If a, b, and c are real numbers, is a/b b/c ?

Question

If a, b, and c are real numbers, is a/b > b/c ?

(1) a > c
(2) ac > b^2

shrouded1 · Answer

Is a/b > b/c ?
 \frac{a}{b} \gt \frac{b}{c} 
 \frac{a}{b} - \frac{b}{c} \gt 0 
 \frac{ac-b^2}{bc} \gt 0

(1) Clearly inssufficient, as it doesnt say anything about b. Consider the simple case where ac=b and where ac is not equal to b, in the former case the answer is always no and in the latter it could be yes or no.

(2) ac>b^2 ... Only sufficient if know about the sign of bc, which is unknown. Insufficient

(1+2) ac>b^2 so numerator is >0. But a>c tells us nothing about denominator. Insufficient, could be true or false.

Answer is (e)

vitamingmat · Answer

ac > b^2 .... i have a doubt with the B option.

i can write the above one as ac/b > b 
 ====>a/b > b/c

so i can say this is stright to to ans ....

Please let me know if i am wrong

shrouded1 · Answer

In an inequality, when you divide both sides, the sign of the inequality remains the same if the number you are dividing by is positive otherwise it flips. So you are assuming b>0, which is why you are going wrong. Eg. 4>2 hence 4/2> 2/1 OR 2>1 4>2 hence 4/-2 < 2/-2 OR -2 < -1

vitamingmat · Answer

Thanks shrouded1 .. I did not consider it ...thxs for the reply

Bunuel · Answer

Is a/b > b/c?

(1) a > c
(2) ac > b^2

rohit8865 · Answer

Is a/b-b/c>0
(ac-b^2) / bc > 0 ??

(1) no info of b ...thus insuff

(2) ac > b^2
or ac-b^2>0 thus we know numerator is >0 but we don't have info of denominator( bc) 
let a=5 , c=3 && b=2 then YES
but if a=5 , c=3 && b= -2 then NO

thus insuff

Combining also we have no info on value b
thus insuff

Ans E

Bunuel · Answer

The highlighted part above is redundant. All numbers on the GMAT are real by default.

bumpbot · Answer

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If a, b, and c are real numbers, is a/b > b/c ?

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If a, b, and c are real numbers, is a/b > b/c ?

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