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.
OAC
Please explain.
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A certain number of marbles
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Question stem: What is the value of Y-R?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.
Statement 1: To guarantee that a red marble is removed, the smallest number of marbles that must be removed from the box is 14.
Implication:
It is possible to remove 13 NON-RED marbles, with the result that AT LEAST 14 marbles must be removed to guarantee that a red marble is removed.
Since there are 13 non-red marbles, we get:
Y+B = 13.
No way to determine the value of Y-R.
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.
Implication:
It is possible to remove 7 NON-YELLOW marbles, with the result that AT LEAST 8 marbles must be removed to guarantee that a yellow marble is removed.
Since there are 7 non-yellow marbles, we get:
B+R = 7.
No way to determine the value of Y-R.
INSUFFICIENT.
Statements combined:
Subtracting B+R=7 from Y+B=13, we get:
(Y+B) - (B+R) = 13-7
Y-R = 6.
SUFFICIENT.
The correct answer is C.
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Mitch has shown a nice fast way to deal with the COMBINED STATEMENTS:
1) B + Y = 13
2) R + B = 7
If you missed that approach, here's a different approach:
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,
Brent
1) B + Y = 13
2) R + B = 7
If you missed that approach, here's a different approach:
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,
Brent
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Hi Needgmat,
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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich
