Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 26 Sep 2016, 19:51

### GMAT Club Daily Prep

#### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If p is a prime number, what is the value of p ? (1) \sqrt

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 34862
Followers: 6485

Kudos [?]: 82734 [0], given: 10116

If p is a prime number, what is the value of p ? (1) \sqrt [#permalink]

### Show Tags

03 Oct 2010, 10:30
00:00

Difficulty:

95% (hard)

Question Stats:

37% (02:25) correct 63% (01:54) wrong based on 88 sessions

### HideShow timer Statistics

If $$p$$ is a prime number, what is the value of $$p$$?

(1) $$\sqrt[3]{1-p^2}=-n$$, where $$n$$ is a prime number.
(2) $$8p^2+1=m$$, where $$m$$ is a prime number.
[Reveal] Spoiler: OA

_________________
VP
Joined: 08 Jul 2010
Posts: 1250
Location: India
GMAT: INSIGHT
WE: Education (Education)
Followers: 52

Kudos [?]: 1178 [2] , given: 40

Re: If p is a prime number, what is the value of p ? (1) \sqrt [#permalink]

### Show Tags

20 Jul 2016, 11:18
2
This post received
KUDOS
Expert's post
Bunuel wrote:
If $$p$$ is a prime number, what is the value of $$p$$?

(1) $$\sqrt[3]{1-p^2}=-n$$, where $$n$$ is a prime number.
(2) $$8p^2+1=m$$, where $$m$$ is a prime number.

Please find the solution as attached.

Answer: option D
Attachments

File comment: www.GMATinsight.com

Untitled2.jpg [ 137.45 KiB | Viewed 361 times ]

_________________

Prosper!!!

GMATinsight

Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com
Call us : +91-9999687183 / 9891333772
http://www.GMATinsight.com/testimonials.html

Contact for One-on-One LIVE ONLINE (SKYPE Based) or CLASSROOM Quant/Verbal FREE Demo Class

READ: http://gmatclub.com/forum/620-to-760-getting-reborn-161230.html
Classroom Centre Address:
GMATinsight
107, 1st Floor, Krishna Mall, Sector-12 (Main market), Dwarka, New Delhi-110075

______________________________________________________
Please press the if you appreciate this post !!

Manager
Joined: 04 Sep 2010
Posts: 51
Followers: 2

Kudos [?]: 1 [1] , given: 1

Re: If p is a prime number, what is the value of p ? (1) \sqrt [#permalink]

### Show Tags

03 Oct 2010, 12:06
1
This post received
KUDOS
A is ans
on solving a we get
1+ n^3 = P^2
so it will be satisfied with n=2 and p=3..
the reason is..p will be alws greater than n..so p will alws be odd no..so its square will be alws odd...
so n^3 must be even which is possible with only prime no 2..
so 1+n^3 will bcome odd...
so satisfied...

2) on solving eq bcom 8p^2 +1 =m..so I m unable to find any prime no which is 24k+1..where k is any + integer.. so not satisfied
Retired Moderator
Joined: 02 Sep 2010
Posts: 805
Location: London
Followers: 102

Kudos [?]: 877 [1] , given: 25

Re: If p is a prime number, what is the value of p ? (1) \sqrt [#permalink]

### Show Tags

03 Oct 2010, 12:11
1
This post received
KUDOS
Bunuel wrote:
If $$p$$ is a prime number, what is the value of $$p$$?

(1) $$\sqrt[3]{1-p^2}=-n$$, where $$n$$ is a prime number.
(2) $$8p^2+1=m$$, where $$m$$ is a prime number.

(1) $$\sqrt[3]{1-p^2}=-n$$ OR $$p^2=1+n^3=(1+n)(n^2-n+1)$$
If n=2, p=3
If n>2, then n is odd, (n+1) is even, hence p^2 is even, but this is only possible if p=2 and if p=2, n is cube_root(-3) which is not an integer
So only possibility is p=3
Sufficient

(2) $$8p^2+1=m$$
p is an integer and a prime so it can either be of the form 3k+1 or 3k-1 or be 3 (all other numbers of form 3k are composite)
8*(3k+1)^2+1=8*(9k^2+6k+1)+1=3*(24k^2+16k+3) .. which cannot be a prime since k>=1
8*(3k-1)^2+1=8*(9k^2-6k+1)+1=3*(24k^2-16k+3) .. which cannot be a prime since k>=1
8*3^2+1=73 is a prime
So only possible value of p is 3
Sufficient

Answer is (D)
_________________
Manager
Joined: 04 Sep 2010
Posts: 51
Followers: 2

Kudos [?]: 1 [1] , given: 1

Re: If p is a prime number, what is the value of p ? (1) \sqrt [#permalink]

### Show Tags

03 Oct 2010, 12:27
1
This post received
KUDOS
hey Man
p is an integer and a prime so it can either be of the form 6k+1 or 6k-1... not 3k+1 and 3k-1
Manager
Joined: 04 Sep 2010
Posts: 51
Followers: 2

Kudos [?]: 1 [1] , given: 1

Re: If p is a prime number, what is the value of p ? (1) \sqrt [#permalink]

### Show Tags

03 Oct 2010, 12:43
1
This post received
KUDOS
ya agreed D is ans..Thnx
CEO
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2795
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 222

Kudos [?]: 1531 [1] , given: 235

Re: If p is a prime number, what is the value of p ? (1) \sqrt [#permalink]

### Show Tags

03 Oct 2010, 22:08
1
This post received
KUDOS
Statement 2: take prime = 6k+1 and 6k-1

$$8*((6k+1)^2 + 1) = 8*36k^2 + 12k +9 =$$ 3* something => not a prime
$$8*((6k-1)^2 + 1) = 8*36k^2 - 12k +9 = 3*$$ something => not a prime

so any prime number of the form 6k+1 and 6k-1 is not possible.
lowest prime of the above form is for k=1 i.e. 5.

Thus only 2 possibilities p=2 and p=3. Only p=3 satisfies.

BUNUEL- Great question.
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned

Jo Bole So Nihaal , Sat Shri Akaal

Support GMAT Club by putting a GMAT Club badge on your blog/Facebook

GMAT Club Premium Membership - big benefits and savings

Gmat test review :
http://gmatclub.com/forum/670-to-710-a-long-journey-without-destination-still-happy-141642.html

Retired Moderator
Joined: 02 Sep 2010
Posts: 805
Location: London
Followers: 102

Kudos [?]: 877 [0], given: 25

Re: If p is a prime number, what is the value of p ? (1) \sqrt [#permalink]

### Show Tags

03 Oct 2010, 12:29
sudhanshushankerjha wrote:
hey Man
p is an integer and a prime so it can either be of the form 6k+1 or 6k-1... not 3k+1 and 3k-1

You can always divide all integers into 3 sets : 3k , 3k+1 , 3k-1
In case of primes, it is easy to see only one element in the first set, i.e., 3
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 34862
Followers: 6485

Kudos [?]: 82734 [0], given: 10116

Re: If p is a prime number, what is the value of p ? (1) \sqrt [#permalink]

### Show Tags

03 Oct 2010, 15:32
Expert's post
3
This post was
BOOKMARKED
Bunuel wrote:
If $$p$$ is a prime number, what is the value of $$p$$?

(1) $$\sqrt[3]{1-p^2}=-n$$, where $$n$$ is a prime number.
(2) $$8p^2+1=m$$, where $$m$$ is a prime number.

I wrote this question, so below is my solution:

(1) $$\sqrt[3]{1-p^2}=-n$$, where $$n$$ is a prime number.

It's clear that $$p\neq{2}$$ as in this case $$\sqrt[3]{1-p^2}\neq{integer}$$, so $$p$$ is a prime more than 2, so odd. Then $$1-p^2=odd-odd=even$$ --> cube root from even is either an even integer or not an integer at all, we are told that $$\sqrt[3]{1-p^2}=-n=integer$$, so $$-n=even=-prime$$ --> $$n=2$$ (the only even prime) --> $$\sqrt[3]{1-p^2}=-2$$ --> $$p=3$$. Sufficient.

(2) $$8p^2+1=m$$, where $$m$$ is a prime number.

$$p$$ can not be any prime but 3 for $$8p^2+1$$ to be a prime number: because if $$p$$ is not 3, then it's some other prime not divisible by 3, but in this case $$p^2$$ (square of a not multiple of 3) will yield the remainder of 1 when divided by 3 (not a multiple of 3 when squared yields remainder of 1 when divided by 3), so $$p^2$$ can be expressed as $$3k+1$$ --> $$8p^2+1=8(3k+1)+1=24k+9=3(8k+3)$$ --> so $$8p^2+1$$ becomes multiple of 3, so it can not be a prime. So $$p=3$$ and in this case $$8p^2+1=73=m=prime$$. Sufficient.

Answer: D.
_________________
Manager
Joined: 20 Apr 2010
Posts: 210
Schools: ISB, HEC, Said
Followers: 4

Kudos [?]: 68 [0], given: 28

Re: If p is a prime number, what is the value of p ? (1) \sqrt [#permalink]

### Show Tags

05 Oct 2010, 00:01
great question Bunuel
Intern
Joined: 25 Jul 2009
Posts: 11
Followers: 0

Kudos [?]: 3 [0], given: 2

Re: If p is a prime number, what is the value of p ? (1) \sqrt [#permalink]

### Show Tags

05 Oct 2010, 10:55
I am really confused. Can someone please explain me,

Statement 2:

I understand that if we work out the
8P^2 + 1 : where P = 2
we get m = 33, which is NOT a prime.

Great! I am on-board till here.

Is the strategy to try every prime number from 2, onwards??

How is the value of P chosen??

You state P cannot be any prime but 3 for 8P^2 + 1 to be a prime number. How can you be so sure? I do not have an exhaustive list of all prime number, but this claim is little far fetched.

Please clear my confusion.
_________________

Failure it not and option -- Gene Kranz

Math Expert
Joined: 02 Sep 2009
Posts: 34862
Followers: 6485

Kudos [?]: 82734 [0], given: 10116

Re: If p is a prime number, what is the value of p ? (1) \sqrt [#permalink]

### Show Tags

05 Oct 2010, 11:04
vrajesh wrote:
I am really confused. Can someone please explain me,

Statement 2:

I understand that if we work out the
8P^2 + 1 : where P = 2
we get m = 33, which is NOT a prime.

Great! I am on-board till here.

Is the strategy to try every prime number from 2, onwards??

How is the value of P chosen??

You state P cannot be any prime but 3 for 8P^2 + 1 to be a prime number. How can you be so sure? I do not have an exhaustive list of all prime number, but this claim is little far fetched.

Please clear my confusion.

There are infinitely many prime numbers so there is no "list of all primes".

Next, $$p$$ can not be any prime but 3 for $$8p^2+1$$ to be a prime number: because if $$p$$ is not 3, then it's some other prime not divisible by 3, but in this case $$p^2$$ (square of a not multiple of 3) will yield the remainder of 1 when divided by 3 (not a multiple of 3 when squared yields remainder of 1 when divided by 3), so $$p^2$$ can be expressed as $$3k+1$$ --> $$8p^2+1=8(3k+1)+1=24k+9=3(8k+3)$$ --> so $$8p^2+1$$ becomes multiple of 3, so it can not be a prime. So $$p=3$$ and in this case $$8p^2+1=73=m=prime$$.
_________________
Intern
Joined: 25 Jul 2009
Posts: 11
Followers: 0

Kudos [?]: 3 [0], given: 2

Re: If p is a prime number, what is the value of p ? (1) \sqrt [#permalink]

### Show Tags

05 Oct 2010, 12:47
Hi Bunuel,

OK.
But I am still not clear about why is it important to be divisible by 3.

"because if $$p$$ is not 3, then it's some other prime not divisible by 3, but in this case $$p^2$$ (square of a not multiple of 3) will yield the remainder of 1 when divided by 3 (not a multiple of 3 when squared yields remainder of 1 when divided by 3)"

Bunuel wrote:
There are infinitely many prime numbers so there is no "list of all primes".

Next, $$p$$ can not be any prime but 3 for $$8p^2+1$$ to be a prime number: because if $$p$$ is not 3, then it's some other prime not divisible by 3, but in this case $$p^2$$ (square of a not multiple of 3) will yield the remainder of 1 when divided by 3 (not a multiple of 3 when squared yields remainder of 1 when divided by 3), so $$p^2$$ can be expressed as $$3k+1$$ --> $$8p^2+1=8(3k+1)+1=24k+9=3(8k+3)$$ --> so $$8p^2+1$$ becomes multiple of 3, so it can not be a prime. So $$p=3$$ and in this case $$8p^2+1=73=m=prime$$.

I guess, you will have to explain this a little more.
_________________

Failure it not and option -- Gene Kranz

Math Expert
Joined: 02 Sep 2009
Posts: 34862
Followers: 6485

Kudos [?]: 82734 [0], given: 10116

Re: If p is a prime number, what is the value of p ? (1) \sqrt [#permalink]

### Show Tags

05 Oct 2010, 13:05
vrajesh wrote:
Hi Bunuel,

OK.
But I am still not clear about why is it important to be divisible by 3.

"because if $$p$$ is not 3, then it's some other prime not divisible by 3, but in this case $$p^2$$ (square of a not multiple of 3) will yield the remainder of 1 when divided by 3 (not a multiple of 3 when squared yields remainder of 1 when divided by 3)"

I guess, you will have to explain this a little more.

Because if $$p$$ IS NOT divisible by 3 then $$8p^2+1$$ IS divisible by 3 and thus can not be a prime, so $$p$$ must be divisible by 3, only prime divisible by 3 is 3.
_________________
CEO
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2795
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 222

Kudos [?]: 1531 [0], given: 235

Re: If p is a prime number, what is the value of p ? (1) \sqrt [#permalink]

### Show Tags

16 Oct 2010, 07:58
Raths wrote:
tough one...

Yes nice question- 700+
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned

Jo Bole So Nihaal , Sat Shri Akaal

Support GMAT Club by putting a GMAT Club badge on your blog/Facebook

GMAT Club Premium Membership - big benefits and savings

Gmat test review :
http://gmatclub.com/forum/670-to-710-a-long-journey-without-destination-still-happy-141642.html

Intern
Joined: 10 Jul 2010
Posts: 44
Followers: 0

Kudos [?]: 4 [0], given: 34

Re: If p is a prime number, what is the value of p ? (1) \sqrt [#permalink]

### Show Tags

23 Oct 2010, 04:28
D ...intially i thought it as A coz i was wrongly marked 57 as prime Silly mistake :0
Senior Manager
Status: Not afraid of failures, disappointments, and falls.
Joined: 20 Jan 2010
Posts: 294
Concentration: Technology, Entrepreneurship
WE: Operations (Telecommunications)
Followers: 17

Kudos [?]: 218 [0], given: 253

Re: If p is a prime number, what is the value of p ? (1) \sqrt [#permalink]

### Show Tags

23 Oct 2010, 19:32
Tough one, I could solve the question by plugging in the numbers but didn't think of trying (especially for 2nd statement) the above concepts, despite knowing for a number to be prime it should be either $$6k+1$$ or $$6k-1$$. Similarly, for statemet1 despite knowing that $$p$$ can not be $$2$$ and it would be more than didn't think that it must be odd and apply Odd & Even concept here.

Thank you! for reminding me to use concepts rather than just guessing and then getting doubtful solutions (and doing silly mistakes).
_________________

"I choose to rise after every fall"
Target=770
http://challengemba.blogspot.com
Kudos??

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 11690
Followers: 527

Kudos [?]: 144 [0], given: 0

Re: If p is a prime number, what is the value of p ? (1) \sqrt [#permalink]

### Show Tags

14 Jan 2015, 00:54
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.
_________________
Director
Joined: 26 Mar 2013
Posts: 548
Followers: 3

Kudos [?]: 98 [0], given: 81

If p is a prime number, what is the value of p ? (1) \sqrt [#permalink]

### Show Tags

21 Jul 2016, 09:16
GMATinsight wrote:
Bunuel wrote:
If $$p$$ is a prime number, what is the value of $$p$$?

(1) $$\sqrt[3]{1-p^2}=-n$$, where $$n$$ is a prime number.
(2) $$8p^2+1=m$$, where $$m$$ is a prime number.

Please find the solution as attached.

Answer: option D

Dear GMATinsight,

Thanks for you explanation. I did the same as you did in solving those question. But I had a doubt that there maybe a higher prime number that satisfy fact 2 so I kept doing this to 13 & 17. How should I be confident to stop at 11 like you?
VP
Joined: 08 Jul 2010
Posts: 1250
Location: India
GMAT: INSIGHT
WE: Education (Education)
Followers: 52

Kudos [?]: 1178 [0], given: 40

Re: If p is a prime number, what is the value of p ? (1) \sqrt [#permalink]

### Show Tags

21 Jul 2016, 20:14
Mo2men wrote:
GMATinsight wrote:
Bunuel wrote:
If $$p$$ is a prime number, what is the value of $$p$$?

(1) $$\sqrt[3]{1-p^2}=-n$$, where $$n$$ is a prime number.
(2) $$8p^2+1=m$$, where $$m$$ is a prime number.

Please find the solution as attached.

Answer: option D

Dear GMATinsight,

Thanks for you explanation. I did the same as you did in solving those question. But I had a doubt that there maybe a higher prime number that satisfy fact 2 so I kept doing this to 13 & 17. How should I be confident to stop at 11 like you?

Mo2men

To be Confident

1) You need to find out a pattern in solutions because there are always patterns followed among all acceptable or unacceptable solutions

2) To find a pattern you need three instances/examples to observe

I saw the pattern in solutions that each of the solutions that I was finding was a multiple of 3 so I concluded that this pattern is going to continue

Trusting the pattern based on three instances usually gets you the correct answer in 99% cases and the remaining 1% are usually made by Manhattan intentionally to prove this thought process incorrect. Thankfully Manhattan doesn't make GMAT so the chances are bleak that you get wrong answer trusting the pattern
_________________

Prosper!!!

GMATinsight

Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com
Call us : +91-9999687183 / 9891333772
http://www.GMATinsight.com/testimonials.html

Contact for One-on-One LIVE ONLINE (SKYPE Based) or CLASSROOM Quant/Verbal FREE Demo Class

READ: http://gmatclub.com/forum/620-to-760-getting-reborn-161230.html
Classroom Centre Address:
GMATinsight
107, 1st Floor, Krishna Mall, Sector-12 (Main market), Dwarka, New Delhi-110075

______________________________________________________
Please press the if you appreciate this post !!

Re: If p is a prime number, what is the value of p ? (1) \sqrt   [#permalink] 21 Jul 2016, 20:14
Similar topics Replies Last post
Similar
Topics:
If p is a negative number, what is the value of p ? 1 26 May 2016, 11:05
1 If p is an integer greater than 1, is p a prime number? 1 21 Dec 2015, 16:00
13 If p is a prime number greater than 2, what is the value of 16 28 Mar 2010, 05:56
8 If p, s, and t are positive prime numbers, what is the value 9 23 Jan 2010, 00:18
5 If p is a prime number greater than 2, what is the value of 9 12 Jul 2008, 15:46
Display posts from previous: Sort by

# If p is a prime number, what is the value of p ? (1) \sqrt

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.