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Which of the following could be the units digit in A + B, if m and n
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19 Aug 2024, 03:19
19 Aug 2024, 03:19
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0% (00:00) correct
100% (02:03) wrong based on 8 sessions
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\(A=4^m\) and \(B=9^n\)
Which of the following could be the unit’s digit in \(A + B\), if m and n are non-negative integers?
A. 0
B. 1
C. 2
D. 3
E. 4
F. 5
G. 6
H. 7
I. 8
J. 9
Which of the following could be the unit’s digit in \(A + B\), if m and n are non-negative integers?
A. 0
B. 1
C. 2
D. 3
E. 4
F. 5
G. 6
H. 7
I. 8
J. 9
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Free Materials for the GRE General Exam - Where to get it!!
Shorter GRE - Preparing for the Quantitative Reasoning Measure
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Re: Which of the following could be the units digit in A + B, if m and n
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20 Sep 2024, 00:28
20 Sep 2024, 00:28
1
Not sure why the answers are only A (0) and E (4). Here's how I approach this problem, would appreciate if there are any errors in the logic below
m and n are non-negative integers, so there are 3 base cases:
1. m = 0, n = 0 => A + B = 2
2. m = 0, n = 1 => A + B = 10, units digit is 0
3. m = 1, n = 0 => A + B = 5
Since 4^1 = 4, 4^2 = 16, 4^3 = 64, 4^4 = 256, cycle of unit digits of 4 is 4 and 6
Since 9^1 = 9, 9^2 = 81, 9^3 = 729, 9^4 = 6561, cycle of unit digits of 9 is 9 and 1
Then we have the following unit digits combination:
4 + 9 = 13, units digit is 3
4 + 1 = 5
6 + 9 = 15, units digit is 5
6 + 1 = 7
Possible unit digits: 2,0,5,3,7
m and n are non-negative integers, so there are 3 base cases:
1. m = 0, n = 0 => A + B = 2
2. m = 0, n = 1 => A + B = 10, units digit is 0
3. m = 1, n = 0 => A + B = 5
Since 4^1 = 4, 4^2 = 16, 4^3 = 64, 4^4 = 256, cycle of unit digits of 4 is 4 and 6
Since 9^1 = 9, 9^2 = 81, 9^3 = 729, 9^4 = 6561, cycle of unit digits of 9 is 9 and 1
Then we have the following unit digits combination:
4 + 9 = 13, units digit is 3
4 + 1 = 5
6 + 9 = 15, units digit is 5
6 + 1 = 7
Possible unit digits: 2,0,5,3,7
Re: Which of the following could be the units digit in A + B, if m and n
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20 Sep 2024, 01:39
20 Sep 2024, 01:39
Expert Reply
The OA's are correct sir.
What is your doubt ?
Please let me know
What is your doubt ?
Please let me know
