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Question

If X and Y are the sets of all positive divisors of 400 and 1000, respectively (including 1 and the number). Then, n(XintersectionY) is equal to:


A

4

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B

6

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C

8

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D

10

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E

12

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Solution

The correct option is E

12


Explanation for the correct option.

Since, X and Yare the sets of all positive divisors of 400 and 1000, respectively. So, we will find the factors of 400 and 1000

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

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

X∩Y=1,2,4,5,8,10,20,25,40,50,100,200

nX∩Y=12

Hence, option E is correct.


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