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# Plugging In: Invisible Plugging In - Fractions

David paid off $$\frac{1}{5}$$ of his total loan in January and $$\frac{1}{6}$$ of the remainder in February. Of the rest of the loan owed, David paid off $$\frac{1}{3}$$ in March, $$\frac{1}{6}$$ in April, $$\frac{1}{3}$$ in May, and $$\frac{1}{6}$$ in June. What fraction of his total loan did David pay in April and May combined?
Incorrect. [[snippet]]
Incorrect. [[snippet]]
Correct. [[snippet]] The invisible variable in this problem is David's total loan. However, therein lies a dilemma: if you multiply all the fractions present in the problem, you end up with a very large, unfavorable number. Did you try to multiply all the numbers in the problem?
Incorrect. [[snippet]]
Incorrect. [[snippet]]
Check out the following explanation to make sure you really get this advanced application of __Hidden Plugging In__: Choose a good number to work with, such as $$5\times 6\times 3=90$$. Then David paid >$$\frac{1}{5}$$ of $90 in January ($18), and >$$\frac{1}{6}$$ of $72 in February ($12). This leaves $60 remaining. Now focus on what the question is asking: David paid >$$\frac{1}{6}$$ of$60 ($10) in April, and >$$\frac{1}{3}$$ of$60 ($20) in May. Thus, the answer is that David paid $$10+20=30$$ out of$90, or $$\frac{1}{3}$$ of the loan, in April and May combined.
Multiplying all the bottoms of the fractions in the problem is near suicide on the GMAT. Be wiser and multiply only the bottoms of those fractions that use different numbers. Take one of each kind so the result is comfortably divisible by all the fractions presented in the problem.
$$\frac{1}{9}$$
$$\frac{1}{6}$$
$$\frac{1}{3}$$
$$\frac{1}{2}$$
$$\frac{2}{3}$$
No, I didn't. I tried something slightly different.
Unfortunately, I did and got stuck….
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