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

 It is currently 19 May 2019, 23:42

### 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

# What is the digit at the unit's place in the expansion

Author Message
TAGS:

### Hide Tags

Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3386
Location: India
GPA: 3.12
What is the digit at the unit's place in the expansion  [#permalink]

### Show Tags

10 Apr 2018, 13:19
1
1
00:00

Difficulty:

55% (hard)

Question Stats:

49% (01:17) correct 51% (01:20) wrong based on 61 sessions

### HideShow timer Statistics

What is the digit at the unit's place in the expansion of $$X^{40}$$?

1. X is even
2. X is not a multiple of five

Source: Experts Global

_________________
You've got what it takes, but it will take everything you've got
Manager
Joined: 30 Mar 2017
Posts: 132
GMAT 1: 200 Q1 V1
Re: What is the digit at the unit's place in the expansion  [#permalink]

### Show Tags

10 Apr 2018, 15:24
Statement 1
x is even --> units digit of x can be 0,2,4,6,8
if units digit is 0, then x^40 has units digit 0
if units digit is 2, then x^40 has units digit 6 because 2 raised to a power that's a multiple of 4 has 6 as the units digit.
if units digit is 4, then x^40 has units digit 6 because 4=2^2 --> (2^2)^40=2^80 --> 80 is a multiple of 4
if units digit is 6, then x^40 has units digit 6
if units digit is 8, then x^40 has units digit 6 because 8=2^3 --> (2^3)^40=2^120 --> 120 is a multiple of 4
So units digit of x^40 can be 0 or 6.
Not sufficient

Statement 2
x is not a multiple of 5 --> units digit of x can be 1,2,3,4,6,7,8,9
Not sufficient

Combining 1&2
Units digit of x can be 2,4,6,8, thus x^40 will have 6 as the units digit.
Sufficient

Intern
Joined: 28 Apr 2014
Posts: 49
GMAT 1: 640 Q50 V25
Re: What is the digit at the unit's place in the expansion  [#permalink]

### Show Tags

11 Apr 2018, 08:07
imo C

st 1 gives 0&6
St2 insufficient
Both gives 6
Director
Joined: 02 Oct 2017
Posts: 729
Re: What is the digit at the unit's place in the expansion  [#permalink]

### Show Tags

19 Apr 2018, 22:52
I)X is even . For every even to power 4 always give 6 except the ones which include 5 eg 20 or 10 which will end with zero.

So not sufficient.

II)not multiple of 5 includes 2,3 etc which have 6 and 1 values when raise to power 4.
Not sufficient.

Combining 1 and 2
Even nos excluding multiple of 5 will always end in 6.

Posted from my mobile device
_________________
Give kudos if you like the post
Re: What is the digit at the unit's place in the expansion   [#permalink] 19 Apr 2018, 22:52
Display posts from previous: Sort by

# What is the digit at the unit's place in the expansion

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne 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®.