Find the number of integers divisible by 3...

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BTGmoderatorLU: Moderator; Posts: 2598; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Tue Nov 21, 2017 7:52 am

Find the number of integers divisible by 3 in the interval from 10 to 200 inclusive.

(A) 61.
(B) 62.
(C) 63.
(D) 64.
(E) 65.

The OA is C.

I'm really confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.

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Source: Beat The GMAT — Problem Solving | Tue Nov 21, 2017 7:52 am

EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pmFollowed by: 12 members; Thanked: 180 times

by EconomistGMATTutor » Tue Nov 21, 2017 9:14 am

Hello LUANDATO.

We just need to find the first and the last multiple of 3 in that range, that is to say, the value of n such that $$10\le3\cdot n\le200.$$ By inspection we can conclude that $$4\le n\le66.$$ In this range there are $$\left(66-4\right)+1=63\ integers.$$ So, there are 63 numbers divisible by 3 in the given range,

The correct answer is C.

I really hope this can help you.

Feel free to ask me if you have a doubt.

Regards.

GMAT Prep From The Economist
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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 » Tue Nov 21, 2017 9:55 am

LUANDATO wrote:Find the number of integers divisible by 3 in the interval from 10 to 200 inclusive.

(A) 61.
(B) 62.
(C) 63.
(D) 64.
(E) 65.

A nice rule says: the number of integers from x to y inclusive equals y - x + 1
Example: the number of integers from 6 to 18 inclusive = 18 - 6 + 1 = 13

We can use the above rule to answer a wide range of questions.
First list a few values IN THE GIVEN RANGE:
12, 15, 18, 21, . . . . 195, 198

We can also write:
12 = 3(4)
15 = 3(5)
18 = 3(6)
.
.
.
195 = 3(65)
198 = 3(66)

So, the number of multiples is the same as the number of integers from 4 to 66 inclusive
The number of integers from 4 to 66 inclusive = 66 - 4 + 1 = 63
Answer: C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8199; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Sat Oct 12, 2019 4:06 pm

BTGmoderatorLU wrote:Find the number of integers divisible by 3 in the interval from 10 to 200 inclusive.

(A) 61.
(B) 62.
(C) 63.
(D) 64.
(E) 65.

The OA is C.

I'm really confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.

The number of multiples of 3 is:

(198 - 12)/3 + 1 = 63

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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