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

 It is currently 18 Jun 2018, 13:45

### 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

# Events & Promotions

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

# If P is a prime number greater than 5, what is the remainder when P^2

Author Message
TAGS:

### Hide Tags

BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2642
GRE 1: 323 Q169 V154
If P is a prime number greater than 5, what is the remainder when P^2 [#permalink]

### Show Tags

03 Aug 2016, 04:19
00:00

Difficulty:

5% (low)

Question Stats:

82% (00:43) correct 18% (00:21) wrong based on 100 sessions

### HideShow timer Statistics

If P is a prime number greater than 5, what is the remainder when P^2 is divided by 8.
A) 4
B) 3
C) 2
D) 1
E) Cannot be determined

Note => Kudos for an algebraic approach

_________________

MBA Financing:- INDIAN PUBLIC BANKS vs PRODIGY FINANCE!

Getting into HOLLYWOOD with an MBA!

The MOST AFFORDABLE MBA programs!

STONECOLD's BRUTAL Mock Tests for GMAT-Quant(700+)

AVERAGE GRE Scores At The Top Business Schools!

Director
Joined: 05 Mar 2015
Posts: 969
If P is a prime number greater than 5, what is the remainder when P^2 [#permalink]

### Show Tags

Updated on: 03 Aug 2016, 09:25
stonecold wrote:
If P is a prime number greater than 5, what is the remainder when P^2 is divided by 8.
A) 4
B) 3
C) 2
D) 1
E) Cannot be determined

Note => Kudos for an algebraic approach

take square of any prime number
remainder will be 1

Ans D

Originally posted by rohit8865 on 03 Aug 2016, 08:28.
Last edited by rohit8865 on 03 Aug 2016, 09:25, edited 2 times in total.
Math Expert
Joined: 02 Aug 2009
Posts: 5887
Re: If P is a prime number greater than 5, what is the remainder when P^2 [#permalink]

### Show Tags

03 Aug 2016, 08:49
3
3
stonecold wrote:
If P is a prime number greater than 5, what is the remainder when P^2 is divided by 8.
A) 4
B) 3
C) 2
D) 1
E) Cannot be determined

Note => Kudos for an algebraic approach

Hi,

here is the algebric approach..
these prime numbers are of teh form 6n+1 or 6n-1..
so P= 6n+1..
$$P^2 = (6n+1)^2 = 36n^2+12n+1$$...
Now $$36n^2+12n = 4n(9n+3)$$ ....
if n is even... 4n will be div by 8....
if n is odd.. 4n will be div by 4 and 9n+3 will become even and be div by 2,hence 4n*(9n+3) will be div by 4*2=8..
so in $$P^2=36n^2+12n+1$$ only 1 is left, Remainder = 1..
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

GMAT online Tutor

Senior Manager
Joined: 23 Apr 2015
Posts: 322
Location: United States
WE: Engineering (Consulting)
Re: If P is a prime number greater than 5, what is the remainder when P^2 [#permalink]

### Show Tags

03 Aug 2016, 09:04

How to solve :
Given,
$$P^2$$ mod 8 = x,remainder. Then $$P^2$$ - x would be divisible by 8 giving remainder zero.
So $$P^2$$ - x = (P -$$\sqrt{x}$$)(P + $$\sqrt{x}$$) divisible by zero when divided by 8.

Let's consider the choices, 4 would make \sqrt{4} = 2, which would make both factors as odd numbers.
Obviously 3 and 2 are irrational. Left is 1 and when tried P-1 and P+1 would be even and since P is greater than 5, it is the right answer.
BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2642
GRE 1: 323 Q169 V154
If P is a prime number greater than 5, what is the remainder when P^2 [#permalink]

### Show Tags

11 Jan 2017, 08:04
Here is one more way to solve this one=>

All prime numbers greater than 2 are odd.
Hence p must be of the form => 2k+1
p^2=> 4k^2+4k+1=> 4k(k+1)+1= 8k'+1
Hence it will always leave a remainder 1 with 8.

Another important takeaway ->
For any odd number k => k^2 will always leave a remainder 1 with 8.

_________________

MBA Financing:- INDIAN PUBLIC BANKS vs PRODIGY FINANCE!

Getting into HOLLYWOOD with an MBA!

The MOST AFFORDABLE MBA programs!

STONECOLD's BRUTAL Mock Tests for GMAT-Quant(700+)

AVERAGE GRE Scores At The Top Business Schools!

Senior Manager
Joined: 25 Mar 2013
Posts: 267
Location: United States
Concentration: Entrepreneurship, Marketing
GPA: 3.5
Re: If P is a prime number greater than 5, what is the remainder when P^2 [#permalink]

### Show Tags

14 Jan 2017, 17:54
P > 5 ( 7,11,13 .. )
p^2 : two odd prime numbers always result odd, not divisible by 8
$$\frac{p^2}{8}$$
Reminds either 0 or 1
D
_________________

I welcome analysis on my posts and kudo +1 if helpful. It helps me to improve my craft.Thank you

Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3505
Location: India
GPA: 3.5
Re: If P is a prime number greater than 5, what is the remainder when P^2 [#permalink]

### Show Tags

16 Jan 2018, 10:56
stonecold wrote:
If P is a prime number greater than 5, what is the remainder when P^2 is divided by 8.
A) 4
B) 3
C) 2
D) 1
E) Cannot be determined

Note => Kudos for an algebraic approach

Plug in some values and check

Let P = 7, 11 , 13

Result will be 1 in each case, thus answer will be (D)

_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2738
Location: United States (CA)
Re: If P is a prime number greater than 5, what is the remainder when P^2 [#permalink]

### Show Tags

18 Jan 2018, 14:14
stonecold wrote:
If P is a prime number greater than 5, what is the remainder when P^2 is divided by 8.
A) 4
B) 3
C) 2
D) 1
E) Cannot be determined

If we let P = 7, then the remainder when P^2 is divided by 8 is 1 since 49/8 = 6 remainder 1.

If we let P = 11, then the remainder when P^2 is divided by 8 is 1 since 121/8 = 15 remainder 1.

If we let P = 13, then the remainder when P^2 is divided by 8 is 1 since 169/8 = 21 remainder 1.

At this point, you might wonder: is the remainder always 1? If it is, then the answer will be D; otherwise, the answer will be E. Let’s prove it algebraically.

Since any prime number greater than 5 is odd, and an odd number can be written as 4n + 1 or 4n + 3 for some positive integer n, we can express P as P = 4n + 1 or P = 4n + 3.

Case 1: If P = 4n + 1, we have:

P^2 = (4n + 1)^2 = 16n^2 + 8n + 1

We see that the first two terms are divisible by 8; thus, the remainder must be the last term, which is 1.

Case 2: If P = 4n + 3, we have:

P^2 = (4n + 3)^2 = 16n^2 + 24n + 9

We see that the first two terms are divisible by 8 and the last term 9 has a remainder of 1 when it’s divided by 8; thus, the remainder must be 1.

Thus, we see that when the square of a prime (greater than 5) is divided by 8, the remainder will always be 1.

Alternate Solution:

Let’s consider P^2 - 1 = (P - 1)(P + 1).

Since P > 5, both P - 1 and P + 1 are even because P is prime. Moreover, since P - 1 and P + 1 are consecutive even integers, one of them is divisible by 4. Since each of P - 1 and P + 1 are even and since, furthermore, one of them is divisible by 4, their product, which is P^2 - 1, is divisible by 8. Since P^2 - 1 is divisible by 8, P^2 will leave a remainder of 1 when divided by 8.

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: If P is a prime number greater than 5, what is the remainder when P^2   [#permalink] 18 Jan 2018, 14:14
Display posts from previous: Sort by