It is currently 18 Nov 2017, 20:22

### 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

# A Mersenne number is a positive integer that is one less tha

Author Message
TAGS:

### Hide Tags

Manager
Joined: 09 Feb 2013
Posts: 121

Kudos [?]: 1173 [4], given: 17

A Mersenne number is a positive integer that is one less tha [#permalink]

### Show Tags

11 Mar 2013, 23:25
4
KUDOS
1
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

63% (01:38) correct 37% (01:33) wrong based on 177 sessions

### HideShow timer Statistics

A Mersenne number is a positive integer that is one less than any power of 2. A Mersenne prime is a Mersenne number that also happens to be prime. The largest known prime number, 2^(43112609) - 1, is a Mersenne prime. If the largest known Mersenne prime were multiplied by the smallest Mersenne prime, which of the following would represent the units digit of the product?

A. 2
B. 3
C. 4
D. 6
E. 8
[Reveal] Spoiler: OA

_________________

Kudos will encourage many others, like me.
Good Questions also deserve few KUDOS.

Last edited by Bunuel on 12 Mar 2013, 04:50, edited 1 time in total.
Edited the question.

Kudos [?]: 1173 [4], given: 17

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7736

Kudos [?]: 17781 [1], given: 235

Location: Pune, India
Re: A Mersenne number is a positive integer that is one less tha [#permalink]

### Show Tags

11 Mar 2013, 23:43
1
KUDOS
Expert's post
emmak wrote:
A Mersenne number is a positive integer that is one less than any power of 2. A Mersenne prime is a Mersenne number that also happens to be prime. The largest known prime number, ((2^[43112609])-1), is a Mersenne prime. If the largest known Mersenne prime were multiplied by the smallest Mersenne prime, which of the following would represent the units digit of the product?
a) 2
b) 3
c) 4
d) 6
e) 8

First of all, think which is the smallest Mersenne prime?
The smallest prime 1 less than a power of 2 is 3.

We need the last digit of 2^{43112609} - 1. What will be the last digit of 2^{43112609}?
Recall cyclicity of last digits. After every 4 powers, the last digit repeats itself. Let's look at the last digits of powers of 2.
2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 6
2^5 = 2
2^6 = 4
and so on...
When 43112609 is divided by 4, you get remainder 1 (divide just the last two digits by 4. Whatever remainder you get will be the remainder when you divide the actual number by 4)
So the last digit of 2^{43112609} is 2
Last digit of 2^{43112609} - 1 is 1

Product of the last digits is 1*3 = 3

_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Kudos [?]: 17781 [1], given: 235

Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 627

Kudos [?]: 1386 [10], given: 136

Re: A Mersenne number is a positive integer that is one less tha [#permalink]

### Show Tags

12 Mar 2013, 01:21
10
KUDOS
emmak wrote:
A Mersenne number is a positive integer that is one less than any power of 2. A Mersenne prime is a Mersenne number that also happens to be prime. The largest known prime number, (2^[43112609])-1), is a Mersenne prime. If the largest known Mersenne prime were multiplied by the smallest Mersenne prime, which of the following would represent the units digit of the product?
a) 2
b) 3
c) 4
d) 6
e) 8

The smallest Mersenne prime is 3. Now we know that any power of 2 ends with a even integer. Thus the units digit of (2^[43112609])-1) will be an odd integer. This when multiplied by 3 will still be an odd integer. Thus the answer is the only odd integer.

B.
_________________

Kudos [?]: 1386 [10], given: 136

Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132623 [2], given: 12326

Re: A Mersenne number is a positive integer that is one less tha [#permalink]

### Show Tags

12 Mar 2013, 04:55
2
KUDOS
Expert's post
vinaymimani wrote:
emmak wrote:
A Mersenne number is a positive integer that is one less than any power of 2. A Mersenne prime is a Mersenne number that also happens to be prime. The largest known prime number, (2^[43112609])-1), is a Mersenne prime. If the largest known Mersenne prime were multiplied by the smallest Mersenne prime, which of the following would represent the units digit of the product?
a) 2
b) 3
c) 4
d) 6
e) 8

The smallest Mersenne prime is 3. Now we know that any power of 2 ends with a even integer. Thus the units digit of (2^[43112609])-1) will be an odd integer. This when multiplied by 3 will still be an odd integer. Thus the answer is the only odd integer.

B.

Good solution.

The smallest Mersenne prime = 2^2 - 1 = 3 = Odd;
2^(43112609) - 1 = Even - Odd = Odd;

Odd*Odd = Odd --> the units digit must be odd. Only B fit.

_________________

Kudos [?]: 132623 [2], given: 12326

Intern
Joined: 23 Apr 2013
Posts: 22

Kudos [?]: 23 [0], given: 1

Re: A Mersenne number is a positive integer that is one less tha [#permalink]

### Show Tags

04 May 2013, 23:23
emmak wrote:
A Mersenne number is a positive integer that is one less than any power of 2. A Mersenne prime is a Mersenne number that also happens to be prime. The largest known prime number, 2^(43112609) - 1, is a Mersenne prime. If the largest known Mersenne prime were multiplied by the smallest Mersenne prime, which of the following would represent the units digit of the product?

A. 2
B. 3
C. 4
D. 6
E. 8

The smallest Mersenne Prime is $$2^2 - 1 = 3$$
We know that any prime other than '2' is odd.
Hence the product of these two primes should be odd.

From the options, only option B is possible.

Hence option B is the answer.

Kudos [?]: 23 [0], given: 1

Non-Human User
Joined: 09 Sep 2013
Posts: 15704

Kudos [?]: 282 [0], given: 0

Re: A Mersenne number is a positive integer that is one less tha [#permalink]

### Show Tags

30 May 2014, 06:29
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.
_________________

Kudos [?]: 282 [0], given: 0

Non-Human User
Joined: 09 Sep 2013
Posts: 15704

Kudos [?]: 282 [0], given: 0

Re: A Mersenne number is a positive integer that is one less tha [#permalink]

### Show Tags

07 Oct 2016, 15:41
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.
_________________

Kudos [?]: 282 [0], given: 0

Intern
Joined: 07 Jun 2016
Posts: 47

Kudos [?]: 7 [0], given: 106

GPA: 3.8
WE: Supply Chain Management (Manufacturing)
Re: A Mersenne number is a positive integer that is one less tha [#permalink]

### Show Tags

07 Oct 2016, 15:43
mau5 wrote:
emmak wrote:
A Mersenne number is a positive integer that is one less than any power of 2. A Mersenne prime is a Mersenne number that also happens to be prime. The largest known prime number, (2^[43112609])-1), is a Mersenne prime. If the largest known Mersenne prime were multiplied by the smallest Mersenne prime, which of the following would represent the units digit of the product?
a) 2
b) 3
c) 4
d) 6
e) 8

The smallest Mersenne prime is 3. Now we know that any power of 2 ends with a even integer. Thus the units digit of (2^[43112609])-1) will be an odd integer. This when multiplied by 3 will still be an odd integer. Thus the answer is the only odd integer.

B.

That is exactly how I did it but I was worried it I was missing something just in case. You explained it really well, thank you

Kudos [?]: 7 [0], given: 106

Re: A Mersenne number is a positive integer that is one less tha   [#permalink] 07 Oct 2016, 15:43
Display posts from previous: Sort by