Multiples of 4 between 12 and 96

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money9111: Legendary Member; Posts: 2109; Joined: Sun Apr 19, 2009 10:25 pmFollowed by: 79 members; Location: New Jersey; Thanked: 109 times; GMAT Score:640

by money9111 » Mon Feb 01, 2010 8:34 pm

How many multiples of 4 are there between 12 and 96, inclusive?

a. 21
b. 22
c. 23
d. 24
e. 25

didn't know where to begin with this one either... this is the last question out of my problem set that I did not get... if you'll notice there's a theme with the questions I've just posted... all the same topic... Exponents, Odds & Evens, Postives, Negatives, and Roots were all easy for me... ::sigh::

OA B

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Source: Beat The GMAT — Problem Solving | Mon Feb 01, 2010 8:34 pm

kabirmohammed: Junior | Next Rank: 30 Posts; Posts: 15; Joined: Mon Nov 23, 2009 6:23 pm; Thanked: 1 times

by kabirmohammed » Mon Feb 01, 2010 8:44 pm

How many multiples of 4 are there between 12 and 96, inclusive?

a. 21
b. 22
c. 23
d. 24
e. 25

Multiples of 4 are : 12, 16, 20, 24, ........, 96
for a evenly spaced set: total no of terms = (last - first)/increment
= 96-12/4
= 21
as the question ask for inclusive = 21+1 =22

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money9111: Legendary Member; Posts: 2109; Joined: Sun Apr 19, 2009 10:25 pmFollowed by: 79 members; Location: New Jersey; Thanked: 109 times; GMAT Score:640

by money9111 » Mon Feb 01, 2010 8:52 pm

ah ha... "Last-First/increment"... going in my notecards... thanks!

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Cally627: Newbie | Next Rank: 10 Posts; Posts: 9; Joined: Sun Mar 11, 2012 7:42 pm

by Cally627 » Sun Apr 29, 2012 9:22 am

quick question,

if the problem mentions "inclusive" - we add the 1.

large - small / 2 + 1

if the problem doesn't mention inclusive - do we not add the 1?

thanks.

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LalaB: Master | Next Rank: 500 Posts; Posts: 425; Joined: Wed Dec 08, 2010 9:00 amFollowed by: 7 members; Thanked: 56 times; GMAT Score:690

by LalaB » Sun Apr 29, 2012 9:53 am

Cally627 wrote:quick question,

if the problem mentions "inclusive" - we add the 1.

large - small / 2 + 1

if the problem doesn't mention inclusive - do we not add the 1?

thanks.

no.

as for the q. above it can be solved this way-

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

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vinokayal: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Thu Sep 26, 2013 7:52 am

by vinokayal » Thu Sep 26, 2013 7:57 am

Where

First Term = 12

Difference = 4

Last Term = 96

As per the formula

a+(n-1)d

12+(n-1)4 = 96

(n-1)4 = 96-12

(n-1)4 = 84

n-1 = 84/4

n-1 = 21

n=22

12 + (

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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 Sep 26, 2013 8:03 am

money9111 wrote:How many multiples of 4 are there between 12 and 96, inclusive?

a. 21
b. 22
c. 23
d. 24
e. 25

If you'd rather not memorize formulas, you can also try listing and looking for a pattern.
Let's list the multiples of 4 from 12 to 96 inclusive.

12 = 4(3)
16 = 4(4)
20 = 4(5)
24 = 4(6)
.
.
.
88 = 4(22)
92 = 4(23)
96 = 4(24)

As you can see, the number of multiples of 4 from 12 to 96 inclusive is equal to the number of integers from 3 to 24 inclusive.

Well, we know that the number from integers from x to y inclusive equals y - x + 1

So, the number of integers from 3 to 24 inclusive equals 24 - 3 + 1 = 22

Answer: B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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by [email protected] » Thu Sep 26, 2013 11:38 am

Hi All,

Certain versions of these questions can be solved by including (and then removing) elements to "round out" the math.

In this case, it would be pretty easy to count the multiples of 4 from 1 to 100: there are 25 of them......25(4) = 100

So, which multiples of 4 must we REMOVE from this group of 25?

We want 12 to 96, inclusive, so we should REMOVE: 4, 8, 100. That's 3 values.

25 - 3 = 22

Final Answer:B

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Rich

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Mon Dec 11, 2017 4:11 pm

money9111 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 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

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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