Suppose that x = -2 is the only number that satisfices 2^x^2 + Bx

Question

Suppose that x = -2 is the only number that satisfies  2^{x^2 + Bx + \frac{11}{2}} = \sqrt{8} . What is the value of B?

A. 3/4
B. 15/4
C. 4
D. 9/2
E. 19/4

gmatophobia · Accepted Answer

We can equate powers on both sides of the equation and obtain the value of B.

Option C

JeffTargetTestPrep · Answer

√8 = (2^3)^(1/2) = 2^(3/2)

We see that each side of the equation in the question stem can be written as 2 raised to some exponent.

If two exponential expressions that have the same base are equal and the same base is not -1, 0, or 1, then their exponents must be equal as well.

x^2 + Bx + 11/2 = 3/2

Since x = -2, we have:

(-2)^2 – 2B + 11/2 = 3/2

8 – 4B + 11 = 3

16 = 4B

B = 4

Answer: C

DanTheGMATMan · Answer

Classic exponents situation. Make the bases equal and then set the exponents equal:
 https://www.youtube.com/watch?v=HDZFSqmbHFY

GMATinsight · Answer

TRICK: It's important to bring both sides in same base so that their exponents may be equated. So in this question it's best to bring the right side in form of  2^a

We know,  2^{x^2 + Bx + \frac{11}{2}} = \sqrt{8}

but we also know that  \sqrt{8} = 2^{3/2}

therefore,  2^{x^2 + Bx + \frac{11}{2}} = 2^{3/2}

i.e.  x^2 + Bx + \frac{11}{2} = \frac{3}{2}

i.e.  x^2 + Bx + 4 = 0

Now, we have been given that x = -2

i.e.  (-2)^2 + B*(-2) + 4 = 0

i.e. B = 4

Answer: Option C

Suppose that x = -2 is the only number that satisfices 2^x^2 + Bx

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GMAT Problem Solving (PS) Questions

Suppose that x = -2 is the only number that satisfices 2^x^2 + Bx

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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