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What is the total number of integers between 101 and 202 that are divi

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What is the total number of integers between 101 and 202 that are divi  [#permalink]

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New post 21 Oct 2014, 20:05
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What is the total number of integers between 101 and 202 that are divisible by 3?

(A) 31
(B) 32
(C) 33
(D) 34
(E) 35
Spoiler: OA

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Re: What is the total number of integers between 101 and 202 that are divi  [#permalink]

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New post 21 Oct 2014, 23:28
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PareshGmat wrote:
What is the total number of integers between 101 and 202 that are divisible by 3?

(A) 31
(B) 32
(C) 33
(D) 34
(E) 35


\(# \ of \ multiples \ of \ x \ in \ the \ range = \frac{Last \ multiple \ of \ x \ in \ the \ range \ - \ First \ multiple \ of \ x \ in \ the \ range}{x}+1\)

(201 - 102)/3 + 1 = 34.

Answer: D.
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Re: What is the total number of integers between 101 and 202 that are divi  [#permalink]

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New post 21 Oct 2014, 21:57
PareshGmat wrote:
What is the total number of integers between 101 and 202 that are divisible by 3?

(A) 31
(B) 32
(C) 33
(D) 34
(E) 35


First no divisible by 3: 102
Last no divisible by 3: 201

Note that any number is divisible by 3 if the sum of the digits is divisible by 3

So total numbers divisible by 3:

202=102+(n-1)*3 where n is total numbers

3n=102, n=34
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Re: What is the total number of integers between 101 and 202 that are divi  [#permalink]

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New post 20 May 2017, 21:14
First integer divisible by 3 in this range = 102 = 3*34
Last integer divisible by 3 in this range = 201 = 3*67

So the list is like this:
3*34, 3*35, 3*36, ......, 3*67

So basically we have to calculate the number of consecutive integers from 34 to 67
67-34 +1 = 34

Hence answer is D
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Re: What is the total number of integers between 101 and 202 that are divi  [#permalink]

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New post 21 May 2017, 04:35
102-201=99

number of integers divisible by 3 is 99/3 +1 = 34.

u can get it in 35 seconds
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Re: What is the total number of integers between 101 and 202 that are divi  [#permalink]

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