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## Comment on

Introduction to GMAT Data Sufficiency## This video on Data

## Hi Francena,

Hi Francena,

Thanks for taking the time to say that. I'm glad you liked the video.

Cheers,

Brent

## Hi Brent, I´m wondering if

-If a real estate agent received a commission of 6 percent of the selling price of a certain house, what was the selling price of the house?

(1) The selling price minus the real estate agent's commission was $84,600.

(2) The selling price was 250 percent of the original purchase price of $36,000.

## Here's my full solution:

Here's my full solution: https://gmatclub.com/forum/if-a-real-estate-agent-received-a-commission-...

## Thank you so much for all the

On her way home from work, Janet drives through several tollbooths. Is there a pair of these tollbooths that are less than 10 miles apart?

(1) The first tollbooth and the last tollbooth are 25 miles apart.

(2) Janet drives through 4 tollbooths on her way home from work.

## Here's my full solution:

Here's my full solution: https://gmatclub.com/forum/on-her-way-home-from-work-janet-drives-throug...

## This is one of the D/S

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

17, x, 35, 12, y

Is the range of the five numbers in the list above less than 30 ?

(1) 6 ≤ x ≤ 20

(2) y = 2x

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

The correct answer is ''BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.''

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

However, I'm confused with the explanation below.

Given (1) and (2) together, it follows that 6 ≤ x ≤ 20 and y = 2x. Since the minimum and/or maximum of the numbers in the list will depend on the values of x and y, it will be useful to divide the range 6 ≤ x ≤ 20 into the three intervals 6 ≤ x < 12, 12 ≤ x < 17.5, and 17.5 ≤ x ≤ 20. First, if 6 ≤ x < 12, then 12 ≤ y < 24, and so the least of the numbers is x and the greatest of the numbers is 35. Therefore, the range is 35 – x ≤ 35 – 12 = 23, which is less than 30. Next, if 12 ≤ x < 17.5, then 24 ≤ y < 35, and so the least of the numbers is 12 and the greatest of the numbers is 35. Therefore, the range is 35 – 12 = 23, which is less than 30. Finally, if 17.5 ≤ x ≤ 20, then 35 ≤ y ≤ 40, and so the least of the numbers is 12 and the greatest of the numbers is 40. Therefore, the range is 40 – 12 = 28, which is less than 30. Since in each of the three cases the range is less than 30, it follows that the range is less than 30 when 6 ≤ x ≤ 20 and y = 2x.

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

How did 35 result from this (this is quoted from the explanation above)?: First, if 6 ≤ x < 12, then 12 ≤ y < 24, and so the least of the numbers is x and the greatest of the numbers is 35.

Thanks!

## GIVEN: The five numbers are:

GIVEN: The five numbers are: 17, x, 35, 12, y

Since we're dealing with range, we need only examine the maximum and minimum possible values of x and y.

The MINIMUM value of x = 6

Since y = 2x, the minimum value of y = 12

So, the five numbers are: 17, 6, 35, 12, 12

In this case, the range = 35 - 6 = 29, which is less than 30

So, the answer to the target question is "YES, the range is less than 30"

The MAXIMUM value of x = 20

Since y = 2x, the maximum value of y = 40

So, the five numbers are: 17, 20, 35, 12, 40

In this case, the range = 40 - 12 = 28, which is less than 30

So, the answer to the target question is "YES, the range is less than 30"

From this we can be certain that the range is less than 30.

Does that help?

Cheers,

Brent

## Yes, very much so. Your

## Why is negative 3 (-3) not an

## x = 3 is a solution to the

x = 3 is a solution to the equation 2x = 6, because (2)(3) = 6

However, x = -3 is a not solution, because (2)(-3) = -6 [not 6]

I believe you may thinking of the quadratic equation x² = 9

With this equation, we have two solutions: x = 3 and x = -3

We know that x = 3 is a solution, because 3² = 9

And we know that x = -3 is a solution, because (-3)² = 9

Does that help?

## What is the difference

## Those three answer choices

Those three answer choices have some similarities, but there is a significant distinction.

The answer is A if statement 1 is sufficient, and statement 2 is not sufficient.

Here's an example where the correct answer is A:

Target question: What is the value of x?

(1) 2x = 10

(2) x < 100

The answer is B if statement 1 is not sufficient, and statement 2 is sufficient.

Here's an example where the correct answer is B:

Target question: What is the value of x?

(1) x < 100

(2) 2x = 10

The answer is D if statement 1 is sufficient, and statement 2 is sufficient.

Here's an example where the correct answer is D:

Target question: What is the value of x?

(1) x + 1 = 6

(2) 2x = 10

Keep in mind that EVERYONE struggles with Data Sufficiency questions at first. Once you answer a few dozen questions, you'll have no trouble distinguishing between the five answer choices.

## Thanks mate, i think you are

A 1 Correct, 2 Not correct

B 1 Not Correct, 2 correct

C 1 + 2 Both combined correct

D 1 Correct 2 correct (Mutually exclusive)

E 1 + 2 Both combined Not correct

## Exactly!

Exactly!

Although I'd replace "correct" with "sufficient"

## Hi Brent, Been bouncing

I had a look at the 650-800 difficulty question you linked below the video and had a question. https://www.beatthegmat.com/product-of-abc-t288448.html

I note one of the commenters/instructors on that thread stated that

"Since the two statements cannot contradict each other, the one case that satisfies statement 1 -- 1, 2 and 4 -- must also satisfy statement 2."

I've not come across this before, is this accurate?

If I have another similar question like 'is the value of Y known?'

Can it be possible to have 2 sufficient equations for finding Y that give different values?

Many thanks

## I'm glad to hear your

I'm glad to hear your enjoying the lessons!

Yes, Mitch is correct to say that the two statements can't contradict each other. I talk about that feature in the following lesson: https://www.gmatprepnow.com/module/gmat-data-sufficiency/video/1104

So, for example, the following would never be an official Data Sufficiency question since it yields contradictory information about the value of x:

What is the value of x?

(1) 2x = 10

(2) x - 1 = 2

Keep in mind that this concept is different from having more than one possible solution to an equation. Consider this example:

What is the value of x?

(1) x² - 5x + 6 = 0

(2) x² + 2x - 8 = 0

When we factor statement 1, we get (x - 2)(x - 3) = 0, which means either x = 2 OR x = 3.

Since there are two possible values of x, we can't answer the target question with certainty.

So, statement 1 is not sufficient.

Likewise, when we factor statement 2, we get (x - 2)(x + 4) = 0, which means either x = 2 OR x = -4.

Since there are two possible values of x, we can't answer the target question with certainty.

So, statement 2 is not sufficient.

When we COMBINE the two statements we see that...

Statement 1 tells us x = 2 OR x = 3

Statement 2 tells us x = 2 OR x = -4

Since both statements must be true, it MUST be the case that x = 2, in which case the combined statements are sufficient, and the correct answer is C.

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