By inserting parentheses, it is possible to give the expression 2 × 3 + 4 × 5 several values. How many different values can be obtained?

2009 AMC 12B Problem 6 — Solution

2009 AMC 12B Problem 6

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By inserting parentheses, it is possible to give the expression $2 \times 3 + 4 \times 5$ several values. How many different values can be obtained?

$2$

$3$

$4$

$5$

$6$

Answer: C

Concepts:order of operations systematic listing

Difficulty rating: 1250

Solution:

The genuinely different groupings give

$(2 \times 3) + (4 \times 5) = 26,$ $\ ((2 \times 3) + 4) \times 5 = 50,$ $\ 2 \times (3 + (4 \times 5)) = 46,$ and $\ 2 \times (3 + 4) \times 5 = 70.$

These are all distinct, so $4$ values can be obtained.

Thus, the correct answer is C.

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