A full glass of juice is a mixture of 20% grape juice and 80% apple ju

Question

A full glass of juice is a mixture of 20% grape juice and 80% apple juice. The contents of the glass are poured into a pitcher that is 200 percent larger than the glass. The remainder of the pitcher is filled with 16 ounces of water. What was the original volume of grape juice in the mixture?

(A) 1.6 ounce
(B) 3.2 ounce
(C) 4.8 ounce
(D) 6.4 ounce
(E) 8 ounces

(A) 1.6 ounce 
(B) 3.2 ounce 
(C) 4.8 ounce
(D) 6.4 ounce
(E) 8 ounces

Tulkin987 · Answer

According to the constraints, the remainder, which is  16  ounces, is equal to the full glass.

Hence,  16*0.2=3.2

Answer: B

Hero8888 · Answer

Hi Tulkin,

It's a trap: 200% larger means x + 2x = 3x (3 times larger), so the remaining part is 2x = 16 oz, x = 8 oz. So the the original volume of grape juice = 0.2 * 8 oz=1.6 oz. Answer (A)

Tulkin987 · Answer

You are right. I mistakenly translated '200% larger'.
I should work more on concentration.

generis · Answer

To find the volume of grape juice in the original mixture, we need the volume of the glass (the volume of liquid in the glass).

Traps 
This question has two traps:

(1) "16 ounces" is relevant  only  to calculation of the volume of the glass.

The added water in the pitcher does not affect the original concentration (and hence volume) of grape juice in the glass because

(a) the volume of liquid that the pitcher can hold (200% more than the glass) tells us how much the glass can hold, and

(b) the volume of liquid that the glass can hold will yield the original volume of grape juice: 20% of whatever amount of liquid was in the glass

2) 200 percent more than*?

Analogize: 
--  10  percent more than A:  A = (1A + .10A)= 1.10A

-- The multiplier for 200 percent is 2
10 percent =  \frac{10}{100}=.10 
200 percent =  \frac{200}{100}=2

Solve 
• Find the volume of the glass in terms of the volume in the pitcher

Let  x  = the volume of the glass in ounces

The pitcher's volume is 200 percent more than  x :
Pitcher:  x + (2)(x) = 3x

• The equation depends on the 16-ounce volume difference

The pitcher can hold the amount in the glass plus 16 ounces of water
  + 16 oz = pitcher ounces, so

x + 16 = 3x 
 2x = 16 
 x = 8  ounces = volume of   the glass

• Volume of grape juice in the original mixture?
Volume of grape juice = 20% of the original liquid's total volume of 8 ounces:
    .20(8)=1.6   ounces

Answer A

Translation: 200 "percent   larger than  "   =   "percent   greater than  "   =   "percent   MORE THAN  "

JeffTargetTestPrep · Answer

Let’s let the capacity of the glass = n. Since the volume of the pitcher is 200% larger than that of the glass, we see that the volume of the pitcher is 3n. We can now create the equation:

n + 16 = 3n

16 = 2n

8 = n

Thus, there are 8 ounces of juice in the glass and since grape juice is 20% of it, grape juice is 8 x 0.2 = 1.6 ounces.

Alternate Solution:

The problem states that the pitcher needs 16 ounces of water to fill it, after the juice has been poured into it. Thus, 16 ounces is twice the capacity of the glass, so the capacity of the glass is 8 ounces. Since grape juice is 20% of the original juice in the glass, grape juice is 8 x 0.2 = 1.6 ounces.

Answer: A

RohitSaluja · Answer

Assume the size of the original glass be x, size of the new glass is 3x (as it is mentioned the new glass is 200% larger, which means 300% of the original).

Now it says when contents are transferred to new glass, remaining glass is filled by adding 16 ounces of water, thus we can write the equation as x + 16 = 3x => x = 8
Now we can find the amount of grape juice easily that would be 20% off 8 => 1.6

billionaire999 · Answer

Original glass
apple juice = 20/100 units

Pitcher volume = 200%(100) + 100 =300 units

200 units added are water, which is 16 ounces.

16 ounces = 200 units

20 units of apple juice = ?

cross multiply

(20x16)/200 = 1.6

answer A hope it helps

Eduardo86 · Answer

Can you check if my concept is right please?

Number strategy. Glass 10 lt of solution 8 lt apple and 2 lt grape.

Filled in a 200% larger backet. Pitcher volume 30 lt. Empty 20l. 2/3 of the pitcher are filled with 16 lt. 
2/3x= 16 
x=24

3y is 3 time the volume of the glass. 3y=24, y=8 
0.2 x 8= 1.6

jamiedimonn · Answer

Bunuel, please explain in a simpler way please

sujoykrdatta · Answer

Grape juice : Apple juice = 1 : 4
Total = 1 + 4 = 5
Capacity of larger pitcher = 3 * 5 = 15
Water in pitcher = 15 - 5 = 10

However, it is mentioned that this 10 is actually 16 => scale factor = 1.6
=> Grape juice = 1 * 1.6 = 1.6 ounces

Ans A

A full glass of juice is a mixture of 20% grape juice and 80% apple ju

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A full glass of juice is a mixture of 20% grape juice and 80% apple ju

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