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a, b and c are positive integers. If b equals the square roo

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a, b and c are positive integers. If b equals the square roo [#permalink] New post 04 Dec 2017, 05:27
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a, b and c are positive integers. If b equals the square root of a, and if c equals the sum of a and b, which of the following could be the value of c?

Indicate all such values.

A. 21
B. 30
C. 45
D. 72
E. 100
F. 331

[Reveal] Spoiler: OA
B and D


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Re: a, b and c are positive integers. If b equals the square roo [#permalink] New post 04 Dec 2017, 12:42
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Bunuel wrote:
a, b and c are positive integers. If b equals the square root of a, and if c equals the sum of a and b, which of the following could be the value of c?

Indicate all such values.

A. 21
B. 30
C. 45
D. 72
E. 100
F. 331

[Reveal] Spoiler: OA
B and D




Here

b = \(\sqrt{a}\)

or we can write as \(b^2 = a\)

Now c = a + b

or c = \(b^2\) + b

or c= b(b+1) ; now looking at the equation we need the value b as two consecutive integer then only the equation will satisfy.

Now looking at the option we find two options :-

30 as one possible option because 5 * 6 = 30 ; 5 and 6 are two consecutive integer

72 is another possible option because 8 * 9 = 72 ; 8 and 9 are two consecutive integer
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Re: a, b and c are positive integers. If b equals the square roo   [#permalink] 04 Dec 2017, 12:42
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a, b and c are positive integers. If b equals the square roo

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