# 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 ## Get to 170 in GRE Quant #### Online GRE Courses From INR 2999 ### Video Explanation ## GRE Live Online Classes #### Starts Fri, August 26, 2022 ### 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 #### GRE Online Course - QuantTry it free! Register in 2 easy steps and Start learning in 5 minutes! #### Already have an Account? #### GRE Live Online Classes Next Batch August 26, 2022 ##### Where is Wizako located? Wizako - GMAT, GRE, SAT Prep An Ascent Education Initiative 14B/1 Dr Thirumurthy Nagar 1st Street Nungambakkam Chennai 600 034. India Work @ Wizako ##### How to reach Wizako? Mobile:$91) 93800 48484
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