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Questions on base system

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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by Brent@GMATPrepNow » Sun Jul 10, 2016 4:26 am
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?
That kind of question would be out of scope for the GMAT.

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by [email protected] » Sun Jul 10, 2016 5:25 am
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?

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by Abhey Kharbanda » Mon Jul 11, 2016 12:51 am
[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?

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Thanks Rich, no I haven't been working on them but thought of asking it here
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by 800_or_bust » Tue Jul 12, 2016 6:10 am
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)
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by regor60 » Wed Jul 13, 2016 7:39 am
Can't have a "4" in base 4, etcetera.

The base number is always written as 10 in the base system
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by OptimusPrep » Sun Jul 17, 2016 8:37 pm
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.
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by Matt@VeritasPrep » Fri Jul 22, 2016 1:31 am
edit
Last edited by Matt@VeritasPrep on Fri Apr 28, 2017 12:41 am, edited 1 time in total.
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by Matt@VeritasPrep » Fri Jul 22, 2016 1:35 am
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.
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by Matt@VeritasPrep » Fri Nov 11, 2016 1:42 pm
Should of course add explicitly again that BASE SYSTEMS ARE NOT TESTED ON THE GMAT AS OF 2016.
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by Matt@VeritasPrep » Fri Nov 11, 2016 1:42 pm
... which is a shame, because they're great fun (hint hint, GMAC! :))
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by Matt@VeritasPrep » Wed Mar 15, 2017 4:48 pm
Matt@VeritasPrep wrote:... which is a shame, because they're great fun (hint hint, GMAC! :))
Still holding out hope for these in GMAT 2017 ...
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by Matt@VeritasPrep » Wed Mar 15, 2017 4:49 pm
... though the newer inequalities and quadratics and whatever else are cool too :)
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by Matt@VeritasPrep » Thu May 11, 2017 8:00 pm
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)
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by Matt@VeritasPrep » Thu May 11, 2017 8:03 pm
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.
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