Discussion
Calculate the total number of singers needed to make it 70, if the rank of a singer in that group is 19th from the top and 38th from the bottom.
Answer: A
Fourteen more singers are needed. A singer who is 19th from the top and 38th from the bottom stands in a group of \(19 + 38 - 1 = 56\) singers, because that singer is counted in both ranks. To make the group 70 the number to add is \[ 70 - 56 = 14 \] so 14 more are needed. The options 16 and 18 overshoot the gap, and 10 leaves the group at 66. If the question were read as asking for the group itself, the answer would be 56, which is not offered, so the question is read as the number to be added, which the key confirms.
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