Blog

Concerning our last discussion on Absolute value, let us try solving the following questions:

E.g. 1. What is the value of?

1. x/|x| = 1

1. x2– x – 6 = 0

Explanation:

Statement 1: x/|x| = 1

With the above equation, we know x > 0

But, we cannot determine the exact value of x.

So, we cancel out A and D.

Statement 2: x2 – x- 6 = 0

Thus, we know, (x – 3) X ( x + 2) = 0

So, either x – 3 = 0 or x + 2 = 0

x = 3 or x = -2

Here, we don’t get one specific value, so we cancel out B also.

Thus, by combining statements 1 and 2:

We know x > 0 and x = 3 or -2.

Hence, x must be 3.

Eg. 2: Is |x + y| < |x| + |y|?

1. xy < 0

1. |x| = 7 and |y| ≠ 7

Explanation:

To have |x + y| < |x| + |y|, we must know that they have opposite signs.

Either, (+, -) or (-, +)

Statement 1:

From xy < 0, we get that x and y both have opposite signs.

Thus, |x + y| < |x| + |y|

In this case, we get a specific answer (‘Yes’) from statement 1. So, we cancel out B, C, and E.

Statement 2:

|x| = 7 which means, x = 7 or -7

|y| ≠ 7, which means y ≠ 7 or y ≠ -7

Combining x and y for the values of |x + y| and |x| + |y|, we do not get a specific value, thus no specific answer.

Thus, we now cancel out D.

September 21, 2023

Concerning our last discussion on Absolute value, let us try solving the following questions: E.g. 1. What is the value of? Explanation: Statement 1: x/|x| = […]
September 13, 2023

Well begun is well done!

This is a wake-up call for all those about to step into junior year and plan to take the SAT. You have just transitioned from one […]
September 7, 2023

Ask yourself – Why Option Training Institute

Option has dedicatedly worked on understanding the different tests and evolving effective classroom strategies to tackle even the worst questions these tests are so good at […]
August 28, 2023

More Facts on Factorial

In our last article, we discussed finding some zeroes at the end of any factorial. For example, to find the number of zeroes in 22! we […]
August 23, 2023

FUNDAMENTAL CONCEPTS AND TECHNIQUES IN ALGEBRAIC EXPRESSIONS

Introduction to Algebraic Expressions Algebraic expressions are the cornerstone of mathematics, serving as a fundamental building block for solving equations, making predictions, and understanding complex relationships. […]
August 16, 2023

The October – November GMAT Syndrome

While preparing for the GMAT, it is not uncommon for test takers to come up against a wall and discover they still have an Achilles ’ […]
August 10, 2023

Remainders – Important Question Type

Based on our last discussion of remainders, let’s start with a frequently asked question type on the GMAT. Many GMAT questions could have a piece of […]
July 28, 2023

Make a Choice Right – Right Now!

This is something oft-discussed and written about – how does one select a business school to do his MBA from? Maybe the answer was not as […]
July 7, 2023

Number Properties – Factors

As promised in the last post, we will investigate the number of properties tested frequently on the GMAT. We first begin with prime numbers. Prime Numbers […]