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• ### $450 Tuition Credit & Official CAT Packs FREE January 15, 2019 January 15, 2019 10:00 PM PST 11:00 PM PST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • ### The winning strategy for a high GRE score January 17, 2019 January 17, 2019 08:00 AM PST 09:00 AM PST Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL. # How many multiples of 4 are there between 12 and 96, inclusive?  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Math Expert Joined: 02 Sep 2009 Posts: 52108 How many multiples of 4 are there between 12 and 96, inclusive? [#permalink] ### Show Tags 26 May 2010, 11:21 5 42 00:00 Difficulty: 15% (low) Question Stats: 73% (00:36) correct 27% (00:42) wrong based on 713 sessions ### HideShow timer Statistics How many multiples of 4 are there between 12 and 96, inclusive? (A) 21 (B) 22 (C) 23 (D) 24 (E) 25 Problem Solving Question: 11 Category: Arithmetic Properties of numbers Page: 63 Difficulty: 550 The Official Guide For GMAT® Quantitative Review, 2ND Edition _________________ ##### Most Helpful Expert Reply Math Expert Joined: 02 Sep 2009 Posts: 52108 Re: How many multiples of 4 are there between 12 and 96, inclusive? [#permalink] ### Show Tags 26 May 2010, 11:55 66 97 marcusaurelius wrote: How many multiples of 4 are there between 12 and 96, inclusive? 21 22 23 24 25 My answer was 21 and that's incorrect. $$# \ of \ multiples \ of \ x \ in \ the \ range = \frac{Last \ multiple \ of \ x \ in \ the \ range \ - \ First \ multiple \ of \ x \ in \ the \ range}{x}+1$$. In the original case: $$\frac{96-12}{4}+1=22$$. If the question were: how many multiples of 5 are there between -7 and 35, not inclusive? Last multiple of 5 IN the range is 30; First multiple of 5 IN the range is -5; $$\frac{30-(-5)}{5}+1=8$$. OR: How many multiples of 7 are there between -28 and -1, not inclusive? Last multiple of 7 IN the range is -7; First multiple of 7 IN the range is -21; $$\frac{-7-(-21)}{7}+1=3$$. Hope it helps. _________________ ##### Most Helpful Community Reply Manager Joined: 27 Jul 2010 Posts: 154 Location: Prague Schools: University of Economics Prague Re: How many multiples of 4 are there between 12 and 96, inclusive? [#permalink] ### Show Tags 02 Feb 2011, 03:20 5 Thanks Bunuel. One day, after my GMAT is over, and that day will come soon, you should bake a cake for you _________________ You want somethin', go get it. Period! ##### General Discussion Manager Joined: 06 Aug 2011 Posts: 51 Concentration: Entrepreneurship, Finance GPA: 3.87 Re: How many multiples of 4 are there between 12 and 96, inclusive? [#permalink] ### Show Tags 31 Oct 2013, 19:46 Why add one to the final result? I can count from 12-96 by four and come up with 22 that way, but I want to know the logic behind it. Math Expert Joined: 02 Sep 2009 Posts: 52108 Re: How many multiples of 4 are there between 12 and 96, inclusive? [#permalink] ### Show Tags 01 Nov 2013, 00:20 4 6 Stoneface wrote: Why add one to the final result? I can count from 12-96 by four and come up with 22 that way, but I want to know the logic behind it. Set of consecutive multiples of 4 is an evenly spaced set (arithmetic progression). If the first term of arithmetic progression is $$a_1$$ and the common difference of successive members is $$d$$, then the $$n_{th}$$ term of the sequence is given by: $$a_ n=a_1+d(n-1)$$ --> $$n=\frac{a_n-a_1}{d} + 1$$. Hope it helps. _________________ Manager Status: GMATting Joined: 21 Mar 2011 Posts: 105 Concentration: Strategy, Technology GMAT 1: 590 Q45 V27 Re: How many multiples of 4 are there between 12 and 96, inclusive? [#permalink] ### Show Tags 30 Dec 2013, 21:56 2 My approach would be this way: 12/4 = 3; 96/4 = 24; Since both are inclusive, I will go with (Last - First + 1) concept: 24 - 3 + 1 = 22; Ans is (B) EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 13325 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: How many multiples of 4 are there between 12 and 96, inclusive? [#permalink] ### Show Tags 23 Mar 2015, 21:30 1 Hi All, This is an example of a "fencepost" problem, since you have to include the "posts" (the numbers 12 and 96) in your calculation. There are a couple of different ways to approach these types of prompts, depending on what you're given and how comfortable you are with the 'technical aspects' of the math. Here, we have a pretty easy situation: we're asked for all the multiples of 4 between 12 and 96, INCLUSIVE (meaning we have to include the 12 and the 96). (4)(25) = 100, so there are 25 positive multiples of 4 when dealing with all positive integers from 1 to 100. (4)(24) = 96, so there are 24 positive multiples of 4 when dealing with all positive integers from 1 to 96, INCLUSIVE. We now have to remove the multiples of 4 that DO NOT fit the given range.... There are two: 4 and 8 24 - 2 = 22 total multiples of 4 Final Answer: GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: How many multiples of 4 are there between 12 and 96, inclusive?  [#permalink]

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19 Mar 2018, 15:10
marcusaurelius wrote:
How many multiples of 4 are there between 12 and 96, inclusive?

A. 21
B. 22
C. 23
D. 24
E. 25

We can determine the number of multiples of 4 from 12 to 96, inclusive, by using the following formula:

(largest multiple of 4 - smallest multiple of 4)/4 + 1

(96 - 12)/4 + 1 =84/4 + 1 = 21 + 1 = 22

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Re: How many multiples of 4 are there between 12 and 96, inclusive?  [#permalink]

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31 Oct 2018, 13:52
Is there a difference in the equation, when the numbers are not inclusive?
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Re: How many multiples of 4 are there between 12 and 96, inclusive?  [#permalink]

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31 Oct 2018, 18:07
Hi TestTaker9,

To answer your immediate question: YES - the equation would change IF we were NOT including 12 and 96. Since both of those numbers are multiples of 4, we would have to subtract 2 from the total. As an alternative, you could recalculate using the lower-most and upper-most multiples of 4 that would be in the range of what you were looking for. In your hypothetical, that would be 16 and 92.

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Re: How many multiples of 4 are there between 12 and 96, inclusive? &nbs [#permalink] 31 Oct 2018, 18:07
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