Transcript Seven cards in a pile are numbered 1 through 7.

Seven cards in a pile are numbered 1 through 7. One card is drawn. The units digit
of the sum of the numbers on the remaining cards is 7. What is the number on the
drawn card?
a) 1
Difficulty:
Medium
b) 3
c) 5
d) 6
e) 7
HINT
The sum of the numbers on all seven cards is 1 + 2 + 3 + 4 + 5 + 6 + 7, or 28. If,
say, the card numbered 5 were drawn, the sum on the remaining cards would be
28 – 5 = 23, a number whose units digit is 3. You want to remove one card and get
a sum whose units digit is 7.
A: 1
Explanation
The sum of the numbers on all seven cards is 1 + 2 + 3 + 4 + 5 + 6 + 7, or 28.
Removing a numbered card reduces the sum of the remaining cards by the number
on that card. For example, if the card drawn were numbered 5, then the sum of the
remaining cards would be 28 – 5 = 23, a number whose units digit is 3. Similarly, if
the card drawn is numbered 1, then the sum of the numbers on the remaining cards
is 27, whose units digit is 7. Therefore, the drawn card was numbered 1.