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P* is defined as the number of positive even integers less than P, if [#permalink]
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20 Oct 2017, 00:17
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Re: P* is defined as the number of positive even integers less than P, if [#permalink]
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20 Oct 2017, 00:43
Hi Bunuel, 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?
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Re: P* is defined as the number of positive even integers less than P, if [#permalink]
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20 Oct 2017, 00:57
pushpitkc wrote: Hi Bunuel, 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? 7* = 6* 7* = 3 ( 2,4,6) 6* = 3 (2,3,5)



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P* is defined as the number of positive even integers less than P, if [#permalink]
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20 Oct 2017, 00:59
pushpitkc wrote: Hi Bunuel, 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
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)*



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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, 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)* Hi avaneeshvyas0 is neither positive nor negative. 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



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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)* Hi avaneeshvyas0 is neither positive nor negative. 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.



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Re: P* is defined as the number of positive even integers less than P, if [#permalink]
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22 Oct 2017, 05:53



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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. Check below for more: ALL YOU NEED FOR QUANT ! ! !Ultimate GMAT Quantitative MegathreadHope it helps. Just to Add to Bunuel 's point for 0 being even number despite 0 being divisible by Odd number but still it is not an Odd no. Any even number is of the form 2k (that is a multiple of 2) and Odd no is of the form 2k+1, where k is an integer. so 2k=0 => k=0 (an integer). Hence 0 is even but if 0 were Odd, then 2k+1=0 => k=1/2 =not an integer. Hence 0 is not odd Also Odd ± Odd = Even, so if 0 were Odd, then 0+0=0, so 0 becomes even despite being an Odd as per our earlier assumption. Hence the assumption is invalid Therefore, 0 is even as Even ± Even=Even so we can say 0+0=0=Even perfectly fine assumption In conclusion 0 is a unique no that is Even and neither positive nor negative.



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Re: P* is defined as the number of positive even integers less than P, if [#permalink]
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24 Oct 2017, 06:40
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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