StudyPattern

A higher score startswith the right practice.

Online exam prep with a guided study path, exam-style questions, and explanations that help you fix your mistakes.

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StudyPattern connects your study plan, practice, and progress. Spend your session on the work that needs it.

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Lesson · Quantitative reasoning

Solving for Multiple Variables

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Up nextSolving for Multiple VariablesPractice

Score Estimate

Quant154
Verbal151

Based on practice.
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Your topic strengths

ProbabilityNeeds attention48%
Sentence EquivalenceBuilding66%
Linear EquationsStrong82%
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Go from “I don’t know how to start” to a method you can use. Focused lessons explain the concept before you put it to work in practice.

Quant and Verbal live in the same study space. You can pick up an unfinished lesson where you left it.

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StudyPatternGRE · Study

Solving for Multiple Variables

Translate two-category problems

In a two-category problem, let one variable represent one category and express the other category using the known total.

23 cartons. Two kinds of contents.

xcartons with 11 lamps
23 − xcartons with 7 lamps

11x + 7(23 − x) = 197

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GRE lesson preview · example from the free practice question

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StudyPatternGRE · Review

Solving for Multiple Variables

At a warehouse, each of 23 cartons contains either 7 lamps or 11 lamps. The cartons contain 197 lamps in all. How many cartons contain 11 lamps?

B36Your answer
A9Correct answer
Answer and explanation

Let x be the number of cartons that contain 11 lamps. Then 23 - x cartons contain 7 lamps. Since there are 197 lamps in all, 11x + 7(23 - x) = 197. Simplifying gives 11x + 161 - 7x = 197, so 4x = 36 and x = 9. Therefore, 9 cartons contain 11 lamps.

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GRE Quant

149157

10 weeks of study
I kept doing more questions without understanding what I was getting wrong. Having the lesson and explanation in the same place finally made the algebra stick.
Maya · working full-time
GRE Verbal

152158

8 weeks of study
I used to pick words that sounded right. Reviewing the sentence clues helped me slow down and actually explain why the answer fit.
Daniel · applying to graduate school
GRE total

304315

12 weeks of study
The best part was opening the app and knowing what to work on. I could fit a lesson and a short practice set around my classes without replanning my whole week.
Leah · final-year student

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Quantitative + Verbal Reasoning

GRE Quant + Verbal.

Practice the math and reasoning tested on the GRE. Start here with a real algebra question and its worked solution.

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GRE Quantitative ReasoningSample

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At a warehouse, each of 23 cartons contains either 7 lamps or 11 lamps. The cartons contain 197 lamps in all. How many cartons contain 11 lamps?
Answer and explanation

The correct answer is A. Let x be the number of cartons that contain 11 lamps. Then 23 - x cartons contain 7 lamps. Since there are 197 lamps in all, 11x + 7(23 - x) = 197. Simplifying gives 11x + 161 - 7x = 197, so 4x = 36 and x = 9. Therefore, 9 cartons contain 11 lamps.

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How does StudyPattern adapt to different exams?

Each exam has its own Study Path, concepts, and practice. The same learn, practice, and review rhythm carries across them. GRE is the launch exam. MCAT is still in development; its website examples are previews.

Do I need to take a Diagnostic first?

No. The Diagnostic is an optional way to get a starting picture. You can also begin with a concept on your Study Path and work through its lesson and practice.

What happens when I get a question wrong?

You can read the explanation to understand the reasoning, then return to the concept. Needs-Work Review keeps missed questions available for another pass. A wrong answer is useful information about where to focus.

What does my Score Estimate mean?

It is an estimate based on your practice, not an official result or a guarantee of an exam-day score. Strength describes your progress with a concept. Use both as guidance for what to study next.

Can I try it before creating an account?

Yes. The interactive preview above includes a lesson excerpt and a real practice question for each exam. You do not need an account to try them. Create an account in the StudyPattern app to save your study progress.