inequalities problem

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hazelnut: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Sat Jun 18, 2011 6:46 am

by hazelnut » Wed Jun 22, 2011 7:08 am

Hi,

Came across the following inequalities problem

If m and n are negative, is m/n less than 1 ?
(1) mn < 1
(2) m - n > n

Any help with be highly appreciated

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Source: Beat The GMAT — Data Sufficiency | Wed Jun 22, 2011 7:08 am

Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Wed Jun 22, 2011 7:20 am

Hi,
From(1): m and n are interchangeable. So we cannot say m/n is less than 1
example: if m = -1/2, n = -1/4, m/n = 2(greater than 1)
if m = -1/4, n = -1/2, m/n = 1/2(less than 1)
Not sufficient

From(2): m-n>n
So, m > 2n
As n is negative, m/n < 2
We can't say whether m/n is less than 1 or not
Not sufficient

Both(1)&(2): mn<1 and m>2n
if m = -1/2, n = -1/3, m/n = 3/2(>1)
if m = -1/6, n = -1/3, m/n = 1/2(<1)
Not sufficient

Hence, E

Cheers!

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