Question

# If two different numbers are taken from the set {0, 1, 2, 3,.... 10}, then the probability that their sum as well as absolute difference are both multiple of 4, is ?

A
655
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B
1255
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C
1445
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D
755
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Solution

## The correct option is A 655Total number of ways os selecting 2 different numbers from {0,1,2,....10}=11C2=55 Let two numbers selected be x and y. Then, x + y = 4m ...(i) and x - y = 4n .....(ii) ⇒2x=4(m+n) and 2y=4(m−n) ⇒x=2(m+n) and y=2(m−n) ∴ x and y both are even numbers. xy04,826,1040,862,1080,4102,6 But here arrangement of x & y does not matter. Only selection of two numbers is necessary. Therefore, total 6 combinations are possible ∴ Required probability =655

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