A grocery store sells two varieties of jellybean jars ...

[Blackbox]

Hello experts,

I am stuck on a MGMAT homework problem (Q10 in Extra FDPs pg 72 (pg number is online resource, not paper back)). Below is how I approached to solve:

Q. A grocery store sells two varieties of jellybean jars, and each type of jellybean jar contains only red and yellow beans. If jar B contains 20% more Red jellybeans than Jar A, but 10% fewer yellow jellybeans, and Jar A contains twice as many red jellybeans as yellow jellybeans, by what percent is the number of jellybeans in Jar B larger than the number of jellybeans in Jar A?

Given,
Yellow beans(Jar A), henceforth Y(A) = y
Red Beans(Jar A), henceforth R(A) = 2y
Total Jar(A)= 3y

Yellow beans (Jar B), henceforth Y(B) = 90%y
Red beans (Jar B), henceforth R(B) = 240%y
Total Jar(B)=330%y

Asking
Total Jar(B)/Total Jar(A) = ?

Therefore,
Total Jar(B)/Total Jar(A) = (330y/100)/3y = 110/100 = 110%

Apparently, my answer is incorrect. The OA is 10%. Can someone explain where I went wrong, please?

[jnelson0612]

Whenever I see all percents with no real numbers, my first thought is to make up some numbers that fit the problem and solve. Let's try it!

Let's have Jar A contain 20 red and 10 yellow for a total of 30.

Since Jar B contains 20% more red but 10% less yellow than Jar A, Jar B contains 24 red and 9 yellow for a total of 33.

The question: by what percent is the number of jellybeans in Jar B larger than the number of jellybeans in Jar A? Percent greater is difference over the smaller amount, or 3/30 = 10%. Way easier! :-)

By the way, all your math was right until the end. If A has 3y and B has 3.3y, the percent GREATER is .3y/3y or 10%. You have solved that B is 110% of A, which it is, but it is 10% GREATER than A. You just answered the wrong question. :-)

[Blackbox]

Percent greater is difference over the smaller amount

Aha! That ... I did not know. So, whenever the question asks for percent larger/greater, I will remember to take the difference over the other number in question.

Can I assume, for percent lesser, I could total the two?

Thanks!
Jay
p.s: Also, may I know why this concept - percent greater means the difference of the values over the other number in question has not been discussed in the strategy guide? Am I missing something?

[jnelson0612]

Percent greater is difference over the smaller amount

Aha! That ... I did not know. So, whenever the question asks for percent larger/greater, I will remember to take the difference over the other number in question.

Can I assume, for percent lesser, I could total the two?

Thanks!
Jay
p.s: Also, may I know why this concept - percent greater means the difference of the values over the other number in question has not been discussed in the strategy guide? Am I missing something?

Hey Jay,
Just remember this:
percent greater=difference/smaller amount
percent less=difference/larger amount

percent change=difference/original amount

Let me know if there's anything else that you need to know!

[Blackbox]

Hey Jay,
Just remember this:
percent greater=difference/smaller amount
percent less=difference/larger amount

percent change=difference/original amount

Let me know if there's anything else that you need to know!

Thank you, Jnelson! Those tips are awesome!

[RonPurewal]

you can also just invoke real-life situations, in which you'll be much more likely to have the correct instincts.

e.g.,
i weigh 200 pounds. my cousin weighs 220 pounds.
my cousin's weight is what percent greater than mine?

i very strongly doubt that you're tempted to answer "110%" to this problem; even if you were, common sense would stop you in your tracks.

you should try to import those instincts into the test. when you're doing "academic" tasks, there's a strong tendency to just start shuttling meaningless symbols around a page. try not to let yourself get to that point.

[Blackbox]

you can also just invoke real-life situations, in which you'll be much more likely to have the correct instincts.

e.g.,
i weigh 200 pounds. my cousin weighs 220 pounds.
my cousin's weight is what percent greater than mine?

i very strongly doubt that you're tempted to answer "110%" to this problem; even if you were, common sense would stop you in your tracks.

you should try to import those instincts into the test. when you're doing "academic" tasks, there's a strong tendency to just start shuttling meaningless symbols around a page. try not to let yourself get to that point.

Great explanation and I agree. Thank you for all the wonderful work you guys are doing.

[RonPurewal]

sure.

remember, the language of the problems will always mean exactly what it means in The Big Bad Real World.

if these problems were written so that only specialists could understand them, the test would be unfair.