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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*)*?

For an odd P, P* is defined as the number of positive even integers less than P For an even P, P* is defined as the number of prime integers less than P.

Since we are asked the value of (5* + 10*)*

5* = 2,4(2) 10* = 2,3,5,7(4)

Therefore we have been asked to find (2+4)* = 6*

But I do not find that answer option. Am i doing something wrong?
_________________

For an odd P, P* is defined as the number of positive even integers less than P For an even P, P* is defined as the number of prime integers less than P.

Since we are asked the value of (5* + 10*)*

5* = 2,4(2) 10* = 2,3,5,7(4)

Therefore we have been asked to find (2+4)* = 6*

But I do not find that answer option. Am i doing something wrong?

For an odd P, P* is defined as the number of positive even integers less than P For an even P, P* is defined as the number of prime integers less than P.

Since we are asked the value of (5* + 10*)*

5* = 2,4(2) 10* = 2,3,5,7(4)

Therefore we have been asked to find (2+4)* = 6*

But I do not find that answer option. Am i doing something wrong?

hi .. 6* means prime number LESS than 6 so 2,3,5 - ans 3 in choices 7* means EVEN integers LESS than 7 so 2,4,6 again answer 3 EDIT - SOMEONE has already clarified above...
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Re: P* is defined as the number of positive even integers less than P, if [#permalink]

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21 Oct 2017, 12:47

1

This post received KUDOS

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*

The answer choices are in the form <integer>* and not what that integer would evaluate to.

I think 5* should be {0,2,4}, since 0 is considered and even positive integer, hence it evaluates to 3 10* would be {2,3,5,7} so (3+4)* = (7)*

Re: P* is defined as the number of positive even integers less than P, if [#permalink]

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21 Oct 2017, 13:04

avaneeshvyas wrote:

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*

The answer choices are in the form <integer>* and not what that integer would evaluate to.

I think 5* should be {0,2,4}, since 0 is considered and even positive integer, hence it evaluates to 3 10* would be {2,3,5,7} so (3+4)* = (7)*

Consider this: if 0 is positive, then on multiplying it with a negative number, say -1, it should become negative because positive*negative=negative. But 0 multiplied by any number is 0.

For this solution 5* ={2,4}= 2 values 10*={2,3,5,7}=4 values hence (5*+10*)*=(2+4)*=6* again 6*={2,3,5}= 3 values and 7*={2,4,6}= 3 values

Re: P* is defined as the number of positive even integers less than P, if [#permalink]

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22 Oct 2017, 04:10

niks18 wrote:

avaneeshvyas wrote:

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*

The answer choices are in the form <integer>* and not what that integer would evaluate to.

I think 5* should be {0,2,4}, since 0 is considered and even positive integer, hence it evaluates to 3 10* would be {2,3,5,7} so (3+4)* = (7)*

Consider this: if 0 is positive, then on multiplying it with a negative number, say -1, it should become negative because positive*negative=negative. But 0 multiplied by any number is 0.

For this solution 5* ={2,4}= 2 values 10*={2,3,5,7}=4 values hence (5*+10*)*=(2+4)*=6* again 6*={2,3,5}= 3 values and 7*={2,4,6}= 3 values

Hence 6*=7*

So option C

I would like others to pitch in with their thoughts on this since for GMAT, as far as I know, 0 is an even number. Positive/negative/otherwise I am not very sure.

I would like others to pitch in with their thoughts on this since for GMAT, as far as I know, 0 is an even number. Positive/negative/otherwise I am not very sure.

ZERO:

1. 0 is an integer.

2. 0 is an even integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even.

3. 0 is neither positive nor negative integer (the only one of this kind).

4. 0 is divisible by EVERY integer except 0 itself.

Re: P* is defined as the number of positive even integers less than P, if [#permalink]

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22 Oct 2017, 07:03

Bunuel wrote:

avaneeshvyas wrote:

I would like others to pitch in with their thoughts on this since for GMAT, as far as I know, 0 is an even number. Positive/negative/otherwise I am not very sure.

ZERO:

1. 0 is an integer.

2. 0 is an even integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even.

3. 0 is neither positive nor negative integer (the only one of this kind).

4. 0 is divisible by EVERY integer except 0 itself.

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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