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
How many positive integers less than 28 are prime numbers,
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Any even integer other than 2 and 4 can be expressed as the sum of a positive multiple of 2 and a positive multiple of 4, yielding the following options less than 28:BTGmoderatorDC 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
6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26 --> 11 options.
Prime numbers less than 28:
2, 3, 5, 7, 11, 13, 17, 19, 23 --> 9 options.
Odd multiples of 5 not yet listed:
15, 25 --> 2 options.
Total options = 11+9+2 = 22.
The correct answer is D.
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The following are sums of multiples of 2 and 4:BTGmoderatorDC 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
6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26
The following are prime numbers less than 28:
2, 3, 5, 7, 11, 13, 17, 19, 23
The following are odd multiples of 5 (excluding 5) that are less than 28:
15 and 25
In the lists above there are 11 + 9 + 2 = 22 values.
Answer: D
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