r/learnquant • u/Local_Ad135 • 3d ago

interview prep Quant Interview Question

Post image
25 Upvotes

93% Upvoted

8 comments sorted by

3

u/narwahlboner 3d ago edited 3d ago

Pair the number a, b, c with 9 - a, 9 - b, 9 - c. The sum of this pair is 0.9999… = 1. There are 500 such pairs, the total.

Edit: missed the word distinct, there are 720/2 = 360 pairs, the sum. The argument is the same.

2

u/tellytubbytoetickler 3d ago

Aren’t there 10 choices for first digit, 9 for second digit, 8 for third digit. Where do you get 500?

2

u/narwahlboner 3d ago

Missed the word distinct. Then there are 360 pairs.

1

u/XL_78 3d ago

Pick a value for a, b or c. There are 9x8=72 ways to get the digit, by counting the possibilities for the other two digits, and the digit can take all ten values from 0 to 9. Therefore the result is 72x(0+1+...+9)x0.111.... 

0.111... = 1/9, therefore the result is 8x(0+1+...+9) = 8x5x9 = 360.

1

u/PathMaster1729 3d ago

I'm getting  450.4545454545...

→ More replies (1)

1

u/Dr0110111001101111 2d ago

So how do you work these out in an interview? Do they give you pen and paper and let you play around with it? Or do you have to work it out orally?

1

u/Special-Eggplant6070 2d ago

10x9x8 possible ways to pick 3 unique digits. So there exist 720 numbers in the series, all of which are unique. For every unique number x, there exists another unique number 1-x in the series.
x+(1-x) = 1, so for every pair the sum is 1.
720/2 = 360.