Problem Solving

A breakfast that consists of 1 ounce of corn puffs and 8 ounces of fruit X provides 257 calories. When 8 ounces of fruit Y is substituted for the 8 ounces of fruit X, the total number of calories is reduced to 185. If fruit X provides 1.8 times as many calories as fruit Y, how many calories does 8 ounces of fruit Y alone provide ?
(A) 11.25
(B) 72
(C) 90
(D) 95
(E) 129.6

OA is C

I don't understan how OA is C ?

1C + 8(1.8y) = 257

1C + 8y = 185

Subtracting 2 from 1 we get y = 11.25 (A)

when you replace fruit x with fruit y, you go from 257 calories to 185, or a difference of 72. That means X - Y = 72. You could think about this way: you know that with fruit X you have 257 calories, but when you take it away (subtract X) and add fruit Y (add Y), then you have 72 calories less:

-X + Y = -72, rearranging you get X - Y = 72.

You also know that X = 1.8Y, so plug it in:

X - Y = 72
1.8Y - Y = 72
0.8Y = 72
Y = 90

Choice C.

mp2437 wrote:when you replace fruit x with fruit y, you go from 257 calories to 185, or a difference of 72. That means X - Y = 72. You could think about this way: you know that with fruit X you have 257 calories, but when you take it away (subtract X) and add fruit Y (add Y), then you have 72 calories less:

-X + Y = -72, rearranging you get X - Y = 72.

You also know that X = 1.8Y, so plug it in:

X - Y = 72
1.8Y - Y = 72
0.8Y = 72
Y = 90

Choice C.

I can't comprehend your solution, although I understand it. In the test i will do what I just did, because I don't understand the difference between the two ways.

heshamelaziry wrote:

mp2437 wrote:when you replace fruit x with fruit y, you go from 257 calories to 185, or a difference of 72. That means X - Y = 72. You could think about this way: you know that with fruit X you have 257 calories, but when you take it away (subtract X) and add fruit Y (add Y), then you have 72 calories less:

-X + Y = -72, rearranging you get X - Y = 72.

You also know that X = 1.8Y, so plug it in:

X - Y = 72
1.8Y - Y = 72
0.8Y = 72
Y = 90

Choice C.

I can't comprehend your solution, although I understand it. In the test i will do what I just did, because I don't understand the difference between the two ways.

You are solving for y. which turns out to be 11.25/ The problem asks you to answer how many calories there are in 8 oz of y. which would be 8*y. In this case 11.25*8=90. So both solutions are applicable. One is just faster than another.

Firstly, The question is wrongly typed. Also, MG368, please use Spoilers like this for OA. [spoiler]OA:C[/spoiler]. Corrected question below.

MG368 wrote:A breakfast that consists of 1 ounce of corn puffs and 8 ounces of fruit X provides 257 calories. When 8 ounces of fruit X is substituted for the 8 ounces of fruit Y, the total number of calories is reduced to 185. If fruit X provides 1.8 times as many calories as fruit Y, how many calories does 8 ounces of fruit Y alone provide ?
(A) 11.25
(B) 72
(C) 90
(D) 95
(E) 129.6

OA is C

From the question these are the equations:
p + 8x = 257 -- (1)
p + 8y = 185 -- (2)
x = 1.8 y. -- (3)

What's the question? Find 8y. (Not y)
Replace equation 3 in equation 1 and subtract equation 1 - equation 2.
You will get,
8(1.8y) - 8y = 72.
=> 8y (1.8 - 1) = 72
=> 8y = 72/0.8
=> 8y = 90.
Which is the answer.

heshamelaziry wrote:I don't understan how OA is C ?

1C + 8(1.8y) = 257

1C + 8y = 185

Subtracting 2 from 1 we get y = 11.25 (A)

As pointed out in another post, your mistake is that you didn't read the question carefully enough - up until that point your math was great.

You let y = the number of calories in 1 ounce of fruit y. Since the question asks for the number of calories in 8 ounces of y, you need to multiply your result by 8.

It's not even slightly surprising that your calculated result was among the choices. One of the most common traps on the GMAT is to provide answer choices that are interim calculations in arriving at the final solution, especially on more complex questions.

Here are some examples:

Question asks: how long does it take x and y to paint 2 rooms?
Trap answer: how long it takes them to paint 1 room.

Question asks: how much money does Bob have left?
Trap answer: how much money Bob spent.

Question asks: what's the revenue from the sale of 2 donuts and 3 cups of coffee?
Trap answer: revenue from the sale of 1 donut.
Trap answer: revenue from the sale of 1 cup of coffee.
Trap answer: revenue from the sale of 2 donuts.
Trap answer: revenue from the sale of 3 cups of coffee.

So, what's the key to happiness? It's:

Step 4 of the Kaplan Method for PS: after doing all your calculations, always double check the question.