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P* is defined as the number of positive even integers less
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19 Oct 2017, 22:41
19 Oct 2017, 22:41
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Question Stats:
44% (01:54) correct
55% (01:15) wrong based on 9 sessions
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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*
Kudos for correct solution.
(A) 3*
(B) 4*
(C) 7*
(D) 10*
(E) 11*
Kudos for correct solution.
Re: P* is defined as the number of positive even integers less
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20 Oct 2017, 07:01
20 Oct 2017, 07:01
1
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
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
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08 Jan 2018, 11:03
08 Jan 2018, 11:03
Expert Reply
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*
(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
