying x > |y| SUFFICIENT

With 2) y is negative and when you plug it into the first equation you will convert the neg value to a positive value [eg: x > -(-5)]. Therefore no matter what y is, x will always be a greater positive number. SUFFICIENT
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