Lesson: Properties of Real Numbers

Comment on Properties of Real Numbers

a + 0 = a
1 x a = a
a x 0 = 0
Is this stuff actually tested on the GMAT?
gmat-admin's picture

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 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
gmat-admin's picture

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 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.
gmat-admin's picture

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,

In this link below
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
gmat-admin's picture

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 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 covered in this video with almost any of all the exercises under the related resources. What am I missing?
gmat-admin's picture

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.

Trying to sign up and am getting the message your Paypal is down? Please advise?
gmat-admin's picture

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

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?
gmat-admin's picture

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 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
gmat-admin's picture

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

Hi Brent,

could you please explain how we should interpret bracket and multiplication
6÷2(1+2) = 9 or 1 ??
gmat-admin's picture

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,

I didn't understand your answer in this question: http://www.beatthegmat.com/og13-ds-133-t124839.html

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
gmat-admin's picture

Question link: http://www.beatthegmat.com/og13-ds-133-t124839.html

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
+ 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
gmat-admin's picture

Question link: https://www.beatthegmat.com/a-and-b-represent-digits-t111247.html

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,
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?

Thanks in advance!!
gmat-admin's picture

Hi Pradeep,

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,

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
gmat-admin's picture

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

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
gmat-admin's picture

Question link: https://gmatclub.com/forum/if-x-y-and-z-are-three-digit-positive-integer...

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 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
gmat-admin's picture

Hi Fatima-Zahra,

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

Cheers,
Brent

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