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Re: a = b + 1 and 5 < ab < 8 [#permalink]
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I am a bit confused with the solution posted. If a = 1 and b=6, wouldn't that not satisfy the requirement that a = b +1?
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Re: a = b + 1 and 5 < ab < 8 [#permalink]
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rubytuesdays21 wrote:
I am a bit confused with the solution posted. If a = 1 and b=6, wouldn't that not satisfy the requirement that a = b +1?


Good catch!
I've edited my response accordingly

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a=b+1 and 5<ab<8 [#permalink]
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\(a=b+1\) and \(5<ab<8\)


Quantity A
Quantity B
\(2a + b^2\)
\( a^2+2b \)



A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.



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Re: a=b+1 and 5<ab<8 [#permalink]
The key here is that a and b are either both positive or both negative, since the product of two positives is a positive and the product of two negatives is also positive.

\(ab = (b+1)b = b^2 + b\)
\(5 < b^2 + b < 8\)

1) a and b are both positive
Pick a positive value for b that satisfies the inequality. If \(b = 2\), then \(a = 3\)

Quantity A: \(2a + b^2 = 2(3) + 2^2 = 10\)
Quantity B: \(a^2 + 2b = 3^2 + 2(2) = 13\)

13 > 10, so Quantity B is greater.

2) a and b are both negative
Pick a negative value for b that satisfies the inequality. If \(b = -3\), then \(a = -2\)

Quantity A: \(2a + b^2 = 2(-2) + (-3)^2 = 5\)
Quantity B: \(a^2 + 2b = (-2)^2 + 2(-3) = -2\)

-2 < 5, so Quantity A is greater.

Since there are values of a and b that make the Quantity relationships different, the answer is D.
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