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# How many positive integers less than 20 are either a multipl

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Director
Joined: 30 Jun 2008
Posts: 980
How many positive integers less than 20 are either a multipl  [#permalink]

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04 Oct 2008, 04:06
2
12
00:00

Difficulty:

45% (medium)

Question Stats:

68% (01:28) correct 32% (01:35) wrong based on 463 sessions

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How many positive integers less than 20 are either a multiple of 2, an odd multiple of 9, or the sum of a positive multiple of 2 and a positive multiple of 9 ?

A. 19
B. 18
C. 17
D. 16
E. 15

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Director
Joined: 30 Jun 2008
Posts: 980

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04 Oct 2008, 04:39
I get the 9 + 1 part. I am not sure how to get the 5 ??
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Manager
Joined: 27 Sep 2008
Posts: 75

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04 Oct 2008, 04:50
2
amitdgr wrote:
I get the 9 + 1 part. I am not sure how to get the 5 ??

{2,4,6,8,10,12,14,16,18} = 9

{9} = 1

{11,13,15,17,19} = 5
Director
Joined: 30 Jun 2008
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04 Oct 2008, 05:10
Greenberg wrote:
amitdgr wrote:
I get the 9 + 1 part. I am not sure how to get the 5 ??

{2,4,6,8,10,12,14,16,18} = 9

{9} = 1

{11,13,15,17,19} = 5

how do you derive the set {11,12,13,14,15} ?
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Manager
Joined: 31 Jul 2008
Posts: 249

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04 Oct 2008, 10:35
then the answer shud be 16 : 9+2+5

gud one vrIndian
Intern
Joined: 06 Jul 2008
Posts: 24

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04 Oct 2008, 16:42
What is the official answer ? I also thinkit should be 15. (9+1+5).

Out of 9 1nd 18, 18 is not odd multiple, hence we get 1 only here.
Manager
Joined: 24 Sep 2008
Posts: 169
Schools: MIT / INSEAD / IIM - ABC

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04 Oct 2008, 16:51
1
Between 0 & 20

Multiple of 2: 2,4,6,8,10,12,14,16,18 = 9
ODD Multiple of 9: 9 = 1
Sum of +ve multiple of 2 & 9: 11,13,15,17,19 = 5

9+1+5=15
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04 Oct 2008, 17:18
1
amitdgr wrote:
How many positive integers less than 20 are either a multiple of 2, an odd multiple of 9, or the sum of a positive multiple of 2 and a positive multiple of 9 ?

* 19
* 18
* 17
* 16
* 15

even is 10, less than 20 = 9

multiples of 9 = 20/9 = 2 one odd other is even = 1

total = 10

or

9+2 , 9+4,9+6,9+8,9+10 = 5

total = 5

10+5 = 15
Director
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04 Oct 2008, 20:05
1
The OA is 15. Thanks guys !!
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Posts: 52294
Re: How many positive integers less than 20 are either a multipl  [#permalink]

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28 Jan 2014, 23:44
amitdgr wrote:
How many positive integers less than 20 are either a multiple of 2, an odd multiple of 9, or the sum of a positive multiple of 2 and a positive multiple of 9 ?

A. 19
B. 18
C. 17
D. 16
E. 15

Similar questions to practice:
how-many-positive-integers-less-than-20-can-be-expressed-as-106559.html
how-many-positive-integers-less-than-30-are-either-a-127362.html
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Intern
Joined: 20 Nov 2009
Posts: 18
Re: How many positive integers less than 20 are either a multipl  [#permalink]

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03 Mar 2014, 18:09
answer is 15 it is based on simple counting I did it manually as the number list was small from 1 to 20
Intern
Joined: 30 Nov 2014
Posts: 3
Location: India

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12 Feb 2015, 21:07
How many positive integers less than 20 are either a multiple of 2, an odd multiple of 9, or the sum of a positive multiple of 2 and a positive multiple of 9?

A. 19
B. 18
C. 17
D. 16
E. 15
Math Expert
Joined: 02 Aug 2009
Posts: 7206
Re: How many positive integers  [#permalink]

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12 Feb 2015, 21:20
ans E ..15
there are 3 cases..
1) multiple of 2 till 20.. so number = (18-2)/2 + 1=9..
2) odd multiple of 9= 9*1..1
3) sum of a positive multiple of 2 and a positive multiple of 9...only 9*1 is valid as 9*2 + 2=20 and ans <20..
the numbers will be 11,13,15,17,19.... 5
total = 9+1+5=15
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Re: How many positive integers  [#permalink]

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12 Feb 2015, 21:32
Hi call2aks,

This question is essentially about thoroughness (making sure that you find all of the 'acceptable' values). You can solve it with "brute force" and some basic math concepts.

Here's an alternative that most Test Takers would not think about though:

We're asked to deal with the positive integers LESS than 20. There are only 19 numbers in that group (1 to 19, inclusive). We're asked to find all of the numbers that fit one (or more) of the given descriptions. Looking at the answer choices, we have every value form 15 to 19, inclusive, so most (if not all) of the numbers from 1 to 19 fit one (or more) of the descriptions. How long would it take you to find the ones that DON'T fit.....?

The first several should be pretty easy to find - the prompt wants us to focus on multiples of 2 and 9 (and sums of those multiples). So what ODD numbers are less than 9?

1, 3, 5, 7

None of these values fit the given descriptions. That's 4 out of 19 that we know for sure do NOT fit. 19 - 4 = 15. THAT is the smallest answer amongst the choices. The answers don't get any smaller, so 15 MUST be the answer. We don't have to look any further (and we don't have to do any more work).

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Re: How many positive integers less than 20 are either a multipl  [#permalink]

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31 Oct 2017, 05:50
If the question would have asked the number of non-negative integers instead of the number of positive integers, would the answer be 16? (including 2x0 in the first set)
Intern
Joined: 10 May 2018
Posts: 34
How many positive integers less than 20 are either a multipl  [#permalink]

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22 Nov 2018, 13:18
amitdgr wrote:
How many positive integers less than 20 are either a multiple of 2, an odd multiple of 9, or the sum of a positive multiple of 2 and a positive multiple of 9 ?

A. 19
B. 18
C. 17
D. 16
E. 15

Multiples of 2: 2, 4, 6...18 --> 9
Odd multiple of 9: 9 --> 1
Sum of a positive multiple of 2 and a positive multiple of 9: 11, 13, 15, 17, 19 --> 5

Total: 9+1+5 = 15 (check for no overlap among integers)

E.
How many positive integers less than 20 are either a multipl &nbs [#permalink] 22 Nov 2018, 13:18
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