Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
If each of the 20 bolts of fabric on a shelf is either 100 percent cotton, 100 percent wool, or a mixture of cotton and wool, how many bolts contain both cotton and wool?
(1) Of the 20 bolts, 18 contain some wool and 14 contain some cotton.
(2) Of the 20 bolts, 6 are 100 percent wool.
This is a typical ‘2 by 2 question’, a commonly observed type of question in GMAT math. We can represent the original condition using the table below:
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GCDS If each of the 20 bolts of fabric on(20151008).jpg [ 23.1 KiB | Viewed 4801 times ]
There is no fabric that is neither cotton nor wool, so this can be written ‘0’, and a+b+c=20,
Giving 3 variables (a,b,c) and an equation. We need 2 more equations in order to solve for the variables, and 2 equations are given from the 2 conditions, making (C) likely to be the answer.
However, looking at condition 1,
a+b=18, a+c=14 (2 equations), making the condition sufficient,
and condition 2 gives b=6, being insufficient, makes the answer (A).
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