Last visit was: 21 May 2024, 18:29 It is currently 21 May 2024, 18:29
Close
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
Your Progress

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.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
Tags:
Show Tags
Hide Tags
User avatar
Intern
Intern
Joined: 14 Mar 2013
Posts: 36
Own Kudos [?]: 223 [16]
Given Kudos: 119
Location: United States
Concentration: General Management, Leadership
GMAT Date: 12-03-2013
WE:General Management (Retail)
Send PM
User avatar
Economist GMAT Tutor Instructor
Joined: 01 Oct 2013
Posts: 62
Own Kudos [?]: 181 [3]
Given Kudos: 7
Send PM
User avatar
Economist GMAT Tutor Instructor
Joined: 01 Oct 2013
Posts: 62
Own Kudos [?]: 181 [2]
Given Kudos: 7
Send PM
User avatar
Intern
Intern
Joined: 22 Sep 2009
Posts: 19
Own Kudos [?]: 40 [2]
Given Kudos: 3
Send PM
Re: What is the units digit of the expression 14^7−18^4? [#permalink]
1
Kudos
1
Bookmarks
14^7−18^4 = 2^7*7^7 - 2^4*9^4
= 2^4 (2^3*7^7 - 9^4)
=16[ 8* (unit digit 3) - unit digit 1 ]
= 16 (unit digit 4 - unit digit 1)
= 16 *unit digit 3
= unit digit 8

unit digit = 8
avatar
SVP
SVP
Joined: 27 Dec 2012
Status:The Best Or Nothing
Posts: 1559
Own Kudos [?]: 7233 [3]
Given Kudos: 193
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
Send PM
Re: What is the units digit of the expression 14^7−18^4? [#permalink]
2
Kudos
1
Bookmarks
First expression = 14^7 it cycles around 4,6,4,6............ seventh power would have 4 in units place
Second expression = 18^4 it cycles around 8,4,2,6,............ seventh power would have 6 in units place

14 - 6 = 8 (1 has to be borrowed from tens place as 6>4)

Answer = E
User avatar
VP
VP
Joined: 06 Sep 2013
Posts: 1343
Own Kudos [?]: 2401 [1]
Given Kudos: 355
Concentration: Finance
Send PM
Re: What is the units digit of the expression 14^7−18^4? [#permalink]
1
Kudos
I think answer on this one should be E too. Since we know that 14^7>18^4, as Will said one should always check if the number is positive.

Is the OA shown as D correct for any reason?

Please clarify
Cheers
J
Math Expert
Joined: 02 Sep 2009
Posts: 93373
Own Kudos [?]: 625647 [1]
Given Kudos: 81918
Send PM
What is the units digit of the expression 14^7−18^4? [#permalink]
1
Kudos
Expert Reply
jlgdr wrote:
I think answer on this one should be E too. Since we know that 14^7>18^4, as Will said one should always check if the number is positive.

Is the OA shown as D correct for any reason?

Please clarify
Cheers
J


The OA is E. Thank you. Edited.

Units digits, exponents, remainders problems to practice: https://gmatclub.com/forum/units-digits ... 75004.html

Hope it helps.
User avatar
Manager
Manager
Joined: 10 Jun 2015
Posts: 89
Own Kudos [?]: 72 [0]
Given Kudos: 0
Send PM
Re: What is the units digit of the expression 14^7−18^4? [#permalink]
amgelcer wrote:
What is the units digit of the expression 14^7−18^4?

(A) 0
(B) 3
(C) 4
(D) 6
(E) 8

answer is (E)
you have to use pattern method.
powers of 4 ends with unit digits: 4,6,4,6 and so on); if the power is odd it is 4 otherwise 6
powers of 8 ends with unit digits: 8,4,2,6,8,4,2,6 and so on); it is cycle of four
so the unit digit is 4-6=8
avatar
Manager
Manager
Joined: 18 Feb 2015
Posts: 71
Own Kudos [?]: 573 [0]
Given Kudos: 15
Send PM
Re: What is the units digit of the expression 14^7−18^4? [#permalink]
Hi,

In the example mentioned above, does anyone know why do we borrow 1, make 14 and subtract 6 from it to get 8 as the answer? What about if the questions were "Whats the unit digit of 18^4 - 14^7?" In that case the unit digit would have been 6 - 4 = 2 OR?

Thanks for your help!

WillEconomistGMAT wrote:
I love this type of question. It looks scary until you know how to handle it.

Start by finding the units digit of each of the components:

14^7 --> all that matters is the 4, so figure out the pattern 4^1=...4 4^2=...6 4^3=...4, so 4^7=...4 (odd power)

18^4 --> same approach. 8^1=...8 8^2=...4 8^3=...2 8^4=...6. (Not quite confirming the pattern, but we got what we needed)

So, we have

...4
-...6
_____
Borrow a 1, and we have
User avatar
Intern
Intern
Joined: 24 Jan 2016
Posts: 16
Own Kudos [?]: 10 [0]
Given Kudos: 0
Send PM
Re: What is the units digit of the expression 14^7−18^4? [#permalink]
Answer:E
Units digit of 14^7−18^4:
Consider the following unit digits:
4^1: 4
4^2: 6
4^3: 4
4^4: 6
⇒ unit digit of 4^7 is: 4
The unit digit of 14^7 will also be 4

Also:
8^1: 8
8^2: 4
8^3: 2
8^4: 6
⇒ unit digit of 8^4 is: 6
The unit digit of 18^4 will also be 6

Finally, 4-6 (or 14-6) = 8
Board of Directors
Joined: 11 Jun 2011
Status:QA & VA Forum Moderator
Posts: 6069
Own Kudos [?]: 4705 [0]
Given Kudos: 463
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Send PM
Re: What is the units digit of the expression 14^7−18^4? [#permalink]
amgelcer wrote:
What is the units digit of the expression 14^7−18^4?

(A) 0
(B) 3
(C) 4
(D) 6
(E) 8


Cyclicity of units digit of 4 is 2

So, 4^7 will have units digit as 4

Units digit of 8^4 is 6

Now, 4 - 6 = 8

Hence, units digit will be (E) 8
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18886
Own Kudos [?]: 22291 [1]
Given Kudos: 285
Location: United States (CA)
Send PM
Re: What is the units digit of the expression 14^7−18^4? [#permalink]
1
Kudos
Expert Reply
amgelcer wrote:
What is the units digit of the expression 14^7−18^4?

(A) 0
(B) 3
(C) 4
(D) 6
(E) 8


Since we only care about units digits, we can rewrite the expression as:

4^7 − 8^4

Let’s start by evaluating the pattern of the units digits of 4^n for positive integer values of n. That is, let’s look at the pattern of the units digits of powers of 4. When writing out the pattern, notice that we are ONLY concerned with the units digit of 4 raised to each power.

4^1 = 4

4^2 = 6

4^3 = 4

4^4 = 6

The pattern of the units digit of powers of 4 repeats every 2 exponents. The pattern is 4–6. In this pattern, all positive exponents that are odd will produce a 4 as its units digit. Thus:

4^7 has a units digit of 4.

Next, we can evaluate the pattern of the units digits of 8^n for positive integer values of n. That is, let’s look at the pattern of the units digits of powers of 8. When writing out the pattern, notice that we are ONLY concerned with the units digit of 8 raised to each power.

8^1 = 8

8^2 = 4

8^3 = 2

8^4 = 6

8^5 = 8

The pattern of the units digit of powers of 8 repeats every 4 exponents. The pattern is 8–4–2–6. In this pattern, all positive exponents that are multiples of 4 will produce an 8 as its units digit. Thus:

8^4 has a units digit of 6.

Thus, the “units digit” of 4^7 − 8^4 is 4 − 6 = –2. However, we can’t have a negative number as the unit digit. When we encounter such a case, we add 10 to make it positive. Thus, the the units digit of 4^7 − 8^4 is –2 + 10 = 8.

Answer: E
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 33142
Own Kudos [?]: 829 [0]
Given Kudos: 0
Send PM
Re: What is the units digit of the expression 14^718^4? [#permalink]
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.
GMAT Club Bot
Re: What is the units digit of the expression 14^718^4? [#permalink]
Moderator:
Math Expert
93373 posts