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10 Dec 2021, 03:15
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Difficulty:
95%
(hard)
Question Stats:
50% (02:38) correct
50%
(02:55)
wrong
based on 56
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A family consists of 6 persons - A, B, C, D, E and F. Age of A, B, C, D, E and F are distinct and are in descending order. The average of their ages is a two digit odd palindromic number. Age of each family member is a 2 digit number and no one is more than 70 years old. Age of E and F is below 15. After 7 years, A dies. After 3 more years, G is born and after 2 more years B dies. The average age now is 4 less than the average age in the beginning. What is the sum of the age of A when he dies and the age of B when he dies?
A. 138
B. 130
C. 122
D. 124
E. None of the above
Are You Up For the Challenge: 700 Level Questions
A. 138
B. 130
C. 122
D. 124
E. None of the above
Are You Up For the Challenge: 700 Level Questions
19 Dec 2021, 06:19
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Bunuel
We have A<B<C<D<E<F.
Average age is a 2 digit odd palindrome, so 11,33,55,77,99 are the possible values.
No one is above 70, so average age <70. Eliminate 77 and 99.
All ages are 2 digit number, so average age has to be greater than 12. Least possible ages = 10,11,12,13,14,15. Eliminate 11.
So we are left with 33 and 55.
Two of the members are less than 15, so maximum possible values are 14 and 13.
Let us look for maximum average, so take all other ages as maximum possible- 69,68,67,66.
Sum = 270+14+13 = 297. Average = 297/6 <50.
Thus average age is 33.
After 7 years the sum of age = 6*(33+7) = 240.
Sum without A = 240-A.
In next 3 years, 3*5 years are added.
In the next 2 years, 2*6 are added as a mew member gets added.
Sum = 240-A+15+12 = 267-A
As B dies, the Sum = 267-A-B
The average now is 33-4 or 29, so sum = 5*29 = 145
Thus, 267-A-B = 145 or A+B = 122.
C
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