Backsolving is a technique of trying out the answer choices in GMAT questions. Each choice is selected one at a time and is assumed to be the right choice. Analyze the value or conditions by injecting the choices into the question. Backsolving is incredibly time saving in algebraic equations and number properties problems.

Case 1: To find the value of an equation

Example: Which number gives the lowest value for the equation?

1/X + (1/X) ^2 + 5X

Approach 1: Start from the middle value in the answer choice.

For example, if the five answer choices are 14,5,19,8,21

Plug 14 into the equation and check the value. If the value is too high, find out an answer choice with a much smaller value, like 5.

Approach 2: If you inspect the equation, the first two terms will result in small numbers, smaller than 1, according to the given answer choices. However, the 3rd term of the equation is the leading one. A small value in 5X will make the equation’s net value smaller, and a big value in 5X will make the equation’s net value bigger. So, the answer is almost immediately x = 5.

Case 2: To satisfy a condition

Example: If y # 3 and 2x/y is a prime integer greater than 2, which of the following must be true?

I. x = y

II. y = 1

III. x and y are prime integers.

(A) None

(B) I only

(C) II only

(D) III only

(E) I and II

For 1: Let us plug-in x=y=1

2x/y = 2, which is not greater than 2

For 2: y=1

Therefore 2x/y = 2x

Plug-in value for x:

x = 1, 2x = 2 which is equal to 2 and not greater than 2

For 3: x and y are prime integers

x = 13 y= 2

2x/y = 13, which is a prime integer greater than 2

x=2 y=13

2x/y = 0.3, which is less than 2 and not a prime integer

Note: If a certain value satisfies the condition, always try with other values before confirming the answer.

Correct Answer : A

For 3: x=13, y=2 satisfied the condition (Where x is a large prime number and y, a small one), but when we plugged in opposite numbers, x=2 and y =13 (Where x is a small prime number and y, a large prime number) the condition failed. Always test with opposite numbers to validate the condition.

Credits: Leo John, Luis R. Villegas H

Recommended Books

- Kaplan GMAT Math Workbook
- Word Translations GMAT Preparation Guide, 4th Edition (Manhattan GMAT Preparation Guides)
- Geometry GMAT Strategy Guide, 4th Edition (Manhattan GMAT Preparation Guides)
- Equations, Inequalities, and VIC's, GMAT Preparation Guide, 4th Edition (Manhattan GMAT Preparation Guides)
- Number Properties GMAT Strategy Guide, 4th Edition (Manhattan GMAT Preparation Guides)
- The Official Guide for GMAT Quantitative Review, 2nd Edition
- Kaplan GMAT 800: Advanced Prep for Advanced Students (Kaplan Gmat Advanced)

Essential GMAT Reading Comprehension Guide

After you read F1GMAT’s Essential GMAT Reading Comprehension Guide, you will:

1. Complete GMAT RC Questions in less than 1 minute and 50 seconds

2. Read Faster

3. Take Notes Effectively

4. Collect and Interpret Facts

5. Speed up Summary Creation

6. Remember Information

7. Question the Author

8. Learn to answer GMAT Reading Comprehension Title question

9. Learn to Solve GMAT Reading Comprehension Main Idea Question

10.Learn to Solve GMAT Reading comprehension inference question

11. Learn to Solve GMAT Reading Comprehension Detail Questions

12. Learn to Organize passage in GMAT Reading Comprehension

13. Learn to Identify style/tone or attitude of the author

14. Learn to Improve GMAT Reading Comprehension Score

Download Essential GMAT Reading Comprehension Guide

Mastering GMAT Critical Reasoning

After you read F1GMAT’s Mastering GMAT Critical Reasoning Guide, you will:

1) Learn to eliminate out of scope answer choices

2) Learn to spot logical fallacies

3) Learn to read questions by focusing on the holy trinity – premise, assumption, and conclusion.

4) Learn to disregard filler information

5) Complete GMAT CR Questions in less than 1 minute and 40 seconds

Download Mastering GMAT Critical Reasoning