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How many multiples of 4 are there between 12 and 96, inclusive?
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26 May 2010, 11:21
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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
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Re: How many multiples of 4 are there between 12 and 96, inclusive?
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26 May 2010, 11:55
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: \(\frac{9612}{4}+1=22\). 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.
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Re: How many multiples of 4 are there between 12 and 96, inclusive?
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02 Feb 2011, 03:20
Thanks Bunuel. One day, after my GMAT is over, and that day will come soon, you should bake a cake for you




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Re: How many multiples of 4 are there between 12 and 96, inclusive?
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31 Oct 2013, 19:46
Why add one to the final result? I can count from 1296 by four and come up with 22 that way, but I want to know the logic behind it.



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Re: How many multiples of 4 are there between 12 and 96, inclusive?
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01 Nov 2013, 00:20
Stoneface wrote: Why add one to the final result? I can count from 1296 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: \(a_ n=a_1+d(n1)\) > \(n=\frac{a_na_1}{d} + 1\). Hope it helps.
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Re: How many multiples of 4 are there between 12 and 96, inclusive?
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30 Dec 2013, 21:56
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)



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Re: How many multiples of 4 are there between 12 and 96, inclusive?
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23 Mar 2015, 21:30
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
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Re: How many multiples of 4 are there between 12 and 96, inclusive?
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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 Answer: B
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Re: How many multiples of 4 are there between 12 and 96, inclusive?
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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?
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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 lowermost and uppermost multiples of 4 that would be in the range of what you were looking for. In your hypothetical, that would be 16 and 92. GMAT assassins aren't born, they're made, Rich
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How many multiples of 4 are there between 12 and 96, inclusive?
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16 May 2019, 19:02
Total multiples of 4 to 96 =96/4=24 4 has two multiples up to 12 which are 4 & 8. So, multiples of 4 for 12 to 96 inclusive= 242=22 (Ans. B)
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Re: How many multiples of 4 are there between 12 and 96, inclusive?
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18 May 2019, 14:36
Since all the numbers will be in ap So the first number will be 12 and last is 96. An=a+(n1)d 96=12+(n1)4 21=n1 N=22
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Re: How many multiples of 4 are there between 12 and 96, inclusive?
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18 May 2019, 14:37
Since all the numbers will be in ap So the first number will be 12 and last is 96. An=a+(n1)d 96=12+(n1)4 21=n1 N=22
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Re: How many multiples of 4 are there between 12 and 96, inclusive?
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18 Aug 2019, 23:47
TestTaker9 wrote: Is there a difference in the equation, when the numbers are not inclusive? Yes there will be a difference then. The range would be 16 to 92 and in between there are 76 numbers out of which 19 will be divisble by 4 and +1, 20 would be the answer.
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Re: How many multiples of 4 are there between 12 and 96, inclusive?
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