nafiul9090 wrote:How many positive integers less than 30 are either a multiple
of 2, an odd multiple of 9, or the sum of a positive multiple of
2 and a positive multiple of 9 ?
(A) 27
(B) 26
(C) 25
(D) 24
(E) 23
i am totally lost in this problem. please someone shed some eco-friendly light
First check the answer choices. They range from 23 to 27.
Since there are 29 positive integers less than 30, it might be easiest to find the values that
don't meet any of the criteria and subtract this value from 29.
Observe
1) Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, . . . 28
2) Odd multiples of 9: 9, 27
3) Sum of a positive multiple of 2 and a positive multiple of 9: By adding an even number to 9 (e.g., 9+2, 9+4, 9+6, etc), we can get every odd number from 11 to 29.
Summarize
The first condition gives us every even number from 2 to 28.
The second condition gives us 9
The third condition gives us every odd number from 11 to 29.
So, it appears that the only numbers that can't be derived are the
4 odd numbers from 1 to 7 (1, 3, 5, and 7)
So, the number of integers that meet the conditions = 29 -
4 = [spoiler]25 = C[/spoiler]
Cheers,
Brent
