p^2 = 28r
p= +- 2 * \(\sqrt{(7r)}\)

Of the values given in the options, p will be an integer only if r = 7

Ans:D

Ans: D

Solution: for p to be an int 28 r must be whole square of a number.
28r= 7*2*2*r
to make it whole square we need 7
so r can must be divisible by 7y where y is itself a whole square.
so D is the ans
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If p and r are integers, and p^2 = 28r, then r must be divisible by which of the following?

28 has 2 twos and 1 seven. That means r must contain a 7 for 28r to be divisible by p

Answer: D) 7

28r is a square number
2^2*7r is a square number
Therefore, r has to be 7.
7 is divisible by 1 as well as 7
Therefore, the correct option is D

P^2=28r and 28=2^2*7
Therefore, since p^2 is a square, r needs to have a 7.
Answer D

Economist GMAT Tutor Official Solution:

First, we want to know for what, precisely, the question asks. This is a “must be” question. We can see that there are lots of possible values for p and r, but we are asked to find the factor (from among the answer choices) that must be present regardless of our choice of p or r.

So, what information is available to help us solve this problem?

(1) p and r are integers
(2) p^2=28r

From (1), we know that p^2 is a perfect square, and by extension, we know that 28r is a perfect square.

What do we know about perfect squares and their prime factors? Each must have a partner!

So, if we factor 28r, we get 2 • 2 • 7 • r. So, whatever other factors r contains, it must, at least, have the partner for 7. So, r must be divisible by 7.
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We are given that p^2 = 28r, which means that 28r is a perfect square. We must remember that all perfect squares break down to unique prime factors, each of which has an exponent that is a multiple of 2. So, let’s break down 28 into its prime factors to determine the minimum value of r.

28 = 7 x 4 = 7 x 2^2
In order to make 28r a perfect square, the smallest value of r is 7^1, so that 28r = x 3^1) = 2^2 x 7^2, which is a perfect square.

Answer: D
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p^2 = 28r
p*p= 28*r
by putting value from options into r and then finding a square.
by putting 7 we get value,
p*p= 28*7
p*p=196
since we know 196 is the square of 14 .
r is divisible by 7

p -> is the square of a number
which means that the power of every factor of p^2 must be even.
we have,
p^2=28*r
p^2= (2^2)*7*r
we see that 7 has an odd power and for p^2 = 28*r,
r must be a multiple of 7.
ans. D