If k is a positive integer, which of the following must be

Oldest

Best Reply

Author

Message

TAGS:

Manager

Joined: 16 Jan 2011

Posts: 87

Followers: 5

Kudos [?]: 8 [0], given: 12

If k is a positive integer, which of the following must be [#permalink]

05 Apr 2012, 13:04

00:00

Question Stats:

31% (02:24) correct

68% (01:25) wrong

based on 1 sessions

[Reveal] Spoiler: OA

GMAT Club team member

Joined: 02 Sep 2009

Posts: 11515

Followers: 1791

Kudos [?]: 9536 [3] , given: 826

Re: If k is a positive integer, which of the following must be [#permalink]

05 Apr 2012, 14:17

This post received
KUDOS

If k is a positive integer, which of the following must be divisible by 24?

(A) (k – 4)(k)(k + 3)(k + 7)
(B) (k – 4)(k – 2)(k + 3)(k + 5)
(C) (k – 2)(k + 3)(k + 5)(k + 6)
(D) (k + 1)(k + 3)(k + 5)(k + 7)
(E) (k – 3)(k + 1)(k + 4)(k + 6)

24=8*3.

Note that the product of two consecutive even integers is always divisible by 8 (since one of them is divisible by 4 and another by 2). Only option B offers two consecutive even numbers for any integer value of k: k-4 and k-2, if k=even or k+3 and k+5 if k=odd.

Also from the following 3 consecutive integers: (k-4), (k-3), (k-2) one must be divisible by 3, if it's not k-4 or k-2 then it must be k-3 (if it's k-4 or k-2 option B is divisible by 3 right away). But if it's k-3 then (k-3)+6=k+3 must also be divisible by 3.

So, option B: (k – 4)(k – 2)(k + 3)(k + 5) is divisible by 8 and 3 in any case.

Answer: B.
_________________

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!!

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!

What are GMAT Club Tests?
25 extra-hard Quant Tests

Find out what's new at GMAT Club - latest features and updates

Veritas Prep GMAT Instructor

Joined: 16 Oct 2010

Posts: 3105

Location: Pune, India

Followers: 567

Kudos [?]: 1994 [0], given: 92

Re: If k is a positive integer, which of the following must be [#permalink]

05 Apr 2012, 20:19

Galiya wrote:

Ideally, you should use the logical approach suggested by Bunuel above. If it doesn't come to mind during the test, you can also test the options for values of k.
Try putting k = 5, 6, 7 and 8 (0 is divisible by all numbers so k = 2, 3 and 4 doesn't make sense. Also, divisibility of a negative number does not have physical meaning)

The options will keep falling out one after the other and you will be left will only the answer.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save 10% on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Manager

Joined: 16 Jan 2011

Posts: 87

Followers: 5

Kudos [?]: 8 [0], given: 12

Re: If k is a positive integer, which of the following must be [#permalink]

06 Apr 2012, 12:15

Bunuel, Karishma
thank you so much for help!

Manager

Joined: 12 Oct 2011

Posts: 136

GMAT 1: 700 Q48 V37
GMAT 2: 720 Q48 V40

Followers: 2

Kudos [?]: 36 [0], given: 23

Re: If k is a positive integer, which of the following must be [#permalink]

15 Apr 2012, 03:52

I have a question. 0 is a multiple of every number, and thus 0 would also be divisible by 24, correct? So if k=3, E would also be divisble by 24, wouldn't it?

GMAT Club team member

Joined: 02 Sep 2009

Posts: 11515

Followers: 1791

Kudos [?]: 9536 [1] , given: 826

Re: If k is a positive integer, which of the following must be [#permalink]

15 Apr 2012, 03:59

This post received
KUDOS

BN1989 wrote:

I have a question. 0 is a multiple of every number, and thus 0 would also be divisible by 24, correct? So if k=3, E would also be divisble by 24, wouldn't it?

Zero is a multiple of every integer, except zero itself - true.

Next, the question asks "which of the following MUST be divisible by 24" not COULD be divisible. Now, every option COULD be divisible by 24 (for example A if k=4, C if k=2, D if k=-1, and E for k=3. Notice that these are not the only values of k for which these options are divisible by 24). But the only option which is divisible by 24 for ANY integer value of k is B.

Hope it's clear.
_________________

Re: If k is a positive integer, which of the following must be [#permalink] 15 Apr 2012, 03:59

		Similar topics	Author	Replies	Last post
Similar Topics:		If x and y are positive, which of the following must be	M8	6	12 May 2006, 05:03
	1	If x and y are positive, which of the following must be	ns	5	17 Jun 2006, 15:15
		If x and y are positive, which of the following must be	gmacvik	2	22 Sep 2006, 22:50
		If x and y are positive, which of the following must be	eagerbeaver	9	11 Oct 2006, 19:04
		If k^(xy)=1, where k#0, which of the following must be true	LM	5	26 Jan 2012, 06:46

If k is a positive integer, which of the following must be

Main navigation

GMAT Resources

Partners

MBA Resources

GMAT ® is a registered trademark of the Graduate Management Admission Council ® (GMAC ®). GMAT Club's website has not been reviewed or endorsed by GMAC.