Caringbah 2020 trials q10 (1 Viewer)

[jane1820]

answer says D (w no explanation) but the only answer i keep getting is 1/6

 

[ivanradoszyce]

Hi,

D is the correct answer. The highest product of the 3 scores one can get if one rolls 3 dice is . List all the perfect squares less than 216. These are:

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196

So let's consider them individually.

1 - we could have a 1 on the first die, 1 on the second die and 1 on the last die. I'll write it as (1, 1, 1) - 1 option only
4 - (1,2,2), (2,1,2), (2,2,1) or (4,1,1), (1,4,1), (1,1,4) - 6 options
9 - (3,3,1),(3,1,3), (1,3,3) - 3 options

I'll use a bit of combinatorics theory here - It's not that hard!

16 - Arrange 3 numbers in a row (4,2,2) of which 2 are identical. Also arrange 3 numbers in a row (4,4,1) of which 2 are identical - 6 options in total
25 - (5,5,1) Arrange 3 numbers in a row (5,5,1) of which 2 are identical - 3 options
36- (6,6,1) arrange 3 numbers in a row of which 2 are identical. (4,3,3). Arrange 3 numbers in a row of which 2 are identical. Arrange (2,3,6) in a row - 12 options in total
49 - No combinations (product of 2 primes, each prime is greater than 6.
64- (4,4,4) - 1 option only
81 - No combinations since factor 9 is greater than 6.
100 - (5,5,4) arrange 3 numbers in a row of which 2 are identical. 3 options
144 - (6,6,4) arrange 3 numbers in a row of which 2 are identical. 3 options

Total number of options

The probability that the product of the 3 scores is a perfect square is

What a nice little question.

 

[jane1820]

thank you @ivanradoszyce !!
but in the exam do i have to list all the factors? doesnt that take more than a minute since multiple choice should take maximum a minute?

is there a quicker way?

 

[ivanradoszyce]

You could automatically eliminate A and B, since the number of options(just by quick examination) is more than 6 or 13.