Data Sufficiency

From GMAT Prep: Data sufficiency

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

1. Linda packed 30 percent of the total number of boxes of books
2. Robert packed 10 more boxes of books than Pat did.

--> I get that both are not sufficient on their own. But I thought I could play around with both to come up with a ratio for R to P.

Explanations greatly appreciated!

1 is obviously not sufficient since it speaks about linda
2 .says R = P+10
not sufficient cant get R/p
combine them
since linda packed 30 percent therefore r and P packed
70 percent ..let total no be x
R + P = .7x
from statement 2
p+10 + P = .7x
cant still find P and hence cant find r
E

san2009 wrote:WHY couldn't we pick a smart number, say 100 for the total number of boxes and just work with that??

If u wish to pick a number and then proceed, u will certainly get ratio of R over P. But will that ratio be consistent??

Always see to that you get a consistent answer be it a YES or a strong NO .In this case ratio will vary as total number of boxes vary. So you cant select C.

san2009 wrote:WHY couldn't we pick a smart number, say 100 for the total number of boxes and just work with that??

You could; but when you pick numbers in DS, you have to make sure that picking different numbers gives you the same answer to the question.

In this case, if you pick b=100, then:

Linda packs 30
R + P = 70
R - P = 10

R = 40; P = 30
R:P = 4:3

However, if we pick b = 50, then:

Linda packs 30
R + P = 20
R - P = 10

R = 15; P = 5
R:P = 3:1

So, picking numbers is a great approach, because it shows us that the information given is not sufficient to answer the question.

Let me rephrase/fine-tune my query.
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

san2009 wrote:Let me rephrase/fine-tune my query.
Because in the exam, one may quickly assume

Here's a huge tip for DS: never assume anything.

In Data Sufficiency, we only know what we're explicitly told. Every time you make an assumption about a situation, you're running the risk of falling for a trap.

If you haven't done so recently, I advise looking at the DS directions at the front of the Official Guide (page 24 of the 12th edition), so you can see what you can and can't take for granted.

Great, thank you. That is helpful.

Hi,

I have two questions regarding the above:

1) P+10/P is not a ratio?

2)How about if the second statement says that "Robert packed 10 times more boxed than Pat did", then the equation is: 10p/p, and this would make a ratio and thus is sufficient.

Am I right? Thank you!

Thouraya wrote:Hi,

I have two questions regarding the above:

1) P+10/P is not a ratio?

2)How about if the second statement says that "Robert packed 10 times more boxed than Pat did", then the equation is: 10p/p, and this would make a ratio and thus is sufficient.

Am I right? Thank you!

Hi,

(P+10)/P is a ratio, but it's not a constant ratio; in other words, the value of the ratio changes dependent on the value of P.

You're dead on for (2)!

Hi @Stuart,

Can you please elaborate further on your reply above? I'm not sure I understand what you mean, thanks!:)

Thouraya wrote:Hi @Stuart,

Can you please elaborate further on your reply above? I'm not sure I understand what you mean, thanks!:)

Sure!

When we say that two items are in a constant ratio, we mean that one is a multiplier of the other. For example, if:

x/y = 2/3

we can also express the relationship as:

3x = 2y

by cross multiplying by the denominators.

However, if we don't have a simple "x/y" on the left side, we won't be dealing with simple multipliers. For example, if our original ratio had been:

(x+3)/(y-4) = 2/3

Then when we cross multiply we get:

3x + 9 = 2y - 8

and even if we gather the numbers on the same side, we have:

3x - 1 = 2y

Since there's a "-1" term, there's no constant ratio between x and y.

We can see that this is true by plugging in numbers.

If x=1, we get:

3 - 1 = 2y
2 = 2y
1=y

So when x=1, y=x

However, when x=2, we get:

6 - 1 = 2y
5 = 2y
5/2 = y

So, when x=2, y no longer equals x.

Similarly, in the example posted above:

(P+10)/P

when P = 1, the ratio is 11/1
when P = 2, the ratio is 12/2 = 6/1

Since varying the value of P changes the ratio, it's not a constant ratio.