2010 AMC 12B Problem 5

Attempt Problem 5 of the 2010 AMC 12B 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 2010 AMC 12B solutions, or check the answer key.

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

Lucky Larry’s teacher asked him to substitute numbers for

a,

b,

c,

d,

and

e

in the expression

a-(b-(c-(d+e)))

and evaluate the result. Larry ignored the parentheses but added and subtracted correctly and obtained the correct result by coincidence. The numbers Larry substituted for

a,

b,

c,

and

d

were

1,

2,

3,

and

4,

respectively. What number did Larry substitute for

e?

-5

-3

0

3

5

Answer: D

Concepts:order of operations linear equation

Difficulty rating: 1100

Small hint:

Expand the correct expression to

a-b+c-d-e

Big hint:

Larry instead computed

a-b-c-d+e;

set the two equal

Solution:

The correct value is

a-(b-(c-(d+e)))=

a-b+c-d-e.

With

a, b, c, d=1, 2, 3, 4,

this equals

1-2+3-4-e=-2-e.

Larry dropped the parentheses and computed

1-2-3-4+e=-8+e.

Setting

-2-e=-8+e

gives

2e=6,

e=3.

Thus, the correct answer is D.