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

 It is currently 19 May 2019, 17:51 ### 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 28 are prime numbers

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

### Hide Tags

Intern  Joined: 06 Mar 2012
Posts: 32
How many positive integers less than 28 are prime numbers  [#permalink]

### Show Tags

2
3 00:00

Difficulty:   85% (hard)

Question Stats: 56% (02:48) correct 44% (02:42) wrong based on 216 sessions

### HideShow timer Statistics

How many positive integers less than 28 are prime numbers, odd multiples of 5, or the sum of a positive multiple of 2 and a positive multiple of 4?

A. 27
B. 25
C. 24
D. 22
E. 20

My thought process and correct solution:

List the prime numbers from 0-28 (3,5,7,11,13,17,19,23), odd multiples of 5 (5,15,25), and sum of a positive multiple of 2 and a positive multiple of 4 (since it has to be a sum the first integer starts at 6 onwards (6,8,10,12,14, 16,18, 20, 22, 24 and 26). The total integers add up to 8 + 3 + 11= 22
This seems rather time consuming. Is this really the quickest way to answer the question? Thanks in advance.
Intern  Joined: 16 Feb 2012
Posts: 34
Location: United States
Concentration: Entrepreneurship, Technology
GMAT 1: 690 Q47 V38 GPA: 3.7
Re: How many positive integers...  [#permalink]

### Show Tags

Did not understand the third part of the question correctly. Anyways, baseline is that I followed the same approach as you mentioned above.

Created 4 Columns (actually there should be only 3), First had all the prime numbers, Second had 5's multiple, and third for the third set (which I messed up, but ) approach was similar to yours.

Will wait for some to post smarter way of tackling this.
_________________
Keeping up the spirit. Target = 750
Intern  Joined: 03 Feb 2012
Posts: 7
Re: How many positive integers less than 28 are prime numbers  [#permalink]

### Show Tags

damham17 wrote:
How many positive integers less than 28 are prime numbers, odd multiples of 5, or the sum of a positive multiple of 2 and a positive multiple of 4?

A. 27
B. 25
C. 24
D. 22
E. 20

My thought process and correct solution:

List the prime numbers from 0-28 (3,5,7,11,13,17,19,23), odd multiples of 5 (5,15,25), and sum of a positive multiple of 2 and a positive multiple of 4 (since it has to be a sum the first integer starts at 6 onwards (6,8,10,12,14, 16,18, 20, 22, 24 and 26). The total integers add up to 8 + 3 + 11= 22
This seems rather time consuming. Is this really the quickest way to answer the question? Thanks in advance.

Regarding your thought process, you missed the number "2" for your prime numbers, and you should eliminate one of the 5's (since 5 is in both the "prime number" and "odd multiples of 5" category). But other than that, I solved the problem the same way you did.
Intern  Joined: 11 Jul 2012
Posts: 40
Re: How many positive integers less than 28 are prime numbers  [#permalink]

### Show Tags

The answer sets is wrong
First there are only 9 integers thess than 28 whore are prime numbers (2 3 5 7 11 13 17 19 23) how come you your answers choices are all greater than 9?
Math Expert V
Joined: 02 Sep 2009
Posts: 55150
Re: How many positive integers less than 28 are prime numbers  [#permalink]

### Show Tags

2
1
Ousmane wrote:
The answer sets is wrong
First there are only 9 integers thess than 28 whore are prime numbers (2 3 5 7 11 13 17 19 23) how come you your answers choices are all greater than 9?

We wan to determine how many numbers less than 28 are primes OR odd multiples of 5 OR the sum of a positive multiple of 2 and a positive multiple of 4.

How many positive integers less than 28 are prime numbers, odd multiples of 5, or the sum of a positive multiple of 2 and a positive multiple of 4?

A. 27
B. 25
C. 24
D. 22
E. 20

9 prime numbers less than 28: {2, 3, 5, 7, 11, 13, 17, 19, 23}

3 odd multiples of 5: {5, 15, 25}

11 numbers which are the sum of a positive multiple of 2 and a positive multiple of 4: {6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26}

Notice, that 5 is in two sets, thus total # of integers satisfying the given conditions is 9+3+11-1=22.

Answer: D.

Hope it's clear.
_________________
Manager  Joined: 25 Sep 2012
Posts: 237
Location: India
Concentration: Strategy, Marketing
GMAT 1: 660 Q49 V31 GMAT 2: 680 Q48 V34 Re: How many positive integers less than 28 are prime numbers  [#permalink]

### Show Tags

What is meant by the sum of a positive multiple of 2 and a positive multiple of 4
First of all does it actually means --- the sum of a positive multiple of 2 and 4?

Multiple of 2 - 2,4,6,8,10,12,14,16,18,20,22,24,26
Multiple of 4 - 4,8,12,16,20,24

What is sum of these Didn't understand
Veritas Prep GMAT Instructor D
Joined: 16 Oct 2010
Posts: 9218
Location: Pune, India
Re: How many positive integers less than 28 are prime numbers  [#permalink]

### Show Tags

4
b2bt wrote:
What is meant by the sum of a positive multiple of 2 and a positive multiple of 4
First of all does it actually means --- the sum of a positive multiple of 2 and 4?

Multiple of 2 - 2,4,6,8,10,12,14,16,18,20,22,24,26
Multiple of 4 - 4,8,12,16,20,24

What is sum of these Didn't understand

It means you need to find those numbers which can be written as 2a + 4b where a and b are positive integers.

n = 2(a + 2b)
Note that a + 2b can take all values starting from 3
a = 1, b = 1, a+2b = 3
a = 2, b = 1, a+2b = 4
a = 1, b = 2, a+2b = 5
a= 2, b = 2, a+2b = 6
etc...
Hence the numbers which are "sum of a positive multiple of 2 and a positive multiple of 4" all are even numbers starting from 6 onwards.
n = 6, 8, 10, 12 etc

You can also do this question by figuring out the number of integers which are none of these three: not prime, not odd multiples of 5, not even (6 and above). The reason you will do that is there will be few such numbers since most numbers less than 28 are either even or prime. Also the options are close to 27 so they tell you that there are few such numbers

Start from 1.
1 - not prime, not multiple of 5, not even (6 and above)
4 - not prime, not multiple of 5, not even (6 and above)
Just focus on the odd numbers now and keep ignoring primes: 5/7 - ignore
9 - not prime, not multiple of 5, not even (6 and above)
11/13/15/17/19 - Ignore
21 - not prime, not multiple of 5, not even (6 and above)
23/25 - Ignore
27 - not prime, not multiple of 5, not even (6 and above)

So there are 5 numbers that do not fall in any of these categories out of a total of 27 numbers which are less than 28.

This gives us 27 - 5 = 22 relevant numbers

Answer (D)
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Target Test Prep Representative G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2823
Re: How many positive integers less than 28 are prime numbers  [#permalink]

### Show Tags

1
damham17 wrote:
How many positive integers less than 28 are prime numbers, odd multiples of 5, or the sum of a positive multiple of 2 and a positive multiple of 4?

A. 27
B. 25
C. 24
D. 22
E. 20

We can start by listing the number of prime numbers less than 28:

2, 3, 5, 7, 11, 13, 17, 19, 23

There are 9 prime numbers less than 28.

Next we list the odd multiples of 5 less than 28:

5, 15, 25

There are 3 odd multiples of 5. However, since 5 is also a prime number and we don't want to count it twice, we can remove that number from this list and thus there are only 2 odd multiples of 5 left.

Finally, we need to determine the number of sums from adding positive multiples of 2 and positive multiples of 4 that are less than 28:

Since the smallest positive multiple of 2 is 2 and the smallest multiple of 4 is 4, we see that all even numbers from 2 + 4 = 6 to 26, inclusive, will be a sum of a multiple of 2 and (a multiple of) 4. This is because any even number greater than or equal to 6 can be expressed as 4 + some even number. There are (26 - 6)/2 + 1 = 11 even numbers from 6 to 26, inclusive.

Thus, we have a total of 9 + 2 + 11 = 22 numbers that fit the given criteria.

Answer: D
_________________

# Jeffrey Miller

Head of GMAT Instruction

Jeff@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.

Senior Manager  G
Joined: 02 Apr 2014
Posts: 477
Location: India
Schools: XLRI"20
GMAT 1: 700 Q50 V34 GPA: 3.5
How many positive integers less than 28 are prime numbers  [#permalink]

### Show Tags

Prime numbers < 28 = {2,3,5,7,11,13,17,19,23} = total 9

odd multiples of 5 < 28 = {5,10,15} => excluding 5 as prime number counted already = total 2

integer = sum of multiple of 2 and sum of multiple of 4 < 28 => basically all positive even numbers(except 2,4) < 28 (as 2 and 4 cannot be expressed as sum of multiple of 2 and multiple of 4) = total = (13 - 2) = 11

total = 9 + 2 + 11 = 22 => (D)
Math Expert V
Joined: 02 Aug 2009
Posts: 7671
Re: How many positive integers less than 28 are prime numbers  [#permalink]

### Show Tags

damham17 wrote:
How many positive integers less than 28 are prime numbers, odd multiples of 5, or the sum of a positive multiple of 2 and a positive multiple of 4?

A. 27
B. 25
C. 24
D. 22
E. 20

My thought process and correct solution:

List the prime numbers from 0-28 (3,5,7,11,13,17,19,23), odd multiples of 5 (5,15,25), and sum of a positive multiple of 2 and a positive multiple of 4 (since it has to be a sum the first integer starts at 6 onwards (6,8,10,12,14, 16,18, 20, 22, 24 and 26). The total integers add up to 8 + 3 + 11= 22
This seems rather time consuming. Is this really the quickest way to answer the question? Thanks in advance.

Another way is to find THOSE that don't fit the bill..

1) the sum of a positive multiple of 2 and a positive multiple of 4 MEANS 2x+4y but x and y cannot be 0
so all even numbers other than 2 and 4 fall into this category..
2) Prime numbers - the above 2 also gone and other prime number
3) All multiples of 5 gone

so we are looking at 1,4 and possible multiples of ODD numbers..
a) if 3 - $$3^2, 3^3$$ and 3*7
b) if 5 - None
c) if 7 - cannot be more than 7*3 as 28 is 7*4

so final list 1,4,9,27,21 - 5 numbers

ans 27-5=22
_________________ Re: How many positive integers less than 28 are prime numbers   [#permalink] 28 Dec 2017, 06:27
Display posts from previous: Sort by

# How many positive integers less than 28 are prime numbers

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.

#### MBA Resources  