RudeWall927
The average (arithmetic mean) of the 5 positive integers, u, w ,x, y, and z is 14, and u < w <x < y < z. If z is 26, what is the least possible value of the median of the 5 integers?
(A) 3
(B) 7
(C) 8
(D) 9
(E) 10
can anybody get a fastest way of solving such questions
If the average of 5 numbers is 14, its sum would be 14*5 = 70. The biggest number is 26 so now we know that the other 4 numbers should add up to 70-26 = 44.
Now to minimize the median, we need to give as much of this 44 as we can to the 4th number y but we know that y has to be less than z so y = 25
Now the sum of u, w and x is 44-25 = 19. Again, we need to give as much of this 19 as we can to u and w so we get the minimum value of x. After this point, we can use the options.
Substitute the values one by one for x and see how we can split u and w and see if we satisfy the condition u<w<x. You’ll see that we can’t substitute 3 because then u and w would be higher than x. We can’t substitute 7 because then you can’t split the remaining 12 in two so that it satisfies the condition. You either have to do 6,6,7 or 5,7,7. We can substitute 8 for x because then u and w can be 5 and 6 or 4 and 7.
Hence answer is (C) 8. I hope this helps and that it is right.