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If a and b are positive integers, is 2*a^(1/3) < (a + b)^(1/3) ?

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If a and b are positive integers, is 2*a^(1/3) < (a + b)^(1/3) ? [#permalink] If a and b are positive integers, is 2*a^(1/3) < (a + b)^(1/3) ?   23 Sep 2022, 06:38
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If a and b are positive integers, is \(2\sqrt[3]{a} < \sqrt[3]{a + b}\)?

(1) 7a < b
(2) 7a < a + b
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If a and b are positive integers, is 2*a^(1/3) < (a + b)^(1/3) ? [#permalink] If a and b are positive integers, is 2*a^(1/3) < (a + b)^(1/3) ?   23 Sep 2022, 06:52
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Bunuel wrote:
If a and b are positive integers, is \(2\sqrt[3]{a} < \sqrt[3]{a + b}\)?

(1) 7a < b
(2) 7a < a + b


Answer: Option A

Tip: Always simplify the question stem if possible




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Re: If a and b are positive integers, is 2*a^(1/3) < (a + b)^(1/3) ? [#permalink] If a and b are positive integers, is 2*a^(1/3) < (a + b)^(1/3) ?   18 Mar 2023, 01:16
Could someone please elaborate on the answer choice ?
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Re: If a and b are positive integers, is 2*a^(1/3) < (a + b)^(1/3) ? [#permalink] If a and b are positive integers, is 2*a^(1/3) < (a + b)^(1/3) ?   20 Mar 2023, 02:37
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If a and b are positive integers, is 2a^(1/3)< (a+b)^(1/3)?
2a^(1/3)< (a+b)^(1/3)
Since, a and b are both positive integers, we can raise both sides to power 3, we get
2^3 * a < (a+b)
=> 8a < a +b
=> 7a < b
So, we need to find is b > 7a?

(1) 7a < b
Sufficient.

(2) 7a < a + b
=> 7a - a < b
=> 6a < b. We find that b > 6a but from statement 2, we don't whether b>7a.
Not sufficient.
Answer A.
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Re: If a and b are positive integers, is 2*a^(1/3) < (a + b)^(1/3) ? [#permalink]
20 Mar 2023, 02:37
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Bunuel
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