GRE® Quant Practice | Algebra Q1

GRE Sample Questions | Linear Equations Word Problem

The GRE maths sample question given below is a word problem in Linear Algebra. Framing and solving linear equations are the concepts tested in this practice question.

Question 1 : When four is added to six times a number and the result squared, the result obtained is four times the square of the sum of the number and its next multiple. What is the number?

  1. \\frac{1}{3})
  2. \\frac{-1}{3})
  3. 3
  4. -3
  5. -1

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Explanatory Answer

Step 1 of solving this GRE Algebra Question: Frame equations from statements

Let 'n' be the number.
Step a: Four is added to six times a number: 4 + 6n
Step b: The result is squared (step a is squared): (4 + 6n)2
Step c: Sum of the number and its next multiple: (n + 2n)
Step d: Four times square of step 3: 4(n + 2n)2

Step 2 of solving this GRE Algebra Question: Equate and solve for "n"

Equating Step b and Step d,
(4 + 6n)2 = 4 (n + 2n)2
(2 + 3n)2 × 4 = 4 × (3n)2
(2 + 3n)2 = 9n2
4 + 12n + 9n2 = 9n2
4 + 12n = 0
12n = -4
n = \\frac{-4}{12}) → n = \\frac{-1}{3})

Choice B is the correct answer

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