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GRE Math Strategies Part IV of VI: Logical Deduction

If the Textbook approach is the formal method of solving math problems, Logical Deduction could be called the informal approach. This strategy relies on careful reading, insight, and common sense.

Example #1:
Six beads, each a different color, are put into a bag. How many different three-color combinations are possible if 3 beads are drawn out of the bag simultaneously? (Assume the order of the colors does not matter.)
(A) 6
(B) 9
(C) 18
(D) 20
(E) 120

(D) is the correct answer.
There are six possible colors that could be chosen for the first bead. If there are 5 beads left in the bag, there are five possible colors for the second bead or 6 * 5 = 30 possible combinations of two colors after the second draw.
Now there are 4 beads left in the bag. For each of the 30 two-color combinations, there are four possible choices for the 3rd bead. Altogether, then, there are 6 * 5 * 4 = 120 possible combinations of three different colored beads drawn from six different colored beads. But, because the order of the colors doesn’t matter, and because there are 3 * 2 * 1 = 6 ways to pick any combination of three colors, we divide: {6 * 5 * 4}/{3 * 2 * 1} = 120/6 = 20. Note that (E) is a good wrong answer.

Example #2:
The product of n consecutive integers equals P. Which of the following is true for n >= 2″ title=”n >= 2″/> ?<br />
I. <img src= is an even number
II. P is an odd number
III. P is positive

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) II and III only

(A) is the correct answer.
If we have at least two consecutive integers, then at least one of them is even. If we multiply an even number by any other number(s), the result is always an even number. Hence, the product of n consecutive integers (provided n >= 2″ title=”n >= 2″/>) is always even. Thus, Statement I is true and Statement II is false.</p>
<p>The consecutive integers could be positive or negative. An odd number of negative<br />
integers multiplied together gives a negative product, and an even number of<br />
negative integers multiplied together yields a positive number, so <img src= does not have
to be positive. Thus, Statement III is not necessarily true.

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