Each of the 75 children in a line was assigned one of the integers from 1 through 75 by counting off in order. Then, standing in the same order, the children counted off in the opposite direction, so that the child who was assigned the number 75 the first time was assigned the number 1 the second time. Which of the following is a pair of numbers assigned to the same child?
(A) 50 and 25
(B) 49 and 24
© 48 and 26
(D) 47 and 29
(E) 45 and 32
Ans: D
Hint: look at the sum of the two numbers each child has.
Ah! I got it, but does the same method apply? @MITer94
Yes
1 75
2 74
3 73
…
75 1
Where is this question from? It’s a good one! It evokes the method that Gauss is said to have used in elementary school when assigned the busy work task of adding up the first 100 whole numbers…
This is not difficult at all, honestly.
Counting one way, 74 is the 2nd child (-1 from 75). And 2 is the 2nd child counting the other way (+1 from 1). The problem people have, I guess, is that 2 is +2 from ZERO and 73 is -2 from 75, so some people may match 2 with 73 instead of 2 with 74. As long as you have your counting procedures down, this question is easy.