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## Comment on

Common GMAT Data Sufficiency Myths - Part II## hello again :)

another question, when we are dealing with a quadratic and we know that only positive numbers fulfil our conditions (for instance in geometry), could we skip the calculation in this case? or is it also possible to get 2 positive solution from a quadratic ?

## Yes, it's possible to get to

Yes, it's possible to get to two positive solutions to a quadratic equation.

Take, for example, x² - 5x - 6 = 0

Factor to get: (x - 2)(x - 3) = 0

So, x = 2 or x = 3

Cheers,

Brent

## Hello admin... From the

## Is this the question you're

Is this the question you're referring to: https://gmatclub.com/forum/if-x-and-y-are-positive-integers-what-is-the-... ?

If so, I'm not sure what you are asking. I don't have x = 1 and y = 1 as a solution anywhere in my answer (https://gmatclub.com/forum/if-x-and-y-are-positive-integers-what-is-the-...)

Can you please elaborate on your question?

Cheers,

Brent

## You assumed the statement is

## I believe you're referring to

I believe you're referring to the question that starts at 2:15 in the above video.

We're told that x and y are positive integers, and we want to determine the value of x.

STATEMENT 1 tells us that 10x + 5y = 15

When we simplify this equation, we get: 2x + y = 3

Keep in mind that, in Data Sufficiency questions, each statement is true, so it MUST be the case that 2x + y = 3

Since there is ONLY ONE pair of values that satisfy this equation (x = 1 and y = 1), we can be certain that x MUST EQUAL 1.

If you feel that x could have values other than 1, you must find a DIFFERENT pair of x and y values that satisfy the equation 2x + y = 3.

For example, you are suggesting that x could equal 2. However, in order to satisfy the given equation (2x + y = 3), we must find a POSITIVE value of y to go along with x = 2.

However, if x = 2, then y must equal -3, and -3 is not positive.

Does that help?

Cheers,

Brent

## Hi Brent,

1. I know that we can find the value of 2 variables provided there are 2 equations such that the equations are neither Identical nor Inconsistent.

2. I also know that in DS questions we should be careful about declaring a statement sufficient in scenarios where both LHS and RHS contain variables as the variables might get cancelled.

With these 2 points in mind I attempted this Q : https://gmatclub.com/forum/each-person-attending-a-fund-raising-party-for-a-certain-club-was-101572.html#p787212

My questions are whether the assumptions above are correct or not and whether I could have stopped further calculation after the 1st step i.e. xn=(x−0.75)(n+100) ? Furthermore, if I get 2 unique equations then can I conclude that the equations could be solved without actually having to solve those equations? Any exceptions to the rule?

Thanks & Regards,

Abhirup

## Hi Abhirup,

Hi Abhirup,

Link: https://gmatclub.com/forum/each-person-attending-a-fund-raising-party-fo...

Once you have two different LINEAR equations, you can be certain that the system can be solved for each variable.

So, once we spend a few seconds confirming that we have two different LINEAR equations, then we can conclude that we have sufficient information.

Cheers,

Brent

## Thanks Brent!! That helps a

## Hi Brent,

I am really struggling with Min-Max problems like the one here : https://gmatclub.com/forum/six-countries-in-a-certain-region-sent-a-total-of-93368.html#p718376

I am unable to list down the combination of numbers quickly enough. Often its taking almost 3-4 mins to solve such problems. Do you have any specific video lesson on tackling Min-Max problems? Please suggest how may I improve in such problems and demonstrate the right strategy to tackle such questions with help of any example.

Really appreciate your help.

Thanks & Regards,

Abhirup

## Sorry, we don't have a

Sorry, we don't have a specific lesson on max/min questions.

That said, this question type almost always involves the same approach:

If we want to maximize one value, then we must minimize the other values, and if we want to minimize one value, then we must maximize the other values.

If you're looking for extra practice questions, try this link: https://gmatclub.com/forum/search.php?selected_search_tags%5B%5D=63&t=0&...

I hope that helps.

Cheers,

Brent

## Thanks Brent!!

## Dear Brent, could you please

1 question: from the lecture on 5:25 min there is a question: If 2x + 3y=11, what is the value of x?

Statement 1: 3x – 5y = 7

How did you solve this system of equations to get x=4, y=1? I tried few times and my x cancel each other out.

2 question: https://gmatclub.com/forum/if-x-and-y-are-positive-integers-what-is-the-value-of-x-238519.html

Statement 2: |9x² + 30xy + 25y²| = 21²

First factor the part inside the absolute value to get: |(3x + 5y)²| = 21².

How did you factor inside the absolute value?

## 1. We want to solve the

Question #1. We want to solve the following system of equations:

2x + 3y = 11

3x – 5y = 7

I prefer to use the elimination method described in the following video: https://www.gmatprepnow.com/module/gmat-algebra-and-equation-solving/vid...

Take the top equation and multiply both sides by 5, and take the bottom equation and multiply both sides by 3. When we do this, we get the following EQUIVALENT equations:

10x + 15y = 55

9x – 15y = 21

Now, when we ADD the two equations, the y-terms disappear to get: 19x = 76

Divide both sides by 19 to get: x = 4

From here, we can find the value of y by plugging x = 4 into one of our given equations.

Take: 2x + 3y = 11

Replace x with 4 to get: 2(4) + 3y = 11

Simplify: 8 + 3y = 11

Subtract 8 from both sides: 3y = 3

Solve: y = 1

So, the solution to our system of equations is x = 4 and y = 1

---------------------------

Question #2: https://gmatclub.com/forum/if-x-and-y-are-positive-integers-what-is-the-...

In most cases on the GMAT, quadratic expressions will be in the form x² + ax + b

In other words, the coefficient of x² is typically 1, which makes it relatively easy to factor the quadratic expression

When we have quadratic expressions where the coefficient of x² is NOT 1 (as in 9x²), it's typically the case that the expression can be factored in the form (a + b)(a + b) OR (a - b)(a - b)

So, when I see 9x² + 30xy + 25y², I recognize that 9x² can be written as (3x)² and 25y² can be written as (5y)²

So, it's possible that 9x² + 30xy + 25y² = (3x + 5y)(3x + 5y)

When I expand and simplify (3x + 5y)(3x + 5y), it turns out that this is the correct factorization.

All of this is covered later in the course at https://www.gmatprepnow.com/module/gmat-algebra-and-equation-solving/vid...

Cheers,

Brent

## Joanna bought only $0.15

(1) She bought $4.40 worth of stamps.

(2) She bought an equal number of $0.15 stamps and $0.29 stamps.

Please share an easy way to calculate 1st statement.

## That's a tricky (and often

That's a tricky (and often discussed) question!

Here's my full solution: https://gmatclub.com/forum/joanna-bought-only-0-15-stamps-and-0-29-stamp...

Please let me know if you need any clarification.

Cheers,

Brent