M15 Q11

Question

Is  |x - y| \gt |x + y|  ?

x^2 - y^2 = 9 
  x - y = 2

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
 Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
 BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
 EACH statement ALONE is sufficient
 Statements (1) and (2) TOGETHER are NOT sufficient

Statement (1) by itself is insufficient. S1 gives us information about  (x - y)(x + y)  but does not tell how  (x - y)  and  (x + y)  compare to each other.

Statement (2) by itself is insufficient. S2 gives no information about  (x + y)  .

Statements (1) and (2) combined are sufficient. From S1 and S2 it follows that  2(x + y) = 9  from where  (x + y) = 4.5  . Now we can state that  |x - y| = 2 \lt |x + y| = 4.5  .
The correct answer is C.

I can't get the right numbers to test statement 2 to prove it Insuff. Please help. All the numbers I tried have me NO. Please help.

souvik101990 · Answer

statement 1
 x^2 - y^2 = 9 
or, (x+y)(x-y)=9
Clearly not sufficient (different combinations of x+y and x-y are possible)

statement 2
x-y=2
not sufficient with no info on (x+y)

combining both together
x+y=9/2
x-y=2

so |x-y|<|x+y|
Sufficient
Hence C

teal · Answer

can you please suggest some numbers to prove statement 2 insuff??

souvik101990 · Answer

consider x=2 and y=4
in this case |x+y| i.e 6>|x-y| i.e 2
Again consider x=2 and y=-4
in this case |x+y| ie 2 < |x-y| i.e 6
hope this helps.

souvik101990 · Answer

in general if you want to plug in numbers in questions like these, you need to consider positive, negative and fractional values of all the variables to eleminate/consider one option
Cheers

palsays · Answer

For statement 2, use these values to prove that the statement alone is insufficient.

x=2 and y=0 
x=3 and y=1
x=-1 and y=-3

Always make a point to check for the inequality with 0 as a value.

Kind Regards,
Ravender

souvik101990 · Answer

@palsays 
I dont think your values provide insufficiency
for x=2, y=0 |x+y|>|x-y|
for x=3, y=1 |x+y|>|x-y|
for x=-1, y=-3 |x+y|>|x-y|

You have to make one variable negative and one variable postive to show that |x+y|<|x-y|
Cheers

EvaJager · Answer

In fact, the given inequality can be rewritten as  (x-y)^2>(x+y)^2  - we can square both sides, as they are both positive. Rearranging the terms, the question becomes  xy<0  (is the product xy negative)?

Then, it is much easier to understand that neither (1), nor (2) alone is sufficient.
Taking both statements, one can explicitly find the values of x and y (although not necessary), and check whether their product is negative.
That's why the correct answer should be C.

souvik101990 · Answer

yeah true that. Precisely my point.

M15 Q11

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