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

Redeem

Inequality - Kaplan Instructor please help!

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Senior | Next Rank: 100 Posts
Posts: 35
Joined: Mon Jul 11, 2011 11:47 am
Thanked: 1 times
Followed by:1 members

Inequality - Kaplan Instructor please help!

by AVbyT » Wed Aug 24, 2011 10:19 am
Question is from Kaplan Premier Practice Test 3 (CAT) - Online

If it is true that -6 <= n <= 10, which of the following must be true?

A. n < 8
B. n = -6
C. n > -8
D. -10 < n < 7
E. none of the above

Please explain why answer B is wrong and more importantly how C is correct?

Correct Choice: [spoiler](C)

We should start with answer choice (D) and move up the choices to see which one MUST be true. Choice (D) may be true, but if 7 n 10, then this statement is not true. Choice (C) must be true because all possible values of n specified by the inequality in the question stem are greater than -8. This is the correct choice. We can stop here. Choice (B) is incorrect because there are more values within the range in the question stem than just -6. Choice (A) may be true, but does not have to be. If 8 n 10, choice (A) is not true.[/spoiler]

Thanks,
Amit
Last edited by AVbyT on Thu Aug 25, 2011 5:51 am, edited 1 time in total.
Top
Source: — Quantitative Reasoning |
User avatar
Senior | Next Rank: 100 Posts
Posts: 64
Joined: Sun Jul 24, 2011 9:11 am
Thanked: 13 times
GMAT Score:610

by sumgb » Wed Aug 24, 2011 2:31 pm
choice B is wrong because it says n can take only value of -6 however given info says n could be from -6 to 10. so B is not necessarily true always. -3 is a legitimate value of n as per the given info. so n = -6 is not always true.

choice C says n > -8 and n lies between -6 and 10 both inclusive and hence is ALWAYS true.

hope this helps...
Top
User avatar
Senior | Next Rank: 100 Posts
Posts: 35
Joined: Mon Jul 11, 2011 11:47 am
Thanked: 1 times
Followed by:1 members

by AVbyT » Thu Aug 25, 2011 5:29 am
Sumgb,

n > -8 means that n can be -7 but that value does not fall between -6 and 10 so what am I missing here?

Thanks
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Thu Aug 25, 2011 10:13 am
AVbyT wrote:Sumgb,

n > -8 means that n can be -7 but that value does not fall between -6 and 10 so what am I missing here?

Thanks
You are accidentally reversing the order of the conditional (if then).

The "if" portion is that -6 < x < 10. In other words, it is definitely the case that -6 < x < 10. Our goal is to determine which conclusion can be drawn (the "then" portion).

So, if -6 < x < 10, then we know that x must be greater than -8 (answer choice C)

You state that "n > -8 means that n can be -7, but that value does not fall between -6 and 10"

Here, you are reversing the "if" and the "then." You are suggesting that n > -8 is the given information (the "if" part), when it is not. Since we are told that -6 < x < 10, it would be impossible for x to equal -7.

I hope that helps.

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Thu Aug 25, 2011 10:26 am
AVbyT wrote:Sumgb,

n > -8 means that n can be -7 but that value does not fall between -6 and 10 so what am I missing here?

Thanks
Here's another way to look at it. Consider this analogous question:

If x equals either 2 or 10, which of the following must be true?
(A) x < 6
(B) x > 0
etc

So, the given info (the "if" part) tells us that x can have 1 of 2 values.

(A) is incorrect. x could be less than 6 (if x=2), but x could also be greater than 6 (if x=10)

(B) is correct. If x equals 2 or 10, x must be positive. We can be certain of this.
Now, some might say, "If x is positive then x could equal 7" but this would be making the mistake of confusing the given (if) information with the consequence (then) part.

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
User avatar
Senior | Next Rank: 100 Posts
Posts: 35
Joined: Mon Jul 11, 2011 11:47 am
Thanked: 1 times
Followed by:1 members

by AVbyT » Thu Aug 25, 2011 12:03 pm
Ok, finally got my "aha moment" that each value of n from the question has to satisy the test in the answer choices

-6<=n<10 => n = -6, -5,..,0,...,9,10 and all these values are greater than -8 so therefore n > -8 is correct!

Thanks!
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 106
Joined: Fri Feb 05, 2010 9:39 am
Thanked: 4 times
Followed by:1 members

by czarczar » Fri Aug 26, 2011 7:41 am
Should be C only.
Top
Post new topic Post Reply
• Page 1 of 1