How many positive integers less than 30 are either

guerrero wrote:How many positive integers less than 30 are either a multiple of 2, an odd prime number, or the sum of a positive multiple of 2 and an odd prime?

Note that any odd integer greater than 3 can be expressed as the sum of a positive multiple of 2 and an odd prime. For example, 5 = 2 + 3, 17 = 4 + 13, 27 = 4 + 23 etc.

Now, all the positive integer less than 30 except 1 are either even (multiple of 2), or odd (sum of a positive multiple of 2 and an odd prime), or odd prime (3).

So, number of such integers = 30 - 1 = 29

The correct answer is A.

guerrero wrote:How many positive integers less than 30 are either a multiple of 2, an odd prime number, of the sum of a positive multiple of 2 and an odd prime?

A. 29
B. 28
C. 27
D. 25
E. 23

OA A

How to tackle ?

There are 29 positive integers that are less than 30 (1, 2, 3, ... 28, 29)

Multiples of 2: 2, 4, 6, 8, ... (all even numbers)

Sum of a positive multiple of 2 and an odd prime: 3+2, 3+4, 3+6, 3+8, . . .
In other words, 5, 7, 9, 11, 13 (all odd numbers > 5)

At this point, we've accounted for all positive integers less than 30 EXCEPT for 1 and 3

Since 3 is a prime number, it is also accounted for.

The only number NOT accounted for is 1.

So, the answer is 29 - 1 = [spoiler]28 = B[/spoiler]

Cheers,
Brent

sana.noor wrote:isn't zero a multiple of 2 and 3?

Yes, but the question refers to positive integers only.
Zero is neither positive nor negative.

Cheers,
Brent