If a/b is less than 1, what has to be greater than 1?

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umaa: Legendary Member; Posts: 727; Joined: Sun Jun 08, 2008 9:32 pmFollowed by: 1 member; Thanked: 8 times

by umaa » Wed Jul 09, 2008 10:56 pm

If a/b is less than 1, what has to be greater than 1?

a.) b/a
b.) b/(a^2)
c.) a/2b
d.) sqrt(a/b)
e.) a/(b^2)

Answer is, A.

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Source: Beat The GMAT — Problem Solving | Wed Jul 09, 2008 10:56 pm

preetha_85: Senior | Next Rank: 100 Posts; Posts: 95; Joined: Sun Jul 06, 2008 6:41 am; Location: INDIA; Thanked: 2 times

by preetha_85 » Thu Jul 10, 2008 12:07 am

Hi

If a/b <1 this implies a<b>a
dividing both side by a
b/a >1

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bhuman111: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Sun Jul 06, 2008 6:34 pm

by bhuman111 » Thu Jul 10, 2008 1:02 am

The question as its stated must be wrong because it does not exclude negative numbers.

The OA is A. Lets take the two values:
a= -1
b= 4

(-1)/(4)

and

(4)/(-1)

Both are less than 1.

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umaa: Legendary Member; Posts: 727; Joined: Sun Jun 08, 2008 9:32 pmFollowed by: 1 member; Thanked: 8 times

by umaa » Thu Jul 10, 2008 1:07 am

right. I also believe that the answer is not A.

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CappyAA: Master | Next Rank: 500 Posts; Posts: 124; Joined: Mon Jun 16, 2008 11:07 amFollowed by: 14 members; Thanked: 21 times; GMAT Score:750

by CappyAA » Thu Jul 10, 2008 3:17 am

The question is stated wrong. Set a = 2 and b = 3

a/b = 2/3 <1> 1
b) b/a^2 = 3/4 < 1 - RULE OUT
c) a/2b = 2/6 < 1 - RULE OUT
d) sqrt(a/b) = sqrt(2/3) < 1 - RULE OUT
e) a/b^2 = 2/9 < 1 - RULE OUT

So it is valid in this case for A

But in negative numbers as a previous poster said, where a = 2 and b = -3, both a/b and b/a are negative. So A is the answer assuming both a and b are positive.

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olika: Senior | Next Rank: 100 Posts; Posts: 55; Joined: Sat Nov 10, 2007 10:35 am; Thanked: 1 times

by olika » Thu Jul 10, 2008 10:01 am

preetha_85 wrote:Hi

If a/b <1 this implies a<b>a
dividing both side by a
b/a >1

How can you divide by a, if you know nothing about it? Maybe a=0? You can't divide by zero.

I agree something seems to be missing in the problem.

If the statement 'a/b<1' is true, we have three cases:
1) both a and b >0, and a<b
2) a=0, b = any number
3) a - negative, b - positive, and visa versa a - positive, b - negative.

Thus, we should check all tree cases to come up with the answer.

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