Aug 22 09:00 PM PDT  10:00 PM PDT What you'll gain: Strategies and techniques for approaching featured GMAT topics, and much more. Thursday, August 22nd at 9 PM EDT Aug 24 07:00 AM PDT  09:00 AM PDT Learn reading strategies that can help even nonvoracious reader to master GMAT RC Aug 25 09:00 AM PDT  12:00 PM PDT Join a FREE 1day verbal workshop and learn how to ace the Verbal section with the best tips and strategies. Limited for the first 99 registrants. Register today! Aug 25 08:00 PM PDT  11:00 PM PDT Exclusive offer! Get 400+ Practice Questions, 25 Video lessons and 6+ Webinars for FREE. Aug 28 08:00 AM PDT  09:00 AM PDT Join a FREE live webinar with examPAL and Admissionado and learn how to master GMAT Critical Reasoning questions and the 6pointed star of MBA application essay glory. Save your spot today! Aug 30 08:00 PM PDT  11:00 PM PDT We'll be posting questions in DS/PS/SC/CR in competition mode. Detailed and quickest solution will get kudos. Will be collecting new links to all questions in this topic. Here you can also check links to fresh questions posted.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 10 Aug 2018
Posts: 218
Location: India
Concentration: Strategy, Operations
WE: Operations (Energy and Utilities)

Re: What is the remainder when (25^99 x 4^99)^99 is divided by 11?
[#permalink]
Show Tags
19 Jul 2019, 08:46
1 is the answer. (25^99 x 4^99)^99 could be written as (100^99)^99> ((10^2)^99)^99 11 will leave 1 remainder with 10, and this 1 on squaring will become +1. then finally 11 will leave 1 remainder with (1^99)^99 pretty bad explanation but I think 1 has to be answered.
_________________
On the way to conquer the GMAT and I will not leave it until I win. WHATEVER IT TAKES. Target 720+ " I CAN AND I WILL"Your suggestions will be appreciated: https://gmatclub.com/forum/youroneadvicecouldhelpmepoorgmatscores299072.html1) Gmat prep: 620 Q48, V27 2) Gmat prep: 610 Q47, V28 3) Gmat prep: 620 Q47, V28 4) Gmat prep: 660 Q47, V34 5) Gmat prep: 560 Q37, V29 6) Gmat prep: 540 Q39, V26 7) Veritas Cat: 620 Q46, V30 8) Veritas Cat: 630 Q45, V32



Manager
Joined: 06 Aug 2018
Posts: 98

Re: What is the remainder when (25^99 x 4^99)^99 is divided by 11?
[#permalink]
Show Tags
19 Jul 2019, 08:49
We can write expression as
100^99*99
So 100 mod 11 is always 1
So remainder will always be 1
Hence answer is A
Posted from my mobile device



Director
Status: Manager
Joined: 27 Oct 2018
Posts: 554
Location: Egypt
Concentration: Strategy, International Business
GPA: 3.67
WE: Pharmaceuticals (Health Care)

Re: What is the remainder when (25^99 x 4^99)^99 is divided by 11?
[#permalink]
Show Tags
19 Jul 2019, 08:50
It can be rewritten as: \(100^{99*99}\) = \(10^{2*99*99}\) = \((111)^{2*99*99}\) > \((1)^{2*99*99}\) > \(1\) (because the power is even) or can be rewritten as : \(100^{99*99}\) = \((99 + 1)^{99*99}\) > \((1)^{99*99}\) > \(1\) so A
_________________



Manager
Joined: 26 Mar 2019
Posts: 100
Concentration: Finance, Strategy

Re: What is the remainder when (25^99 x 4^99)^99 is divided by 11?
[#permalink]
Show Tags
19 Jul 2019, 08:54
Quote: What is the remainder when (25^99∗4^99)^99 is divided by 11?
\(25 * 4 = 100\) \(100 = 11* 9 + 1\) => 1 is remainder \(25^2 * 4^2 = 10,000\) \(10,000 = 11*909+1\) => 1 is remainder Independent of the degree, the remainder in this calculation is always 1. Thus, (25^99∗4^99)^99 / 11 will have 1 as a remainder. Answer: A



Manager
Joined: 28 Jan 2019
Posts: 118
Location: Peru

What is the remainder when (25^99 x 4^99)^99 is divided by 11?
[#permalink]
Show Tags
Updated on: 19 Jul 2019, 19:41
What is the remainder when (25^99∗4^99)^99 is divided by 11:
First, we can simplify this expression by multiplying 25*4 and power it to 99, so we will have:
(100^99)^99
Then we have that when we divide 100 by 11, the reminder is 1, so we can replace this reminder in the expression:
(1^99)^99, so the reminder will be also 1.
So (A) is our answer.
Originally posted by Mizar18 on 19 Jul 2019, 08:56.
Last edited by Mizar18 on 19 Jul 2019, 19:41, edited 1 time in total.



Senior Manager
Joined: 12 Dec 2015
Posts: 427

Re: What is the remainder when (25^99 x 4^99)^99 is divided by 11?
[#permalink]
Show Tags
19 Jul 2019, 08:56
What is the remainder when (25^99 * 4^99)^99 is divided by 11? Solution: (25^99 * 4^99)^99 = ((25*4)^99)^99=100^(99*99) if 100 is divided by 11, reminder is 1 => 100 = 11*9+1 => 100^2=10000 = 11*909+1 => 100^3=1000000 = 11*90909+1 similarly: if 100^n is divided by 11, reminder is 1, so if 100^(99*99) is divided by 11, reminder is 1
A. 1 > correct B. 3 C. 7 D. 9 E. 10



Manager
Joined: 11 Feb 2018
Posts: 73

Re: What is the remainder when (25^99 x 4^99)^99 is divided by 11?
[#permalink]
Show Tags
19 Jul 2019, 09:06
(25^99 ∗ 4^99)^99 ==>> (5^(2(99)) * 2^(2(99)))^99 (factoring out the common exponents) ==>> (5 * 2)^(2(99^2)) ==>> 10^(2(99^2)).
Now we need to find the remainder when 10^(2(99^2)) is divided by 11. Lets try to find the remainder with lesser powers of 10 and see if there is a pattern:
10^1=10 divided by 11  r=10 10^2=100 divided by 11  r=1 10^3=1,000 divided by 11  r=10 (990 is 90 times 11) 10^4=10,000 divided by 11  r=1 (9,999 is 99 times 11)
So what is the pattern we see here? For every odd power of 10, dividing the number by 11 gives a remainder of 10 and dividing any even power of 10 by 11 gives a remainder of 1. Now we know that 10^(2(99^2)) is an even power of 10 (because of 2 is being multiplied with 99^2), we know for certain that the remainder when 10^(2(99^2)) is divided by 11 will be 1.
Answer is thus A



Manager
Joined: 24 Jun 2019
Posts: 108

Re: What is the remainder when (25^99 x 4^99)^99 is divided by 11?
[#permalink]
Show Tags
19 Jul 2019, 09:08
What is the remainder when \((25^{99}∗4^{99})^{99}\) is divided by 11?
This can be rewritten as \((100^{99})^{99}\)
So, Numerator is a power of 100, and denominator is 11
100/11 gives remainder of 1
10000/11 also gives remainder of 1 ... and so on
all powers of 100 when divided by 11 always give remainder of 1
ANSWER: A  1



Intern
Joined: 17 Jul 2017
Posts: 34

Re: What is the remainder when (25^99 x 4^99)^99 is divided by 11?
[#permalink]
Show Tags
19 Jul 2019, 09:18
When 25 is multiplied by 4 it will give 100 No matter what power 100 is raised to when divided by 11, Remainder will always be 1 Answer is A
_________________
I am alive, because I have a dream Give kudos if it helped. Comment if I am wrong to help me learn more.



Manager
Joined: 12 Jul 2017
Posts: 206
GMAT 1: 570 Q43 V26 GMAT 2: 660 Q48 V34

Re: What is the remainder when (25^99 x 4^99)^99 is divided by 11?
[#permalink]
Show Tags
19 Jul 2019, 09:19
Given (25^99 * 4^ 99) ^ 99 and we need to find the remainder of this number to 11. The number can be written as ((25*4)^99)^99 Why? Since power is same, bases can be multiplied This becomes ((100)^99)^99 => (100)^99^2
So our number is 100000000... Now here is the beauty of this number. Irrespective of the trailing zeros, this number will always give remainder as 10 when divided by 11.
Say X = 1000000000... X + 1 = 100000.... 1 Notice that X + 1 is divisible by 11 So X + 1 = 11n X = 11n 1 => X = 11n  (1110) => X = 11n' + 10 So remainder 10
Answer E. Regards, Rishav



Manager
Joined: 08 Jan 2018
Posts: 143
Location: India
Concentration: Operations, General Management
WE: Project Management (Manufacturing)

Re: What is the remainder when (25^99 x 4^99)^99 is divided by 11?
[#permalink]
Show Tags
19 Jul 2019, 09:25
IMOA
Easier Approach : (25^99 x 4^99)^99= (100^99)^99= 100^9801
Therefore ques is, 100^9801 / 11 = (Rem 100/11)^9801 = 1^9801= 1
Another approach Note Any Number N of form, {N^(p1)}/p leaves remainder 1  Where p=prime no. and N,p are coprime Now, (25^99 x 4^99)^99= (100^99)^99= 100^9801 Therefore ques is, {100^9801}/11
Comparing with above, N=100 & p=11 .... Clearly, N & p are coprimes so, 100^(111)/11 remainder 1 i.e. 100^10/11remainder 1
100^9801/11= [(100^10)^9800 X 100] /11= [(100^10)^9800]/11 x 100/11= Rem (1) x Rem (1)= Rem (1)



Manager
Joined: 18 Sep 2018
Posts: 100

Re: What is the remainder when (25^99 x 4^99)^99 is divided by 11?
[#permalink]
Show Tags
19 Jul 2019, 09:26
IMO E
What is the remainder when (25^99∗4^99)^99 is divided by 11?
A. 1 B. 3 C. 7 D. 9 E. 10
Given, (25^99*4^99)^99 = (100)^99*99 = (100)^…1 [99*99 = “…1” => some odd integer ending with 1]
Now, when the even power of 10 (for e.g. 100, 10000 and so on…) is divided by 11, the remainder is 1 And when the odd power of 10 (for e.g. 10, 1000 and so on…) is divided by 11, the remainder is 10
From above expression we get the power of equation is odd, as 99*99 = “…1” => some odd integer ending with 1 So, when this expression is divided by 11, the remainder will be 10



Manager
Joined: 30 Sep 2017
Posts: 237
Concentration: Technology, Entrepreneurship
GPA: 3.8
WE: Engineering (Real Estate)

What is the remainder when (25^99 x 4^99)^99 is divided by 11?
[#permalink]
Show Tags
19 Jul 2019, 09:31
\((25^{99}\) x \(4^{99})^{99} =\) \((100^{99})^{99} =\) \((100)^{99 * 99} = (100)^{9801}\) Note that \(99*99\) can easily be calculated as \((1001)^2 = 100^2 + 1 2*100 = 9801\)
Let's find the pattern of the remainder when \((100)^n\) is divided by 11 (\(n\) is positive integer). \(n=1\) > \(\frac{100}{11}\) has quotient of 9 and remainder of 1; \(n=2\) > \(\frac{10,000}{11}\) has quotient of 909 and remainder of 1; \(n=3\) > \(\frac{1,000,000}{11}\) has quotient of 90,909 and remainder of 1, etc.
Thus, we can confidently say that when \((25^{99}\) x \(4^{99})^{99} = 100^{9801}\) is divided by 11, the remainder is 1.
Correct answer is (A) \(\) one.



Manager
Joined: 30 Nov 2017
Posts: 186
WE: Consulting (Consulting)

Re: What is the remainder when (25^99 x 4^99)^99 is divided by 11?
[#permalink]
Show Tags
19 Jul 2019, 09:38
Given (25^99 x 4^99)^99 is divided by 11 Firstly, 25^99 x 4^99 = (25 x 4)^99 = (100)^99 Therefore, (100^99)^99 divided by 11 is as follows: 100/11 gives a remainder of 1 (100^2)/11 gives a remainder of 1 (100^3)/11 gives a remainder of 1 therefore, (100^99)^99 divided by 11 will give a remainder of 1 Hence answer choice A.
Thank you for the Kudos.
_________________
Be Braver, you cannot cross a chasm in two small jumps...



Senior Manager
Joined: 13 Feb 2018
Posts: 448

Re: What is the remainder when (25^99 x 4^99)^99 is divided by 11?
[#permalink]
Show Tags
19 Jul 2019, 09:43
1) Let's make prime factorization: \(25^99=5^198\) \(4^99=2^198\)
2) Let's use the formula: \(a^n*b^n=(ab)^n\) to get the value in the brackets: \(5^198*2^198=10^198\)
3) now let's open the brackets to get (10^198)^99=10^{198*99} The only thing we will pick from this huge power is that it is even
4) Now lets give 10 more convenient form 10=111, so we have (111)^{even positive integer} 11 will always be divisible by 11 whatever the positive power 1 will transform into 1 as the power is even and 1/11 will always leave remainder 1
IMO Ans: A



Intern
Joined: 25 Mar 2019
Posts: 4

Re: What is the remainder when (25^99 x 4^99)^99 is divided by 11?
[#permalink]
Show Tags
19 Jul 2019, 09:43
As per exponent laws (25^99 * 4^99)^99 = (100^99)^99. It does not matter what the power is, if we divide by 11 the remainder will always be 1. Option A in my opinion.



Manager
Joined: 27 Mar 2016
Posts: 110

Re: What is the remainder when (25^99 x 4^99)^99 is divided by 11?
[#permalink]
Show Tags
19 Jul 2019, 10:02
(25^99 *4^99)^99 =(100^99)^99 when divided 11 should leave remainder 1 as 100/11 leaves 1 Hence A



Manager
Joined: 15 Jun 2019
Posts: 147

What is the remainder when (25^99 x 4^99)^99 is divided by 11?
[#permalink]
Show Tags
Updated on: 20 Jul 2019, 03:52
What is the remainder when\((25^99 x 4^99)^99\) is divided by 11 A. 1 B. 3 C. 7 D. 9 E. 10 inside the bracket, same power we can multiply to give (100^99)^99.. which gives so ans as 100 power something.. for 100 the remainder is 1 if divided by 11 . so (100^99)^99 gives 1 power something so 1 power anything will give only 1. so ans is 1 ie A
_________________
please do correct my mistakes that itself a big kudo for me,
thanks
Originally posted by ccheryn on 19 Jul 2019, 10:12.
Last edited by ccheryn on 20 Jul 2019, 03:52, edited 1 time in total.



Director
Joined: 19 Oct 2018
Posts: 778
Location: India

Re: What is the remainder when (25^99 x 4^99)^99 is divided by 11?
[#permalink]
Show Tags
19 Jul 2019, 10:14
What is the remainder when (25^99∗4^99)^99 is divided by 11?
\((25^{99}∗4^{99})^{99}\) = \([(25*4)^{99}]^{99}\) =\([(100)^{99}]^{99}\)
100=1 [MOD 11]
\(100^{99}\)= \((1)^{99}\) (Mod 11) \(100^{99}\)= (1) (Mod 11)
\([(100)^{99}]^{99}\)= (1)^{99} (Mod 11) \([(100)^{99}]^{99}\)= (1) (Mod 11)
Remainder is 1 when \((25^{99}∗4^{99})^{99}\) is divided by 11.
IMO A



Manager
Joined: 07 Dec 2018
Posts: 111
Location: India
Concentration: Technology, Finance

Re: What is the remainder when (25^99 x 4^99)^99 is divided by 11?
[#permalink]
Show Tags
19 Jul 2019, 11:12
What is the remainder when \((25^{99}∗4^{99})^{99}\) is divided by 11? 99*99=9801
So, \(25^{9801}*4^{9801}\)
\(25^1\) /11 => Reminder 3 \(25^2\) /11 => Reminder = 3*3= 9 \(25^3\) /11 => Reminder = 9*3/11 = 5 \(25^4\) /11 => Reminder = 5*3/11 = 4 \(25^5\) /11 => Reminder = 4*3 / 11 = 1 \(25^6\) /11 => Reminder = 1*3 / 11 = 3
Pattern has formed.
Reminder cyclicity will be : 3, 9, 5, 4, 1
9801/5 => Reminder =1 =>\(25^{9801}\)/11 => Reminder should be 3
Similarly,
\(4^1\) /11 => Reminder 4 \(4^2\) /11 => Reminder = 4*4/11= 5 \(4^3\) /11 => Reminder = 5*4/11 = 9 \(4^4\) /11 => Reminder = 9*4/11 = 3 \(4^5\) /11 => Reminder = 3*4 / 11 = 1 \(4^6\) /11 => Reminder = 1*4 / 11 = 4
Pattern has formed.
Reminder cyclicity will be : 4, 5, 9, 3, 1
9801/5 => Reminder = 1 =>\(4^{9801}\)/11 => Reminder should be 4
Finally, \(25^{9801}/11*4^{9801}/11\) => Reminder = 3*4 = 12/11
So, Ans should be 1. That's option (A)




Re: What is the remainder when (25^99 x 4^99)^99 is divided by 11?
[#permalink]
19 Jul 2019, 11:12



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



