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12 Days of Christmas GMAT Competition - Day 1: In a jar of 300 marbles

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Re: 12 Days of Christmas GMAT Competition - Day 1: In a jar of 300 marbles [#permalink]
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Given: In a jar of 300 marbles, 98% are red.
Asked: How many red marbles need to be removed to bring the percentage of red marbles down to 95%?

Total marbles = 300
Red marbles = 98%*300 = 294

Let x be number of red marbles to be reduced to bring the percentage of red marbles down to 95%
Total marbles = 300-x
Red marbles = 294 - x
% of red marbles = (294-x)/(300-x) = 95% = .95 = 19/20
6/(300-x) = 1/20
120 = 300 - x
x = 300 - 120 = 180

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Re: 12 Days of Christmas GMAT Competition - Day 1: In a jar of 300 marbles [#permalink]
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98% of 300 is 294 red marbles to begin with. If you subtract 180 from the original 294 you are left with 114 red marbles. You must also subtract 180 from the original total of 300 marbles so you now have 120 marbles in total. Taking the new amount of red marbles (114) and the new total amount of marbles (120) and dividing 114/120 yields 0.95 (multiply by 100 to get 95%).

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Re: 12 Days of Christmas GMAT Competition - Day 1: In a jar of 300 marbles [#permalink]
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Currently the % of red marble is 98% out of 300 marbles. → total red marble = 294 and non red marbles =6
After removing X marbles the % becomes 95%

(294-x)/(300-x)=95/100
29400-100x=28500-95x
900=5x
X= 180
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Re: 12 Days of Christmas GMAT Competition - Day 1: In a jar of 300 marbles [#permalink]
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Bunuel wrote:
12 Days of Christmas 🎅 GMAT Competition with Lots of Questions & Fun

In a jar of 300 marbles, 98% are red. How many red marbles need to be removed to bring the percentage of red marbles down to 95%?

A. 60
B. 120
C. 160
D. 180
E. 240

 This question was provided by GMAT Club for the 12 Days of Christmas Competition Win \$25,000 in prizes: Courses, Tests & more

We can backsolve as well...

Option D
98% of 300=294
300-180=120
294-180=114

New percentage= 114/120= 95%

IMO: D
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Re: 12 Days of Christmas GMAT Competition - Day 1: In a jar of 300 marbles [#permalink]
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Kudos
- If in the jar of 300 marbles, 98% are red => in the jar we have {98*300/100 red; 2*300/100 blue} = {294 red; 6 blue}
- So the question is, how many red marbles x should we remove to have 95% of red marbles in the jar.
After removing x red marbles the percentage of red marbles can be written like this:
(294-x/300-x ) =95/100 => (294-x)*100 = 95(300-x) => 29400-28500=5x => 5x=900 therefore x=180

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Re: 12 Days of Christmas GMAT Competition - Day 1: In a jar of 300 marbles [#permalink]
Options are not matching with my answer please correct me if i am wrong

Total marbles is 300
98% of 300 is 294 ( 294 red marbles)

If we want to make it 95% of red marbles then it would be 285
So we need to remove 9 balls

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Re: 12 Days of Christmas GMAT Competition - Day 1: In a jar of 300 marbles [#permalink]
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In a jar of 300 marbles, 98% are red. How many red marbles need to be removed to bring the percentage of red marbles down to 95%?

98% of 300 = 294
$$\frac{(294-x)}{(300-x)}$$ = $$\frac{95}{100}$$
294 - x = 0.95 (300 - x)
294 - x = 285 - 0.95x
294 - 285 = -0.95x + x
9 = 0.05x
180 = x

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Re: 12 Days of Christmas GMAT Competition - Day 1: In a jar of 300 marbles [#permalink]
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Since, no of non-red marbles remains same.
Therefore,
(2/100)*300 = (5/100)*(300-x)
=> 300-x = 120
=> x = 180
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Re: 12 Days of Christmas GMAT Competition - Day 1: In a jar of 300 marbles [#permalink]
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No. of red marbles = 0.98 * 300 =294

Let x marbles removed

$$\frac{294-x}{300-x}$$ = 0.95

x= 180

Ans D
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12 Days of Christmas GMAT Competition - Day 1: In a jar of 300 marbles [#permalink]
­Assuming 5% of the new total number of marbles (X) equals 6 marbles (Colours other than Red)

0.05 × X = 6

X = 120

and 120 - 6 (colours other than Red) = 114 Red Marbles.

Initially, there were 294 red marbles. (98% of 300)

and 294 − 114 = 180­
12 Days of Christmas GMAT Competition - Day 1: In a jar of 300 marbles [#permalink]
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