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a, b and c are positive integers. If b equals the square root of a, an

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a, b and c are positive integers. If b equals the square root of a, an [#permalink] a, b and c are positive integers. If b equals the square root of a, an   04 Dec 2017, 06:28
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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?

I. 21
II. 30
III. 72

A. I only
B. II only
C. III only
D. II and III only
E. I, II and III
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D
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Re: a, b and c are positive integers. If b equals the square root of a, an [#permalink] a, b and c are positive integers. If b equals the square root of a, an   04 Dec 2017, 07:05
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Bunuel
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?

I. 21
II. 30
III. 72

A. I only
B. II only
C. III only
D. II and III only
E. I, II and III


\(b=\sqrt{a}..............a=b^2\)..
and \(c=a+b = b^2+b =b(b+1)\)
so C is PRODUCT of two consecutive integers
21=3*7 or 1*21 ......NO
\(30 = 5*6\) ................YES
\(72 = 8*9\) ................ YES

D
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Re: a, b and c are positive integers. If b equals the square root of a, an [#permalink] a, b and c are positive integers. If b equals the square root of a, an   04 Dec 2017, 06:47
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c= \(\sqrt{a}\) + a
a= 25, c= 5+25 = 30
a= 64, c= 8+ 64 = 72
a= 16, c= 4+16 = 20 (1 eliminated)
II and III only possible
--D--
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Re: a, b and c are positive integers. If b equals the square root of a, an [#permalink] a, b and c are positive integers. If b equals the square root of a, an   04 Dec 2017, 06:56
Option D.
a,b,c
=> b2, b, c
c=b*(b+1)

Product of 2 consecutive +ve integers
30 &72

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Re: a, b and c are positive integers. If b equals the square root of a, an [#permalink] a, b and c are positive integers. If b equals the square root of a, an   12 Jan 2018, 07:12
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Bunuel
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?

I. 21
II. 30
III. 72

A. I only
B. II only
C. III only
D. II and III only
E. I, II and III

We have the following equations:

b = √a

b^2 = a

and

c = a + b

Thus,

c = a + a^2

So c is the sum of an integer + that integer squared.

Statement I is not true, since 4^2 + 4 = 20 and 5^2 + 5 = 30; thus the value of a that satisfies a^2 + a = 21 is not an integer, but some real number between 4 and 5.

Looking at the answer choices we see that II and III can work since 30 = 5 + 25, and 72 = 8 + 64.

Answer: D
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Re: a, b and c are positive integers. If b equals the square root of a, an [#permalink] a, b and c are positive integers. If b equals the square root of a, an   19 Jun 2021, 08:28
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If b equals the square root of a => \(b^2 = a\)

If c equals the sum of a and b => \(c = a + b = b^2 + b = b ( b + 1)\)

Therefore, c is the product of two consecutive integers

I. 21 = 4 * 5 = 20 - NOT POSSIBLE

II. 30 = 5 * 6 = 30 - POSSIBLE

III. 72 = 8 * 9 = 72 - POSSIBLE

Only Option II and III are possible.

Answer D
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Re: a, b and c are positive integers. If b equals the square root of a, an [#permalink] a, b and c are positive integers. If b equals the square root of a, an   15 Aug 2022, 23:52
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Re: a, b and c are positive integers. If b equals the square root of a, an [#permalink]
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