Fractions - MCAT Exam

[clarence.booth]

Hi,

I had trouble on some of the algebra for the following DS problem on a CAT Exam:

Wendy, Jim, and Pedro are golfing. Collectively, they have 24 golf balls. How many golf balls does Jim have?

(1) Jim has 1/5 of the number of golf balls that Wendy and Pedro have combined.

(2) Pedro and Wendy collectively have 5/6 of the golf balls.

Regarding statement (1), I did not understand why the explanation (below) stated we should multiply both equations by 5. What fundamental math concept am I missing?

(1) SUFFICIENT: Let j = the number of Jim's golf balls, w = the number of golf balls Wendy has, and p = the number of balls Pedro has. We start knowing that j + p + w = 24. Statement (1) tells us that j = 1/5( p + w). Multiplying both equations by 5, we get:

5 j + 5 p + 5 w = 120
5 j = p + w

Substituting, we get:

5 j + 5(5 j) = 120
30 j = 120

From this we know that Jim has 4 golf balls.

[RonPurewal]

Multiplying by 5 is just a way of avoiding the unpleasantness of dealing with fractions.

You could just as well work with the equations without multiplying them by 5. But then you'd have to deal with terms that are multiplied by 1/5.

[RobertS114]

I understand why you multiply the equation with the fraction by 5, but why multiply "j+p+w"? When I put in "j + 5j= 24", I get J = 4. Is this just a coincidence?

[RonPurewal]

oh, hmm, yeah, that's clearly unnecessary—and it makes the existing solution less efficient, too.
if that equation is left as j + p + w = 24, then 5j can be put directly in for (p + w).

getting "5j" on both sides would help if the objective were to eliminate "j", but, that's not the objective.
HMM.

i'll submit this for review/improvement, since your point is a good one.
thanks.

[AmyL562]

"Submitting something for review" must not do much, seeing as this post is from 6 years ago and the confusing explanation to the CAT exam question has yet to change.

[Whit Garner]

"Submitting something for review" must not do much, seeing as this post is from 6 years ago and the confusing explanation to the CAT exam question has yet to change.

Thank you so much for bringing this to our attention! This solution has been updated