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Smita04
If xy < 4, is x < 2 ?

(1) y > 1
(2) y > x

From F.S 1, when y = 4, x = 0.5, xy<4 and x<2.Hence a YES for the question stem. However, for y = 3/2 and x = 2, xy<4 and x=2, hence a NO for the question stem.Insufficient.

From F. S 2, we know that y>x.

Had y been equal to x, we would have x*x<4 --> |x|<2 --> -2<x<2

However, as y>x, to maintain the above given inequality, the value of x will have to reduce even further. Thus, x <2. Sufficient.

B.
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Have a somewhat different solution for this one.

Given that XY <4 ...... Is X<2???

(1). Y > 1 => Y = GT 1 (Where GT = Greater than)

XY < 4 => X < (4/Y) (We can divide by a number >1 both sides)

=> X < (4/GT1) = > X < LT4 = > X < 4 Not sufficient as X can be 3 , 2 ,1 and so on so forth.

(2). Y>X

=> X GTX < 4

Substituting values X=2 , 2*3 < 4 Not true
X=1 , 1*2 < 4 true

Hence (B) !!
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Smita04
If xy < 4, is x < 2 ?

(1) y > 1
(2) y > x

Alternate solution (rather alternate interpretation) for this problem -
xy < 4 or x < 4/y

(1) y > 1: Interpret 4/y as 4/(1 and increasing). This implies x can be <2 or >2 - So not sufficient

(2) y > x: Interpret xy < 4 as x\(2\)<4 and since y is greater than x, it implies that x < 2 - So sufficient

Ans.
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- A is insufficient.
- Option B. what if x or y is negative integer. I don't see you mentioned it in your answer.
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nguyenduong
- A is insufficient.
- Option B. what if x or y is negative integer. I don't see you mentioned it in your answer.

nguyenduong,

Interpretation should be based on given (true) statements. Given here xy<4 and for pt. (2) y>x.

Take any signs, y has to be greater than x or greater part of the multiplication with x resulting in a product smaller than 4.
Consider if xy was 4 (xy=4) and y=x then both x & y would have been + /- 2. Now when the product reduces (product < 4), x has to be always less than the equal contribution i.e. 2.

Hope I could explain.
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nguyenduong
- A is insufficient.
- Option B. what if x or y is negative integer. I don't see you mentioned it in your answer.

The question asks whether x<2. Now, for (2) if x is negative, then x<0<2 and if y is negative, then x<y<0<2. In either case we have an YES answer to the question.
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why is E the right answer?
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Shouldn't statement 2 be sufficient?

If xy < 4 and y > x, then x must be less than 2.
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Shouldn't statement 2 be sufficient?

If xy < 4 and y > x, then x must be less than 2.

Yes, the correct answer is B, not E. Fixed the OA. Thank you.
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