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GRE Math Strategies Part V of VI: Estimation

Some GRE problems invite Estimation. In fact, if you find yourself immersed in irksome computations, you may want to consider estimating the answer, especially when the answer choices are numerically well spaced.

Example #1:
Which of the following is nearest to (98.6/{16.2*100})*({81.9*20}/103.4)
(A) 20
(B) 15
(C) 10
(D) 5
(E) 1

(E) is the correct answer.
The numerator of the first factor and denominator of the second factor are nearly equal, approximately 100, and can be cancelled. Then the remaining expression can be easily estimated.
(1/{16.2*100})*({81.9*20}/1) approx (1/{16*100})*({80*20}/1) approx {1/1600} * {1600/1} approx 1

Some questions may involve unfamiliar symbolism and minor calculations yet are still good candidates for Estimation.

Example #2:
{(sqrt{3}+1)(sqrt{3}-1)}/{(1+sqrt{8})(1-sqrt{8})} =

(A) -8
(B) -2
(C) -2/7
(D) sqrt{3}
(E) 12

(C) is the correct answer.

Because sqrt{3} approx 2 and sqrt{8} approx 3, we can estimate the expression as {(2+1)(2-1)}/{(1+3)(1-3)} = -3/8, which is very close to -2/7

Note:
Textbook Approach: If you remember this formula, the problem is easily solved: (a+b)(a-b) = a^2-b^2, so {sqrt{3}^2-1^2}/{1^2 - sqrt{8}^2} = {3-1}/{1-8} = -2/7

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