Consider Algebra, Not Arithmetic

by on June 6th, 2017

calculations_mathMany test takers fail to make the connection between not being permitted to use a calculator on the quantitative section of the GMAT and, well, not making intensive, calculator-required calculations.

The reality is, when you are working through a question and think a calculator is needed and/or there is some simplistic, obscure formula that is required, you are not using the right strategy. This proves most true for arithmetic questions, when tedious calculations take test takers down the road where an algebraic approach should be considered instead.

Let’s look at an example:

5^10 + 5^10 + 5^10 + 5^10 + 5^10 = 5^x. What is x?

A) 8

B) 10

C) 11

D) 40

E) 50

Most test takers get started by going down the route of (5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5) +(5 x 5 x 5 … ) and either a) take 10 minutes trying to do some intense multiplication calculations and potentially getting the correct answer if careless mistakes are not made or b) give up and just add the exponents, well knowing that it is not the correct direction to take, but hoping there is an exception to the rule they have forgotten about.

Operating on hope does not typically lead to success!

The reality is, think of a parallel example with a variable, say:

x^2 + x^2 + x^2 + x^2 = 4x^2

OR

2^3 + 2^2 + 2^1 = 2(2^2 + 2 + 1)

Would help test takers realize there is a different approach to this question—combining like terms and factoring—that would them to the right answer quickly and efficiently.

For this particular problem, 5^10 + 5^10 + 5^10 + 5^10 + 5^10 is the same as 5(5^10), which is the same as 5^(1+10) making x = 11 or (C).

Take a similar problem:

What is the greatest prime factor of 12!11! + 11!10!?

A) 2

B) 7

C) 11

D) 19

E) 23

Multiplying out these factorials makes it impossible to get to the right answer efficiently—while prime factorization is an important component of the test, a combination of strategies need to be used for this particular question. Instead, trying to factor out the factorials makes the most sense:

11!10!(12*11 + 1) = 11!10!(133)

By factoring out 133 we get 7*19, and there are no numbers within 11! or 10! that are greater than 19 making the correct answer choice (D).

Whenever you see a question that requires combining terms and/or additional or subtraction of variables, exponents, and roots consider factoring as your primary strategy, not diving down the road of endless times tables.

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