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

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Math Expert
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a, b and c are positive integers. If b equals the square root of a, an [#permalink]

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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
[Reveal] Spoiler: OA

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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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04 Dec 2017, 06:47
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
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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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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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Math Expert
Joined: 02 Aug 2009
Posts: 5776
Re: a, b and c are positive integers. If b equals the square root of a, an [#permalink]

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04 Dec 2017, 07:05
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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?

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]

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12 Jan 2018, 07:12
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Expert's post
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?

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.

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

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