(159,919)/((409)*(17))

I think the easiest approach is rounding numbers + scanning answer choices:

> 17*409 = 6953 ~ 7000;

> 7.000*23 ~ 161.000, which is close to 159.919;

Therefore the answer is C, 23;

Okay, I know that it comes out as an integer, so I know that the big number on top must be divisible by both 409 and 17.

Since I already know it's divisible, I'll just divide them! I call this the 'caveman approach' in my classes. You can either waste time looking for the elegant, 'smart' approach - or, if you're quick with arithmetic, you can just do the 'obvious' approach and it won't take 2 minutes.



Now I have a much more manageable problem: 9407 / 409. There are a few ways to proceed:

- approximate. This is about 9400/400, or 94/4 = 47/2 = 23.5. Guess 23.

- Look at the units digits. Something ending in 7, divided by something ending in 9, will result in a final digit of 3. Choose 23.

- Finish the division the old-fashioned way.

Hey!!

I tried solving this question using estimation and got 20 as the answer.

Here is the method:
160000/(400*20)
= 160/8
= 20

What went wrong? Please guide.
Thanks.

I think the easier way to approach this is to divide the numerator by denominator one by one.

159,919/409 x 17
9407/409
23

Answer D

That's a great way to solve such questions. But it would be great if someone could tell what went wrong while estimating so that I could work on the gap.

Thanks

When I first read your answer, I thought you meant any number divided by a number ending in 3 will equal a number ending in 3. The second time, I read "a number ending in 9 divided by a number ending in 3 must equal number ending in 3"..

Yeah, I was going for that second thing. I just stated it a bit casually.

Was so close but have to do some additional calcs:
(159,919)/(409*17)=(160000-81)/(409*17)=((400-9)(400+9))/((400+9)*(17))=((20-3)(20+3))/(20-3)=20+3=23. D it is

My take on this:
159,919/(409(17)) = 159,919/6,953

6,953 * (answer) must have a units digit of 9

A. 17 -> units digit of 1
B. 19 -> units digit of 7
C. 21 -> units digit of 3
D. 23 -> units digit of 9
E. 27 -> units digit of 1

Therefore, D (23) is the correct answer.

So my method was a little different yet somehow the answer was correct. I'm not sure if I should use the same in the future, this is how it goes:

round up 159,919 to 160,000
round 409 down to 400 and 17 up to 20

--> this roughly becomes 160,000/8,000

This step helps me rule out the first two options

next, I come back to the original numbers:
159,919/(409*17)

Here, 409*17 gives 3 in units place
Dividing 159,919 by a number with 3 in units place with give me a quotient with 3 in the units place

--> brings us to option D - 23

Units digit of denominator is 3 you will get units digit 9 when multiplied by 3. Thus 23.

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Iterative use of difference of squares formula:

(159,919)/[(409)*(17)] = (160,000-81)/[(400+9)*(20-3)] = [(400ˆ2-9ˆ2)]/[(400+9)*(20-3)] = [(400-9)*(400+9)]/[(400+9)*(20-3)] = (400-9)/(20-3) = [(20-3)*(20+3)]/(20-3) = 20+3 = 23