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P* is defined as the number of positive even integers less

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P* is defined as the number of positive even integers less [#permalink] New post 19 Oct 2017, 22:41
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P* is defined as the number of positive even integers less than P, if P is odd. If P is even, P* is defined as the number of prime integers less than P. What is (5* + 10*)*?

(A) 3*

(B) 4*

(C) 7*

(D) 10*

(E) 11*


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Re: P* is defined as the number of positive even integers less [#permalink] New post 20 Oct 2017, 07:01
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Since 5 is odd, 5* = 2 because the odd numbers less than 5 are 2 and 4. Since 10 is even, 10* = 4, given that the prime numbers less than 10 are 2, 3, 5, 7.

Thus, we get (2+4)* = 6* = 3, i.e. 2, 3, 5 the prime numbers less than 6.

Among the choices only 7* = 3 because there three even numbers less than 7.

Answer C
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Re: P* is defined as the number of positive even integers less [#permalink] New post 08 Jan 2018, 11:03
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Bunuel wrote:
P* is defined as the number of positive even integers less than P, if P is odd. If P is even, P* is defined as the number of prime integers less than P. What is (5* + 10*)*?

(A) 3*

(B) 4*

(C) 7*

(D) 10*

(E) 11*


Since 5 is odd, 5* represents the number of even integers less than 5. Since the even integers less than 5 are 4 and 2, 5* = 2.

Since 10 is even, 10* represents the number of primes less than 10. Since the primes less than 10 are 7, 5, 3, and 2, 10* = 4.

So, (5* + 10*)* = (2 + 4)* = 6* = 3, since 6 is even and the primes less than 6 are 5, 3, and 2.

We need to find an answer choice that is equal to 3.

We see that 7* = 3, since there are 3 even numbers less than 7, namely, 6, 4, and 2.

Answer: C
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Re: P* is defined as the number of positive even integers less   [#permalink] 08 Jan 2018, 11:03
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