Question from MGMAT CAT

[aakhoja]

QUESTION - If x and y are integers such that x < y < 0, what is x - y?
(1) (x + y)(x - y) = 5
(2) xy = 6

(1) (x + y)(x - y) = 5 can be rephrased to x square - y square = 5. Knowing that x < y < 0, x = -3 and y = -2 will be SUFFICIENT to ans x - y.
(2) NOT SUFFICIENT.

Hence the ans is 'A'

QUESTION - What is the ratio of r to s?
(1) r + s = 7
(2) r square - s square = 7

(1) Using the rational used in the above question to ans x square - y square = 5, r can be either 4 or -4 and s can be either 3 or -3. With this info, can we determine the ratio of r to s which will confirm 'B' to be the ans? The official ans is NO we can't determine the ratio just using (2) and we will also require (1). Is that because that helps (1) helps us to narrow the possibilities down to '3' and '4' so it helps eliminate -3, -4? Can ratios be negative? Therefore, the ans is 'C'. Just trying to better understand what am I missing.

Appreciate the help! Best wishes to all!

[aakhoja]

QUESTION - If x and y are integers such that x < y < 0, what is x - y?
(1) (x + y)(x - y) = 5
(2) xy = 6

(1) (x + y)(x - y) = 5 can be rephrased to x square - y square = 5. Knowing that x < y < 0, x = -3 and y = -2 will be SUFFICIENT to ans x - y.
(2) NOT SUFFICIENT.

Hence the ans is 'A'

QUESTION - What is the ratio of r to s?
(1) r + s = 7
(2) r square - s square = 7

(1) Using the rational used in the above question to ans x square - y square = 5, r can be either 4 or -4 and s can be either 3 or -3. With this info, can we determine the ratio of r to s which will confirm 'B' to be the ans? The official ans is NO we can't determine the ratio just using (2) and we will also require (1). Is that because (1) helps us to narrow the possibilities down to '3' and '4' so it helps eliminate -3, -4? Can ratios be negative? Therefore, the ans is 'C'. Just trying to better understand what am I missing.

Appreciate the help! Best wishes to all!

[RonPurewal]

QUESTION - If x and y are integers such that x < y < 0, what is x - y?
(1) (x + y)(x - y) = 5
(2) xy = 6

(1) (x + y)(x - y) = 5 can be rephrased to x square - y square = 5. Knowing that x < y < 0, x = -3 and y = -2 will be SUFFICIENT to ans x - y.
(2) NOT SUFFICIENT.

Hence the ans is 'A'

QUESTION - What is the ratio of r to s?
(1) r + s = 7
(2) r square - s square = 7

(1) Using the rational used in the above question to ans x square - y square = 5, r can be either 4 or -4 and s can be either 3 or -3. With this info, can we determine the ratio of r to s which will confirm 'B' to be the ans? The official ans is NO we can't determine the ratio just using (2) and we will also require (1). Is that because that helps (1) helps us to narrow the possibilities down to '3' and '4' so it helps eliminate -3, -4? Can ratios be negative? Therefore, the ans is 'C'. Just trying to better understand what am I missing.

Appreciate the help! Best wishes to all!

i don't really understand this post 100%. in particular, it doesn't look as though you're even using the first question you posted.

in any case, if r^2 = 16 and s^2 = 9, then there are actually FOUR possibilities:
r = 4, s = 3;
r = 4, s = -3;
r = -4, s = 3;
r = -4, s = -3.
for the first and last of these, the ratio is 4/3. for the second and third, the ratio is -4/3. (yes, ratios can be negative.)

taking the first statement as well eliminates all but the first possibility.