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Peter combines two different . . .

by Vincen » Fri Sep 15, 2017 7:16 pm
Peter combines two different types of trail mix, A and B, to make 400 ounces of his own mix, which includes 48 ounces of raisins. Trail mix A is 10% raisins by weight, and Trail mix B is 20% raisins by weight. How many ounces of trail mix A does Peter use to make his mix?

A) 80
B) 160
C) 240
D) 320
E) 360

The OA is D.

The calculus I did gave as the result 360. It seems I did something wrong. Experts, please help me.
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by Jay@ManhattanReview » Tue Sep 19, 2017 12:02 am
Vincen wrote:Peter combines two different types of trail mix, A and B, to make 400 ounces of his own mix, which includes 48 ounces of raisins. Trail mix A is 10% raisins by weight, and Trail mix B is 20% raisins by weight. How many ounces of trail mix A does Peter use to make his mix?

A) 80
B) 160
C) 240
D) 320
E) 360

The OA is D.

The calculus I did gave as the result 360. It seems I did something wrong. Experts, please help me.
Say the weight of trail mix A = a, and the weight of trail mix B = b

Thus, we have a + b = 400 ---(1)

Also, the weight of raising by mix A = 10% of a = a/10; and
the weight of raising by mix B = 20% of b = b/5

Thus, a/10 + b/5 = 48

a + 2b = 480---(2)

Upon solving (1) and (2), we get a = 320 ounces.

The correct answer: D

Hope this helps!

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by Jeff@TargetTestPrep » Fri Dec 22, 2017 10:40 am
Vincen wrote:Peter combines two different types of trail mix, A and B, to make 400 ounces of his own mix, which includes 48 ounces of raisins. Trail mix A is 10% raisins by weight, and Trail mix B is 20% raisins by weight. How many ounces of trail mix A does Peter use to make his mix?

A) 80
B) 160
C) 240
D) 320
E) 360
We can let a = the amount of trail mix A and b = the amount of trail mix B. We have two equations:

a + b = 400

b = 400 - a

and

0.1a + 0.2b = 48

a + 2b = 480

Substituting b = 400 - a in a + 2b = 480, we have:

a + 2(400 - a) = 480

a + 800 - 2a = 480

320 = a

Answer: D

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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by [email protected] » Fri Dec 22, 2017 11:50 am
Hi Vincen,

We're told that Peter combines two different types of trail mix, A and B, to make 400 ounces of his own mix, which includes 48 ounces of raisins. Trail mix A is 10% raisins by weight, and Trail mix B is 20% raisins by weight. We're asked for the number of ounces of trail mix A Peter uses to make his mix. This question can be approached in a number of ways; here's how you can solve it with some basic arithmetic and TESTing THE ANSWERS:

To start, we need to know what PERCENTAGE of the overall mixture is raisins. 48/400 = 24/200 = 12/100 = 12%. Since Mix A is 10% raisins and Mix B is 20% raisins, we will clearly have a LOT MORE of Mix A than Mix B (If we had an equal amount of each, then the overall mixture would be (10+20)/2 = 15% raisins). Thus, the correct answer must be a LOT GREATER than 200.

Let's TEST Answer D: 320 ounces of Mix A... meaning that there would also be 80 ounces of Mix B

Mix A: (.1)(320) = 32 ounces of raisins
Mix B: (.2)(80) = 16 hours of raisins
Total raisins = 32 + 16 = 48 ounces
This is an exact MATCH for what we were told, so this MUST be the answer!

Final Answer: D

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