Lesson: Introduction to Decimals

Comment on Introduction to Decimals

Hi Brent

In the Manhattan Prep practice question my thought pattern was similar to what you have provided in your model answer. However, I can’t make sense of the final part;

"If 1.43b5 rounded to the nearest THOUSANDTH = 1.436, then b MUST equal 5
So, x must equal 1.4355, which means 10 - x MUST equal 8.5645
Since we can answer the target question with certainty, statement 2 is SUFFICIENT”

Why MUST B equal 5? Why can’t B equal 6,7,8 or 9?

TIA!
gmat-admin's picture

Hi Matt,

Question link: https://gmatclub.com/forum/in-the-number-1-4ab5-a-and-b-represent-single...

KEY POINT: 1.43b5 rounded to the nearest THOUSANDTH = 1.436

Let's examine some cases...

If b = 5, the number becomes 1.4355
When we round 1.4355 to the nearest THOUSANDTH, we get 1.436
This MEETS the given condition

If b = 6, the number becomes 1.4365
When we round 1.4365 to the nearest THOUSANDTH, we get 1.437
This does NOT meet the given condition

If b = 7, the number becomes 1.4375
When we round 1.4375 to the nearest THOUSANDTH, we get 1.438
This does NOT meet the given condition

If b = 8, the number becomes 1.4385
When we round 1.4385 to the nearest THOUSANDTH, we get 1.439
This does NOT meet the given condition

Etc.

So, it must be the case that b = 5

Sir, your videos are amazing. But, are these videos alone sufficient to get a 700 on the gmat?

Please advise sir.
gmat-admin's picture

Absolutely. Our lessons cover all of the concepts and strategies required to achieve a 800 score on the GMAT. Each module (especially the Arithmetic module) begins with the most fundamental/basic concepts, and slowly works towards more advanced topics/techniques.

Cheers,
Brent

Hi Brent,

Please consider adding the following time saver to your lessons, as I personally have found it very helpful:
9x0.6 = 9x6/10 = 54/10 = 5.4

Thank you,
Ana
gmat-admin's picture

That's a great technique, Ana.
Thanks for sharing!!

Cheers,
Brent

Hi Brent,

Wondering of there's a quicker method to solve the below question, I followed a very lengthy process and still got the answer wrong.

https://gmatclub.com/forum/list-t-consist-of-30-positive-decimals-none-of-which-is-an-integer-131755.html
gmat-admin's picture

That is a CRAZY hard question! In most students, the best approach is to guess and use your time to answer questions that are much less insane.

That said, here's my full solution: https://gmatclub.com/forum/list-t-consist-of-30-positive-decimals-none-o...

Cheers,
Brent

Hey Brent for https://gmatclub.com/forum/there-are-24-different-four-digit-integers-than-can-be-141891.html

I did a different approach. I knew each number would get a spot 6 times (24/4). So the sum of all the numbers multiplied by 6 totaled to 84. Staggered them and added them to get the last 3 digits to be -324
gmat-admin's picture

HI Brent,

If Φ is a digit in the number n and n = 3.Φ6, what is Φ?

(1) When rounded to the nearest tenth n is 3.9
(2) When rounded to the nearest integer n is 4

In the second part, we have only one definite answer right? If I were to round off 3.Φ6 to the nearest integer - n is 4. That means, if we round off 3.96, N= 4. If we were to round off 3.86, rounding off would give us 3.9 not 4.

I am not understanding why the answer A and not D.
gmat-admin's picture

Be careful, 3.9 is not an integer.
The integers are: ...-3, -2, -1, 0, 1, 2, 3, 4....

So if we round 3.86 to the nearest integer, we get 4 (not 3.9)

Here's my full solution: https://gmatclub.com/forum/if-is-a-digit-in-the-number-n-and-n-3-6-what-...

https://gmatclub.com/forum/what-is-the-sum-of-all-3-digit-positive-integers-that-can-be-formed-us-78143.html
would you please give your approch for repitition problem?
gmat-admin's picture

Thanks a ton.
One last query.
If you notice, you will see bunuel posted similar type questions in that question comments thread. I thought we those can be solve by yours method.
So i tried every question (with repeating or non repeating way) but couldn’t able to do!
gmat-admin's picture

Those linked practice questions aren't very good.
Is there one you'd like me to solve?

If possible, can you post each ones (linked) with repeating and non-repeating ways?
gmat-admin's picture

Sorry, I'm not sure what you mean by repeating and non-repeating ways.

In the meantime here's an official question that's similar to the question I solved: https://gmatclub.com/forum/there-are-27-different-three-digit-integers-t...

I. E
, if the digits are allowed to repeat or no repeat within a number?
This line is written in the last question which i give you for solving.
gmat-admin's picture

Among the four linked practice questions, only one does not allow for repetition (https://gmatclub.com/forum/find-the-sum-of-all-the-four-digit-numbers-fo...), however that question has been locked, which means I can't submit a solution to it.

Here's my solution to the 4th linked practice question from Bunuel's list: https://gmatclub.com/forum/find-the-sum-of-all-the-four-digit-numbers-wh...

Note: Regardless of whether the digits can be repeated or not, the solution method will be the same each time.

I feel a little silly asking as it seems like I'm missing something very fundamental but at 03:1 minutes into this video you have 14.24800 - 3.18749. I am not sure I follow how you are subtracting the decimal points from each other. (I am doing it in my head in a very round about way, but I don't think I am grasping the fundamental process)
gmat-admin's picture

Once you add to zeros to the end of 14.248 to get 14.24800 - 3.18749, you can subtract the same way you'd calculate 1424800 - 318749, just be sure to keep track where the decimal point goes at the end.

For more practice and additional instruction, see: https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-arithmetic-o...

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