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# How many integers between 1 and 200, inclusive, are divisible by both

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Math Expert
Joined: 02 Sep 2009
Posts: 59728
How many integers between 1 and 200, inclusive, are divisible by both  [#permalink]

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11 Jul 2019, 02:51
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15% (low)

Question Stats:

83% (01:09) correct 17% (01:44) wrong based on 83 sessions

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How many integers between 1 and 200, inclusive, are divisible by both 3 and 4?

A. 8

B. 12

C. 15

D. 16

E. 24

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Joined: 29 Jun 2019
Posts: 470
Re: How many integers between 1 and 200, inclusive, are divisible by both  [#permalink]

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11 Jul 2019, 03:00
In this sequence we need just numbers which are divisible by 12.
Totally we have 200 numbers.
200/12 ~=16
Option (D)

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Re: How many integers between 1 and 200, inclusive, are divisible by both  [#permalink]

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11 Jul 2019, 03:04
1
Bunuel wrote:
How many integers between 1 and 200, inclusive, are divisible by both 3 and 4?

A. 8

B. 12

C. 15

D. 16

E. 24

# of integers divisible by both 3 & 4 are divisible by 12

= [200/12] = 16

IMO D
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Joined: 14 Nov 2018
Posts: 38
Location: Austria
How many integers between 1 and 200, inclusive, are divisible by both  [#permalink]

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11 Jul 2019, 03:11
In order to make this process work for all cases, would the best approach be to

First, find the least common multiple (“LCM”)of the two numbers 3 and 4, then divide by the LCM?

The answer would be the same (explained above).

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Manager
Joined: 27 Mar 2016
Posts: 116
GMAT 1: 590 Q44 V22
Re: How many integers between 1 and 200, inclusive, are divisible by both  [#permalink]

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11 Jul 2019, 03:18
It has to be multiple of 12 and there are 16 multiples of 12
Hence 16

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Posts: 31
Re: How many integers between 1 and 200, inclusive, are divisible by both  [#permalink]

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11 Jul 2019, 05:03
2
Q. How many integers between 1 and 200, inclusive, are divisible by both 3 and 4?

LCM of 3 and 4 is 12.

We need to look for multiples of 12 up to 200.

First multiple of 12 is 12.
Last multiple of 12 is 192

Total integers = (192 - 12)/12 + 1 => 15+1 = 16.

Ans - D.
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Re: How many integers between 1 and 200, inclusive, are divisible by both  [#permalink]

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11 Jul 2019, 11:14
Bunuel wrote:
How many integers between 1 and 200, inclusive, are divisible by both 3 and 4?

A. 8

B. 12

C. 15

D. 16

E. 24

LCM of 3,4 = 12 so
integers divisible from 1 to 200 ; 200/12 ; 16
IMO D
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Re: How many integers between 1 and 200, inclusive, are divisible by both  [#permalink]

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11 Jul 2019, 14:32
we have to find the LCM for both 3 and 4.

least common multiple is 3x4=12

first multiple=12
last multiple =12x16=192

total number of integers =(192 - 12)/12 + 1 =16 ==> choice D
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Re: How many integers between 1 and 200, inclusive, are divisible by both  [#permalink]

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12 Jul 2019, 18:58
Bunuel wrote:
How many integers between 1 and 200, inclusive, are divisible by both 3 and 4?

A. 8

B. 12

C. 15

D. 16

E. 24

The number of integers divisible by 3 and 4 is equal to the number of integers divisible by 12:

(192 - 12)/12 + 1 = 16

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Joined: 07 Dec 2018
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Re: How many integers between 1 and 200, inclusive, are divisible by both  [#permalink]

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13 Jul 2019, 00:21

((192-12)/12) + 1 == 15 + 1 == 16

Why cant we just do 192/12 == 16?

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Re: How many integers between 1 and 200, inclusive, are divisible by both   [#permalink] 13 Jul 2019, 00:21
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