GRE Prep 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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
How many positive integers less than 20 can be expressed as the sum of
[#permalink]
21 Sep 2021, 20:54
21 Sep 2021, 20:54
2
Expert Reply
1
Bookmarks
00:00
Question Stats:
46% (02:33) correct
53% (02:45) wrong based on 13 sessions
Hide Show timer Statistics
How many positive integers less than 20 can be expressed as the sum of a positive multiple of 2 and a positive multiple of 3?
(A) 14
(B) 13
(C) 12
(D) 11
(E) 10
(A) 14
(B) 13
(C) 12
(D) 11
(E) 10
How many positive integers less than 20 can be expressed as the sum of
[#permalink]
22 Sep 2021, 00:14
22 Sep 2021, 00:14
Positive multiple of \(2 = 2, 4, 6, 8, 10, 12, 14, 16, 18\)
Positive multiple of \(3 = 3, 6, 9, 12, 15, 18\)
The sum should be less than \(20\) with the combination of the above numbers.
They can be \(5, 8, 11, 14, 17, 7, 10, 13, 16, 19, 9, 12, 15, 18\)
Total \(14\) nos
Answer A
Positive multiple of \(3 = 3, 6, 9, 12, 15, 18\)
The sum should be less than \(20\) with the combination of the above numbers.
They can be \(5, 8, 11, 14, 17, 7, 10, 13, 16, 19, 9, 12, 15, 18\)
Total \(14\) nos
Answer A
Moderator
Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1131
Given Kudos: 9
Location: India
Concentration: General Management
Schools: XLRI Jamshedpur, India - Class of 2014
GMAT 1: 700 Q51 V31
GPA: 2.8
WE:Engineering (Computer Software)
Re: How many positive integers less than 20 can be expressed as the sum of
[#permalink]
01 Oct 2022, 02:50
01 Oct 2022, 02:50
1
We need to find How many positive integers less than 20 can be expressed as the sum of a positive multiple of 2 and a positive multiple of 3
Let's try to express each number from 5 to 19 as a positive multiple of 2 and 3
We are considering only between 5 and 19 because
- 5 is the least number which can be formed with positive multiples of 2 and 3
- 19 because we need to find numbers less than 20
Using following format: Number = multiple of 2 + multiple of 3
5 = 2 + 3
6 = NOT POSSIBLE to express
7 = 4 + 3
8 = 2 + 6
9 = 6 + 3
10 = 4 + 6
11 = 8 + 3
12 = 6 + 6
13 = 10 + 3
14 = 8 + 6
15 = 12 + 3
16 = 10 + 6
17 = 14 + 3
18 = 12 + 6
19 = 16 + 3
Total numbers = (19-5 + 1 ) - 1 = 14
So, Answer will be A
Hope it helps!
Watch the following video to learn How to Sequence problems
Let's try to express each number from 5 to 19 as a positive multiple of 2 and 3
We are considering only between 5 and 19 because
- 5 is the least number which can be formed with positive multiples of 2 and 3
- 19 because we need to find numbers less than 20
Using following format: Number = multiple of 2 + multiple of 3
5 = 2 + 3
6 = NOT POSSIBLE to express
7 = 4 + 3
8 = 2 + 6
9 = 6 + 3
10 = 4 + 6
11 = 8 + 3
12 = 6 + 6
13 = 10 + 3
14 = 8 + 6
15 = 12 + 3
16 = 10 + 6
17 = 14 + 3
18 = 12 + 6
19 = 16 + 3
Total numbers = (19-5 + 1 ) - 1 = 14
So, Answer will be A
Hope it helps!
Watch the following video to learn How to Sequence problems
