BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

0 < a < 2 < b

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 am
Location: India
Thanked: 267 times
Followed by:80 members
GMAT Score:760

0 < a < 2 < b

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

[spoiler]Source: made by me for
www.avenuesabroad.org[/spoiler]
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
Top
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 1052
Joined: Fri May 21, 2010 1:30 am
Thanked: 335 times
Followed by:98 members

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?

-Patrick
  • Ask me about tutoring.
Top
User avatar
Legendary Member
Posts: 1893
Joined: Sun May 30, 2010 11:48 pm
Thanked: 215 times
Followed by:7 members

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
Top
User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 am
Location: India
Thanked: 267 times
Followed by:80 members
GMAT Score:760

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



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
Top
User avatar
GMAT Instructor
Posts: 1052
Joined: Fri May 21, 2010 1:30 am
Thanked: 335 times
Followed by:98 members

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

-Patrick
  • Ask me about tutoring.
Top
Post new topic Post Reply
• Page 1 of 1