Linda and the BOXEs

[GMAT PREP 2]

Linda, Robert and Pat packed a certain number of boxes with books. What is the ration of the number of boxes of books that Robert packed to the number of boxes of books that PAt packed?

1 Linda packed 30% of all the boxes
2 Robert packed 10 boxes more than Pat.

Thanks!!

Ruben

[StaceyKoprince]

First, I assume that "ration" is supposed to read "ratio"? :) Also, is this definitely a GMATPrep problem? I would have expected them to say that there were no partial boxes packed or something like that - I guess it doesn't really matter. Just surprising.

A ratio tells us the relative amounts of something but not the absolute amounts. Since they're asking for a ratio, we only need to know how much Robert packs relative to Pat - we don't necessarily need to know their exact, actual amounts. The ratio, however must be constant - that is, I have to find one definitive ratio.

Statement 1 tells us that Linda packed 30% relative to the others. The others, therefore, combined to pack 70%. This doesn't let us know what Robert packed relative to Pat, though. Not sufficient; eliminate A and D.

Statement 2 tells us that Robert packed 10 boxes more than Pat. This tells us a relative amount but is not sufficient to calculate a single, constant ratio. For example, Robert could have packed 20 to Pat's 10, for a ratio of 20:10 or 2:1. Or Robert could have packed 30 to Pat's 20, for a ratio of 30:20, or 3:2. Those are different ratios, so not sufficient. Eliminate B.

Combining the statements: If the boxes total 100, then according to the first statement, L packed 30 and R+P packed 70. The second statement means that R packed 40 and P packed 30, for a ratio of 40:30 or 4:3. If the boxes total 20, then L packed 4 and R+P packed 16. In this case, R packed 13 and P packed 3, for a ratio of 13:3, which can't be simplified. Those are different ratios, so not sufficient. Eliminate C. (Note: you can pick any numbers you want to test this, so use numbers that are easy for you.)

Answer is E.

[hardwick1010]

If the boxes total 20, then L packed 4 and R+P packed 16. In this case, R packed 13 and P packed 3, for a ratio of 13:3, which can't be simplified

Wouldn't 30% of 20 be 6, leaving 14 to be packed by R and P? Just to clarify...

[RonPurewal]

If the boxes total 20, then L packed 4 and R+P packed 16. In this case, R packed 13 and P packed 3, for a ratio of 13:3, which can't be simplified

Wouldn't 30% of 20 be 6, leaving 14 to be packed by R and P? Just to clarify...

heh, yes. looks good.

of course, this doesn't affect the fact that the answer to the problem is (e). but, good eyes.

[sudaif]

How do we know when we can pick smart numbers, and when we can't? Because in the exam, one may quickly assume 100 to be the total, in which case statements 1 and 2 would be sufficient. Without realizing that if you picked a different total you would have a different ratio, one would move on. Thanks

[RonPurewal]

How do we know when we can pick smart numbers, and when we can't? Because in the exam, one may quickly assume 100 to be the total, in which case statements 1 and 2 would be sufficient. Without realizing that if you picked a different total you would have a different ratio, one would move on. Thanks

"smart numbers" is absolutely not a technique that should be used for data sufficiency!

the "smart numbers" technique is meant to be used on problem-solving questions -- i.e., questions on which "sufficiency" and "what we know and what we don't know" are NOT issues. if you pick smart numbers on problem solving, you are basically converting a variable into a hard number, with the advance knowledge that the problem must work out the same way if you do so. that is the essence of problem solving.

on the other hand, the essence of data sufficiency is that you have to determine exactly what you do and don't know!
this is precisely what data sufficiency is all about: in general, you will know some of the information, but you will not know other information. the issue is whether the information that you DO know is sufficient to answer the problem.
therefore, if you mistakenly apply the "smart numbers" techniques to data sufficiency -- i.e., cavalierly picking hard values for quantities that are actually unknown -- you should not be surprised if you conclude that statements are sufficient when in fact they are not.

[sudaif]

Ron:
On that note....if I'm trying to figure out on a DS question if I have enough information to solve for the "average speed over the entire trip"...and one of the statements tells me that the distance travel back and forth was the same...i should keep the distance as a variable, say "2d", and not plug in a number for it...even though the distance traveled in essence is fixed? I can't remember where I saw this question, but it was on one of the GMAT tests....thus the abstract rephrasing above.

[RonPurewal]

Ron:
On that note....if I'm trying to figure out on a DS question if I have enough information to solve for the "average speed over the entire trip"...and one of the statements tells me that the distance travel back and forth was the same...i should keep the distance as a variable, say "2d", and not plug in a number for it...even though the distance traveled in essence is fixed? I can't remember where I saw this question, but it was on one of the GMAT tests....thus the abstract rephrasing above.

in this sort of instance, picking any SINGLE number is an incredibly bad idea -- if the statement turns out to be insufficient, you'll never find out (because your single chosen number will always yield some single answer).

so, in response to your question, there are two things that you can do in such a situation:
(1) as you've stated, stick with a variable, and see if you can get the algebra to work out.
(2) pick MULTIPLE numbers and plug them into the same quantity, one at a time. if all of these numbers yield the same numerical result, then you can place fairly confident bet on "sufficient". if, at any point, any two of them yield different numerical results, then you're done and the statement is definitely insufficient.

[jp.jprasanna]

First, I assume that "ration" is supposed to read "ratio"? :) Also, is this definitely a GMATPrep problem? I would have expected them to say that there were no partial boxes packed or something like that - I guess it doesn't really matter. Just surprising.

A ratio tells us the relative amounts of something but not the absolute amounts. Since they're asking for a ratio, we only need to know how much Robert packs relative to Pat - we don't necessarily need to know their exact, actual amounts. The ratio, however must be constant - that is, I have to find one definitive ratio.

Statement 1 tells us that Linda packed 30% relative to the others. The others, therefore, combined to pack 70%. This doesn't let us know what Robert packed relative to Pat, though. Not sufficient; eliminate A and D.

Statement 2 tells us that Robert packed 10 boxes more than Pat. This tells us a relative amount but is not sufficient to calculate a single, constant ratio. For example, Robert could have packed 20 to Pat's 10, for a ratio of 20:10 or 2:1. Or Robert could have packed 30 to Pat's 20, for a ratio of 30:20, or 3:2. Those are different ratios, so not sufficient. Eliminate B.

Combining the statements: If the boxes total 100, then according to the first statement, L packed 30 and R+P packed 70. The second statement means that R packed 40 and P packed 30, for a ratio of 40:30 or 4:3. If the boxes total 20, then L packed 4 and R+P packed 16. In this case, R packed 13 and P packed 3, for a ratio of 13:3, which can't be simplified. Those are different ratios, so not sufficient. Eliminate C. (Note: you can pick any numbers you want to test this, so use numbers that are easy for you.)

Answer is E.

Hi Isnt the question asking abt the ratio of books packed by R and P and not boxes

"What is the ration of the number of books that Robert packed to the number of books that PAt packed? "

Since both the statements are talking about boxes they packed so it is a direct E right?

[RonPurewal]

jp, good eyes -- actually, the original problem was transcribed incorrectly. i've gone back and fixed it.