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

Question

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

chetansood · Answer

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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chetansood · Answer

Why isnt the answer 18 ?

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Bunuel · Answer

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: https://gmatclub.com/forum/how-many-posi ... 06559.html https://gmatclub.com/forum/how-many-posi ... 27362.html https://gmatclub.com/forum/how-many-pos ... 15992.html https://gmatclub.com/forum/how-many-pos ... 94190.html https://gmatclub.com/forum/how-many-pos ... 44535.html

Kinshook · Answer

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

Archit3110 · Answer

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

Sayon · Answer

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

ScottTargetTestPrep · Answer

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

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