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a and b are positive numbers such that

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SamaunParvez
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a and b are positive numbers such that [#permalink] New post   14 Feb 2021, 22:27
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a and b are positive numbers such that √(a+b)=5

Quantity A
Quantity B
a
25-2b


A)The quantity in Column A is greater.
B)The quantity in Column 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 and b are positive numbers such that [#permalink] New post   15 Feb 2021, 02:26
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SamaunParvez wrote:
a and b are possitive numbers such that √(a+b)=5

Column A
a

Column B

25-2b


Kindly, abide by the rules of posting a question here!

The Answer would be A.
\(\sqrt{a + b} = 5\)
Squaring both sides;
\(a + b = 25\)

Col. A: \(a\)
Col. B: \(25 - 2b\)

Plug \(25 = a + b\) in Col. B

Col. A: \(a\)
Col. B: \(a + b - 2b = a - b\)

Subtract a from both columns;
Col. A: \(a - a = 0\)
Col. B: \(-b\)

Since, b is a positive number, Col. B will have a negative value.

Therefore, \(0 > -b\)
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Re: a and b are positive numbers such that [#permalink] New post   15 Feb 2021, 04:03
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Follow the rules for posting BEFORE to post a question on the forum

https://gre.myprepclub.com/forum/how-to-po ... 12752.html

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a and b are positive numbers such that [#permalink] New post   15 Feb 2021, 05:22
As, √(a+b) = 5, So, a + b = 25.

Now As both a and b are positive number, Think of two extreme cases here,
First, a = 0, b = 25, for these values Qnt A = 0, Qnt B = -25, So Qnt A > Qnt B.
Second, a = 25, b = 0, for these values Qnt A = 25, Qnt B = 23, So Qnt A > Qnt B.

So, for the minimum and maximum values for a we get Qnt A is greater than Qnt B, Hence We can deduct for the whole range here.

The answer will be Qnt A.
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Re: a and b are positive numbers such that [#permalink] New post   27 Oct 2022, 17:53
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: a and b are positive numbers such that [#permalink]
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