Heavy division shortcut

[smehmood]

Pg 26, Q6 in the FDP guide is related to heavy division shortcut. The explanation is not very clear, could you please explain the method particulary how do we change the numerator and denominator before the division?
Thanks

[jnelson0612]

Hi there,
Our numbers are as follows:
4,509,982,344
5.342 * 10^4

The first thing we should do is convert the denominator to a real number. 10^4 is 10,000, so 5.342 * 10,000 is 53,420.

Now, let's round the top and bottom numbers so we can easily divide the bottom into the top. I notice that I have a 45 on top and a 5 on the bottom; since 45 is divisible by 5 let's convert every other number to 0.

Thus,
4,500,000,000
50,000

Now you can cancel four zeros on the top and bottom and arrive at 450,000/5, or 90,000.

[christinebruton]

This was posted a while ago but I'll try a question since I was also fuzzy on the explanation. The question asks to "estimate to the nearest 10,000." How does that factor into the steps? Is it just luck that the end result is given in the 10,000's?

[jlucero]

This was posted a while ago but I'll try a question since I was also fuzzy on the explanation. The question asks to "estimate to the nearest 10,000." How does that factor into the steps? Is it just luck that the end result is given in the 10,000's?

Most estimation problems will be written in a way that an easy estimation takes place, so I wouldn't worry about this too much. In this problem, Jamie noticed that 45 and 9 are easily divisible and then didn't worry about the other numbers. In fact, I've never seen an estimation question that didn't have some sort of trick that made the computation very straightforward.

That said, estimation is simply a faster way of dividing and then rounding. So if you do get stuck finding easy numbers to use, round the numbers to something manageable, divide like normal, and then stop once you get to the accuracy you are aiming for. Technically you should go one past the value you want to round to and use the next spot, in this case thousands, to estimate whether to round up or down

[GagandeepS790]

what if we just follow the above explanation that is provided in the book
like 454998.2344%5.343

and then 454998%5
that come out to be 9998 and not 90000
and also how can we just me every other digit 0 ,leaving only 45 and 5

[Sage Pearce-Higgins]

I'm struggling to locate this problem in my FDP Strategy Guide. Which edition are you working off please?

It looks like the other solution is using some estimation. Since you don't have a calculator on the quant section of GMAT, you'll never be expected to do such a difficult calculation as 4,509,982,344 / (5.342 * 10^4) precisely. If you approximate it to 4,500,000,000 / 50000, then the answer comes out as 90,000.

and then 454998/5
that come out to be 9998 and not 90000
It looks like you've mislaid a 0 somewhere: I make the answer about 91,000