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a and b are both > 0 and < 1

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a and b are both > 0 and < 1 [#permalink] New post 22 Aug 2018, 08:39
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a and b are both > 0 and < 1

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


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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[Reveal] Spoiler: OA

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Re: a and b are both > 0 and < 1 [#permalink] New post 29 Aug 2018, 04:08
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Carcass wrote:
a and b are both > 0 and < 1

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


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.

Kudos for R.A.E



Since,
0 < a,b < 1

i.e they are positive fraction.

without calculation we can see that QTY A is addition to the square of each fraction , whereas QTY B is addition to each number

we know if the fraction is squared their value decreases the original value

i.e for example \((\frac{1}{2})^2 < \frac{1}{2}\)

So QTY A < QTY B
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Re: a and b are both > 0 and < 1   [#permalink] 29 Aug 2018, 04:08
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a and b are both > 0 and < 1

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