An operation ⊕ is defined for any values a an… | GMAT Sprint

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sub-505

Algebra

An operation ⊕ is defined for any values a and b as $a⊕b = a + b + ab$ . Given that $a⊕b = 2$ and $b ≠ -2$ , how can we express a in terms of b?

Correct answer marked below

\frac{b + 2}{b}

\frac{b - 2}{b + 2}

\frac{2}{b + 2}

\frac{b}{b + 2}

\frac{2 - b}{1 + b}

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Official Explanation

Official

The operation ⊕ is defined as

a⊕b = a + b + ab

. We know that

a⊕b = 2

and

b ≠ -2

. Therefore, we can set up the equation:

2 = a + b + ab

. Rearranging gives us:

2 - b = a(1 + b)

.…

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What this question tests

Your ability to manipulate linear and quadratic expressions, substitute unknowns, and solve equations under time pressure.

Losing a sign when moving terms across the equals sign, or dividing both sides by a variable that could equal zero.