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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.
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Archived GMAT Club Tests question - no more replies possible.
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.
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 _________________
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. _________________
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 _________________
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.
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. _________________
PhD in Applied Mathematics Love GMAT Quant questions and running.