Problem Solving

From MGMAT CHALLENGE PROBLEM Of the week, didn't understand the binary part... if I calculate the powers they do not sum 100,010,000 nor 1,000,100,000. It's the first time I see binary form (as far as I can remember). Learning binary form will be usefull for the GMAT?

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Every digit of a number written in binary is either 0 or 1. To translate a number from binary, multiply the nth digit (reading from right to left) by 2^(n-1)

What is the largest prime number (written in binary) that is a factor of both 100,010,000 and 1,000,100,000 ?

(A) 10
(B) 11
(C) 101
(D) 1011
(E) 10001

[spoiler]Correct Answer (E)[/spoiler]

https://www.beatthegmat.com/mba/2011/04/ ... april-2011

No it does not really help for the GMAT.

Actually he is trying to demonstrate the example of exponents. And you inversed the properties.

The formula is to convert from binary to decimal.

100,010,000 in binary = Sum of (nth digit from right * 2^(n-1))
987,654,321 - digit positions of above number.
So the number indecimal form is
0 * 2^0 + 0 * 2^1 + 0 * 2^2 + 0 * 2^3 + 1 * 2^4 + 0 * 2^5 + 0 * 2^6 + 0 * 2^7 + 1 * 2^8
= 0 + 0 + 0 + 16 + 0 + 0 + 0 + 256 = 272.
Similarly you can convert all other numbers.
Then find the largest prime number.

guess that I should skip this problem then...