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25 Mar 2024, 01:30
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
78% (01:21) correct
22%
(01:52)
wrong
based on 55
sessions
History
Date
Time
Result
Not Attempted Yet
How many marbles are in bowl S?
(1) If 1/4 of the marbles were removed, the bowl would be filled to 1/2 of its capacity.
(2) If 100 marbles were added, the bowl would be full.
(1) If 1/4 of the marbles were removed, the bowl would be filled to 1/2 of its capacity.
(2) If 100 marbles were added, the bowl would be full.
25 Mar 2024, 07:26
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(1) If 1/4 of the marbles were removed, the bowl would be filled to 1/2 of its capacity.
Let the number of marbles already in the bowl = \(m\) and the amount of marbles the bowl can hold = \(b\)
This means that one can write the statement as: \(\frac{3}{4}m = \frac{1}{2}b\)
To solve for the question, we require a secondary equation as the above equation has two unknown variables.
INSUFFICIENT
(2) If 100 marbles were added, the bowl would be full.
Using the same variables as above, one can rewrite this statement as: \(m + 100 = b\)
Once again, without a secondary equation one cannot solve this question.
INSUFFICIENT
(1+2)
Looking at the two equations, both have the same unknown variables. This means that one can easily solve for \(m\) by manipulating the two equations and then subtracting one from the other.
\(\frac{3}{4}m = \frac{1}{2}b\)
Multiply through by 4
\(3m = 2b\) [1]
\(m + 100 = b\)
Multiply through by 2 so that the b's can be subtracted out, leaving m as the only variable
\(2m + 200 = 2b\) [2]
Subtracting [2] from [1]: \(m - 200 = 0\)
\(m = 200\)
SUFFICIENT
ANSWER C
Let the number of marbles already in the bowl = \(m\) and the amount of marbles the bowl can hold = \(b\)
This means that one can write the statement as: \(\frac{3}{4}m = \frac{1}{2}b\)
To solve for the question, we require a secondary equation as the above equation has two unknown variables.
INSUFFICIENT
(2) If 100 marbles were added, the bowl would be full.
Using the same variables as above, one can rewrite this statement as: \(m + 100 = b\)
Once again, without a secondary equation one cannot solve this question.
INSUFFICIENT
(1+2)
Looking at the two equations, both have the same unknown variables. This means that one can easily solve for \(m\) by manipulating the two equations and then subtracting one from the other.
\(\frac{3}{4}m = \frac{1}{2}b\)
Multiply through by 4
\(3m = 2b\) [1]
\(m + 100 = b\)
Multiply through by 2 so that the b's can be subtracted out, leaving m as the only variable
\(2m + 200 = 2b\) [2]
Subtracting [2] from [1]: \(m - 200 = 0\)
\(m = 200\)
SUFFICIENT
ANSWER C
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