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# How many positive integers between 200 and 300 (both inclusive) are no

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Math Expert
Joined: 02 Sep 2009
Posts: 58427
How many positive integers between 200 and 300 (both inclusive) are no  [#permalink]

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03 Feb 2019, 22:35
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Difficulty:

85% (hard)

Question Stats:

46% (02:34) correct 54% (02:40) wrong based on 53 sessions

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How many positive integers between 200 and 300 (both inclusive) are not divisible by 2, 3 or 5?

A. 3
B. 16
C. 24
D. 26
E. 75

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Joined: 11 Dec 2013
Posts: 121
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GMAT Date: 03-15-2015
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How many positive integers between 200 and 300 (both inclusive) are no  [#permalink]

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03 Feb 2019, 22:52
3
3
Divisible by 2 = $$\frac{300-200}{2} +1 = 51$$
Divisible by 3 = $$\frac{300-201}{2} +1 = 34$$
Divisible by 5 = $$\frac{300-200}{5} +1 = 21$$
Divisible by 2 and 3 =$$\frac{300-204}{6} +1 = 17$$
Divisible by 3 and 5 = $$\frac{300-210}{15} +1 = 7$$
Divisible by 5 and 2 = $$\frac{300-200}{10} +1 = 11$$
Divisible by 2,3 and 5 = $$\frac{300-210}{30} +1 = 4$$
positive integers that are not divisible by 2, 3 or 5 = $$101 - (51+34+21) + (17+7+11) - 4 = 26$$
IMO D
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Re: How many positive integers between 200 and 300 (both inclusive) are no  [#permalink]

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03 Feb 2019, 23:16
Bunuel wrote:
How many positive integers between 200 and 300 (both inclusive) are not divisible by 2, 3 or 5?

A. 3
B. 16
C. 24
D. 26
E. 75

IMO D

Total numbers will be 101 (300-200+1)

Not divisible will be, if we can find the numbers divisible by 2, 3 or 5, we can subtract it from Total number

Since the terms will be in an AP, we can use $$a_n$$= a + (n-1)d

Divisible by 2 = 300-200/2 +1 =51

Divisible by 3 = 300-201/3 + 1 = 34

Divisible by 5 = 300-200/5 + 1 = 21

Divisible by 2 or 3 = 300-204/6 + 1 = 17

Divisible by 2 or 5 = 300-200/10 + 1 = 11

Divisible by 3 or 5 = 300-210/15 + 1 = 7

Divisible by 2 ,3 or 5 = 300-210/30 + 1 = 4

101 - (Divisible by all 3) + (common terms of 2) - ( Common terms of all three)
101 -( 51 + 34+21) + (17+11+7) - 4
136- 110
26
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How many positive integers between 200 and 300 (both inclusive) are no  [#permalink]

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04 Feb 2019, 01:56
1
Bunuel wrote:
How many positive integers between 200 and 300 (both inclusive) are not divisible by 2, 3 or 5?

A. 3
B. 16
C. 24
D. 26
E. 75

total integers = 300-200+1 ; 101
+ve integers divisible by 2 = 51
integers divisible by 3 = 34
integers divisible by 5 = 21

integers divisible by both 2& 3 = half of integers divisible by 3 ' ie even integers divisible by 3' ; 17
integers divisible by both 2& 5 = half of integers divisible by 5 ' ie even integers divisible by 5'; 11
integers divisible by 3 & 5 both = 225,255,285 ; 3

so total integers divisible by 2,3 & 5 = (51-17-11)+ ( 34-3) + 21 = 75
integers not divisible by 2,3,5 would be 101- 75 = 26
IMO D
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Re: How many positive integers between 200 and 300 (both inclusi  [#permalink]

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05 Sep 2019, 05:26
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Re: How many positive integers between 200 and 300 (both inclusi   [#permalink] 05 Sep 2019, 05:26
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