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0 < a < 2 < b

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by sanju09 » Thu Jul 22, 2010 4:50 am
If a and b are any numbers such that 0 < a < 2 < b, then which of the following must be true?
(A) a < (a b)/2 < b
(B) 0 < a b < 2 a
(C) a < a b < 2
(D) 0 < a b < 2
(E) a b < b

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by Patrick_GMATFix » Thu Jul 22, 2010 5:24 am
Your answer choices have a lot of (a b). What is the operation between a and b? is it ab? a+b?

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by kvcpk » Thu Jul 22, 2010 5:38 am
If a and b are any numbers such that 0 < a < 2 < b, then which of the following must be true?
put a=1, b=3

(A) a < (a b)/2 < b
1<3/2<3
(B) 0 < a b < 2 a
0<3<2 .. NOt possible
(C) a < a b < 2
1<3<2 .. Not Possible
(D) 0 < a b < 2
0<3<2.. Not possible
(E) a b < b
3<3.. Not possible

pick A
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by sanju09 » Thu Jul 22, 2010 5:51 am
Patrick_GMATFix wrote:Your answer choices have a lot of (a b). What is the operation between a and b? is it ab? a+b?

-Patrick
sorry if it bothered you, well...I represent a multiplied to b as "a b".
The mind is everything. What you think you become. -Lord Buddha



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by Patrick_GMATFix » Thu Jul 22, 2010 6:07 am
Hi Sanju. Thank you for clarifying. It did not bother me at all :-)

I agree with kvcpk's answer. My approach to 'must be true' questions is to make the answer choices false if possible.

0<a<2<b

(A) - must be true
(B) If you divide by a, you will get 0<b<2. Since b is greater than 2, this is always false.
(C) If a=1 and b=100 then ab will not be less than 2. this answer could be false
(D) Same logic as C. This answer could be false
(E) If you divide by b, you will get a<1. This doesn't have to be true (a could be 0.5 or 1.5).

A is the answer.

Alternatively, we could talk about the reason A must be true: (A) a < ab/2 < b

Multiply all by 2 to get 2a<ab<2b:
>> 2a<ab must be true because 2<b
>> 2a<2b must be true because a<b
>> ab<2b must be true because a<2

A is the answer.

To create drills with similar questions, set topic='Inequalities' and difficulty='500-600 & 600-700' in the Drill Generator

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