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

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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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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]
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]
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.

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