# Lesson: Properties of Real Numbers

## Comment on Properties of Real Numbers

### a + 0 = a

a + 0 = a
1 x a = a
a x 0 = 0
Is this stuff actually tested on the GMAT?

### These concepts aren't tested

These concepts aren't tested directly, but many solutions require one to know the basic number properties covered in this video lesson. Keep in mind that you can skip lessons that cover information you already know. I suggest that, with each lesson, you skip to the lesson review at the end of the video. If you find that you already know that content, you can advance to the next lesson.

### Sir i am not understanding

Sir i am not understanding the concept you used in the question: A B
+ B
-----
B A A,B are digits.What is A?
CHOICE:5,6,7,8,9.You said B is odd.Please explain

### You're referring to http:/

You're referring to http://www.beatthegmat.com/a-and-b-represent-digits-t111247.html

Sorry, but I don't see anywhere in my solution where suggested that B is odd.

Am I missing something?

### I am sorry.My mistake. I

I am sorry.My mistake. I typed wrongly.Actually in your explanation you mentioned:
1. When we add B+B,the unit digit of the sum is A. This means that A must be even.
I am not understanding the logic behind this.Could you please explain.Explain the whole solution please.

### Notice that B+B = 2B = an

Notice that B+B = 2B = an even number.
Since the digit A represents the units digit of 2B, then we can be certain that A is even.

Let's look at some examples:
If B = 1, the B + B = 2, so A = 2 (which is even)
If B = 2, the B + B = 4, so A = 4 (which is even)
If B = 3, the B + B = 6, so A = 6 (which is even)
If B = 4, the B + B = 8, so A = 8 (which is even)
If B = 5, the B + B = 10, so A = 0 (which is even)
If B = 6, the B + B = 12, so A = 2 (which is even)
etc

### Hello Brent,

Hello Brent,

http://www.beatthegmat.com/positive-two-digit-integer-t265321.html

You said that greatest possible " Well, 9 is the greatest possible value of any integer" can you helo me on that

Regards,
Abhimanyu

### Thanks for catching that!

Thanks for catching that!

I have edited my response to say "9 is the greatest possible value of any DIGIT."

### Can you please explain tens

Can you please explain tens digit and unit digits? See question below. Thank you!

Is the positive two-digit integer N less than 40 ?

(1) The units digit of N is 6 more than the tens digit
(2) N is 4 less than 4 times the units digit

### I could not relate the topics

I could not relate the topics covered in this video with almost any of all the exercises under the related resources. What am I missing?

### You're right; many of the

You're right; many of the linked practice questions aren't related to the concepts covered in the video. Most of the questions deal with general number sense, so there isn't a specific video I can relate them to. So, I figured this page would be fine.

### Please try again. It looks

Please try again. It looks like PayPal was having some issues.

### Hello Brent,

Hello Brent,
It is suggested that students should first try to solve the reinforcement activities and then decide whether they need to watch the video or not. What should be the targeted correct no of questions, in order to skip the video tutorial?

### That depends entirely on your

That depends entirely on your target score. The higher the target score, the more questions you need to answer correctly.

### Brent- I'm thinking of going

Brent- I'm thinking of going through the videos and solving the questions directed to websites but holding off on solving questions from the OG17 book. What do you think? Do you think that strategy is fine though your learning guide says to watch the videos and then solve the OG probs? I figure doing those problems at a later point AFTER the videos and the online questions might be more beneficial. Let me know if you agree/disagree

### Waiting until you've mastered

Waiting until you've mastered the content before working on Official Guide questions sounds like a reasonable strategy.

### Hi Brent,

Hi Brent,

could you please explain how we should interpret bracket and multiplication
6÷2(1+2) = 9 or 1 ??

### Given: 6 ÷ 2(1 + 2)

Given: 6 ÷ 2(1 + 2)
This is the same as: 6 ÷ 2 x (1 + 2)
Do brackets first to get: 6 ÷ 2 x 3
When given option of division or multiplication, the rule is to perform the operations from left to right.
So, we divide first to get: 3 x 3
Evaluate: 9

### Brent,

Brent,

If we add 156+195=351, it implies that the sum of the hundreds digit of y and z is different from the hundreds digit of x, since the hundreds digit of y+z=2 and the hundreds digit of x is 3.

Please, help me understand this question.

Thanks,
Pedro

In my solution, I note 3 ways for the hundreds digit of x to be DIFFERENT from the sum of the hundreds digits of y and z.

The example that you provide (156 + 195 = 351) is an example of Scenario #2.

Cheers,
Brent

### A B

A B
+ B
____
B A
____

In the correctly worked addition problem above, A and B represent digits. What is A?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9

Hi Bret! Thank you for explaining this problem. But I could not understand why you have chosen B= 8 when you tried to apply it on the answer choice please as detailed below:
Let's check answer choice B, which says A=6
If A = 6, then B must equal 8 (since 8+8=16)
If A=6 and B=8, we get: 68+8=86 (doesn't work, eliminate B

Thanks
Fatima Zahra

In my solution (in the above link), I noted that the sum B+B must be greater than 9. We also know that the sum B+B must have units digit = A.

When we check answer choice B (A=6), we note that the sum B+B must have units digit 6. There are two possible values of B we must consider.

First, we have B=3, since 3+3 = 6 (has units digit 6), but this doesn't meet the condition that the sum B+B must be greater than 9)

Next, we have B=8, since 8+8 = 16 (has units digit 6). Since B=8 meets the condition that the sum B+B must be greater than 9, it MIGHT be correct.

However, when we test A=6 and B=8, we see that it doesn't work.

Does that help?

Cheers,
Brent

### Hi Brent,

Hi Brent,
If x, y, and z are three-digit positive integers and if x = y + z, is the hundreds digit of x equal to the sum of the hundreds digits of y and z?

Is there any shortcut to nail this question, it is very confusing about how to start the explanation?

This is part of a Data Sufficiency (DS) question. So, without any extra information, we cannot determine the sum of the hundreds digits of y and z.

Here's my full solution to the complete DS question: https://gmatclub.com/forum/if-x-y-and-z-are-three-digit-positive-integer...

Cheers,
Brent

### Hi Brent,

Hi Brent,

My question is not related to this topic. But I wanted to know if you have a similar topic wise (arithmatic, probability etc.) breakup of quant and verbal questions from the official quant and verbal review guides. And an improvement chart sheets.

Warm Regards,
Pritish

### Sorry, but I don't have

Sorry, but I don't have Improvement Charts for the Quant-only and Verbal-only guides.

### Hi Brent,

Hi Brent,
If x, y, and z are three-digit positive integers and if x = y + z, is the hundreds digit of x equal to the sum of the hundreds digits of y and z?

could you please make a video on this question? not able to understand it

It's a tricky question!

I don't have a video solution, but I do have a full solution here: https://gmatclub.com/forum/if-x-y-and-z-are-three-digit-positive-integer...

Please let me know if you'd like me to elaborate on any steps of my solution.

Cheers,
Brent

### Hi Brian,

Hi Brent,

Grateful if you could provide me with your answer to the below-mentioned question.

Thanks
Fatima-Zahra

https://gmatclub.com/forum/m-is-the-sum-of-the-reciprocals-of-the-consecutive-integers-from-143703.html

### Hi Fatima-Zahra,

Hi Fatima-Zahra,

Here's my full solution: https://gmatclub.com/forum/m-is-the-sum-of-the-reciprocals-of-the-consec...

Cheers,
Brent

### Hi Brent! I’ve been studying

Hi Brent! I’ve been studying following the Beat the Gmat in 60 days program and using the Gmat review 2018 edition
Do you think it differs from the 2020 edition much?
Should i be studying in a newer version?
Celine

### Good question!

Good question!
Each year GMAC (the GMAT test-makers) issue a "new" edition of the Official Guide for GMAT Review (aka OG).
In most cases, the new edition is 85% to 90% identical to the previous edition. The only change is that some of the practice questions have been replaced with new practice questions.
So, using the OG2018 is perfectly fine.

### Hi Brent,

Hi Brent,

What would be your approach to solve the following?
If the sum of the first n positive integers is x, then which of the following is the sum of the first 2n even positive integers?

Thank you!!

### In the future, please provide

In the future, please provide a link to the question (or post the entire question), since it's often important to see the answer choices.
Here's my full solution: https://gmatclub.com/forum/if-the-sum-of-the-first-n-positive-integers-i...

### Hi Brent,

Hi Brent,

For the overlapping set formula, I saw on Gmatclub from Bunuel's post the following:

Total= A+B+C- (sum of 2 group overlaps)+ all three + neither

Also:
Total=A+B+C- (sum of exactly two group overlaps)- 2*(all three) + neither

I understand how to use each of these, but from one of your videos I remember seeing the following formula: Total= A+B+C- sum of two or more overlaps)- in all 3 groups + none. Are these essentially the same and it's ok to use either?

### The two formulas you're

The two formulas you're referring to are as follows:
#1) Total = Group 1 + Group 2 + Group 3 - (sum of all 2 or more overlaps) + (in all 3 groups) + none.
#2) Total = Group 1 + Group 2 + Group 3 - (sum of members in EXACTLY 2 groups) - 2(All three groups) + none

I've never been a fan of these formulas, and I sincerely doubt that the test-makers would ever create a question that relied on students memorizing the formulas. As such, I don't include those formulas in my lessons.

PS: In the future, please try to write your question under the lesson related to that topic. For example, this question (involving 3 overlapping sets) would fit perfectly under the lesson about 3-Criteria Venn Diagrams (https://www.gmatprepnow.com/module/gmat-word-problems/video/921)