Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized for You
we will pick new questions that match your level based on your Timer History
Track Your Progress
every week, we’ll send you an estimated GMAT score based on your performance
Practice Pays
we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
It appears that you are browsing the GMAT Club forum unregistered!
Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club
Registration gives you:
Tests
Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.
Applicant Stats
View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more
Books/Downloads
Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
If, for all positive integer values of n, P(n) is defined as [#permalink]
Show Tags
25 Apr 2013, 22:43
2
This post received KUDOS
6
This post was BOOKMARKED
00:00
A
B
C
D
E
Difficulty:
75% (hard)
Question Stats:
55% (01:43) correct
45% (02:11) wrong based on 216 sessions
HideShow timer Statistics
If, for all positive integer values of n, P(n) is defined as the sum of the smallest n prime numbers, then which of the following quantities are odd integers?
I. P(10) II. P(P(10)) III. P(P(P(10)))
(A) I only (B) I and II only (C) I and III only (D) II and III only (E) I, II, and III
Re: If, for all positive integer values of n, P(n) is defined as [#permalink]
Show Tags
25 Apr 2013, 23:41
emmak wrote:
If, for all positive integer values of n, P(n) is defined as the sum of the smallest n prime numbers, then which of the following quantities are odd integers? I. P(10) II. P(P(10)) III. P(P(P(10)))
(A) I only (B) I and II only (C) I and III only (D) II and III only (E) I, II, and III
Express appreciation by pressing KUDOS button
2 is the only even prime number. Now, the sum of first 10 prime numbers = 9*odd + 2 = odd. Thus P(10) = odd.
Again, the sum of the first n -odd primes = (n-1)*odd+2 = even.Thus, p(P(10)) = even.
Similarly, the sum of the first m - even primes = (m-1)*odd+2 = odd.
If, for all positive integer values of n, P(n) is defined as the sum of the smallest n prime numbers, then which of the following quantities are odd integers? I. P(10) II. P(P(10)) III. P(P(P(10)))
(A) I only (B) I and II only (C) I and III only (D) II and III only (E) I, II, and III
Express appreciation by pressing KUDOS button
This kind of question can give students fits. The key is to figure out what is being asked. The function P is summing up the first N prime numbers, so for example P(3) = 2 + 3 + 5. The total is 10. If I picked P(4), I'd get the same sum + 7, or 17.
Since the question hinges on whether the sum is even or odd, the only number that's unique in this circumstance is 2, as it is the only even prime number in an otherwise homogenous sea of odd numbers. Thus P(1) is even, P(2) is odd, P(3) is even again and P(4) is odd again. This is the pattern, so clearly P(10) will be 2 + nine odd numbers, so it will be odd. We can eliminate D.
P(P(10)) is where this starts getting interesting. You're doing the same test on a number we don't exactly know, but we know it must be odd. Since we know the pattern, the odd number will give us even. P(P(10)) will not be odd, eliminate B and E.
P(P(10))) will be the same function over a number we just calculated would be even. Hence it must be odd again. Eliminate A, the answer must be C.
Function questions are among the least understood questions on the GMAT, and this type of question can get people spending 3-4 minutes extrapolating numbers. If you understand the pattern using a small sample and reasoning, you can get this question right in under two minutes.
Re: If, for all positive integer values of n, P(n) is defined as [#permalink]
Show Tags
26 Apr 2013, 10:48
VeritasPrepRon wrote:
emmak wrote:
If, for all positive integer values of n, P(n) is defined as the sum of the smallest n prime numbers, then which of the following quantities are odd integers? I. P(10) II. P(P(10)) III. P(P(P(10)))
(A) I only (B) I and II only (C) I and III only (D) II and III only (E) I, II, and III
Express appreciation by pressing KUDOS button
This kind of question can give students fits. The key is to figure out what is being asked. The function P is summing up the first N prime numbers, so for example P(3) = 2 + 3 + 5. The total is 10. If I picked P(4), I'd get the same sum + 7, or 17.
Since the question hinges on whether the sum is even or odd, the only number that's unique in this circumstance is 2, as it is the only even prime number in an otherwise homogenous sea of odd numbers. Thus P(1) is even, P(2) is odd, P(3) is even again and P(4) is odd again. This is the pattern, so clearly P(10) will be 2 + nine odd numbers, so it will be odd. We can eliminate D.
P(P(10)) is where this starts getting interesting. You're doing the same test on a number we don't exactly know, but we know it must be odd. Since we know the pattern, the odd number will give us even. P(P(10)) will not be odd, eliminate B and E.
P(P(10))) will be the same function over a number we just calculated would be even. Hence it must be odd again. Eliminate A, the answer must be C.
Function questions are among the least understood questions on the GMAT, and this type of question can get people spending 3-4 minutes extrapolating numbers. If you understand the pattern using a small sample and reasoning, you can get this question right in under two minutes.
Hope this helps! -Ron
Ah that makes sense... took me a while.
I. Even + 9 odds = odd. II. Even + (odd * (odd - 1)) = even III. Even + (odd * (even - 1)) = odd
Re: If, for all positive integer values of n, P(n) is defined as [#permalink]
Show Tags
26 Feb 2014, 07:35
1
This post received KUDOS
Nice question +1. For this I would identify two cases: First we know that the only even number is 2. Therefore, if the number of prime integers that is n is even then the sum is odd, while if n is odd the sum is even.
In I we have that n is even therefore sum is odd. TRUE.
In II we have that the sum is odd so if we take that n is odd then the sum again will be even. FALSE.
In III, we get that the sum of n=10 is odd. Now the sum of odd is even and again the sum of even is odd. So III is TRUE as well.
Re: If, for all positive integer values of n, P(n) is defined as [#permalink]
Show Tags
26 Apr 2015, 23:03
Hello from the GMAT Club BumpBot!
Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If, for all positive integer values of n, P(n) is defined as [#permalink]
Show Tags
28 Apr 2016, 21:21
Hello from the GMAT Club BumpBot!
Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If, for all positive integer values of n, P(n) is defined as [#permalink]
Show Tags
06 Aug 2017, 09:30
VeritasPrepRon wrote:
emmak wrote:
If, for all positive integer values of n, P(n) is defined as the sum of the smallest n prime numbers, then which of the following quantities are odd integers? I. P(10) II. P(P(10)) III. P(P(P(10)))
(A) I only (B) I and II only (C) I and III only (D) II and III only (E) I, II, and III
Express appreciation by pressing KUDOS button
This kind of question can give students fits. The key is to figure out what is being asked. The function P is summing up the first N prime numbers, so for example P(3) = 2 + 3 + 5. The total is 10. If I picked P(4), I'd get the same sum + 7, or 17.
Since the question hinges on whether the sum is even or odd, the only number that's unique in this circumstance is 2, as it is the only even prime number in an otherwise homogenous sea of odd numbers. Thus P(1) is even, P(2) is odd, P(3) is even again and P(4) is odd again. This is the pattern, so clearly P(10) will be 2 + nine odd numbers, so it will be odd. We can eliminate D.
P(P(10)) is where this starts getting interesting. You're doing the same test on a number we don't exactly know, but we know it must be odd. Since we know the pattern, the odd number will give us even. P(P(10)) will not be odd, eliminate B and E.
P(P(10))) will be the same function over a number we just calculated would be even. Hence it must be odd again. Eliminate A, the answer must be C.
Function questions are among the least understood questions on the GMAT, and this type of question can get people spending 3-4 minutes extrapolating numbers. If you understand the pattern using a small sample and reasoning, you can get this question right in under two minutes.
Hope this helps! -Ron
Thanks for the solution.... Putting numbers to solve this kind of question can take 5 minutes easily.... We must follow the right approach to solve the question quickly...
_________________
If you appreciate my post then please click +1Kudos
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: If, for all positive integer values of n, P(n) is defined as [#permalink]
Show Tags
07 Aug 2017, 23:15
emmak wrote:
If, for all positive integer values of n, P(n) is defined as the sum of the smallest n prime numbers, then which of the following quantities are odd integers?
I. P(10) II. P(P(10)) III. P(P(P(10)))
(A) I only (B) I and II only (C) I and III only (D) II and III only (E) I, II, and III
P(n) = Sum of 1st n prime numbers. Among these prime numbers only 2 i.e. first prime number is even. P(10 )= Sum of 2 and 9 odd numbers = even +9*odd = odd P(P(10)) = P(odd) = even + even *odd = even P(P(P(10))) = P(even) = even + odd * odd = odd.
So I and III only Hence Answer C _________________
Version 8.1 of the WordPress for Android app is now available, with some great enhancements to publishing: background media uploading. Adding images to a post or page? Now...
“Keep your head down, and work hard. Don’t attract any attention. You should be grateful to be here.” Why do we keep quiet? Being an immigrant is a constant...
“Keep your head down, and work hard. Don’t attract any attention. You should be grateful to be here.” Why do we keep quiet? Being an immigrant is a constant...
55% (01:43) correct
15
