GRE Prep 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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
13^x + 12^x = n, where x is a positive integer
[#permalink]
24 Oct 2017, 01:22
24 Oct 2017, 01:22
1
3
Bookmarks
00:00
Question Stats:
46% (01:31) correct
53% (01:24) wrong based on 63 sessions
Hide Show timer Statistics
\(13^x + 12^x = n\), where x is a positive integer
A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Kudos for correct solution.
Quantity A |
Quantity B |
The number of distinct numbers that can be the units digit of n |
4 |
A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Kudos for correct solution.
Re: 13^x + 12^x = n, where x is a positive integer
[#permalink]
18 May 2018, 01:17
18 May 2018, 01:17
I think option A should be the answer since we raise 13 to different first few positive powers I got different units therefore same when we are adding 13^x +12^x then we are ought to get more than 4 types of unit digit.
Please clarify?
Please clarify?
Re: 13^x + 12^x = n, where x is a positive integer
[#permalink]
18 May 2018, 03:25
18 May 2018, 03:25
1
2
Bookmarks
No need to raise 13 and 12 to any digits. Since we are interested in finding the unit digits only we can work with 3 and 2.
We should also keep in mind that the unit digits of any number will reveal a pattern when raised to certain numbers.
For eg.
\(3^1 =3\)
\(3^2 = 9\)
\(3^3 = 27\)
\(3^4 = 81\)
\(3^5 = 243\)
\(3^6 = 729\)
You can notice that the units digit of \(3^5\) is same as \(3^1\) and units digit of \(3^2\) is same as \(3^6\)
Hence the units digits repeat in an interval of 4
Similar is the case for the powers of 2
\(2^1 =2\)
\(2^2 = 4\)
\(2^3 = 8\)
\(2^4 = 16\)
From here on the units digit of powers of 2 will repeat.
Now we just need to add the respective units digit of 2 and 3 for a given digit of power
For x = 1; 3+2 = 5
for x = 2; 9+4 = 13 or, 3
for x = 3; 7+8 = 15 or, 5
for x = 4; 1+6 = 7
since 5 is repeated we count it as 1.
Therefore there are in total 3 distinct unit digits
option B
We should also keep in mind that the unit digits of any number will reveal a pattern when raised to certain numbers.
For eg.
\(3^1 =3\)
\(3^2 = 9\)
\(3^3 = 27\)
\(3^4 = 81\)
\(3^5 = 243\)
\(3^6 = 729\)
You can notice that the units digit of \(3^5\) is same as \(3^1\) and units digit of \(3^2\) is same as \(3^6\)
Hence the units digits repeat in an interval of 4
Similar is the case for the powers of 2
\(2^1 =2\)
\(2^2 = 4\)
\(2^3 = 8\)
\(2^4 = 16\)
From here on the units digit of powers of 2 will repeat.
Now we just need to add the respective units digit of 2 and 3 for a given digit of power
For x = 1; 3+2 = 5
for x = 2; 9+4 = 13 or, 3
for x = 3; 7+8 = 15 or, 5
for x = 4; 1+6 = 7
since 5 is repeated we count it as 1.
Therefore there are in total 3 distinct unit digits
option B
