BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

a and b are different integers. What is the root of (x - a)^2 = (x - b)^2?

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

a and b are different integers. What is the root of (x - a)^2 = (x - b)^2?

by Max@Math Revolution » Mon May 18, 2020 12:40 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

[GMAT math practice question]

a and b are different integers. What is the root of (x - a)^2 = (x - b)^2?

1) a – b = 3
2) a + b = 7
Top
Source: — Data Sufficiency |
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

Re: a and b are different integers. What is the root of (x - a)^2 = (x - b)^2?

by Max@Math Revolution » Wed May 20, 2020 2:57 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

The question (x - a)^2 = (x - b)^2 is equivalent to x = (a + b)/2 for the following reason.
(x - a)^2 = (x - b)^2
⇔ (x - a)^2 - (x - b)^2 = 0
⇔ ((x - a) - (x - b)) ((x - a) + (x - b)) = 0
⇔ (-a + b)(2x - (a + b)) = 0
⇔ (2x - (a + b)) = 0 (by dividing both sides by -a + b since a ≠ b)
⇔ 2x = (a + b) (by adding ( a + b) to both sides)
⇔ x = (a + b)/2 (by dividing both sides by 2)
So, we have to find the value of a + b.
Thus, look at condition (2). It tells us that a + b = 7, which is exactly what we are looking for. The answer is unique, and the condition is sufficient according to Common Mistake Type 2, which states that the number of answers must be only one.
Condition (1) tells us that a – b = 3, from which we cannot determine the unique value of a + b. The answer is not unique, and the condition is not sufficient according to Common Mistake Type 2, which states that the number of answers must be only one.
Condition (2) ALONE is sufficient.
Therefore, B is the answer.
Answer: B
Top
Post new topic Post Reply
• Page 1 of 1