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Bunuel
If the ratio of undergraduate students to graduate students is 7 to 4 and the ratio of graduate students to professors is 2 to 1, which could be the total number of undergraduate students, graduate students, and professors?

I. 520
II. 640
III. 2,600

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


Given: the ratio of undergraduate students(U) to graduate students(G) is 7 to 4 and the ratio of graduate students to professors(P) is 2 to 1
U:G:P = 7:4:2
Asked: Which could be the total number of undergraduate students, graduate students, and professors?

Let U, G & P be 7x, 4x & 2x respectively
total number of undergraduate students, graduate students, and professors = 7x+4x+2x = 13x

I. 520
=13*40 => x =40


II. 640
is not a multiple of 13 => Can not be expressed as 13x


III. 2,600
= 13*200 => x=200


IMO D
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ratio of undergraduate students to graduate students = 7x/4x
ratio of graduate students to professor = 2x/x , lets multiply this to 2 so that graduate student becomes 4x
total = 7x+4x+2x =13x
Hence total has to be a multiple of 13. Only 1st and 3rd satisfy this. so IMO D
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Solution


Given:
    • The ratio of undergraduate students to graduate students is 7 to 4, and
    • The ratio of graduate students to professors is 2 to 1

To find:
    • What could be the total number of undergraduate students, graduate students, and professors?

Approach and Working Out:
We are given that the ratio of undergraduate students to graduate students is 7 to 4
    • Implies, if the number of undergraduate students = 7x, then
    • The number of graduate students = 4x

We are also given that the ratio of graduate students to professors is 2 to 1
    • Since, we know that the number of graduate students = 4x
    • The number of professors will be 2x

So, the total number of students and professors = 7x + 4x + 2x = 13x
    • And we know that the total number of undergraduate students, graduate students, and professors must be an integer

Thus, the answer 13x must be a multiple of 13
    • 520 and 2600 are the multiples of 13 among the given options.

Hence, the correct answer is Option D.

Answer: D

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