Twelve cards are numbered 1 to 12. Amir sorts these cards into pairs. Each pair adds to the same total. Which number must be paired with 3?
A 8 B 9 C 10 D 11 E 12
C
In any sequence of consecutive integers, adding the first and the last, the second and the second last, the third and the third last etc gives the same total. So in this case, 1 + 12 = 13, 2 + 11 = 13, 3 + 10 = 13, etc,; thus 3 must be paired with 10, answer C. This gives a very quick way to add up a sequence of consecutive integers, add together the first and the last, and halve the answer. This represents the average of all the numbers so now multiply by the number of numbers in the sequence to get the total.
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