Oct 15 12:00 PM PDT  01:00 PM PDT Join this live GMAT class with GMAT Ninja to learn to conquer your fears of long, kooky GMAT questions. Oct 16 08:00 PM PDT  09:00 PM PDT EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299) Oct 19 07:00 AM PDT  09:00 AM PDT Does GMAT RC seem like an uphill battle? eGMAT is conducting a free webinar to help you learn reading strategies that can enable you to solve 700+ level RC questions with at least 90% accuracy in less than 10 days. Sat., Oct 19th at 7 am PDT Oct 20 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score. Oct 22 08:00 PM PDT  09:00 PM PDT On Demand for $79. For a score of 4951 (from current actual score of 40+) AllInOne Standard & 700+ Level Questions (150 questions)
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 12 Apr 2017
Posts: 139
Location: United States
Concentration: Finance, Operations
GPA: 3.1

Re: What is the digit on the units place in the expanded value of 97^275 –
[#permalink]
Show Tags
02 Jul 2019, 10:51
7^275 will result with an end unit of 3 2^44 will result with an end unit of 6
36 = 7, D



Intern
Joined: 10 Aug 2017
Posts: 29

What is the digit on the units place in the expanded value of 97^275 –
[#permalink]
Show Tags
Updated on: 03 Jul 2019, 01:19
Find the units digit pattern as follows:
..7^1 = units digit 7 ..7^2 = units digit 9 ..7^3 = units digit 3 ..7^4 = units digit 1 ..7^5 = units digit 7 ..7^6 = units digit 9, etc
Thus, 97^275 will have units digit of 3
32^1 = units digit 2 32^2 = units digit 4 32^3 = units digit 8 32^4 = units digit 6 32^5 = units digit 2 32^6 = units digit 4, dst.
Thus, 32^44 will have a units digit of
97^27532^44 =...3 ...6 =...7
Answer is (D)
Posted from my mobile device
Originally posted by chondroht on 02 Jul 2019, 11:30.
Last edited by chondroht on 03 Jul 2019, 01:19, edited 1 time in total.



Manager
Joined: 19 Apr 2017
Posts: 173
Concentration: General Management, Sustainability
GPA: 3.9
WE: Operations (Hospitality and Tourism)

Re: What is the digit on the units place in the expanded value of 97^275 –
[#permalink]
Show Tags
02 Jul 2019, 11:40
Cyclicity(last digit has repeats after every 4) of 7 is 4, i.e \(7^1 = 7\) \(7^2 = 49\) \(7^3 = 343\) \(7^4 = 2401\)
275=68*4+3 means its the third in the cycle Unit's digit of \(97^275\) is 3
Cyclicity of the digit 2 is 4 \(2^1 = 2\) \(2^2 = 4\) \(2^3 = 8\) \(2^4 = 16\)
44=11*4 means its the 4th in the cycle Units Digit of 32^44 is 6
36=3
Answer B



Intern
Joined: 24 May 2016
Posts: 19

Re: What is the digit on the units place in the expanded value of 97^275 –
[#permalink]
Show Tags
02 Jul 2019, 11:42
97^275–32^44
97^275  Unit's digit 7 has a cyclicity of 4. => unit's digit of 97^275 is equivalent to the unit's digit of 7^3 => Unit's digit of 97^275 = 3
32^44  Unit's digit 2 has a cyclicity of 4. => unit's digit of 32^44 is equivalent to the unit's digit of 2^4 => Unit's digit of 32^44 = 6
36 = 3 which is equivalent to 7.



Senior Manager
Joined: 13 Feb 2018
Posts: 451

What is the digit on the units place in the expanded value of 97^275 –
[#permalink]
Show Tags
02 Jul 2019, 12:21
We can begin with routine work: Calculating cyclicity \(7^1=7\) \(7^2=49\) \(7^3=..3\) \(7^4=..1\)
275/4 leaves remainder 3. The units digit of \(97^{275}\) will be 3
\(2^1=2\) \(2^2=4\) \(2^3=8\) \(2^4=16\)
44/4 leaves no remainder. The units digit of \(32^{44}\) will be 6
here if you think that only 36 is left to calculate BE WARE ALWAYS check which number is greater in such cases In our case \(97^{275}\)>\(32^{44}\) and we can safely deduce that ..3..6=..7 But if the first number is less then we can have different units digit: 1326=13
IMO Ans: D



Manager
Joined: 29 May 2019
Posts: 111

Re: What is the digit on the units place in the expanded value of 97^275 –
[#permalink]
Show Tags
02 Jul 2019, 12:31
97^275: the unit digit will be 3. As any multiple of 7 will have unit digits as 7, 9, 3, 1. This cycle repeats for every 4th exponent. 32^44: the unit digit will be 6. As any multiple of 2 will have unit digits as 2, 4, 8, 6. This cycle repeats for every 4th exponent. 3  6 = unit digit will be 7.
_________________
Pick yourself up, dust yourself off, and start again.
Success is the sum of all small efforts.
MAKE IT HAPPEN



Intern
Joined: 27 Jan 2017
Posts: 10
Location: India

Re: What is the digit on the units place in the expanded value of 97^275 –
[#permalink]
Show Tags
02 Jul 2019, 12:50
Unit digit for 97^275 is 3 unit digit for 32^44 is 6 36 = 7



Senior Manager
Joined: 27 Aug 2014
Posts: 337
Location: Netherlands
Concentration: Finance, Strategy
GPA: 3.9
WE: Analyst (Energy and Utilities)

Re: What is the digit on the units place in the expanded value of 97^275 –
[#permalink]
Show Tags
02 Jul 2019, 12:51
Answer: D
7 has a cyclicity of 4, so last digit of 97^275 > is 3, since 275 can be written as 68*4+3 2 has a cyclicity of 4, so 32^44, last digit > 6 36 = 3 as units digit cannot be negative, subtract 10, which is carried over. So, D



Intern
Joined: 25 Feb 2019
Posts: 3
Location: India

Re: What is the digit on the units place in the expanded value of 97^275 –
[#permalink]
Show Tags
02 Jul 2019, 14:15
7^1 = 7 7^2 = 49 7^3 = ends with 3 7^4 ends with 1 7^5 again ends with 7
2^2 = 4 2^3 = 8 2^4 = ends with 6 2^5 again ends with 2
So 97^275 will have some value as 7^5 which has 7 in units place and 32^44 will have some value 2^(11*4) which has 6 in the units place
Hence, 76 = 1.



Intern
Joined: 11 Dec 2018
Posts: 4

Re: What is the digit on the units place in the expanded value of 97^275 –
[#permalink]
Show Tags
02 Jul 2019, 14:20
Start printing pattern. For first term its 7,9,3,1 Second term tis 2,4,8,6
if first term is multiplied 275 times its goes 68 times with units digit and three additional times giving 3 as units digit. Similar second term is 6.
136 =7



Manager
Joined: 18 Jun 2013
Posts: 134
Location: India
Concentration: Technology, General Management
GPA: 3.2
WE: Information Technology (Consulting)

Re: What is the digit on the units place in the expanded value of 97^275 –
[#permalink]
Show Tags
02 Jul 2019, 14:30
97^275  32^44
Following 7's cyclicity of 4 
7^1 = 7 = ending in 7 7^2 = 49 = ending in 9 7^3 = 343 = ending in 3 7^4 = 2401 = ending in 1
So, 97^275 will be like
7^275 since we are dealing only with digit in units place currently.
Hence,
7^275 is of the type 7^3 and hence will end in a 3
Similarly, following 2's cyclicity of 4 
2^1 = 2 = ending in 2 2^2 = 4 = ending in 4 2^3 = 8 = ending in 8 2^4 = 16 = ending in 6
So, 32^44 will be like
2^44 since we are dealing only with digit in units place currently.
Hence,
2^44 is of the type 2^4 and hence will end in a 6
Now we have 2 numbers each ending in 3 and 6 respectively.
A difference of the 2 numbers will leave a 7 in the units digit of the resulting number. Example: 153  46 = 107
Hence answer is 7 and option D



VP
Joined: 14 Feb 2017
Posts: 1174
Location: Australia
Concentration: Technology, Strategy
GMAT 1: 560 Q41 V26 GMAT 2: 550 Q43 V23 GMAT 3: 650 Q47 V33 GMAT 4: 650 Q44 V36
WE: Management Consulting (Consulting)

What is the digit on the units place in the expanded value of 97^275 –
[#permalink]
Show Tags
Updated on: 04 Jul 2019, 01:55
Made a silly mistake in my working out. 7931 7^275 = 272 (highest multiple of 4 that would repeat the cycle) + 3 = 79 31 2^(some multi of 4) = cyclicity of 4 = 2 4 81 6xxxx3 xxx6 We need to treat the 3 as part of a larger number (Which it is) so we end up with 13  6 (in performing the subtraction) to get 7
_________________
Goal: Q49, V41
+1 Kudos if I have helped you
Originally posted by dcummins on 02 Jul 2019, 15:13.
Last edited by dcummins on 04 Jul 2019, 01:55, edited 1 time in total.



Intern
Joined: 14 Jan 2016
Posts: 20
Location: India
Concentration: Marketing, General Management
GMAT 1: 710 Q50 V35 GMAT 2: 750 Q50 V41

Re: What is the digit on the units place in the expanded value of 97^275 –
[#permalink]
Show Tags
02 Jul 2019, 15:38
Cyclicity of digits. Units digits : 7^1 = 7 7^2 = 9 (49) 7^3 = 3 (343) 7^4 = 1 (2401) As we can see, 7^4 has 1 at its units digit. Thus 7^5 will have a 7 at its units digit and the whole cycle will be repeated. Now, 97 has 7 at its units place and the 7 will dictate the units digit of all its exponents, i.e. 97^1 has 7 at its units digit, 97^2 will have 9(9409) at its units digit and so on. Thus 97^275 = [97^(272)]*[97^3] 272 = 4*68 Units digit of 97^272 = 1 Units digit of 97^3 = 3 Thus units digit of 97^275 = 3 Similarly, 2^1 = 2 2^2 = 4 2^3 = 8 2^4 = 6 (16) 2^5 = 2 (32) So, units digit of 32^44 will be the same as the units digit of 2^44 Which is the same as the units digit of 2^4 = 6. So the units digit of the given equation = 3  6 = 7. Hence (D) P.S. since 97^275 is clearly greater than 32^44, the resulting number when 32^44 is subtracted from 97^275 will be positive.
_________________
The only alternative to hard work is HARDER work.



ISB School Moderator
Joined: 08 Dec 2013
Posts: 594
Location: India
Concentration: Nonprofit, Sustainability
WE: Operations (NonProfit and Government)

Re: What is the digit on the units place in the expanded value of 97^275 –
[#permalink]
Show Tags
02 Jul 2019, 17:38
What is the digit on the units place D, The unit digit o the expression determines the unit digit of the answer Cyclicity of 2 and 7 is 4, so the expression is basically reduced to: 7^3  2^4 = 36 = 7Note: 275= 4K + 3 & 44= 4K'
_________________
Kindly drop a '+1 Kudos' if you find this post helpful.GMAT Math Book I never wanted what I gave up I never gave up what I wanted



Manager
Joined: 28 Jan 2019
Posts: 125
Location: Peru

What is the digit on the units place in the expanded value of 97^275 –
[#permalink]
Show Tags
02 Jul 2019, 18:06
This one is about cyclicity , so you have to consider cyclicity of the unit digits (7 and 2) in order to find the resultant unit digit:
cyclicity units of 7:
7^1=7 7^2=9 7^3=3 7^4=1
cyclicity units of 2:
2^1=2 2^2=4 2^3=8 2^4=6
So, for 97^275:
275=4K+3, so the unit number will have 3 as units
So, for 32^44:
44=4K, so the unit number will have 6 as units
Then, since 97^275 > 32^44, and the units of each are 3 and 6 respectively, the resultant unit digit must be 7.
D is the answer.



Intern
Joined: 05 Jun 2018
Posts: 31

Re: What is the digit on the units place in the expanded value of 97^275 –
[#permalink]
Show Tags
02 Jul 2019, 18:31
7 repeats its unit digits, every 5 numbers Units digits 7^1=7,7^2=9, 7^3=3, 7^4=1, 7^5=7
Thus, 7^275 have a units digit as 7
Similarly, for 2, 2 repeats its unit digits every 5th power (2,4,8,6,2) Thus, 2^44= 2^(40+4), thus unit digit as 2^4= 6
76=1



Intern
Joined: 17 Apr 2019
Posts: 17

Re: What is the digit on the units place in the expanded value of 97^275 –
[#permalink]
Show Tags
02 Jul 2019, 18:48
First of all, look at 97^275, we don't really need to get the full number, all we need to know is the number in the unit place. So we already know the first number in the unite place is 7. Then 97X97, we multiple the number in the unit place 7X7 first, it's equal to 49, so for the second number, the unit place would be 9, we don't need to get the full answer. Then for the next number, no matter what answer we get previously, when it times to 97, the number in unit place would be 9 (the unit digit from last number) X7=63, so number in unit place would be 3. Then times 97 again, 3X7=21, the unit digit would be 1. Then we multiple 97 again, finally we see a train in here, the unit digit will cycles in 4 numbers which are 7,9,3 and 1.
Second, look at 32^44, used the same way and we will see that the unit digit will also cycles in 4 numbers: 2,4,8 and 6
Finally, we used 72, 94, 83 and 61 all the answer are the same, which is number 5
So choose answer C



Intern
Joined: 24 Jan 2019
Posts: 23

Re: What is the digit on the units place in the expanded value of 97^275 –
[#permalink]
Show Tags
02 Jul 2019, 18:53
First, let examize the last unit digit of it:
97^275
We have the reoccurring pattern of the last digit of 7^x: 7^1 ends with 7 7^2 ends with 9 7^3 ends with 3 7^4 ends with 1 7^5 ends with 7 ... So the pattern 7,9,3,1,7,9,3,1... will repeat every four 7^x Plus, we have 275/4=68 with the remainder of 3. So 97^275 ends with 3
Similarly, 32^44 has the repeating pattern of last digit of 2,4,8,6,2... We have 44/4=11, no remainder, so 32^44 ends with 2.
The we have 97^275  32^44 ends with 32=1
I do with A
Posted from my mobile device



Intern
Joined: 25 Nov 2018
Posts: 2

Re: What is the digit on the units place in the expanded value of 97^275 –
[#permalink]
Show Tags
02 Jul 2019, 19:00
This is a simple problem on cyclic nature of last digit of subsequent powers of a number. Cyclicity of last digit for numbers ending with 7  7, 9, 3, 1,7..... (cyclicity=4) and for numbers ending with 2  2,4,8,6,2...(cyclicity=4) here, dividing power by cyclicity will leave a remainder, which will allow us to choose the last digit for that power 275/4 leaves 3 as a remainder, so the last digit for this term will be 3 similarly the right term has 0 remainder and this corresponds to last digit 6



Intern
Joined: 09 Oct 2017
Posts: 11
Location: Viet Nam
GPA: 3.1

Re: What is the digit on the units place in the expanded value of 97^275 –
[#permalink]
Show Tags
02 Jul 2019, 19:32
Answer is C because we use the cyclicity of unit digit.
First number ends with 7 whose cyclicity is 4 => end at 3 Second number ends with 2 whose cyclicity is 4 => end at 8 => 38 = 5




Re: What is the digit on the units place in the expanded value of 97^275 –
[#permalink]
02 Jul 2019, 19:32



Go to page
Previous
1 2 3 4 5 6
Next
[ 107 posts ]



