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Question

Let X and Y be the sets of all positive divisors of 400 and 1000 respectively (including 1 and the number). Then n(XY)=


A

4

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B

6

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C

8

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D

12

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Solution

The correct option is D

12


Explanation for the correct option:

Determine the value of n(XY)

The factors of 400=1,2,4,5,8,10,16,20,25,40,50,80,100,200,400

The factors of 1000=1,2,4,5,8,10,20,25,40,50,100,125,200,250,500,1000

Let X be the sets of all positive divisors of 400

X=1,2,4,5,8,10,16,20,25,40,50,80,100,200,400

Let Y be the sets of all positive divisors of 1000

Y=1,2,4,5,8,10,20,25,40,50,100,125,200,250,500,1000

Calculating n(XY)

XY=x/xXandxY

XY=1,2,4,5,8,10,20,25,40,50,100,200

n(XY)=12

Hence, option (D) is the correct answer


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