Another !$#&!! MATH question

[airvent]

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😡 In a barrel there are 60 pints of a solution that is 20% alcohol. How many pints of pure alcohol must be added to produce a solution that is 40% alcohol?

A)12
B)20
c)24
d)35
E)50

This is from the Kaplan midterm. Answer is 20

 

[airvent]

Other than trying each answer. is there a method?

 

[rocknightmare]

(12+x)/(x+60)=.4

x=20

 

[coodoo]

😡 In a barrel there are 60 pints of a solution that is 20% alcohol. How many pints of pure alcohol must be added to produce a solution that is 40% alcohol?

A)12
B)20
c)24
d)35
E)50

This is from the Kaplan midterm. Answer is 20

yeah, 20% = 1/5

1/5*60=12, so 12 pints of alcohol in the original comprising the 20%

(12+x)/(60+x) *100 = 40 % or (12+x)/(60+x)=.40

now solve for x -- first cross multiply, you get

.4x+24 = 12+x

.6x = 12

12/.6 = 20 pints

 

[CJMPre-Med]

yeah, 20% = 1/5

1/5*60=12, so 12 pints of alcohol in the original comprising the 20%

(12+x)/(60+x) *100 = 40 % or (12+x)/(60+x)=.40

now solve for x -- first cross multiply, you get

.4x+24 = 12+x

.6x = 12

12/.6 = 20 pints

👍

 

[coodoo]

👍

ty, but rocky beat me to the punch. DAMN YOU ROCK, DAMN YOU!

 

[rocknightmare]

you wrote it more professionally.. i was trying to figure out the answer myself had to think for a min... still dont' ahve my alegbra hat on for this damn dat

 

[airvent]

First off, thank you everyone who helped. That was actually easy now that i see it. All the problems i have are not seeing the easy solution.

Anyway here is another:

A triangle has internal angles in the ratio 2 : 6 : 7. What is the differences (in degrees) between the smallest and largest angles?

A) 24
B) 48
C) 60
D) 72
E) 84

Answer: C) 60

 

[CJMPre-Med]

First off, thank you everyone who helped. That was actually easy now that i see it. All the problems i have are not seeing the easy solution.

Anyway here is another:

A triangle has internal angles in the ratio 2 : 6 : 7. What is the differences (in degrees) between the smallest and largest angles?

A) 24
B) 48
C) 60
D) 72
E) 84

Answer: C) 60

The sum of the interior angles of any triangle must be 180 degrees. So you simply set 2x+6x+7x = 180, and solve like so:

2x + 6x + 7x = 180
15x = 180
(180/15) = x = 12 degrees

So the smallest angle was 2x = 24 degrees, and the largest was 7x = 84 degrees.

84 - 24 = 60 degrees, which is choice C. 🙂

 

[1FutureDDS]

If you go down to your local bookstore and buy the Kaplan GRE book for about 18$, it has full length explanations to all of these questions (or atleast everything from the diagnostic) along with much more detail.

 

[coodoo]

The sum of the interior angles of any triangle must be 180 degrees. So you simply set 2x+6x+7x = 180, and solve like so:

2x + 6x + 7x = 180
15x = 180
(180/15) = x = 12 degrees

So the smallest angle was 2x = 24 degrees, and the largest was 7x = 84 degrees.

84 - 24 = 60 degrees, which is choice C. 🙂

👍 😀