If ab, is ac? 1.a/bc/b 2.5ab6bc

Question

If a>b, is a>c?

1.a/b>c/b

2.5ab>6bc

suneeta · Answer

I think the answer is D, Either.

Multiplying or dividing both sides of an inequality gives an equivalent inequality.

Therefore

a/b>c/b is equivalent to a>c
AND
5ab>6bc is equivalent to 5a>6c or a>6/5c

Therefore

a>c in either case.

suneeta · Answer

could someone explain the logic of E to me? I'm missing something obviously.....

brstorewala · Answer

Suneeta,

This is a very common trap.......if ab>ac, this does not imply that b>c.
here is the explanation

suppose a=1, b=3, c=2, which implies that ab>ac

in this case, b>c

however if a=-1, b=2 and c=3, which again implies that ab>ac

but in this case b is not greater than c

so it depends on the sign of the common variable on both sides. you can multiply or divide a variable on both sides of the inequality, only if you know the sign of an inequality. Remember, multiplying or dividing by a negative number changes the inequality sign.

hope that helps

suneeta · Answer

Thanks a lot! That definitely helps...

tzolkin · Answer

Ans : E

Another way to look at it :

1)
if b is +ve then : a>c
if b is -ve then : c>a
Insuff

2)
if b+ve then : 5a > 6c
if b -ve then : 5a < 6c
Insuff

Combined : a/b*(1+5b^2) > c/b*(1+6b^2)

if b=1, then 6a>7c, thus a>c
if b=-1, then 6a<7c thus c couldbe greater than a
try with fractions are ans is insufficient
Insuff

Ans : E

sparky · Answer

reusing the question...

If a>b, is a>c? 1.a/b>c/b 2.5ab>6bc

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