How many multiples of 3 are there between -40 and 40?

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 amFollowed by: 3 members

by VJesus12 » Sat Jan 13, 2018 9:06 am

How many multiples of 3 are there between -40 and 40?
A. 13
B. 17
C. 23
D. 26
E. 27

The OA is the option E.

Is there a fast way to do this PS question? Experts, I would like your explanation. Please.

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Source: Beat The GMAT — Problem Solving | Sat Jan 13, 2018 9:06 am

mariliatgd: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Sun Jan 14, 2018 2:40 pm

by mariliatgd » Sun Jan 14, 2018 3:00 pm

This was my way of solving it:

1) Find the multiples between 1 and 39.
39/3 = 13 >> There are 13 multiples of 3 from 1 to 39.

The same applies to -39 to -1 so it should have also 13 multiple between -39 and -1

And finally, you should count the 0 as a multiple.

13 + 13 + 1 = 27.

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It should also work with ranges. For example, multiples of 4 between 41 and 121:

Multiple right before the smallest >> 40 >> 40/4 = 10
Multiple right before the biggest >> 120 >> 120 / 4 = 30

30 - 10 = 20

Multiples of 4 between 41 and 121: 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120.

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DrMaths: Senior | Next Rank: 100 Posts; Posts: 82; Joined: Mon Jan 15, 2018 2:01 am

by DrMaths » Mon Jan 15, 2018 4:25 am

1 to 40 has 13 multiples of 3 (because 39 = 13 x 3).
-1 to -40 has 13 multiples of 3 too.
And zero is a multiple of all numbers, so is a multiple of 3 too.

So, 13 + 13 + 1 = 27.

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DrMaths: Senior | Next Rank: 100 Posts; Posts: 82; Joined: Mon Jan 15, 2018 2:01 am

Simple Method

by DrMaths » Wed Jan 17, 2018 5:59 am

A quicker way could be to divide everything by 3 and ignore any remainders:
So 40/3=13
How many Multiples of 1 are there between -13 and 13?
Answer = 13 negative + 1 zero + 13 positive = 27

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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 Feb 26, 2018 10:31 am

VJesus12 wrote:How many multiples of 3 are there between -40 and 40?
A. 13
B. 17
C. 23
D. 26
E. 27

We can use the formula:

(largest multiple of 3 - smallest multiple of 3)/3 + 1

[(39 - (-39)]/3 + 1 = 78/3 + 1 = 26 + 1 = 27

Answer: E

Jeffrey Miller
Head of GMAT Instruction
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

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