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

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

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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 than P, if [#permalink]

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New post 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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New post 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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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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New post 21 Oct 2017, 12:47
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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*



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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New post 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 avaneeshvyas

0 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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New post 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 avaneeshvyas

0 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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New post 22 Oct 2017, 05:53
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.


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Hope it helps.
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PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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

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New post 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 Megathread

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