Examination me. IUUUTISIZU
Q51: Mr. X with his eight children of different ages is on a family trip. His oldest child, who is 9 years
old saw a license plate with a 4-digit number in which each of two digits appear two times. “Look
daddy!” she exclaims. "That number is evenly divisible by the age of each of us kids!" "That's
right," replies Mr. X, “and the last two digits just happen to be my age". Which of the following is
not the age of one of Mr. X's children?
Answers
5 is not the age of one of Mr. X's children
Step-by-step explanation:
Given options are 4 , 5 , 6 , 7
Mr. X with his eight children of different ages is on a family trip
Oldest Child is 9 Year old
so Age of 8 Children are from 1 to 9 except any one number
out of 2 , 4 , 6 , 8 at least 3 Child would be there
if its not divisible by 8 then it must be divisible by 2 & 4
& if it divisible by 8 then it automatically divisible by 2 & 4
as it is divisible by 9 so it is also divisible by 3
hence 2 * 3 = 6 (also divisibly by 6)
now we left with only option 5 & 7
if age is not 5
then LCM = 9 * 8 * 7 = 504
& 504 * 11 = 5544
if age is not 7
then LCM = 9 * 8 * 5 = 360 and it does not give any mentioned number
Age of children = 1 , 2 , 3 , 4 , 6 , 7 , 8 , 9
number = 5544
5 is not the age of one of Mr. X's children
X age = 44 Years
Another approach to solve
if 5 is the age of one child then
number must be divisible by 10
then number ends with 0
and number is divisible by 9 also
so other digit would be 9
so possible numbers are
9900 , 9090
9900 is ignored as X age can not be 0
9090 is neither divisible by 7 nor 4 or 8
so we can say age can not be 5 years
this is Quicker solution for the answer but we do not get number here
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