Question

# Let n be four digit positive integer in which all the digits are different. If x is number of odd integers and y is number of even integers, then

A
x<y
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B
x>y
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C
x+y=4500
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D
|xy|=56
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Solution

## The correct option is D |x−y|=56When n is odd: Then units digit can be occupied by 1,3,5,7,9 and 0 cannot be on thousands place The number of such numbers is x=8×8×7×5=2240. When n is even: For any number to be even the last digit should be multiple of 2 i.e., 0,2,4,6,8 Case 1: If unit's place is filled with 0 then the total number is 9×8×7=504. Case 2: If unit's place is other than 0, then the total number is 8×8×7×4=1792. Hence, the total number of even numbers is y=504+1792=2296

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