Questions on base system

[email protected] wrote:Hi Abhey Kharbanda,

All of the questions that you'll face on the Official GMAT are in base-10, so you won't have to worry about working in any other base. That's a rather interesting question to be asking - have you been working with practice materials that expected you to convert your math to a different base?

GMAT assassins aren't born, they're made,
Rich

Thanks Rich, no I haven't been working on them but thought of asking it here

Abhey Kharbanda wrote:Hi guys, does the GMAT ask questions on base system?

For example: how would you write 2234 in base 4 to a number in base 7?

2234 in base 4

(2 x 4^3) + (2 x 4^2) + (2 x 4) + 4 = 128 + 32 + 8 + 4 = 172 (Base 10)

In Base 7... Wasn't sure how to do this formulaically, so I just logically reasoned it out.

172 (Base 10) = (3 x 7^2) + (3 x 7) + 4 = 334 (Base 7)

Can't have a "4" in base 4, etcetera.

The base number is always written as 10 in the base system

Abhey Kharbanda wrote:Hi guys, does the GMAT ask questions on base system?

For example: how would you write 2234 in base 4 to a number in base 7?

Fortunately no.
And even if you are asked one, you would be told in the question itself how to change from one base to another and then the question would be asked.

edit

800_or_bust wrote:
2234 in base 4

(2 x 4^3) + (2 x 4^2) + (2 x 4) + 4 = 128 + 32 + 8 + 4 = 172 (Base 10)

In Base 7... Wasn't sure how to do this formulaically, so I just logically reasoned it out.

172 (Base 10) = (3 x 7^2) + (3 x 7) + 4 = 334 (Base 7)

There are a couple errors here, but the idea is right! Some bases are easier to convert than others (i.e. you don't really have to run them through base 10), but I don't see an obvious way of doing 4 to 7 directly.

Should of course add explicitly again that BASE SYSTEMS ARE NOT TESTED ON THE GMAT AS OF 2016.

... which is a shame, because they're great fun (hint hint, GMAC! )

Matt@VeritasPrep wrote:... which is a shame, because they're great fun (hint hint, GMAC! )

Still holding out hope for these in GMAT 2017 ...

... though the newer inequalities and quadratics and whatever else are cool too

There isn't any base system on the GMAT (yet!), but it does appear on the Indian CAT.

And just for fun, 2234 isn't a number in base 4, since base 4 only has the digits 0, 1, 2, and 3. That said, suppose we have 2233 in base 4, and we want to convert it to base 7. We know that

2233(base 4) = 2*4³ + 2*4² + 3*4¹ + 3 => 175(base 10)

Now we want to put 175 in base 7. We start with the highest power of 7 that has a multiple less than 175: in this case, 7², which has the multiple 3*7². 175 - 3*7² = 28, so we have 28 left over. 28 = 4*7¹, so we're set:

175(base 10) = 3*7² + 4*7¹ + 0 => 340(base 7)

We also could try something like this:

2233 (base 4) =>

2000 + 200 + 30 + 3 (base 4) =>

2*1000 + 2*100 + 3*10 + 3 (base 4)

Since 10� (base 4) = 4� (base 10), we can replace 1000 with 4³, 100 with 10², etc.