DS problem - please help

[mArikIo]

I am having some problems with the follwing question and would really appreciate some help.


If all apples at a certain grocery store are equally priced, all all pears at the grocery store are equally priced, what is the price of a pear?

(1) Eight pears cost eighty cents more than eight apples
(2) Ten apples cost twenty cents more than eight pears

I think that it should be C), but I'm struggeling with the calculation. Please help.

[Brent@GMATPrepNow]

I am having some problems with the follwing question and would really appreciate some help.


If all apples at a certain grocery store are equally priced, all all pears at the grocery store are equally priced, what is the price of a pear?

(1) Eight pears cost eighty cents more than eight apples
(2) Ten apples cost twenty cents more than eight pears

Target question: What is the price of one pear?

Let P = price of 1 pear
Let A = price of 1 apple

We want to find the value of P.

Statement 1: Eight pears cost eighty cents more than eight apples
So, we can write: 8P - 8A = 80
Since we cannot solve this equation for P, statement 1 is NOT SUFFICIENT

Statement 2: Ten apples cost twenty cents more than eight pears
So, we can write: 10A - 8P = 20
Since we cannot solve this equation for P, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
We know that 8P - 8A = 80 and 10A - 8P = 20
Since we now have two different linear equations involving A and P, so we could solve this system for P, so the combined statements are SUFFICIENT

Answer = C

Aside: For those of you who wish to solve this system, take . . .
8P - 8A = 80
10A - 8P = 20

Rearrange the second equation . . .
8P - 8A = 80
-8P + 10A = 20

And add them to get 2A = 100, which means A = 50
If A = 50, then we know that P = 60 (just plug A = 50 into one of the equations and solve for P)


Cheers,
Brent

[mArikIo]

I had the same calculation but made a rookie mistake.

Thanks alot!

[Scott@TargetTestPrep]

I am having some problems with the follwing question and would really appreciate some help.


If all apples at a certain grocery store are equally priced, all all pears at the grocery store are equally priced, what is the price of a pear?

(1) Eight pears cost eighty cents more than eight apples
(2) Ten apples cost twenty cents more than eight pears

We are given that all apples are equally priced and all pears are equally priced, and we need to determine the price of a pear. We can let p = the cost of a pear in cents and a = the cost of an apple in cents.

Statement One Alone:

Eight pears cost eighty cents more than eight apples.

Using the information in statement one, we can create the following equation:

8p = 8a + 80

p = a + 10

While we know a pear costs 10 cents more than an apple, we cannot determine the value of p. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

Ten apples cost twenty cents more than eight pears.

Using the information in statement two, we can create the following equation:

10a = 8p + 20

5a = 4p + 10

While we know 5 apples cost 10 cents more than 4 pears, we cannot determine the value of p. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

Using statements one and two, we know that p = a + 10, or p - 10 = a, and that 5a = 4p + 10. If we substitute (p - 10) for a in the equation 5a = 4p + 10, we have:

5(p- 10) = 4p + 10

5p - 50 = 4p + 10

p = 60

Answer: C