SAT Trial and Error

Algebra Level 1

a b − 2 a − 2 b − 2 = 0 ab - 2a - 2b - 2 = 0

Which of the following pairs of numbers ( a , b ) (a, b) is a solution to the equation above?

I. ( 3 , 8 ) II. ( 4 , 5 ) III. ( 4.5 , 4.5 ) \begin{array}{r r l} &\text{I.}\ &(3, 8)\\ &\text{II.}\ &(4, 5)\\ &\text{III.}\ &(4.5, 4.5)\\ \end{array}

(A) \ \ I only
(B) \ \ II only
(C) \ \ I and II only
(D) \ \ I and III only
(E) \ \ I, II and III

A B C D E

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Tatiana Georgieva by Tatiana Georgieva

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1 solution

Tatiana Georgieva Staff
Mar 26, 2015

Correct Answer: C

Solution:

We try each of the options.

I. If a = 3 a=3 and b = 8 b=8 then a b − 2 a − 2 b − 2 = 3 × 8 − 6 − 16 − 2 = 0. ab - 2a - 2b - 2 = 3 \times 8 - 6 - 16 -2 = 0. Option I is a solution.
II. If a = 4 a=4 and b = 5 b=5 then a b − 2 a − 2 b − 2 = 4 × 5 − 8 − 10 − 2 = 0 ab - 2a - 2b - 2=4 \times 5 - 8 - 10 - 2 = 0 . Option II is a solution.
III. If a = b = 4.5 a=b=4.5 then a b − 2 a − 2 b − 2 = 4.5 × 4.5 − 9 − 9 − 2 = 0.25 ≠ 0 ab - 2a - 2b - 2=4.5 \times 4.5 - 9 - 9 - 2 = 0.25 \neq 0 . Option III is not a solution.

Since only options I and II are solutions to the equation, the correct answer is (C).

Incorrect Choices:

(A) , (B) , (C) , and (D)
See the solution for why these choices are wrong.

If you got this problem wrong, you should review SAT Quadratic Functions .

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