It is currently 23 Oct 2017, 12:12

### 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

# INTEGER & MULTIPLE (DS) QUSTION

Author Message
Intern
Joined: 05 Jun 2014
Posts: 2

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

INTEGER & MULTIPLE (DS) QUSTION [#permalink]

### Show Tags

12 Feb 2017, 02:32
If n is an integer, what is the unit digit of 2^n?

a) n is a multiple of 6
b) n is a multiple of 4

Source: Math Revolution

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

 Math Revolution Discount Codes Optimus Prep Discount Codes Magoosh Discount Codes
Intern
Joined: 02 Oct 2016
Posts: 36

Kudos [?]: 11 [1], given: 20

Schools: HEC Dec '17
Re: INTEGER & MULTIPLE (DS) QUSTION [#permalink]

### Show Tags

12 Feb 2017, 02:48
1
KUDOS
Hi Farjin,

Unit digits of different powers of the integer 2 follow a specific cycle.
2^1 will have 2 as the units digit
2^2 will have 4
2^3 will have 8
2^4 will have 6
2^5 will have 2
2^6 will have 4
2^7 will have 8
2^8 will have 6.

If you look carefully, the cycle 2,4,8,6 is repetitive.
When you can break down the power to the form 4m, 4m+1, 4m+2, 4m+3, where m is any integer, you'll be able to find the units digit.
For example, 2^21 = 2^(20+1) = 2^ [4(5)+1]. In this case, you can ignore the part which is a multiple of 4 and focus on the +1 part.
Hence 2^1 will have the same units digit as 2^21.

Statement 1 says n is a multiple of 6.
Case 1: n = 6
2^6 will have 4 as the unit digit.

Case 2: n = 12
2^12 will have 6 as the unit digit.

You now have two values, so answer isn't unique.

Statement 2 says n is a multiple of 4
N can be 4, 8, 12, 16, 20....
Whatever the value of n, 2^n will have 6 as the units digit. Hence, the answer is unique and sufficient.

Kudos [?]: 11 [1], given: 20

Intern
Joined: 05 Jun 2014
Posts: 2

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

Re: INTEGER & MULTIPLE (DS) QUSTION [#permalink]

### Show Tags

12 Feb 2017, 11:12
Thank you I understand this concept very clearly. Thank you.

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

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4155

Kudos [?]: 2924 [0], given: 0

GPA: 3.82
Re: INTEGER & MULTIPLE (DS) QUSTION [#permalink]

### Show Tags

14 Feb 2017, 16:30
Dear Farjin,

Regarding unit digits of repeated integer multiplication, it has a period as follow.

$$2^1 = 1$$ - Unit digit : 2
$$2^2 = 4$$ - Unit digit : 4
$$2^3 = 8$$ - Unit digit : 8
$$2^4 = 16$$ - Unit digit : 6
$$2^5 = 32$$ - Unit digit : 2
$$2^6 = 64$$ - Unit digit : 4
$$2^7 = 128$$ - Unit digit : 8
$$2^8 = 256$$ - Unit digit : 6

2,4,8,6 happen by repetition.

Therefore, B is the correction answer.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself

Kudos [?]: 2924 [0], given: 0

Re: INTEGER & MULTIPLE (DS) QUSTION   [#permalink] 14 Feb 2017, 16:30
Display posts from previous: Sort by