Is xy 1? (1) x 1/y (2) y is positive

Question

Is xy > 1?

(1) x > 1/y

(2) y is positive

Staphyk · Answer

It a long time I solved Quant questions,but let see
Is xy > 1? Yes? Or xy <or =1? No

(1) x > 1/y
Now since, we don’t know the sign of y we can’t divide nor multiply
So algebra out ,let’s go number picking
When x= 2 , y= 3 —> Yes! xy>1
However, x=2 ,y=-3 —> xy<1
(You! ain’t sufficient)

(2) y is positive
No info. about x (can be -ve /+ve)
(You! ain’t sufficient)

(1+2) y= +ve (since we know the sign of y now we can go the algebra way quickly)

y•x >1/y•y —> xy>1
(O boy! you sufficient

)

C like Capecoast

Posted from my mobile device

) C like Capecoast Posted from my mobile device

CrackverbalGMAT · Answer

This is a Yes/No type of question which involves plugging in values.

Constraints: None. x, y can be any type of number, integers or fractions (negative or positive)

Statement 1: \(x > \frac{1}{y}\)

Most would think that cross multiplying, we get xy is > 1, and therefore it answers our question. This can only be possible if both x and y are positive.

Lets put in some values and see.

Both positive: x = 2, y = 2; \(2 > \frac{1}{2}\) and xy = 4 which is > 1. Therefore YES

Both negative: x = -0.2, y = -2; \(-0.2 > \frac{1}{-2}\) and xy = 0.4 which is < 1. Therefore NO

Statement 1 is Insufficient. Answer options could be B, C or E

Statement 2: y is positive

If x is positive, then xy will be > 0, but can be greater than 1, equal to 1 or less than 1.

Let us check this with some values

x = 0.2, y = 4, xy = 0.8 which is < 1

x = 0.5, y = 2, xy = 1

x = 2, y = 4, xy = 8 which is > 1

If x is negative, then xy will definitely be less than 0.

Statement 2 is Also Insufficient. Answer Options could be C or E

Combining Both Statements: \frac{1}{y}[/m] and y is positive

This, as discussed in statement 1, cross multiplying we get xy > 1

Therefore Both Statements together are sufficient.

Option C

Arun Kumar

IanStewart · Answer

Using Statement 1, if y is positive, we can multiply by y on both sides without reversing the inequality, and then xy > 1 (notice that means that the two Statements together will certainly be sufficient). But if y is negative, 1/y is negative, and then x could be any positive number. In that case, xy will be negative, so certainly will not be greater than 1. So Statement 1 is not sufficient alone. Statement 2 is clearly insufficient alone, so the answer is C.

Is xy > 1? (1) x > 1/y (2) y is positive

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