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GRE Math Strategies Part I of VI: The Textbook Approach

The Textbook Approach can be described best as the way your favorite math teacher would solve the problem.

Many problems on the Math sections of the GRE can be solved using some form of formal mathematical operations and equations.

For questions demanding knowledge of algebraic rules (like the problem below), the Textbook Approach may be the only method available.

Example #1:
Which of the following equations is not equivalent to 36y^2 + 9 = x^2?
(A) 36y^2 = x^2 - 9
(B) 36y^2 = (x - 3)(x + 3)
(C) 108y^2 + 27 = 3x^2
(D) y^2 = {x^2 - 9}/36
(E) 6y = x - 3

(E) is the correct answer.
Manipulate each answer choice, attempting to make it look like the original expression.
(A) is equivalent: Add 9 to both sides of the equation.
(B) is equivalent:(x - 3)(x + 3) = x^2 - 9. So, same as (A).
(C) is equivalent: Divide both sides of the equation by 3.
(D) is equivalent: Multiply both sides of the equation by 36. So, same as (A).
(E) is not equivalent: It incorrectly assumes that (x - 3)^2 = x^2 - 9, if you try to square both sides.

For equations and problems involving proportions (like the ones below), the Textbook Approach is the most reliable.

Example #2
If -2x - 5 = 1 - x, then 1/2x =
(A) -6
(B) -3
(C) 0
(D) 3
(E) 6

(B) is the correct answer.
Solving for x:
-2x - 5 = 1 - x
-6 = x Note that (A) is a good wrong answer
So 1/2x = -3

Example #3:
Operating at the same constant rate, 4 identical machines can produce a total of 220 candles per
minute. At this rate, how many candles could 10 such machines produce in 5 minutes?

(C) is the correct answer.
A logical place to begin problem-solving analysis is at the end of the problem called the question stem. The stem asks for the production of 10 machines in 5 minutes. This is easily found if we know the production of 1 machine in 1 minute.

Each machine produces 220/4, or 55 candles per minute. Ten machines would produce 55(10) = 550 candles per minute, and operating for 5 minutes would yield a
total quantity of 5(550) = 2,750

Algebraic word problems demand an organized, systematic methodology. First, the question involves representation of an unknown quantity by a variable. Second, there’s an equation to create and solve. The Textbook approach provides the best solution process for word problems.

Example #4:
If 1/2 an investment portfolio was invested in stocks, 1/5 in a mutual fund, 1/10 in bonds, and the remaining $25,000 in a savings bond, what was the total amount in the portfolio?
(A) $100,000
(B) $125,000
(C) $150,000
(D) $200,000
(E) $250,000

(B) is the correct answer.
Begin by focusing on the question stem.
Let x equal the total amount of money in the portfolio.
Then, 1/2x + 1/5x + 1/10x + 25,000 = x.
Multiply each term by 10.
5x + 2x + x + 250,000 = 10x
2x = 250,000
x = 125,000

Example #5:
Exactly 8 years ago, Jim’s son was twice as old as Jim’s daughter. If Jim’s son is now 5 years
older than his daughter, how old is Jim’s daughter now?
(A) 5
(B) 10
(C) 13
(D) 16
(E) 18

(C) is the correct answer.
Again, start with the question stem. Let stand for the son’s current age and
d for the daughter’s current age. Then, the first sentence translates to: s - 8 = 2(d - 8) , and the second piece of information translates to: s = d + 5. Plugging the second equation into the first yields one equation in terms of d: (d + 5) - 8 = 2(d - 8), and d - 3 = 2d - 16, so d = 13.

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4 Responses to GRE Math Strategies Part I of VI: The Textbook Approach

  1. Aaron Weber June 14, 2011 at 10:13 am #

    Example #1:
    Which of the following equations is not equivalent to ?

    (C) is equivalent: Divide both sides of the equation by 3.
    (D) is equivalent: Multiply both sides of the equation by 36. So, same as (A).

    C needs to say multiply and D needs to say divide.

    • Chris Lele
      Chris June 14, 2011 at 3:47 pm #

      Hi Aaron,

      I’m not sure if you are saying that C and D need to swap multiply and divide. It seems to me that the explanation is correct as is. That is in (C) you need to divide both sides by 3 and (D) you need to multiply both sides by 36.

      Let me know if I’m interpreting your comment correctly.


      • Muhammad July 21, 2013 at 3:06 pm #

        Aaron is correct.

        For answer choice C, if I were to divide both sides by 3 I would get:

        12y^2 +9 = x^2/3. However, multiplying produces 108y^2 + 27 = 3x^2. For choice D, if I were to multiply both sides of the equation by 36 I would receive the expression:

        1296y^2 + 324 = 36x^2.

        • Chris Lele
          Chris Lele July 22, 2013 at 2:18 pm #

          Yes, you are right. Now it is much clearer what Aron is saying. I was initially confused. But yes, the explanation should say we divide (C) by 3 and we multiply (D) by 36.

          Thanks for catching that 🙂

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