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
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