1996 AJHSME Problems/Problem 6

Problem

What is the smallest result that can be obtained from the following process?

Choose three different numbers from the set $\{3,5,7,11,13,17\}$ .
Add two of these numbers.
Multiply their sum by the third number.

$\text{(A)}\ 15 \qquad \text{(B)}\ 30 \qquad \text{(C)}\ 36 \qquad \text{(D)}\ 50 \qquad \text{(E)}\ 56$

Solution

Since we want the smallest possible result, and we are only adding and multiplying positive numbers over $1$ , we can "prune" the set to the three smallest numbers $\{3,5,7\}$ . Using bigger numbers will create bigger sums and bigger products.

From there, compute the $3$ ways you can do the two operations:

$(3+5)7 = 8\cdot 7 = 54$

$(3 + 7)5 = 10\cdot 5 = 50$

$(7+5)3 = 12\cdot 3 = 36$

The smallest number is 36, giving an answer of $\boxed{C}$

1996 AJHSME (Problems • Answer Key • Resources)
Preceded by Problem 5	Followed by Problem 7
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
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1996 AJHSME Problems/Problem 6

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