1954 AMC 12 Problem 10

Attempt Problem 10 of the 1954 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1954 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

10.

The sum of the numerical coefficients in the expansion of the binomial

(a+b)^6

is:

32

16

64

48

7

The coefficient sum is obtained by choosing convenient values of

a

and

b

Set

a=b=1

Setting

a=b=1

makes every monomial equal to

1,

so the value of the expansion equals the sum of its coefficients. Thus the sum is

(1+1)^6=64.

The correct answer is C.

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