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How many positive integers less than 20 are either a multiple of 2,

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How many positive integers less than 20 are either a multiple of 2,  [#permalink]

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New post Updated on: 29 Jul 2019, 22:01
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How many positive integers less than 20 are either a multiple of 2, an odd multiple of 7, or the sum of a positive multiple of 2 and a positive multiple of 7 ?

(A) 19
(B) 18
(C) 17
(D) 16
(E) 15

Originally posted by robu1 on 29 Jul 2019, 21:21.
Last edited by Bunuel on 29 Jul 2019, 22:01, edited 1 time in total.
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Re: How many positive integers less than 20 are either a multiple of 2,  [#permalink]

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New post 29 Jul 2019, 21:44
Multiples of 2 -> 9
( 2 4 6 8 10 12 14 16 18 )

Odd multiple of 7 -> 1
( 7 )

Sum of 2 and 7 -> 8
( 7x1 + n*2 = 9 11 13 15 17 19 )

( 7x2 + n*2 = 16 18 )

What am i missing ?

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Re: How many positive integers less than 20 are either a multiple of 2,  [#permalink]

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New post 29 Jul 2019, 21:45
Why isnt the answer 18 ?



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Re: How many positive integers less than 20 are either a multiple of 2,  [#permalink]

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New post 29 Jul 2019, 21:58
chetansood wrote:
Multiples of 2 -> 9
( 2 4 6 8 10 12 14 16 18)

Odd multiple of 7 -> 1
( 7 )

Sum of 2 and 7 -> 8
( 7x1 + n*2 = 9 11 13 15 17 19 )

( 7x2 + n*2 = 16 18)

What am i missing ?

Posted from my mobile device


16 and 18 are counted twice.

This question is a copy of the following OG question: https://gmatclub.com/forum/how-many-pos ... 71108.html

Other similar questions to practice:
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https://gmatclub.com/forum/how-many-pos ... 44535.html
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Re: How many positive integers less than 20 are either a multiple of 2,  [#permalink]

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New post 29 Jul 2019, 22:33
robu1 wrote:
How many positive integers less than 20 are either a multiple of 2, an odd multiple of 7, or the sum of a positive multiple of 2 and a positive multiple of 7 ?

(A) 19
(B) 18
(C) 17
(D) 16
(E) 15



How many positive integers less than 20 are either a multiple of 2, an odd multiple of 7, or the sum of a positive multiple of 2 and a positive multiple of 7 ?
multiple of 2 covers all even numbers from 2-18
sum of a positive multiple of 2 and a positive multiple of 7 covers all odd numbers from 7-19
=> numbers 1,3,5 are the only numbers left out.
=> number of positive integers less than 20 = 19-3 = 16

IMO D
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Re: How many positive integers less than 20 are either a multiple of 2,  [#permalink]

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New post 30 Jul 2019, 06:20
robu1 wrote:
How many positive integers less than 20 are either a multiple of 2, an odd multiple of 7, or the sum of a positive multiple of 2 and a positive multiple of 7 ?

(A) 19
(B) 18
(C) 17
(D) 16
(E) 15


need to find +ve integers which are less than 20 are
either a multiple of 2, ; ( 2 to 18 ) total 9
odd multiple of 7,; [; 1
or the sum of a positive multiple of 2 and a positive multiple of 7 ; ( 2,7) ( 4,7), ( 6,7) ( 8,7)(10,7) ( 12,7) ; 6
sum of even multiple of 7 and multiple would be an overlap so 18 is not possible i.e ( 2,14)(4,14) chetansood
so total integers ; 9+1+6 ; 16
IMO D
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Re: How many positive integers less than 20 are either a multiple of 2,  [#permalink]

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New post 30 Jul 2019, 09:03
Positive integers less than 20: So we need to consider numbers from 1 to 19 inclusive.
Are either a multiple of 2: 9 numbers will be multiple of 2. {2, 4, 6, 8, 10, 12, 14, 16, 18} -> (a)
OR an odd multiple of 7: Only 1 odd multiple of 7 will be in the given range. {7} -> (b)

OR the sum of a positive multiple of 2 and a positive multiple of 7: Multiple numbers qualify in the given range. We need to make sure we that we do not double count any "even" value as they will be covered in (a)
Sum of a positive multiple of 2 and a positive multiple of 7: (2 + 7 = 9), (2 + 14 = even), (4 + 7 = 11), (6 + 7 = 13), (8 + 7 = 15), (10 + 7 = 17), (12 + 7 = 19), (4 + 14 = even) - So 8 number out of which 2 are already present in (a). Thus, we count 6 here. -> (c)

(a) + (b) + (c) = 16

Answer D
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Re: How many positive integers less than 20 are either a multiple of 2,  [#permalink]

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New post 05 Aug 2019, 18:16
robu1 wrote:
How many positive integers less than 20 are either a multiple of 2, an odd multiple of 7, or the sum of a positive multiple of 2 and a positive multiple of 7 ?

(A) 19
(B) 18
(C) 17
(D) 16
(E) 15


The multiples of 2 are:

2, 4, 6, 8, 10, 12, 14, 16, 18

The only odd multiple of 7 less than 20 is 7.

The sums of multiples of 2 and multiples of 7 are:

9, 11, 13 ,15 ,16, 17, 18, 19

However since 16 and 18 are already counted, there are 9 + 1 + (8 - 2) = 16 numbers that fit the criteria.

Answer: D
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Re: How many positive integers less than 20 are either a multiple of 2,   [#permalink] 05 Aug 2019, 18:16

How many positive integers less than 20 are either a multiple of 2,

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