If xy x

Question

If xy < 4, is x < 2 ?

Notice that in order xy<4 to hold true at least one of the multiples must be less than 2 (if both x and y are more than or equal to 2 then xy>=2).

(1) y > 1. If for example \(y=1.5>1\) then \(x\) can be 1, so less than 2 or 2 so not less than 2. Not sufficient.

(2) y > x. According to above: \(y>x\geq{2}\) is not possible since in this case \(xy>2\), so \(x\) must be less than 2. Sufficient.

Answer: B.

Hope it's clear.

Smita04 · Answer

Yes Bunuel. It's clear. Thanks!

Bunuel · Answer

Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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Theory on Inequalities:
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mau5 · Answer

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

TGC · Answer

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) !!

Iaintgivinup · Answer

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. B

nguyenduong · Answer

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

Iaintgivinup · 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.

Bunuel · 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.

FlyingCycle · Answer

why is E the right answer?

Basshead · Answer

Shouldn't statement 2 be sufficient?

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

Bunuel · Answer

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

If xy < 4, is x < 2 ? (1) y > 1 (2) y > x

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