CR Example 6 page 110 : Military Alumni

[Kishore]

With reference to Chapter 5 in CR verbal guide question named Military alumni (Example 6 page 110):
I am of the feeling that C can also be logically concluded.

Say Judd has a total of J people in the military across army, navy and airforce; let Knoxworth has K people in military. Given J<K
Let X people out of J be working in airforce from Judd; Let Y out of K people be working for airforce in Knoxworth. Given X>Y

So % of Judd working in airforce is 100X/J; % of Knoxworth alumni working in airforce is 100Y/K

clearly X/J > Y/K
therefore Judd academy has a higher percentage of alumni working in the airforce than Knoxworth does.

Hence C could also be a correct choice.

Don't you all agree

[StaceyKoprince]

Please post the full text of the question. We do not always have our books available while we answer questions. Thanks!

[Kishore]

Question

Of all the high schools in the United States, Judd Academy is the one with the largest number of alumni serving in the Air Force. Knoxworth High Scholl, however, is the school with the most graduates serving in the military as a whole, including the Army, Navy, Air Force, Marines, and Coast Guard.

Which of the following if true, is most clearly supported by the statements above?

(A) Knoxworth is the most patriotic town in the nation.
(B) Judd Academy has fewer graduates serving in the Navy than does Knoxworth high school.
(C) Judd Academy has a higher percentage of alumni serving in the Air Force than does Knoxworth high school.
(D) Some graduates of Knoxworth high school are serving in the military but not in the Air Force.
(E) Knoxworth high school is the school with the second-highest number of alumni serving in the Air Force.

Correct Answer as provided in the booklet: D

I feel that C could also be right because:
Say Judd has a total of J people in the military across army, navy, airforce, .....; let Knoxworth has K people in military. Given J<K
Let X people out of J be working in airforce from Judd; Let Y out of K people be working for airforce in Knoxworth. Given X>Y

So % of Judd working in airforce is 100X/J; % of Knoxworth alumni working in airforce is 100Y/K

clearly X/J > Y/K
therefore Judd academy has a higher percentage of alumni working in the airforce than Knoxworth does.

Hence C could also be a correct choice.

Don't you all agree

[Guest]

Hi,

I tend to agree with Kishore's reasoning. Choice C can also be correct, unless one assumes that total alumni for each school = military and non-military alumni (in which case it can be proven that Choice C is incorrect). Can someone please clarify?

Thanks,
Guest

[RonPurewal]

Say Judd has a total of J people in the military across army, navy, airforce, .....; let Knoxworth has K people in military. Given J<K
Let X people out of J be working in airforce from Judd; Let Y out of K people be working for airforce in Knoxworth. Given X>Y

So % of Judd working in airforce is 100X/J; % of Knoxworth alumni working in airforce is 100Y/K

there's the problem.

statement c says 'percentage of alumni', but you are misinterpreting that phrase as meaning 'percentage of military alumni'. that's bad.

if you want variables - the fractions you want are actually 100x/a and 100y/b, where a and b are the total #s of alumni (whether military or not) from judd and knoxworth, respectively. we have no information about a and b, and thus no grounds for deciding the truth of statement c.

capisce?