A breakfast that consists of 1 ounce of corn puffs

[amontobin]

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

What's the setup for a question like this?

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Hi amontobin,

This is a 3-variable "system" question and can be approached in a couple of different ways. Here's how you can use 'system algebra' to get to the solution. First, we have to translate the prompt into three equations:

1) "1 ounce of corn puffs and 8 ounces of fruit X provides 257 calories" .... C + 8X = 257
2) "8 ounces of fruit Y is substituted...the total number of calories is reduced to 185." ... C + 8Y = 185
3) "fruit X provides 1.8 times as many calories as fruit Y" ... X = 1.8Y

With 3 variables and 3 equations, you can now solve. Note that the question asks for the 'value' of 8Y.

We can start by subtracting the second equation from the first:

(C + 8X = 257) - (C + 8Y = 185) =
8X - 8Y = 72
X - Y = 9

Next, we can substitute in 1.8Y for X...

(1.8Y) - Y = 9
.8Y = 9

Since the question asks for the value of 8Y, we can multiply everything by 10....
8Y = 90

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

[Jay@ManhattanReview]

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
What's the setup for a question like this?

Since fruit X provides 1.8 times as many calories as fruit Y, we have X = 1.8Y; where X = number of calories fruit X provides and Y = number of calories fruit Y provides

=> Y = X/1.8. If we get the value of X, we get the value of Y.

We know that 1 ounce of corn puffs and 8 ounces of fruit X provides 257 calories, thus,

C + 8X = 257 ---(1)

We also know that 1 ounce of corn puffs and 8 ounces of fruit Y provides 185 calories, thus,

C + 8Y = 185 ---(2)

From (1) and (2), we get 8(X-Y) = 72

Thus, 8(1.8Y - Y) = 72

8*0.8Y = 72

8Y = 72/0.8 = 90 calories

The correct answer: C

Hope this helps!

-Jay
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[Matt@VeritasPrep]

I'd put it in words first before assigning variables. This makes it easier to follow your work in case you end up confusing yourself.

1 oz of corn + 8 ounces of X = 257
1 oz of corn + 8 ounces of Y = 185

If we subtract the second equation from the first, we get

8 ounces of X - 8 ounces of Y = 257 - 185 = 72

so

8X - 8Y = 72

X - Y = 9

Now we can add the last equation, X = 1.8Y. Substituting 1.8Y for X in the subtraction equation just above, we get

1.8Y - Y = 9

.8Y = 9

8Y = 90

All set!

[Scott@TargetTestPrep]

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

What's the setup for a question like this?

We see that 8 ounces of fruit X has 257 - 185 = 72 calories more than 8 ounces of fruit Y. Since fruit X provides 1.8 times as many calories as fruit Y, we can create the equations:

X = Y + 72

and

X = 1.8Y

Therefore, we have:

Y + 72 = 1.8Y

72 = 0.8Y

90 = Y

Answer: C