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Yellow marbles - Red marbles?

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Yellow marbles - Red marbles?

by chetan86 » Thu Jul 31, 2014 8:51 pm
A certain number of marbles are to be removed from a box containing only solid-colored red, yellow, and blue marbles. How many more yellow marbles than red marbles are in the box before any are removed?

(1) To guarantee that a red marble is removed, the smallest number of marbles that must be removed from the box is 14.

(2) To guarantee that a yellow marble is removed, the smallest number of marbles that must be removed from the box is 8.

Source: MGMAT
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by GMATinsight » Fri Aug 01, 2014 7:57 am
chetan86 wrote:A certain number of marbles are to be removed from a box containing only solid-colored red, yellow, and blue marbles. How many more yellow marbles than red marbles are in the box before any are removed?

(1) To guarantee that a red marble is removed, the smallest number of marbles that must be removed from the box is 14.

(2) To guarantee that a yellow marble is removed, the smallest number of marbles that must be removed from the box is 8.

Source: MGMAT
If No. of Yellow marbles is Y, No. of Red marbles is R and No. of Blue marbles is B

Question : Y - R = ?

Statement 1) To guarantee that a red marble is removed, the smallest number of marbles that must be removed from the box is 14.

i.e. B+Y+1 = 14
i.e. B+Y = 13
But there is no information about R therefore
Insufficient

Statement 2) To guarantee that a yellow marble is removed, the smallest number of marbles that must be removed from the box is 8.

i.e. B+R+1 = 8
i.e. B+R = 7
No Information about Y therefore,
INSUFFICIENT

Combining the Two statements

B+R = 7 and B+Y = 13
i.e. (B+Y) - (B+R) = 13 - 7
i.e. Y - R = 6
SUFFICIENT

Answer: Option C
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by GMATinsight » Fri Aug 01, 2014 8:19 am
In order to help you understand my working with Statement 1 and Statement 2 in the previous statement, here I am posting another question

Question : What is the minimum number of balls to be extracted to be sure that we have at least 1 balls of each color in the following case:

The box contains 30 balls in total that are 12 red, 8 yellow, blue and 10 green in color.

SOLUTION :
If you pick 12 Balls they can all be Red
If you pick 22 Balls they can all be (12 Red and 10 Green)

But If you pick 23 Balls they at worse will be (12 Red and 10 Green and 1 Yellow)
therefore minimum Number of balls to be picked = 12(Biggest No.) + 10(Second Biggest)+1 = 23
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by [email protected] » Fri Aug 01, 2014 6:51 pm
Hi chetan86,

When a question asks about a "guaranteed" result, you have to account for the "worst case" mathematical scenario.

We're told that there are 3 different colored marbles (Red, Yellow and Blue) and we're asked for the difference in the number of Yellow and Red marbles, so we're essentially asked Y - R = ?

Fact 1: To guarantee removing a red marble, 14 marbles must be removed.

The word-case math scenario here is that ALL the other marbles would have to be removed before the 1st red marble was removed. Since the 14th marble would be the Red one, the other 13 are either Blue or Yellow. This tells us that....

B + Y = 13

Since there's no info about R, this is not enough information to answer the question.
Fact 1 is INSUFFICIENT.

Fact 2: To guarantee removing a yellow marble, 8 marbles must be removed.

This is similar to the situation in Fact 1; 7 marbles are either Red or Blue....

R + B = 7

Since there's no info about Y, this is not enough info to answer the question.
Fact 2 is INSUFFICIENT.

Combined, we have
B + Y = 13
R + B = 7

This can be solved algebraically to find Y - R, but if you don't "see" the algebra approach, there is another way to prove a pattern: TEST VALUES

If...
B = 1
R = 6
Y = 12
Y - R = 12 - 6 = 6

B = 2
R = 5
Y = 11
Y - R = 11 - 5 = 6

B = 3
R = 4
Y = 10
Y - R = 10 - 4 = 6

Notice how the value of Y-R stays the same?
Combined, SUFFICIENT

Final Answer: C

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by Brent@GMATPrepNow » Fri Aug 01, 2014 7:16 pm
Rich has suggested a 2nd way to handle things once we get to the COMBINED STATEMENTS and we've generated the following 2 equations:
1) B + Y = 13
2) R + B = 7


Here's a 3rd way.
If R + B = 7 (from statement 2), then B = 7 - R
Now take the 1st equation (B + Y = 13) and replace B with (7 - R) to get: (7 - R) + Y = 13
Simplify/rearrange to get: Y - R = 6
DONE!

Cheers,
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by chetan86 » Sat Aug 02, 2014 1:51 am
Hi Brent/Rich/GMATInsight,

Thanks a lot for your help and explanation.

Thanks,
Chetan
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