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How many numbers between 101 and 250, exclusive are divisible by three

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Bunuel
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How many numbers between 101 and 250, exclusive are divisible by three [#permalink] New post   Updated on: 15 Jul 2019, 03:40
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Question Stats:

84% (01:14) correct 16% (02:03) wrong based on 134 sessions
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How many numbers between 101 and 250, exclusive are divisible by three?

A. 34
B. 41
C. 50
D. 83
E. 148

Source: Nova GMAT
Difficulty Level: 550
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Official Answer
C

Originally posted by Bunuel on 03 Nov 2016, 02:50.
Last edited by Sajjad1994 on 15 Jul 2019, 03:40, edited 1 time in total.
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Re: How many numbers between 101 and 250, exclusive are divisible by three [#permalink] New post   03 Nov 2016, 08:15
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Bunuel wrote:
How many numbers between 101 and 250, exclusive are divisible by three?

A. 34
B. 41
C. 50
D. 83
E. 148


Numbers upto 250 divisible by 3 is 250/3 = 83
Numbers upto 101 divisible by 3 is 101/3 = 33

Total number of numbers between 101 and 250 that are divisible by 3 is 83 - 33 = 50

Hence correct answer will be (C) 50
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Re: How many numbers between 101 and 250, exclusive are divisible by three [#permalink] New post   05 Nov 2016, 07:13
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rishit1080 wrote:
How many numbers between 101 and 250, exclusive are divisible by three?

A. 34
B. 41
C. 50
D. 83
E. 148





:shock: Then I would cry or try to learn this formula[/quote]

There is no formula to be learnt.. Please understand the basic concept as used in my first explanation in this thread.

You can count multiples of any number x, from 1 to n by taking Integer solution of [n/x]

Calculate multiples of 3 from 1-250 and remove the multiples of 3 from 1-100 to find the number of multiples in the range 101-250

i.e. [250/3] - [100/3] = 83-33=50

I hope this helps!
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Re: How many numbers between 101 and 250, exclusive are divisible by three [#permalink] New post   05 Nov 2016, 10:24
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rishit1080 wrote:
There is no formula to be learnt.. Please understand the basic concept as used in my first explanation in this thread.

You can count multiples of any number x, from 1 to n by taking Integer solution of [n/x]

Calculate multiples of 3 from 1-250 and remove the multiples of 3 from 1-100 to find the number of multiples in the range 101-250

i.e. [250/3] - [100/3] = 83-33=50

I hope this helps!


So, for instance if it was multiples of 3 from 100-999 it would be

(999/3) - (100/3)= 333 - 33 = 300 ??[/quote]

Yes, absolutely correct. :)

Posted from my mobile device
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Re: How many numbers between 101 and 250, exclusive are divisible by three [#permalink] New post   03 Nov 2016, 02:54
Digits are => 102,105,....249
Number of digits => 249-102/3 +1
=> 147/3 +1 = 49+1 => 50.
Wait a minute 50 isn't any of the options.


Am i missing something here Bunuel

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Re: How many numbers between 101 and 250, exclusive are divisible by three [#permalink] New post   Updated on: 03 Nov 2016, 09:18
Bunuel wrote:
How many numbers between 101 and 250, exclusive are divisible by three?

A.34
B. 41
C. 49
D. 83
E. 148


IMO C
numbers between 101 and 250, exclusive is given by {(249-102)/3}+1=49+1=50

Mended my answer. Thanks for the correction Austin.

Originally posted by Vinayak Shenoy on 03 Nov 2016, 02:56.
Last edited by Vinayak Shenoy on 03 Nov 2016, 09:18, edited 1 time in total.
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Re: How many numbers between 101 and 250, exclusive are divisible by three [#permalink] New post   03 Nov 2016, 08:25
Bunuel wrote:
How many numbers between 101 and 250, exclusive are divisible by three?

A. 34
B. 41
C. 50
D. 83
E. 148


fastest way, find multiples of 3.
102 is a multiple of 3
252 is a multiple of 3, thus, 249 must be a multiple of 3.

102 is 34th multiple
249 is 83rd multiple.

83 - 34 = 49
since 102 and 249 are between 101 and 250, we need to add 1 (inclusive counting)
49+1 = 50.

answer is C.
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Re: How many numbers between 101 and 250, exclusive are divisible by three [#permalink] New post   04 Nov 2016, 16:22
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Bunuel wrote:
How many numbers between 101 and 250, exclusive are divisible by three?

A. 34
B. 41
C. 50
D. 83
E. 148


Since we need to determine how many multiples of 3 are between 101 and 250, EXCLUSIVE, we can rewrite this as how many multiples of 3 are between 102 and 249, INCLUSIVE, and use the following equation:

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

(249 - 102)/3 + 1 = 147/3 + 1 = 49 + 1 = 50

Answer: C
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Re: How many numbers between 101 and 250, exclusive are divisible by three [#permalink] New post   04 Nov 2016, 22:21
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Bunuel wrote:
How many numbers between 101 and 250, exclusive are divisible by three?

A. 34
B. 41
C. 50
D. 83
E. 148


Number that are divisible by 3 from 1 to 250 = 250/3 = 83
Number that are divisible by 3 from 1 to 100 = 100/3 = 33

i.e. Number that are divisible by 3 from 101 to 250 = 83-33 = 50

Answer: option C
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Re: How many numbers between 101 and 250, exclusive are divisible by three [#permalink] New post   05 Nov 2016, 02:50
Bunuel wrote:
How many numbers between 101 and 250, exclusive are divisible by three?

A. 34
B. 41
C. 50
D. 83
E. 148


Got C.

Took me 1 minute and 23 seconds to just count it out the old fashion way.
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Re: How many numbers between 101 and 250, exclusive are divisible by three [#permalink] New post   05 Nov 2016, 03:02
rishit1080 wrote:
Bunuel wrote:
How many numbers between 101 and 250, exclusive are divisible by three?

A. 34
B. 41
C. 50
D. 83
E. 148


Got C.

Took me 1 minute and 23 seconds to just count it out the old fashion way.


What if the question said between 101 and 999 :twisted: :twisted: :twisted:
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Re: How many numbers between 101 and 250, exclusive are divisible by three [#permalink] New post   05 Nov 2016, 03:39
These numbers need to count have the common form: 3k
Since 101 = 3*33 + 2, we have k > 33
Since 250 = 3*83 + 1, we have k <=83

So 34 <= k <= 83.

=> There are 83 - 34 + 1 = 50 numbers => OA is C
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Re: How many numbers between 101 and 250, exclusive are divisible by three [#permalink] New post   05 Nov 2016, 04:42
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Bunuel wrote:
How many numbers between 101 and 250, exclusive are divisible by three?

A. 34
B. 41
C. 50
D. 83
E. 148



Alternatively:

Solve it like an Arithmetic Progression (A.P.)

Smallest Number in the given range divisible by 3 = 102
Biggest Number in the given range divisible by 3 = 249

Let, 102 = first term
and 249 = nth term
Common difference, d = 3

nth Term = a+(n-2)d
i.e. 249 = 102+(n-1)*3
i.e. n = 50

Answer: Option C
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Re: How many numbers between 101 and 250, exclusive are divisible by three [#permalink] New post   05 Nov 2016, 06:53
stonecold wrote:
rishit1080 wrote:
Bunuel wrote:
How many numbers between 101 and 250, exclusive are divisible by three?

A. 34
B. 41
C. 50
D. 83
E. 148


Got C.

Took me 1 minute and 23 seconds to just count it out the old fashion way.


What if the question said between 101 and 999 :twisted: :twisted: :twisted:



:shock: Then I would cry or try to learn this formula
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Re: How many numbers between 101 and 250, exclusive are divisible by three [#permalink] New post   05 Nov 2016, 08:53
There is no formula to be learnt.. Please understand the basic concept as used in my first explanation in this thread.

You can count multiples of any number x, from 1 to n by taking Integer solution of [n/x]

Calculate multiples of 3 from 1-250 and remove the multiples of 3 from 1-100 to find the number of multiples in the range 101-250

i.e. [250/3] - [100/3] = 83-33=50

I hope this helps![/quote]

So, for instance if it was multiples of 3 from 100-999 it would be

(999/3) - (100/3)= 333 - 33 = 300 ??
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Re: How many numbers between 101 and 250, exclusive are divisible by three [#permalink] New post   05 Nov 2016, 11:17
Abhishek009 wrote:
Bunuel wrote:
How many numbers between 101 and 250, exclusive are divisible by three?

A. 34
B. 41
C. 50
D. 83
E. 148


Numbers upto 250 divisible by 3 is 250/3 = 83
Numbers upto 101 divisible by 3 is 101/3 = 33

Total number of numbers between 101 and 250 that are divisible by 3 is 83 - 33 = 50

Hence correct answer will be (C) 50


What an amazing approach to this question. So, when dividing 250/3 and 101/3, I just subtract their quotients while ignoring their remainders, and the result is the number of integers within that range that are divisible by 3.
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Re: How many numbers between 101 and 250, exclusive are divisible by three [#permalink] New post   06 Nov 2016, 02:10
diegocml wrote:
Abhishek009 wrote:
Bunuel wrote:
How many numbers between 101 and 250, exclusive are divisible by three?

A. 34
B. 41
C. 50
D. 83
E. 148


Numbers upto 250 divisible by 3 is 250/3 = 83
Numbers upto 101 divisible by 3 is 101/3 = 33

Total number of numbers between 101 and 250 that are divisible by 3 is 83 - 33 = 50

Hence correct answer will be (C) 50


What an amazing approach to this question. So, when dividing 250/3 and 101/3, I just subtract their quotients while ignoring their remainders, and the result is the number of integers within that range that are divisible by 3.


THere are numberous cool ways to solve this problem , including the AP form, however the method I have used to find is as below -
Attachment:
Untitled.png
Untitled.png [ 4.29 KiB | Viewed 5651 times ]


Hope this helps ( Atleast to some extent ) :-D
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Re: How many numbers between 101 and 250, exclusive are divisible by three [#permalink] New post   28 Jan 2021, 12:24
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Re: How many numbers between 101 and 250, exclusive are divisible by three [#permalink]
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