A bag of marbles contains 13 red marbles ...

13 = 65/100 (35-x)
20 = 35 - x
x = 15
15 green should be removed.

Night reader wrote:A bag of marbles contains 13 red marbles and 22 green marbles. How many green marbles must be removed from the bag so that 65 percent of the marbles will be red?

(A) 2
(B) 7
(C) 15
(D) 17
(E) 20

Total Marbles = 22 + 13 = 35

Say x Green Marbles are removed to get the desired answer.

Thus, (35 - x) (0.65) = 13

=> (35 - x) * (0.05) = 1

=> 1.75 - 0.05x = 1

=> -0.05x = -0.75

=> x = 15

This 15 has to be removed only from the 22 Green ones.

IMO C

beat_gmat_09 wrote:13 = 65/100 (35-x)
20 = 35 - x
x = 15
15 green should be removed.

you nailed it!

I solved this question in under 30 seconds.

Here is how


Plug in numbers.The answers are in increasing order.I can test all answer choices by using just B and D!

B) Remove 7 marbles

15 green marbles are left over.

% red marbles -> 13/28.Clearly less than 50% because 13/26 is 50% and fractions get smaller with increasing denominator

Remove 17 green marbles

5 green left over

% red marbles -> 13/18-> clearly it is more than 65%.how? because I know 12/18 -?2/3 or 67% and fractions get larger as denominators grow.

See the trend is up.Percentage of red moved from under 50% to over 67% with increasing numbers.So it's gotta be C=15.

You can confirm

green = 22-15=7
% red = 13/20 =65%

No need to strain your head with algebra,using equations..

rishab1988 wrote:I solved this question in under 30 seconds.

Here is how


Plug in numbers.The answers are in increasing order.I can test all answer choices by using just B and D!

B) Remove 7 marbles

15 green marbles are left over.

% red marbles -> 13/28.Clearly less than 50% because 13/26 is 50% and fractions get smaller with increasing denominator

Remove 17 green marbles

5 green left over

% red marbles -> 13/18-> clearly it is more than 65%.how? because I know 12/18 -?2/3 or 67% and fractions get larger as denominators grow.

See the trend is up.Percentage of red moved from under 50% to over 67% with increasing numbers.So it's gotta be C=15.

You can confirm

green = 22-15=7
% red = 13/20 =65%

No need to strain your head with algebra,using equations..

answers can be posed differently, what now?

are they?

They aren't

GMAT is not gonna check your scratch book as to how you did it.It cares only about whether you got it right.

These are the tricks I used to solve MGMAT in under 70 minutes Q51 [not that you care],in which most students are gasping for time,usually.

By differently what do you mean?

I can still arrange them in sequence and solve!