GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 07 Dec 2019, 11:38 ### 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

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.  # If p is a prime number greater than 2, what is the value of p ?

Author Message
TAGS:

### Hide Tags

Intern  Joined: 08 Dec 2009
Posts: 27
If p is a prime number greater than 2, what is the value of p ?  [#permalink]

### Show Tags

6
1
29 00:00

Difficulty:   5% (low)

Question Stats: 78% (00:58) correct 22% (01:17) wrong based on 538 sessions

### HideShow timer Statistics

If p is a prime number greater than 2, what is the value of p ?

(1) There are a total of 100 prime numbers between 1 and p+1
(2) There are a total of p prime numbers between 1 and 3,912
Math Expert V
Joined: 02 Sep 2009
Posts: 59588
Re: If p is a prime number greater than 2, what is the value of p ?  [#permalink]

### Show Tags

4
2
PhunsukWangdu wrote:
bangalorian2000 wrote:
aljatar wrote:
Please need some help with this one ... thanks a lot

if p is a prime number greater than 2, what is the value of p ?
(1) There are a total of 100 prime numbers between 1 and p+1
(2) There are a total of p prime numbers between 1 and 3,912
Spoiler: :: OA
OA is D

1: p has to be 100th prime number starting from 2 (1st prime number) sufficient.
2: all the prime numbers between 1 and 3912 can be found and the number of prime number will be what we need. Sufficient.
Hence D.

PS: This is a DS question so we do not need to calculate the p till end. calculation will take some time but no need to do.

Using Stmt 1, it's pretty straight forward.

Using Stmt 2, let n = no. of prime numbers between 1 and 3912. How can we be sure that n is a prime number and it is equal to p? Do we have to assume so in questions like these?

Stem and the statements are ALWAYS providing us with correct information.

If it turns out that the quantity of primes between 1 and 3912 is not the prime number itself, this will mean that the question is flawed. GMAT wouldn't give us such question then.

Stem says p is a prime number.
Statement (2) says that "there are a total of p prime numbers between 1 and 3912". So yes the # of primes between 1 and 3912 MUST be prime number itself. We don't know what number it is, but we can calculate it, hence we can calculate p, hence (2) is also sufficient.

Hope it's clear.
_________________
Manager  Joined: 01 Feb 2010
Posts: 174
Re: If p is a prime number greater than 2, what is the value of p ?  [#permalink]

### Show Tags

2
3
aljatar wrote:
Please need some help with this one ... thanks a lot

if p is a prime number greater than 2, what is the value of p ?
(1) There are a total of 100 prime numbers between 1 and p+1
(2) There are a total of p prime numbers between 1 and 3,912
Spoiler: :: OA
OA is D

1: p has to be 100th prime number starting from 2 (1st prime number) sufficient.
2: all the prime numbers between 1 and 3912 can be found and the number of prime number will be what we need. Sufficient.
Hence D.

PS: This is a DS question so we do not need to calculate the p till end. calculation will take some time but no need to do.
##### General Discussion
Intern  Joined: 14 Jan 2010
Posts: 16
Re: If p is a prime number greater than 2, what is the value of p ?  [#permalink]

### Show Tags

1
bangalorian2000 wrote:
aljatar wrote:
Please need some help with this one ... thanks a lot

if p is a prime number greater than 2, what is the value of p ?
(1) There are a total of 100 prime numbers between 1 and p+1
(2) There are a total of p prime numbers between 1 and 3,912
Spoiler: :: OA
OA is D

1: p has to be 100th prime number starting from 2 (1st prime number) sufficient.
2: all the prime numbers between 1 and 3912 can be found and the number of prime number will be what we need. Sufficient.
Hence D.

PS: This is a DS question so we do not need to calculate the p till end. calculation will take some time but no need to do.

Using Stmt 1, it's pretty straight forward.

Using Stmt 2, let n = no. of prime numbers between 1 and 3912. How can we be sure that n is a prime number and it is equal to p? Do we have to assume so in questions like these?
Manager  Joined: 27 Dec 2009
Posts: 124
Re: If p is a prime number greater than 2, what is the value of p ?  [#permalink]

### Show Tags

bangalorian2000 wrote:
1: p has to be 100th prime number starting from 2 (1st prime number) sufficient.

Why can't p+1 be the 100th prime number ?
Math Expert V
Joined: 02 Sep 2009
Posts: 59588
Re: If p is a prime number greater than 2, what is the value of p ?  [#permalink]

### Show Tags

2
msand wrote:
bangalorian2000 wrote:
1: p has to be 100th prime number starting from 2 (1st prime number) sufficient.

Why can't p+1 be the 100th prime number ?

As p is prime more than 2 (given), then p+1 is even so it can not be prime.
_________________
Intern  Joined: 03 Nov 2010
Posts: 1
Re: If p is a prime number greater than 2, what is the value of p ?  [#permalink]

### Show Tags

1
statement A is not sufficient...consider this: how many prime numbers are between 1 and 14 and between 1 and 16,,,same number..you can not conclude anything from statement like there 100 prime less than p+1...
B is sufficient..
Math Expert V
Joined: 02 Sep 2009
Posts: 59588
Re: If p is a prime number greater than 2, what is the value of p ?  [#permalink]

### Show Tags

2
1
lhich2000 wrote:
statement A is not sufficient...consider this: how many prime numbers are between 1 and 14 and between 1 and 16,,,same number..you can not conclude anything from statement like there 100 prime less than p+1...
B is sufficient..

OA for this question is D, not B.

Statement (1) is says that there are 100 primes in the range between 1 and P+1, so this statement basically says that P is the 100th prime --> we can determine the single numerical value of P (we can find 100th prime). As this is DS question no matter what the actual value of P is, the fact that we can find it, is already sufficient.
_________________
Senior Manager  Joined: 13 Aug 2012
Posts: 398
Concentration: Marketing, Finance
GPA: 3.23
Re: If p is a prime number greater than 2, what is the value of p ?  [#permalink]

### Show Tags

2
Statement 1:
Listing the first 100 prime numbers and getting the 100th prime will give us p

Statement 2:
Listing all the prime numbers from 1 to 3912 and counting them will give us p

Manager  B
Joined: 21 Jul 2014
Posts: 80
Location: India
GPA: 4
WE: Project Management (Energy and Utilities)
Re: If p is a prime number greater than 2, what is the value of p ?  [#permalink]

### Show Tags

Incidentally, Bunuel I ran the wolfram to find the number of primes between 1 & 3912. It said 541.

Not to see if 541 is prime or not. We have the closest square root of 541 less than 25 ( considering 625). Thus, we need to check for
2- No
3-No
5-- No
7- No
9-- No ( sum of digits = 10)
11- No
13- No
17- No
19- No
23- No Hence 541 is prime as predicted by you. ( Ohh. by the way, I did countercheck with wolfram again & its correct)

It's good to see the principles in action.

Thanks,
Ankush.
Director  G
Joined: 26 Oct 2016
Posts: 600
Location: United States
Schools: HBS '19
GMAT 1: 770 Q51 V44 GPA: 4
WE: Education (Education)
Re: If p is a prime number greater than 2, what is the value of p ?  [#permalink]

### Show Tags

1
(2) must be sufficient, as there is obviously some fixed number of primes between 1 and 3912. we don't care what that number is, because it's clear that there's only one such number (the number of primes in a fixed range isn't about to change anytime soon).

(1) also sufficient: p is a prime number, so:
if p is the 100th prime, then there are 100 primes - viz., the first 100 primes - between 1 and p + 1.
if p is the 101th prime or later, then there are 101 or more primes, so that's no good.
if p is the 99th prime or earlier, then there are 99 or fewer primes; also no good.
therefore, p is the 100th prime.

_________________
Thanks & Regards,
Anaira Mitch
Target Test Prep Representative V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8622
Location: United States (CA)
Re: If p is a prime number greater than 2, what is the value of p ?  [#permalink]

### Show Tags

aljatar wrote:
If p is a prime number greater than 2, what is the value of p ?

(1) There are a total of 100 prime numbers between 1 and p+1
(2) There are a total of p prime numbers between 1 and 3,912

We are given that p is a prime number greater than 2 and we need to determine the value of p.

Note that even though we are asked for the value of p, we actually need to determine whether the value of p is unique. If we can determine from the given statements that p is unique, then the statement(s) will be sufficient. We do not have to actually determine the value of p, even though it would be possible.

Statement One Alone:

There are a total of 100 prime numbers between 1 and p + 1.

If there are exactly 100 prime numbers between 1 and p + 1, then there are exactly 100 prime numbers in the list: 2, 3, 5, 7, 11, 13, …, p. Whatever value p is, p must be unique. It is the 100th number in the list. Statement one alone is sufficient. We can eliminate answer choices B, C, and E.

Statement Two Alone:

There are a total of p prime numbers between 1 and 3,912.

It is a fact that between two distinct positive integers, there must be a unique number of primes. For example, between 1 and 10 inclusive there are exactly 4 primes: 2, 3, 5, 7. There can’t be 3 primes or 5 primes between 1 and 10. Therefore, if there are exactly p prime numbers between 1 and 3,912, p must be unique, even if we don’t know its exact value. Statement two alone is also sufficient.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

IIMA, IIMC School Moderator V
Joined: 04 Sep 2016
Posts: 1370
Location: India
WE: Engineering (Other)
Re: If p is a prime number greater than 2, what is the value of p ?  [#permalink]

### Show Tags

Bunuel chetan2u niks18

Is my below understanding correct for highlighted text?
Quote:
Statement (1) is says that there are 100 primes in the range between 1 and P+1, so this statement basically says that P is the 100th prime --> we can determine the single numerical value of P (we can find 100th prime). As this is DS question no matter what the actual value of P is, the fact that we can find it, is already sufficient.

Eg 1: 2 is a prime number, numbers that are prime between 1 and 2 is 0

Eg 2: 3 is a prime number, numbers that are prime between 1 and 3 is 1 (2)

Eg 3: 5 is a prime number, numbers that are prime between 1 and 5 is 2 (1,3)

Does the question ask the value in bracket is UNIQUE ? (2 or 1,3) I did not understand significance of P+1 in St 1
_________________
It's the journey that brings us happiness not the destination.

Feeling stressed, you are not alone!!
Retired Moderator D
Joined: 25 Feb 2013
Posts: 1159
Location: India
GPA: 3.82
Re: If p is a prime number greater than 2, what is the value of p ?  [#permalink]

### Show Tags

Bunuel chetan2u niks18

Is my below understanding correct for highlighted text?
Quote:
Statement (1) is says that there are 100 primes in the range between 1 and P+1, so this statement basically says that P is the 100th prime --> we can determine the single numerical value of P (we can find 100th prime). As this is DS question no matter what the actual value of P is, the fact that we can find it, is already sufficient.

Eg 1: 2 is a prime number, numbers that are prime between 1 and 2 is 0

Eg 2: 3 is a prime number, numbers that are prime between 1 and 3 is 1 (2)

Eg 3: 5 is a prime number, numbers that are prime between 1 and 5 is 2 (1,3)

Does the question ask the value in bracket is UNIQUE ? (2 or 1,3) I did not understand significance of P+1 in St 1

First of all note that 1 is not prime.

let's assume p to be 5, so p+1=6

now I can say that there are 3 prime numbers between 1 & 6 (2,3 & 5), which is same as saying there are 3 prime numbers between 1 & p+1, where p is a prime number.

So in this question, we have 100 prime numbers between 1 & p+1, so you can actually count 100 prime numbers starting with 2. the 100th prime number will be p
Manager  S
Joined: 30 May 2018
Posts: 70
Concentration: General Management, Marketing
GMAT 1: 750 Q49 V45 GPA: 3.45
WE: Other (Retail)
Re: If p is a prime number greater than 2, what is the value of p ?  [#permalink]

### Show Tags

1

Statement 1 : Is obvious , you can actually calculate manually and find out the value of P ( though you don't need to coz we know that there will be a unique value ).
Statement 2 : Again , we understand that there will be a unique value for P between 1 and 3912 which we don't need to sit down and calculate coz it is going to be a unique value hence arriving at option D as the answer.

Pls comment in case you disagree with the logic or have a better/shorter way to solve this question , else Kudos would be nice !
Intern  B
Joined: 26 Feb 2019
Posts: 6
Re: If p is a prime number greater than 2, what is the value of p ?  [#permalink]

### Show Tags

Let's take prime numbers between
1 to 14 and 1 to 15
The value of p changes.
The main aim is to find whether we are able to find p value (or)
Whether to find the p value is always same!
Bunuel

Posted from my mobile device
Senior Manager  D
Status: PhD-trained. Education, Research, Teaching, Training, Consulting and Advisory Services
Joined: 23 Apr 2019
Posts: 440
Re: If p is a prime number greater than 2, what is the value of p ?  [#permalink]

### Show Tags

1
GMAT8055 wrote:
Let's take prime numbers between
1 to 14 and 1 to 15
The value of p changes.
The main aim is to find whether we are able to find p value (or)
Whether to find the p value is always same!
Bunuel

Posted from my mobile device

14 and 15 are not prime numbers.

The upper limit of the series of numbers is "p+1", i.e. the upper limit is the number p (a prime number) plus one.

E.g. If you have p=6 prime numbers, then the last number of the series is equal to 6+1=7.

Where are you getting 14 and 15? Perhaps misunderstood your question. Re: If p is a prime number greater than 2, what is the value of p ?   [#permalink] 08 Aug 2019, 20:58
Display posts from previous: Sort by

# If p is a prime number greater than 2, what is the value of p ?  