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Source: Beat The GMAT — Problem Solving |
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ganeshrkamath
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All you need to do here is find the units digit of 3^444 and 4^333 to get to the answer.sanjoy18 wrote:what is the reminder when 3^444+4^333 is divided by 5
A)0
B)1
C)2
D)3
E)4
Now units digits of powers of 3 follow a rule:
3^1 = 3
3^2 = 9
3^3 = 27
3^4 = 81
3^5 = 243
3^6 = __9
3^7 = __7
3^8 = __1
The pattern is : 3,9,7,1,3,9,7,1,....
A similar pattern for powers of 4 exists: 4,6,4,6,....
units digit of 3^444 = units digit of (3^4)^111 = 1
units digit of 4^333 = 4
1+4 = 5
So remainder when divided by 5 is 0.
Choose A
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Kelley School of Business (Class of 2016)
GMAT Score: 750 V40 Q51 AWA 5 IR 8
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GMATGuruNY
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When an integer with a units digit of 3 is raised to successive powers, the units digits of the resulting integers repeat in a cycle of 4:sanjoy18 wrote:what is the reminder when 3^444+4^333 is divided by 5
A)0
B)1
C)2
D)3
E)4
3, 9, 7, 1...3, 9, 7, 1...
Implication: when the exponent is a multiple of 4, the units digit of the resulting integer will be 1.
This, 3^444 has a units digit of 1.
When an integer with a units digit of 4 is raised to successive powers, the units digits of the resulting integers alternate between 4 and 6:
4, 6...4, 6...
Implication: when the exponent is odd, the units digit of the resulting integer will be 4.
Thus, 4^333 has a units digit of 4.
Thus, 3^444 + 4^333 = integer with a units digit of 1 + integer with a units digit of 4 = integer with a units digit of 5.
An integer with a units digit of 5 is a multiple of 5.
Since 3^444 + 4^333 is a multiple of 5, dividing it by 5 will yield a remainder of 0.
The correct answer is A.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
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Student Review #3
