Inequality - Kaplan Instructor please help! - The Beat The GMAT Forum

Inequality - Kaplan Instructor please help!

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AVbyT: Senior | Next Rank: 100 Posts; Posts: 35; Joined: Mon Jul 11, 2011 11:47 amFollowed by: 1 member; Thanked: 1 times

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.

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Source: Beat The GMAT — Quantitative Reasoning | Wed Aug 24, 2011 10:19 am

sumgb: 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...

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AVbyT: Senior | Next Rank: 100 Posts; Posts: 35; Joined: Mon Jul 11, 2011 11:47 amFollowed by: 1 member; Thanked: 1 times

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

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; 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

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; 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

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AVbyT: Senior | Next Rank: 100 Posts; Posts: 35; Joined: Mon Jul 11, 2011 11:47 amFollowed by: 1 member; Thanked: 1 times

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!

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czarczar: Master | Next Rank: 500 Posts; Posts: 106; Joined: Fri Feb 05, 2010 9:39 amFollowed by: 1 member; Thanked: 4 times

by czarczar » Fri Aug 26, 2011 7:41 am

Should be C only.

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