Sep 19 08:00 PM EDT  09:00 PM EDT Strategies and techniques for approaching featured GMAT topics. One hour of live, online instruction. Sep 19 10:00 PM PDT  11:00 PM PDT Join a FREE 1day Data Sufficiency & Critical Reasoning workshop and learn the best strategies to tackle the two trickiest question types in the GMAT! Sep 20 08:00 AM PDT  09:00 AM PDT Feeling perplexed by the paradox? Despairing the disparity? In this webinar, Hailey Cusimano explains how we can use strategy and structure to address premises that don't seem to align. Sept 20, Friday, 8am PST. Sep 19 12:00 PM PDT  10:00 PM PDT On Demand $79, For a score of 4951 (from current actual score of 40+) AllInOne Standard & 700+ Level Questions (150 questions) Sep 21 07:00 AM PDT  09:00 AM PDT Learn reading strategies that can help even nonvoracious reader to master GMAT RC Sep 22 08:00 PM PDT  09:00 PM PDT Exclusive offer! Get 400+ Practice Questions, 25 Video lessons and 6+ Webinars for FREE Sep 23 08:00 AM PDT  09:00 AM PDT Join a free 1hour webinar and learn how to create the ultimate study plan, and be accepted to the upcoming Round 2 deadlines. Save your spot today! Monday, September 23rd at 8 AM PST
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 08 Apr 2011
Posts: 12

Re: What is the digit on the units place in the expanded value of 97^275 –
[#permalink]
Show Tags
02 Jul 2019, 21:20
The units place in the expanded value of 97^275–32^44? 7 raise to any power has cyclicity of 7, 9 , 3, 1 as its unit digit 97^275 = 97^ (272+3) the unit digit for the result would be 3
Similarly, 2 raise to any power has cyclicity of 2, 4 , 8, 6 as its unit digit 32^44 the unit digit for the result would be 6
36 > 136> 7
Answer D



Manager
Joined: 08 Jan 2018
Posts: 129

Re: What is the digit on the units place in the expanded value of 97^275 –
[#permalink]
Show Tags
02 Jul 2019, 22:01
We are only concerned about the digit in the units place. So, even in the above problem \(97^{275}– 32^{44}\) we can only be concerned about \(...7^{275} – ...2^{44}\)
The unit’s digit of powers of 7 are in order of 7, 9, 3, 1 Remainder of \(\frac{275}{4}\) = 3 The unit’s digit of the third power of 7 is 3. Thus, \(7^{275}\) will also have units digit of 3.
Similarly, The unit’s digit of powers of 2 are in order of 2, 4, 8, 6 Remainder \(\frac{44}{4}\) = 0 i.e 4 The unit’s digit of the fourth power of 2 is 6. Thus \(2^{44}\) will also have the unit’s digit of 6.
Hence, Unit’s digit of \(7^{275} – 2^{44}\) = Unit’s digit of \(97^{275} – 32^{44}\) = ….3  ….6 = …7
Answer: D



Manager
Joined: 12 Jan 2018
Posts: 112

Re: What is the digit on the units place in the expanded value of 97^275 –
[#permalink]
Show Tags
02 Jul 2019, 22:03
Numbers ending with 7 will end with 7,9,3,1 based on the power. > Power cycle for 7 is 4. 97^275 will end with 3 since 275 when divided by 4 remainder is 3. Similarly, any number ending with 2 will have 2/4/8/6 in its unit;s digit based on the power. 32^44 will end with 6, as 44 when divided by 4 remainder is 0. Also, notice that 97^275 > 32^44. Hence, 97^275 32^44= .........3 ...........6=............7 OA is D
_________________
"Remember that guy that gave up? Neither does anybody else"



Intern
Joined: 22 Jun 2019
Posts: 41
Location: Canada
Concentration: Operations, Organizational Behavior

Re: What is the digit on the units place in the expanded value of 97^275 –
[#permalink]
Show Tags
02 Jul 2019, 22:03
A)1
I just tried to get the units digit of 7^5 2^4



Manager
Joined: 04 Dec 2017
Posts: 93
Location: India
Concentration: Other, Entrepreneurship
GMAT 1: 570 Q36 V33 GMAT 2: 620 Q44 V32 GMAT 3: 720 Q49 V39
GPA: 3
WE: Engineering (Other)

Re: What is the digit on the units place in the expanded value of 97^275 –
[#permalink]
Show Tags
02 Jul 2019, 22:04
To solve this question we will use the pattern method.
We know that we can find the unit digit of any number from 0 to 9 by finding out if the power is of 4k+1, 4k+2, 4k+3 or 4k.
Using this we get that power 275 is of form 4k+3 and 44 is of form 4k.
Unit digit of 7 for power of form 4k+3 is 3 and unit of 2 for power of the form 4k is 6.
The difference between a number of X3 (where X any interger > 0) and 6 will be 7.
Hence, answer is 7.
Answer: D



Intern
Joined: 27 Jun 2018
Posts: 14

What is the digit on the units place in the expanded value of 97^275 –
[#permalink]
Show Tags
02 Jul 2019, 22:16
Unit digit of 97^275 would be same as 7^275, which would be same as 7^3 (the unit digits of 7^x repeat after x = 4), which is 3. Similarly, unit digit of 32^44 would be same as 2^44, which would be same as 2^4 (the unit digits of 2^x repeat after x = 4), which is 6. Now, ____3____6 will be same as 136 = 7 (where "____x" represents some number string ending with x) Hence, answer should be (D).
_________________



CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2972
Location: India
GMAT: INSIGHT
WE: Education (Education)

What is the digit on the units place in the expanded value of 97^275 –
[#permalink]
Show Tags
02 Jul 2019, 22:29
Quote: What is the digit on the units place in the expanded value of \(97^{275}–32^{44}\)?
A. 1 B. 3 C. 5 D. 7 E. 9 Unit digit of \(97^{275}–32^{44}\) = Unit digit of \(7^{275}–2^{44}\) CONCEPT: The unit digit of any number depends on the unit digit of the number so any digit other than unit digit is irrelevant such as \(97^{275}\) will have same unit digit as \(387^{275}\) or \(7^{275}\)Now, Unit digit of \(7^{275}–2^{44}\) = Unit digit of \(7^3–2^4\) CONCEPT: The cyclicity of unit digit of 7 and 2 is 4 i.e.e unit digits repeat after every 4th power. therefore Remainder (275/4) = 3 hence unit digit of \(7^275\) = unit digit of \(7^3\) Unit digit of \(7^3–2^4\) = 36 = 7 Answer: Option D
_________________
Prosper!!!GMATinsightBhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhihttp://www.GMATinsight.com/testimonials.htmlACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Manager
Joined: 24 Jan 2019
Posts: 105
Location: India
Concentration: Strategy, Finance
GPA: 4

What is the digit on the units place in the expanded value of 97^275 –
[#permalink]
Show Tags
02 Jul 2019, 22:31
Unit digits for the powers of 97: 7, 9, 3, 1, 7, 9, 3........ and so on. Cyclicity = 4
Unit digits for the powers of 32: 2, 4, 8, 6, 2, 4, 8........ and so on. Cyclicity = 4
Now, for the 275th power of 97, unit digit will be "3". (275=68*4+3. So, 3rd term in the series [7,9,3,1])
For the 44th power of 32, unit digit will be "6". (44=11*4, 4th term in the series [2,4,8,6])
So, difference for any number with these unit digits will be "7". (X...X3  X..X6 = X..X7)
ANSWER : D



Manager
Joined: 23 Nov 2016
Posts: 187

What is the digit on the units place in the expanded value of 97^275 –
[#permalink]
Show Tags
02 Jul 2019, 22:52
Last digit of the first no is 7 which a cyclicity of 4 . so last digit will be 3. Similarly last digit of second no is 4. So last digit will be 6. So effective last digit will be 36 =7
_________________
If my post anyway helped you,please spare Kudos !



Senior Manager
Joined: 05 Mar 2017
Posts: 256
Location: India
Concentration: General Management, Marketing
GPA: 3.6
WE: Marketing (Entertainment and Sports)

Re: What is the digit on the units place in the expanded value of 97^275 –
[#permalink]
Show Tags
02 Jul 2019, 23:16
Check for the cyclicity of 7 3M which means unit digit is going to be 3 and then cyclicity of 2 is 4M which means that the unit digit is going to be 6.
So 3  6 which means 13  6 = 7 Answer is D



Senior Manager
Joined: 30 Sep 2017
Posts: 339
Concentration: Technology, Entrepreneurship
GPA: 3.8
WE: Engineering (Real Estate)

What is the digit on the units place in the expanded value of 97^275 –
[#permalink]
Show Tags
02 Jul 2019, 23:21
97^1, 97^5, 97^9, etc. have a units digit of 7 97^2, 97^6, 97^10, etc. have a units digit of 9 97^3, 97^7, 97^11, etc. have a units digit of 3 97^4, 97^8, 97^12, etc. have a units digit of 1
From the abovementioned pattern, one can deduce that 97^275 has a units digit of 3.
32^1, 32^5, 32^9, etc. have a units digit of 2 32^2, 32^6, 32^10,etc. have a units digit of 4 32^3, 32^7, 32^11,etc. have a units digit of 8 32^4, 32^8, 32^12,etc. have a units digit of 6
Similarly, one can deduce that 32^44 has a units digit of 6.
Therefore, the digit on the units place 97^275–32^44 is: ...3  ...6 = ...7
Answer is (D)
Posted from my mobile device



Intern
Joined: 04 Jun 2019
Posts: 3

Re: What is the digit on the units place in the expanded value of 97^275 –
[#permalink]
Show Tags
03 Jul 2019, 00:52
7 follows a cycle of 4 and 2 follows a cycle of 4 The unit digit is of the two number is (32) =1



Manager
Joined: 30 Nov 2016
Posts: 103
Location: India
Concentration: Finance, Strategy

Re: What is the digit on the units place in the expanded value of 97^275 –
[#permalink]
Show Tags
03 Jul 2019, 01:23
97^275:Since the cyclicity is of 4 numbers(7,9,3,1), we can divide the power, 275, by 4 to get a remainder of 3. so the last digit will be 3 32^44:Since the cyclicity is of 4 numbers(2,4,8,6), we can divide the power, 44, by 4 to get a remainder of 0. so the last digit will be 6. so the answer should be 7



Manager
Joined: 29 Nov 2018
Posts: 169

Re: What is the digit on the units place in the expanded value of 97^275 –
[#permalink]
Show Tags
03 Jul 2019, 01:25
What is the digit on the units place in the expanded value of 97275–3244 97 275 – 32 44 ? A. 1 B. 3 C. 5 D. 7 E. 9 Since we are looking for the unit's place, let's figure out the unit's places of the numbers involved 97^275 will have 3 at the unit's place (formula: cyclicity of 4) 32^44 will have 6 at the unit's place (formula: cyclicity of 4) Difference: _ _ _ 3  _ _ _ 6 = _ _ _ 7 IMO, answer is 7
_________________
Hit Kudos to keep the community alive !



Intern
Joined: 31 Jul 2018
Posts: 7

Re: What is the digit on the units place in the expanded value of 97^275 –
[#permalink]
Show Tags
03 Jul 2019, 01:29
97275–3244
The last digit of the number 97^275 is defined by the the power of 7. The power of 7 has the cycle of 4 numbers (7, 9, 3, 1). => 275 = 4*68 + 3 => the last digit of the number 97^275 is 3. The last digit of the number 32^44 is defined by the the power of 2. The power of 2 has the cycle of 4 numbers (2, 4, 8, 6). => 44 = 4*11 => the last digit of the number 32^44 is 6.
XXX3  XXX6 = XXX7 = > Answer is D.



Manager
Joined: 15 Nov 2017
Posts: 171
Location: India
Concentration: Operations, Marketing
GPA: 4
WE: Operations (Retail)

What is the digit on the units place in the expanded value of 97^275 –
[#permalink]
Show Tags
03 Jul 2019, 01:37
\(7^5\) = digit in the unit place would be 7(for square 9, for cube 3 and so on and so forth) \(2^4\) = digit in the unit place would be 6 (for square 4, for cube 8 and so on and so forth) therefore, 76(subtraction, since the last digit can be subtracted directly) would yield answer 1. Option A
_________________



Senior Manager
Joined: 10 Jan 2017
Posts: 254
Location: India

Re: What is the digit on the units place in the expanded value of 97^275 –
[#permalink]
Show Tags
03 Jul 2019, 02:27
the first part is having units digit as 3, as 7 is having a cyclicity of 4,the power 275 when divided by 4, remainder is 3, so 7^3, last digit is 3; similarly the second part is having units digit as 6, as cyclicity of 2 is 5, & 44 divided by 5 gives remainder as 4, 2^4, last digit will be 6; subtraction of XXXX..X3YYY.YY6; last digit will be 7
_________________
Your limitation—it's only your imagination. Please hit +1 Kudos if you like my Post.



Manager
Joined: 21 Jun 2018
Posts: 71

What is the digit on the units place in the expanded value of 97^275 –
[#permalink]
Show Tags
03 Jul 2019, 02:51
Using the cyclical nature of unit digits raised to a power, we can easily calculate the answer. For units digit of 97^275, 7 is the units digit of 97. We know 7^1=7 7^2=9 (the units digit) 7^3=3 7^4=1 The units digits then repeat in 7,9,3,1 order. the power of 97, 275 is in the form of 4n+3. So 97^275 would have 3 as units digit. For units digit of 32^44, 2 is the units digit of 32. We know 2^1=2 2^2=4 2^3=8 2^4=6(the units digit) The units digits then repeat in 2,4,8,6 order. the power of 32, 44 is in the form of 4n. So 32^44 would have 6 as units digit. So the units digit of the substraction of these numbers would be = 36 Since 6 is bigger here than 3, 1 would carry over from the tens side to 3 making it 13. hence, 136=7 is the answer
_________________
_______________________________________________________________________________________________________ Please give Kudos. Kudos encourage active discussions and help the community grow.



Manager
Joined: 06 Aug 2018
Posts: 98

Re: What is the digit on the units place in the expanded value of 97^275 –
[#permalink]
Show Tags
03 Jul 2019, 02:56
It's 7^2752^44
275/4 will.give a remainder of 3 , so units digit will 3
44/4 will.give a remainder of 0 , unit digit will be 2
32=1
Posted from my mobile device



Manager
Joined: 15 Jun 2019
Posts: 167

Re: What is the digit on the units place in the expanded value of 97^275 –
[#permalink]
Show Tags
03 Jul 2019, 03:25
imo 7, question can be written as 7^3  2^4 so 36 gives ans 7
_________________
please do correct my mistakes that itself a big kudo for me,
thanks




Re: What is the digit on the units place in the expanded value of 97^275 –
[#permalink]
03 Jul 2019, 03:25



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



