# Lesson: Introduction to Decimals

## Comment on Introduction to Decimals

### Hi Brent

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!

### Hi Matt,

Hi Matt,

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.

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

Please advise sir.

### Absolutely. Our lessons cover

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,

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

### That's a great technique, Ana

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

Cheers,
Brent

### Hi 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

### That is a CRAZY hard question

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:/

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

### Question link: https:/

Perfectly reasoned - nice work!

### HI Brent,

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.

### Be careful, 3.9 is not an

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-...