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Probability

by harsh.champ » Tue Feb 09, 2010 5:08 am
Suppose that a and b are two integers, not necessarily distinct, chosen from the set S = 1, 2, 3, · · · , 200. What is the probability that the unit digit of 3a + 7b is 6"Œ?

(A)5/16
(B)3/16
(C)3/17
(D)7/17
(E)3/13

The OA is B.
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by shashank.ism » Tue Feb 09, 2010 5:16 am
harsh.champ wrote:Suppose that a and b are two integers, not necessarily distinct, chosen from the set S = 1, 2, 3, · · · , 200. What is the probability that the unit digit of 3a + 7b is 6"Œ?

(A)5/16
(B)3/16
(C)3/17
(D)7/17
(E)3/13

The OA is B.
Consider the powers of 3 and 7 mod 10.
Thus there are 16 pairs of value of 3a and 7b mod 10. They are (3,7), (3,9), (3,3), (3,1), (9,7), (9,9), (9,3), (9,1), (7,7), (7,9), (7,3), (7,1), (1,7), (1,9), (1,3), (1,1)
Of these only 3 have a sum which is 6 mod 10, namely (3,3), (9,7) and (7,9).
Thus the probability is 3/16
[spoiler](B)[/spoiler] is the correct
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by ajith » Tue Feb 09, 2010 6:38 am
harsh.champ wrote:Suppose that a and b are two integers, not necessarily distinct, chosen from the set S = 1, 2, 3, · · · , 200. What is the probability that the unit digit of 3a + 7b is 6"Œ?

(A)5/16
(B)3/16
(C)3/17
(D)7/17
(E)3/13

The OA is B.
Is it 3^a+7^b or 3a+7b?
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