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The contents of a bag of marbles consist of 9 green...

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by BTGmoderatorLU » Sat Dec 30, 2017 6:19 am
The content of a bag of marbles consist of green 9 marbles and 16 blue marbles. How many blue marbles must be removed so that 60% of the marbles in the bag will be green?

(A) 1
(B) 6
(C) 7
(D) 9
(E) 10

The OA is E.

Relatively easy question I'm confused with this PS question, I think I have a problem with the concept. Experts, any suggestion about how can I solve it? Thanks in advance.
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by EconomistGMATTutor » Sun Dec 31, 2017 9:27 am
The content of a bag of marbles consist of green 9 marbles and 16 blue marbles. How many blue marbles must be removed so that 60% of the marbles in the bag will be green?

(A) 1
(B) 6
(C) 7
(D) 9
(E) 10

The OA is E.

Relatively easy question I'm confused with this PS question, I think I have a problem with the concept. Experts, any suggestion about how can I solve it? Thanks in advance.
Hi LUANDATO,
Let's take a look at your question.

There are 9 green and 16 blue marbles in a bag.
Let the 9 green marbles are 60% of a total of 'x' marbles. Then
$$x\times60\%=9$$
$$x\times\frac{60}{100}=9$$
$$x=9\times\frac{100}{60}$$
$$x=15$$

It means that if there are a total of 15 marbles in the bag, only then the 9 green marbles are the 60% of the total marbles in the bag.
Total marbles = 15
Green marbles = 9
We can now calculate the number of blue marbles in the bag.
Blue marbles = 15 - 9 = 6

There were initially 16 blue marbles in the bag, we are asked to find the number of blue marbles that must be removed.
Blue marbles that must be removed = 16 - 6 = 10

Therefore, Option E is correct.

Hope it helps.
I am available if you'd like any follow up.
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by [email protected] » Sun Dec 31, 2017 11:48 am
Hi LUANDATO,

We're told that a bag of marbles contains 9 green marbles and 16 blue marbles. We're asked how many blue marbles must be REMOVED so that 60% of the marbles in the bag will be green. We can answer this question by TESTing THE ANSWERS.

To start, since we need 60% of the marbles to be green, we therefore need there to be MORE green marbles than blue marbles... and this means that we have to remove at least 8 of the 16 blue marbles. Thus, the correct answer has to be either D or E.

Let's TEST Answer E: 10 marbles
If we remove 10 blue marbles, then we'll have...
9 green marbles and 6 blue marbles
(green)/(total) = 9/15 = 3/5 = 60%
This is an exact match for what we were told, so this MUST be the answer.

Final Answer: E

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by GMATWisdom » Mon Jan 01, 2018 1:10 pm
LUANDATO wrote:The content of a bag of marbles consist of green 9 marbles and 16 blue marbles. How many blue marbles must be removed so that 60% of the marbles in the bag will be green?

(A) 1
(B) 6
(C) 7
(D) 9
(E) 10

The OA is E.

Relatively easy question I'm confused with this PS question, I think I have a problem with the concept. Experts, any suggestion about how can I solve it? Thanks in advance.
If finally x blue marbles are left in the bag then 9 and x must be in the ratio of 60 and 40
That means x/40 = 9/60 or x = 9*40/60=6
Hence 16-6=10 blue marbles must be removed
Option E
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by Scott@TargetTestPrep » Sat Aug 24, 2019 4:20 am
BTGmoderatorLU wrote:The content of a bag of marbles consist of green 9 marbles and 16 blue marbles. How many blue marbles must be removed so that 60% of the marbles in the bag will be green?

(A) 1
(B) 6
(C) 7
(D) 9
(E) 10

The OA is E.

Relatively easy question I'm confused with this PS question, I think I have a problem with the concept. Experts, any suggestion about how can I solve it? Thanks in advance.
If 60% of the marbles in the bag must be green, then 40%, or â…–, of the marbles will be blue. Letting n = the number of blue marbles to be removed, we can create the equation:

(16 - n)/(25 - n) = 2/5

80 - 5n = 50 - 2n

30 = 3n

10 = n

Alternate Solution:

Notice that, no matter how many blue marbles are removed, there are still 9 green marbles in the bag, and we want this number to be 60% of all the marbles. Thus, after the removal of blue marbles, there should be 9/0.6 = 15 marbles in the bag. Since there were 9 + 16 = 25 marbles in the bag to begin with, 25 - 15 = 10 blue marbles should be removed.

Answer: E

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by Brent@GMATPrepNow » Sat Aug 24, 2019 6:05 am
BTGmoderatorLU wrote:The content of a bag of marbles consist of 9 green marbles and 16 blue marbles. How many blue marbles must be removed so that 60% of the marbles in the bag will be green?

(A) 1
(B) 6
(C) 7
(D) 9
(E) 10

The OA is E.
GIVEN: Start with 9 green marbles and 16 blue marbles

Let x = the number of BLUE marbles to remove
So, the NEW number of blue marbles remaining = 16 - x
The number of green marbles remaining = 9

How many blue marbles must be removed so that 60% of the marbles in the bag will be green?
We want: (number of GREEN marbles)/(TOTAL number of marbles) = 60%
Rewrite as: (number of GREEN marbles)/(TOTAL number of marbles) = 3/5

Plug in values to get: (9)/(16 - x + 9) = 3/5
Simplify to get: (9)/(25 - x) = 3/5
Cross multiply to get: (5)(9) = 3(25 - x)
Expand to get: 45 = 75 - 3x
Keep going: -30 = -3x
Solve: x = 10

Answer: E

Cheers,
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