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GRE Math Strategies Part II of VI: Plug In (Substitution) Method

The correct answer to a math question is always among the five answer choices. So, for problems with simple equations or answers, it is often quick and easy to substitute each answer choice into the question (the mathematical expression or narrative) and see which one works.

This strategy works best when a symbolic expression (like an equation) is provided and the answer choices are all numerical values.

Example #1:
If (6 + 2/x)(x - 4) = 0, and xdoes not equal 4, then x =
(A) -6
(B) -4
(C) -1/3
(D) 1/3
(E) 3

(C) is the correct answer.
For the product of two factors to equal zero, one (or both) of the factors must equal zero.
It’s given that x does not equal 4, so let’s examine the first factor. What value for x renders the first factor equal to zero?

Examine the choices.
(A) generates 6 + 2/-6 = 5 2/3, a positive mixed number. No.
(B) does also: 6 + 2/-4 = 5 1/2. No.
(C) generates the correct value for the first factor: 6 + 2/{1/-3} = 6 - 6 = 0. Yes!
(D) generates 6 + 2/{1/3} = 12, a positive number. No.
(E) generates 6 + 2/3 = 6 2/3, a positive mixed number. No.

The Plug In approach also works for hard-to-follow word problems when it’s not easy to represent the unknown quantity and create the equation.

Example #2:
Suits at a local clothing store are discounted 20 percent. Despite the discount, the store owner enjoys a net profit (discount price minus cost) equal to 60 percent of the cost of the suits. If the suits cost the clothing store owner $200 each, what was the prediscount retail price of each suit?
(A) $300
(B) $400
(C) $500
(D) $600
(E) $700

(B) is the correct answer.
If the suits cost the owner $200 each, then the net profit (discount price minus cost) on each suit is 60 percent times $200, or $120. Thus, the discount retail price of each suit must be $200 (cost) + $120 (net profit) = $320.

Which of the (prediscount) answer choices discounted by 20 percent equals $320?
(A) $300 times 20 percent discount equals $300-$60 = $240 (incorrect).
(B) $400 times 20 percent discount equals $400-$80 = $320 (correct!).
(C) $500 times 20 percent discount equals $500-$100 = $400 (incorrect)
(D) $600 times 20 percent discount equals $600-$120 = $480 (incorrect).
(E) $700 times 20 percent discount equals $700-$140 = $560 (incorrect).

The Plug In approach demands common sense and confidence in the strategy.
You will have time to use this strategy.
You may choose to abandon your plugging in after securing (B) as the correct answer.
Of course, the Textbook approach is always available:
Let x = the prediscount price of a suit, then 0.8x = discount price.
The net profit (in dollars) is expressed in two ways in the problem.
Set these expressions equal: 0.8x - 200 = 0.6 x 200
Solving for x:
0.8x = 120 + 200
0.8x = 320
x = 400

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