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

Redeem

67 Find x from the inequality

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 226
Joined: Sun Aug 09, 2009 4:34 am

67 Find x from the inequality

by ern5231 » Sat Sep 26, 2009 4:00 am
x is an integer. What is the value of x in the expression 4 <(x-1) ^ 2 <16?

A.0
B.1
C.2
D.3
E.4

Cant we reduce this expression to 2<x-1<4? Then we get the answer as E. But the answer given is C.Please explain.
Last edited by ern5231 on Sun Oct 04, 2009 12:49 am, edited 1 time in total.
Top
Source: — Problem Solving |
Senior | Next Rank: 100 Posts
Posts: 64
Joined: Sat Aug 01, 2009 3:13 am
Thanked: 5 times
Followed by:1 members
GMAT Score:740

Re: Find x from the inequality

by mohitsharda » Sat Sep 26, 2009 6:45 am
ern5231 wrote:x is an integer. What is the value of x in the expression 4 <(x-1) ^ 2 <16?

A.0
B.1
C.2
D.3
E.4

Cant we reduce this expression to 2<x-1<4? Then we get the answer as E. But the answer given is C.Please explain.
x = 2 => expression becomes (2-1)^2 = 1
So, that should clearly not be the answer.
It should be 4.. maybe the given answer is wrong.
MS
Top
User avatar
Newbie | Next Rank: 10 Posts
Posts: 6
Joined: Thu Mar 20, 2008 5:05 pm
Location: Colorado Springs, CO
GMAT Score:550

by rajiishere » Sun Sep 27, 2009 5:47 am
If x is 2, then (x-1)^2 is (2-1)^2 which is 1. 4 is not less than 1. So, 2 could not be the answer. 4 should be the answer.
Top
Master | Next Rank: 500 Posts
Posts: 226
Joined: Sun Aug 09, 2009 4:34 am

by ern5231 » Sun Oct 04, 2009 12:48 am
Ok..but the OA is 2. Any views?
Top
Senior | Next Rank: 100 Posts
Posts: 43
Joined: Tue Mar 31, 2009 9:54 am
Thanked: 2 times

by glorydefined » Sun Oct 04, 2009 3:18 am
wats the source of the question?? answer looks 4 to me as well
Top
Newbie | Next Rank: 10 Posts
Posts: 9
Joined: Fri Sep 21, 2007 8:05 pm

by marie » Sun Oct 04, 2009 6:27 am
The answer is 4. There are multiple ways to attack this problem. Here's one;

4<(x-1)^2<16
4<x^2-2x+1<16
subtract 4 from all segments
0<x^2-2x-3<12
0<(x-3)*(x+1)<12
when x = 3 the quadratic is equal to zero. The above suggests the quadratic must be greater than zero and less than 12. Therefore x must = any number greater than 3 but less than 5. x= 4
Top
Post new topic Post Reply
• Page 1 of 1