Problem Solving

vikkimba17 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

i could not understand what they are asking me to find. please help.
+ ve int less than 28 [2, 3, 5, 7, 11, 13, 17, 19, and 23]
and odd multiples of 5 - (5)
Then im not able to proceed.

Thanks
Vignesh

Hi Vignesh,

The question wants you to find out the count of integers that are less than 28 and have the following characteristics.

1. The count of prime numbers less than 28.

2. The count of positive odd multiples of 5 less than 28.

3. The count of positive integers which have the sum of a positive multiple of 2 and a positive multiple of 4 less than 28.

Hope this makes sense.

-Jay
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vikkimba17 wrote:1) 9
2) 3

3) 13- Multiple of 2 - 2,4,6,8,10,12,14,16,18,20,22,24,26
4) 6 - Multiple of 4 - 4,8,12,16,20,24

9+3+13+6 =

is this the way ?

Hi vikkimba17,

Let's do this way.

1. The count of prime numbers less than 28: {2, 3, 5, 7, 11, 13, 17, 19, 23}: There are 9 integers. You did right.

2. The count of positive odd multiples of 5 less than 28: {5, 15, 25}: There are 3 integers. You did right.

3. The count of positive integers which have the sum of a positive multiple of 2 and a positive multiple of 4 less than 28.

You could not comprehend this one.

The smallest multiple of 2 is '2' and that of 4 is '4', so the smallest sum = 2 + 4 = 6. With each successive addition of 2, we get a set: {6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26}: There are 11 integers.

In other way the set of positive multiples of 2: p: {2,4,6,8,10,12,...} and the set of positive multiples of 4: q: {4,8,12,16...}

We want the sum of (p + q), where p = a positive multiple of 2 and q = a positive multiple of 4. You should choose all possible combinations of ps and qs to make the sum less than 28. You would find that the set would be: {6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26}.

The answer: 9 + (3 -1) + 11 = 22. I subtracted '1' from '3' because '5,' a odd multiple of '5' is also counted in the set of prime numbers.

The correct answer: D

Hope this helps!

Relevant book: Manhattan Review GMAT Number Properties Guide

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Bangkok | Abu Dhabi | Rome | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

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

Primes: 2, 3, 5, 7, 11, 13, 17, 19, 23
Odd multiples of 5: 5, 15, 25
Sum of a positive multiple of 2 and a positive multiple of 4: 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26

We need to ignore one of the 5's since they are listed twice.

TOTAL = [spoiler]22 = D[/spoiler]

Cheers,
Brent

Hi Vignesh,

The other posts in this thread list out the numbers, so I won't rehash any of that here. The 'work' needed to answer this question is essentially 'brute force' math - just list out all of the options (so that you can SEE them all) and make sure to answer the question that is asked. The answer choices give us a bit of a 'nudge' to be careful though - those answers are so close to one another that we have to make sure that we don't miss any of the options OR count an option more than once.

For example, the number 5 is both prime AND an odd multiple of 5... but we're not supposed to count that number twice (just once). Remember that the GMAT Quant section isn't really there to test your math skills (although you will do lots of little calculations as you work through that section) - it's there to test your critical thinking skills. Thus, you should take lots of notes and think about how best to go about dealing with each question (since the question writers often leave 'clues' as how best to proceed).

GMAT assassins aren't born, they're made,
Rich

vikkimba17 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