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

Redeem

inequality (urgent)

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 418
Joined: Wed Jun 11, 2008 5:29 am
Thanked: 65 times

by bluementor » Fri Feb 27, 2009 3:57 am
(X-5) ^ 2 < |X-1| , x is an integer

If x = 2, the inequality will not hold. Therefore choices A, D and E are out.
If x = 0, the inequality will not hold. Therefore choice B is out.

Choose C.

-BM-
Top
Master | Next Rank: 500 Posts
Posts: 353
Joined: Sat Jan 20, 2007 1:29 am
Location: Italy
Thanked: 7 times
GMAT Score:720

by mjjking » Fri Feb 27, 2009 3:58 am
X>5
Beat The GMAT - 1st priority
Enter a top MBA program - 2nd priority
Loving my wife: MOST IMPORTANT OF ALL!

REAL THING 1 (AUG 2007): 680 (Q43, V40)
REAL THING 2 (APR 2009): 720 (Q47, V41)
Top
Senior | Next Rank: 100 Posts
Posts: 33
Joined: Sat Jan 17, 2009 3:48 pm
Thanked: 1 times

by GID09 » Fri Feb 27, 2009 10:36 am
If X>5..say X=10 .....5^2 <9 ....it doesn't hold as well. I am not sure how to pursue. Anybody?
Top
Master | Next Rank: 500 Posts
Posts: 106
Joined: Wed Feb 04, 2009 6:09 am
Location: Louisville, KY
Thanked: 8 times

Re: inequality (urgent)

by marcusking » Fri Feb 27, 2009 11:14 am
mariah wrote:X- integer, if (X-5) ^ 2 < the absolute value of X-1

than x must be


1)X<5
2)X<1
3)X>5
4)X>1
5)X>O
Not sure if there is a good answer

Let's try every answer
A.) -5 < 5 so (-5-5)^2 = 100 < 5-1 false
B.) use the same thing as A (-5) false
C.) 10 > 5 so (10-5)^ = 15 < 10-1 false
D.) use the same as C (10) false
E.) use the same as C & D (10) false.

None are always true. Where is this question from?
Top
Master | Next Rank: 500 Posts
Posts: 221
Joined: Wed Jan 21, 2009 10:33 am
Thanked: 12 times
Followed by:1 members

by krisraam » Fri Feb 27, 2009 1:43 pm
The only values that satisfy the inequation are

3<x<8

Thanks
raama
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 2623
Joined: Mon Jun 02, 2008 3:17 am
Location: Montreal
Thanked: 1090 times
Followed by:355 members
GMAT Score:780

Re: inequality (urgent)

by Ian Stewart » Fri Feb 27, 2009 1:44 pm
marcusking wrote: None are always true.
But the question doesn't ask 'which of the following is always true?' It asks 'which of the following must be true?' There's quite a difference, and this is the reason why you cannot simply plug in different values of x into each inequality. To illustrate, consider the following question:

If x = 1, what must be true?
A) x < 1
B) x < 0
C) x = 5
D) -1 < x < 1
E) x < 1000

That's a perfectly valid question, and the answer is E; if x is equal to 1, then it certainly must be true that x is less than 1000. It doesn't matter that there are numbers less than 1000 which cannot be equal to x.

So, in the question above, we aren't looking for an inequality that describes every possible solution for x; we're only looking for an inequality which contains every possible solution for x, perhaps along with some values that are not solutions for x.

To find the solutions to the inequality, I graphed y = |x-1| and y = (x-5)^2 to see that the only possible solutions for x are close to the value x=5. Since x is an integer, we can find all possible values: x = 4, 5, 6, 7. It's still a badly designed question, because the problem now is that there are then two correct answers - D) and E) - since if x is one of the values 4, 5, 6 or 7, it clearly must be true that x > 1, and also that x > 0.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com
Top
Post new topic Post Reply
• Page 1 of 1