Og 13 number 43 ratio

[hutch27]

If p1 and p2 are the populations and r1 and r2 are the numbers of representatives of district 1 and district 2, respectively, the ratio of the population to the number of representatives is greater for which of the two districts?

1) p1 > p2
2) r2>r1

I'm having trouble finding the sufficiency when both statements are combined

Oa is c

[Brent@GMATPrepNow]

If p1 and p2 are the populations and r1 and r2 are the numbers of representatives of district 1 and district 2, respectively, the ratio of the population to the number of representatives is greater for which of the two districts?

1) p1 > p2
2) r2>r1

Oa is c

Target question: The ratio of the population to the number of representatives is greater for which of the two districts?

This is a great candidate for rephrasing the target question.

Rephrased target question: Which is greater: p1/r1 or p2/r2 ?

Statement 1: p1 > p2
There are several sets of numbers that meet this condition. Here are two:
Case a: p1 = 3, r1 = 1, p2 = 2, r2 = 1, in which case p1/r1 > p2/r2
Case b: p1 = 3, r1 = 3, p2 = 2, r2 = 1, in which case p1/r1 < p2/r2
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: r2 > r1
There are several sets of numbers that meet this condition. Here are two:
Case a: p1 = 12, r1 = 2, p2 = 3, r2 = 3, in which case p1/r1 > p2/r2
Case b: p1 = 2, r1 = 2, p2 = 12, r2 = 3, in which case p1/r1 < p2/r2
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
Let's use big font to show that one value is bigger than another value.
So, from statement 1, we get p1 and p2
From statement 2, we get r2 and r1

Now which is bigger, p1/r1 or p2/r2?
We can see now that p1/r1 is definitely greater than p2/r2
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent

[GMATGuruNY]

If p1 and p2 are the populations and r1 and r2 are the numbers of representatives of district 1 and district 2, respectively, the ratio of the population to the number of representatives is greater for which of the two districts?

1) p1 > p2
2) r2>r1

I'm having trouble finding the sufficiency when both statements are combined

Oa is c

Is P1/R1 > P2/R2?

Since this problem is restricted to positive integers, the question stem can be rephrased:

Is (P1)(R2) > (P2)(R1)?

Statement 1: P1>P2
Without knowing the relationship between R2 and R1, no way to determine whether (P1)(R2) > (P2)(R1).

Statement 2: R2>R1
Without knowing the relationship between P1 and P2, no way to determine whether (P1)(R2) > (P2)(R1).

Statements 1 and 2 combined:
Since each value on the left side (P1 and R2) is greater than the corresponding value on the right side (P2 and R1), (P1)(R2) > (P2)(R1).
SUFFICIENT.

The correct answer is C.

[ceilidh.erickson]

When we're thinking about sufficiency, it's best to frame all DS questions as either yes/no or value questions. One of the trickiest things about this question is that it's not a yes/no question as it's written. Both of my fellow experts have put forth good solutions, but I just want to note a few things that students of mine have struggled with in this problem...

- If you have a non-yes/no question like "which one is greater?", just turn it into a yes/no. You could say "is the first one greater?" or "is the second one greater?" It doesn't matter which inequality you choose, because if you get a definitive answer, you can tell which one is greater.

- when it comes to ratios, it's always better to put things in fractional form than colon form. The ratio of p1 to r1 can be written as p1:r1, but that's not very helpful mathematically (a colon is not an operation). Writing it as p1/r1 is a lot more helpful.

From here, picking values or cross-multiplying and solving algebraically both work well.

[Scott@TargetTestPrep]

If p1 and p2 are the populations and r1 and r2 are the numbers of representatives of district 1 and district 2, respectively, the ratio of the population to the number of representatives is greater for which of the two districts?

1) p1 > p2
2) r2>r1

We are asked to determine which of the values, p1/r1 or p2/r2, is greater.

We can determine which value is greater in either one of the following scenarios:

i) If p1 > p2 and r1 < r2, then p1/r1 > p2/r2.

ii) If p2 > p1 and r2 < r1, then p2/r2 > p1/r1.

Statement One Alone:

p1 > p2

Since we don't know anything about r1 and r2, statement one alone is not sufficient.

Statement Two Alone:

r2 > r1

Since we don't know anything about p1 and p2, statement two alone is not sufficient.

Statements One and Two Together:

Since we know p1 > p2 and r1 < r2, we can see that p1/r1 is the greater ratio.

Answer: C