Is x

Question

Is x < 10 < y?

(1) x < y and xy = 100
(2) x^2 < 100 < y^2

M36-81

grassbird · Answer

This question, from first glance, is asking the positivity or negativity of X and Y.

(1) alone is not sufficient, take x=-20, y=-5, it works; take x=5,y=20, also works. Therefore, not sufficient. 
(2) alone is not sufficient neither, take x=-5, y=-20, it works; take x=5. y=20, it also works. multiple suitable cases means its not sufficient.

Combine (1) and (2) together, X <Y and XY=100 AND X^2 <100 < Y^2. This confirms that X and Y must be >0, while X must be smaller than 10 and Y is bigger than 10. Which means yes its sufficient to determine the statement (The statement is true, but we don't really need that, we just want to know if the info given is enough to DETERMINE the statement)

So C, both statements together are sufficient, but neither statement alone is sufficient.

chetan2u · Answer

(1) x < y and xy = 100 Both x and y could be negative.....x=-20 and y=-5......answer is NO x=5 and y=20....answer is yes Insufficient (2) x^2 < 100 < y^2 -1010 x could be -5 or 5, while y can be 20 or -20 x=-5 and y=-20.....No x=5 and y=20.....Yes Insufficient Combined If -1010, then x10. If y>10 and xy =100, x has to be less than 10.. Thus x<10

Bunuel · Answer

Official Solution: Is x < 10 < y ? (1) x < y and xy = 100 If x=-20 and y=-5 , then the answer is NO but if x=5 and y=20 , then the answer is YES. Not sufficient. Notice that from xy = 100 we can deduce that x and y have the same sign. (2) x^2 < 100 < y^2 The above gives: -10 < x < 10 and |y|>10 . So, y can be more than 10 as well as less than -10. Not sufficient. (1)+(2) Since given that x < y and -10 < x < 10 , then y < -10 is not possible, thus y > 10 . So, we have that x < 10 < y . Sufficient. Answer: C

Bunuel · Answer

Similar question from OG: https://gmatclub.com/forum/if-x-and-y-a ... 39873.html

Serena11 · Answer

Can someone please explain how we will solve taking both statements together?

Bunuel · Answer

Here is slightly rephrased solution, hope it helps. Official Solution: Is x < 10 < y ? (1) x < y and xy = 100 : If x=-20 and y=-5 , then x < y but 10 is not between them, so the answer is NO. However, if x=5 and y=20 , then the answer is YES. Not sufficient. (2) x^2 < 100 < y^2 The first inequality, x^2 < 100 , implies -10 < x < 10 . So, we are left to establish whether y > 10 . The second inequality, 100 < y^2 , implies y > 10 or y < -10 . So, we can have the following two cases: a. If y > 10 , then x < 10 < y is true. b. If y < -10 , then x > y , and therefore x < 10 < y is false. Not sufficient. (1)+(2) Since from (1) we have that x < y , then case b from (2), saying that x > y , cannot be true, hence we are left with case a , and therefore, x < 10 < y . Sufficient. Answer: C

Is x < 10 < y? (1) x < y and xy = 100 (2) x^2 < 100 < y^2

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