Author 
Message 
TAGS:

Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6239
GPA: 3.82

What is the remainder when 7^100 is divided by 50?
[#permalink]
Show Tags
24 May 2018, 18:29
Question Stats:
72% (01:07) correct 28% (01:40) wrong based on 111 sessions
HideShow timer Statistics
[GMAT math practice question] What is the remainder when \(7^{100}\) is divided by \(50\)? \(A. 0\) \(B. 1\) \(C. 7\) \(D. 21\) \(E. 49\)
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $99 for 3 month Online Course" "Free Resources30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons  try it yourself"



Senior Manager
Joined: 24 Aug 2016
Posts: 327
Location: India
Concentration: Entrepreneurship, Operations
GMAT 1: 540 Q49 V16 GMAT 2: 640 Q47 V31 GMAT 3: 630 Q48 V28
GPA: 3.4

Re: What is the remainder when 7^100 is divided by 50?
[#permalink]
Show Tags
24 May 2018, 19:03
MathRevolution wrote: [GMAT math practice question]
What is the remainder when \(7^{100}\) is divided by \(50\)? \(A. 0\) \(B. 1\) \(C. 7\) \(D. 21\) \(E. 49\) This question essentially asking what are the last 2 digits of the expression \(7^{100}\)... as what ever is in the hunderds digit, if the last two are 00, the number is always divided by 50. Now cyclicity of 7 is 4, And the numbers are 7,9,3,1........ Hence the last digit is 1 as 25*4=100 now \(7^{4}\) = 7*7*7*7= 2401 And the expression is \(2401^{25}\)= in that case the last two will be always 01 ( can be tested quickly with \(101^{2}\) & \(101^{3}\)) Hence the reminder is 01.....................Hence , I would go for option B.
_________________
Please let me know if I am going in wrong direction. Thanks in appreciation.



Manager
Joined: 22 Jun 2017
Posts: 72
Location: Brazil
GPA: 3.5
WE: Engineering (Energy and Utilities)

Re: What is the remainder when 7^100 is divided by 50?
[#permalink]
Show Tags
24 May 2018, 19:04
Option B
\(7^1\) = 7 \(7^2\) = 49 \(7^3\) = 343 \(7^4\) = 2401 \(7^5\) = 16807 \(7^6\) = 117649 \(7^7\) = 823543 \(7^8\) = 5764801
...
So, 7^100 is something that ends with 01.
The remander is 1.



Manager
Joined: 20 Feb 2017
Posts: 166
Location: India
Concentration: Operations, Strategy
WE: Engineering (Other)

Re: What is the remainder when 7^100 is divided by 50?
[#permalink]
Show Tags
24 May 2018, 20:35
These type of questions become really simple if you understand the concept of negative remainders. Always try and reduce the dividend to 1 or 1. = Rem [7^100 / 50] = Rem [49^50/50] = Rem [ (1)^50 / 50] = Rem [1 / 50] = 1 hence B
_________________
If you feel the post helped you then do send me the kudos (damn theya re more valuable than $)



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6239
GPA: 3.82

Re: What is the remainder when 7^100 is divided by 50?
[#permalink]
Show Tags
27 May 2018, 18:21
=> The remainder when \(7^{100}\) is divided by \(50\) depends only on the units and tens digits. The units digits of \(7^n\) cycle through the four values \(7, 9, 3\), and \(1\). The tens digits of \(7^n\) cycle through the four values \(0, 4, 4\), and \(0\). We have the following sequence of units and tens digits for \(7^n\): \(7^1 = 07 ~ 07\) \(7^2 = 49 ~ 49\) \(7^3 = 343 ~ 43\) \(7^4 = 2401 ~ 01\) \(7^5 = 16807~ 07\) … So, \(7^{100} = (7^4)^{25}\) has the same units and tens digits as \(7^4\), that is, \(01\). Thus, the remainder when \(7^{100}\) is divided by \(50\) is \(1\). Therefore, B is the answer. Answer : B
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $99 for 3 month Online Course" "Free Resources30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons  try it yourself"



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3528
Location: United States (CA)

Re: What is the remainder when 7^100 is divided by 50?
[#permalink]
Show Tags
29 May 2018, 09:24
MathRevolution wrote: [GMAT math practice question]
What is the remainder when \(7^{100}\) is divided by \(50\)? \(A. 0\) \(B. 1\) \(C. 7\) \(D. 21\) \(E. 49\) We see that 7^2 = 49, which is 50  1. Although 49/50 = 0 R 49, rather than using the remainder of 49, let’s call the remainder “1”. Since 7^100 = (7^2)^50 = 49^50, which is equivalent to (1)^50 when it’s divided by 50, and since (1)^50 = 1, so when (1)^50 is divided by 50, the remainder is 1. Answer: B
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Senior Manager
Joined: 29 Dec 2017
Posts: 383
Location: United States
Concentration: Marketing, Technology
GMAT 1: 630 Q44 V33 GMAT 2: 690 Q47 V37
GPA: 3.25
WE: Marketing (Telecommunications)

What is the remainder when 7^100 is divided by 50?
[#permalink]
Show Tags
27 Aug 2018, 06:43
\(7^{100}/50=49^{50}/50=(501)^{50}/50\)  only \((1)^{50} = 1^{50}=1\)  won't be devisable by 50. The remainder is 1.
Answer B.



Intern
Joined: 03 Feb 2018
Posts: 47

Re: What is the remainder when 7^100 is divided by 50?
[#permalink]
Show Tags
23 Sep 2018, 05:00
ScottTargetTestPrep wrote: MathRevolution wrote: [GMAT math practice question]
What is the remainder when \(7^{100}\) is divided by \(50\)? \(A. 0\) \(B. 1\) \(C. 7\) \(D. 21\) \(E. 49\) We see that 7^2 = 49, which is 50  1. Although 49/50 = 0 R 49, rather than using the remainder of 49, let’s call the remainder “1”. Since 7^100 = (7^2)^50 = 49^50, which is equivalent to (1)^50 when it’s divided by 50, and since (1)^50 = 1, so when (1)^50 is divided by 50, the remainder is 1. Answer: B Hi, thanks for this solution, but I have a doubt. this question doesn't say that there is exponent for 50. then, How can we take (1)^50 ? Waiting for reply. Regards, Kishlay




Re: What is the remainder when 7^100 is divided by 50? &nbs
[#permalink]
23 Sep 2018, 05:00






