Is xyab ?

Question

Is xy > ab ?

(1) b/x > y/a
(2) (ab)^2 > (xy)^2

Kudos for a correct  solution .

Bunuel · Accepted Answer

VERITAS PREP OFFICIAL SOLUTION:

Solution: E

Statement (1) tells us nothing about whether x or a are positive, so we aren’t able to get a definitive answer by multiplying both sides of the equation by x and a, respectively, as we don’t know whether to flip the sign; INSUFFICIENT. Statement (2) is likewise INSUFFICIENT because we still don’t know whether any of the variables are negative. Combined, we still don’t know about what’s positive and what’s negative, so xy could be negative and ab positive or vice versa; (E).

pacifist85 · Answer

Hey,

I would say D.

says that  \frac{b}{x}  >  \frac{y}{a} 
If we cross multiply we get that ab>xy. So the answer is No, so it is sufficient.

gives the same relationship we found for  , but squared. I think it means the same, because if I remember correctly, we only take the positive value of a radical in GMAT.

So, it is also sufficient.

TheKingInTheNorth · Answer

Is xy > ab ?

(1) b/x > y/a
(2) (ab)^2 > (xy)^2

Kudos for a correct solution.

1) b/x > y/a
variable involved and we dont know the sign . therefore cant multiply . not sufficient.

2)(ab)^2 > (xy)^2
since both side are raised to the power 2 .
both ab and xy , can be positive or negative .

(ab)^2 > (xy)^2
let ab =2 and xy = 1 
then (ab)^2 > (xy)^2 satisfied 
 but
 Is xy > ab ? No

let ab = -1 and xy =1/2 
then (ab)^2 > (xy)^2 satisfied 
 but
 Is xy > ab ? yes

st .2 is not sufficient

together both 1 and 2 not sufficient . Since dont give any information that is helpful to solve the question 
Hence E

Regards,

Press Kudos if you like my post .

sahilvijay · Answer

-------------------- Is xy>ab 1) b/x > y/a : b=2 ,a=1, y=1, x =1 yields 2>1 so we can use these values ----> xy=1 ab =2 xy-1 so we can use these values-----------> xy=1 ab =-2 xy>ab A and D eliminated 2) (ab)^2 > (xy)^2 : same values as above same set as above in one case take a=1 and other a=-1 using same values as statement 1) where a=1 we get xy>ab using same values as statement 1) where a=-1 we get xyab Insufficient C eliminated E is the Answer

Mo2men · Answer

(2) (ab)^2 > (xy)^2 It means |ab| > |xy|......We do not know if ab > xy. For example ab = -6 & xy =-5...........Answer to question is Yes ab = 6 & xy =-5...........Answer to question is No Insufficient (1) b/x > y/a If x>0 & a>0.......ab > xy ...........Answer is No (Note: it is the same as x<0 & a<0) If x>0 & a<0.......ab < xy ...........Answer is Yes (Note: it is the same as x<0 & a>0) Insufficient combine 1 & 2 Take same examples above...No clear cut Insufficient Answer: E

azhrhasan · Answer

No. You can't cross multiply because nowhere the signs of any of the variables is specified.
Instead, You have to bring everything on one side of the inequality and then take LCM. If you do this, You will end up noticing that ab>xy depends on the value of a and x. If both have the same sign, then ab>xy, otherwise ab<xy. Therefore, Not sufficient.

You need to take the same approach for the statement 2, you will again end up with insufficiency.

PS: cross multiplication is allowed only when the signs of the variables are known. Even in that situation, you need to be very sure with inequality. Best approach is not to cross multiply but bring all variables on one side of the inequality and then review.

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Is xy>ab ?

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