GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 24 Aug 2019, 13:17 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. ### Request Expert Reply # How many positive integers less than 20 are either a multiple of 2,

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Intern  B
Joined: 08 Jul 2017
Posts: 33
GMAT 1: 620 Q48 V29 How many positive integers less than 20 are either a multiple of 2,  [#permalink]

### Show Tags

2 00:00

Difficulty:   75% (hard)

Question Stats: 40% (01:45) correct 60% (02:04) wrong based on 53 sessions

### HideShow timer Statistics

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, 22:21.
Last edited by Bunuel on 29 Jul 2019, 23:01, edited 1 time in total.
Edited the tags.
Intern  B
Joined: 02 Jun 2014
Posts: 49
Schools: ISB '15
Re: How many positive integers less than 20 are either a multiple of 2,  [#permalink]

### Show Tags

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
Intern  B
Joined: 02 Jun 2014
Posts: 49
Schools: ISB '15
Re: How many positive integers less than 20 are either a multiple of 2,  [#permalink]

### Show Tags

Why isnt the answer 18 ?

Posted from my mobile device
Math Expert V
Joined: 02 Sep 2009
Posts: 57279
Re: How many positive integers less than 20 are either a multiple of 2,  [#permalink]

### Show Tags

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:
http://gmatclub.com/forum/how-many-posi ... 06559.html
http://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
_________________
VP  P
Joined: 03 Jun 2019
Posts: 1080
Location: India
Re: How many positive integers less than 20 are either a multiple of 2,  [#permalink]

### Show Tags

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
_________________
"Success is not final; failure is not fatal: It is the courage to continue that counts."

Please provide kudos if you like my post. Kudos encourage active discussions.

My GMAT Resources: -

Efficient Learning

Tele: +91-11-40396815
Mobile : +91-9910661622
E-mail : kinshook.chaturvedi@gmail.com
GMAT Club Legend  D
Joined: 18 Aug 2017
Posts: 4533
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: How many positive integers less than 20 are either a multiple of 2,  [#permalink]

### Show Tags

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
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
Manager  G
Joined: 08 Jan 2018
Posts: 128
Re: How many positive integers less than 20 are either a multiple of 2,  [#permalink]

### Show Tags

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
Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 7467
Location: United States (CA)
Re: How many positive integers less than 20 are either a multiple of 2,  [#permalink]

### Show Tags

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
_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: How many positive integers less than 20 are either a multiple of 2,   [#permalink] 05 Aug 2019, 19:16
Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

#### MBA Resources  