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(#M40018394) SELF question Keep an EYE

Digits of a four digit numbers are in AP, not necessarily in the same order. Arithmetic mean of any two digits of the number is an integer. How many such numbers are possible?

RAVI PAWAR (12 years ago)

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shakti gupta  (12 years ago)

90
1)abcd are even, 42 possibilities
2)abcd are odd, 48 possibilities
total 90 possibilities

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Vinay Sipani   (12 years ago)

As the arithmetic mean of any two integers is an integer

=>
1) a,b,c,d are equal or
2) a,b,c,d are even and unequal
3) a,b,c,d are odd and unequal

1) If all are equal, 9 possibilities
2) If all are even , 1 possibility
3) If all are odd , 2 possibility

=> Total possibilities = 12

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RAVI PAWAR  (12 years ago)

bt options are
A.84
B.96
C.90
D.70

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Vinay Sipani   (11 years ago)

If order is not necessary
Then total number of possibilities is

90 as explained by Shakti Gupta
+ 9 if all digits are equal

=> 90+9 = 99

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