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Definition of Sets

A number x is...

Question

A number x is selected at random from the set {1,2,3,..............99). A number y is selected from the same set.The probability that the number: $7^{X} + 5^{Y}$ last digit is 8.

A

1/4

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B

1/2

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C

1/16

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D

3/8

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Solution

The correct option is A
1/4

$7^{X}$ will always end is 1,3,7 and 9

$5^{Y}$ will always end in 5

Total cases possible:4

Out of these only one case where 8 is possible

Hence P(E)= $\frac{1}{4}$

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