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x not equal to -y
Source: Beat The GMAT — Data Sufficiency |
If x > -y, then denominator x + y > 0 and the question is "is x - y > x + y"? or "is y < 0?"
If x < -y, then denominator x + y < 0 and the question is "is x - y < x + y"? or "is y > 0?"
Statement 1) this doesn't reveal the relationship between x and -y, so it's not sufficient.
For example, if (x,y) is (5,10), then (5-10)/(5+10) = -5/15 < 1,
but if (x,y) is (5,-2) then [5-(-2)]/[5+(-2)] = 7/3 > 1
Statement 2) this doesn't reveal the relationship between x and -y either, so it's not sufficient.
For example, if (x,y) is (5,-10) then [5-(-10)]/[5+(-10)] = -15/5 = -3 < 1
but if (x,y) is (5,-2) then [5-(-2)]/[5+(-2)] = 7/3 > 1
Combined) The examples listed in statement 2 also adhere to the constraint in statement 1. Nothing is given about x and -y, so even combined the statements are insufficient.
E
If x < -y, then denominator x + y < 0 and the question is "is x - y < x + y"? or "is y > 0?"
Statement 1) this doesn't reveal the relationship between x and -y, so it's not sufficient.
For example, if (x,y) is (5,10), then (5-10)/(5+10) = -5/15 < 1,
but if (x,y) is (5,-2) then [5-(-2)]/[5+(-2)] = 7/3 > 1
Statement 2) this doesn't reveal the relationship between x and -y either, so it's not sufficient.
For example, if (x,y) is (5,-10) then [5-(-10)]/[5+(-10)] = -15/5 = -3 < 1
but if (x,y) is (5,-2) then [5-(-2)]/[5+(-2)] = 7/3 > 1
Combined) The examples listed in statement 2 also adhere to the constraint in statement 1. Nothing is given about x and -y, so even combined the statements are insufficient.
E
