NUMBER PROPERTIES

[\'manpreet singh]

Q.1 answer each question: YES,NO, or CANNOT BE DETERMINED.

1.If j is divisible by 12 and 10, is j divisible by 24?
2.If k is divisible by 6 and 3k is not divisible by 5, is k divisible by 10?

Q.2

A skeet shooting competition awards prizes as follows: the first place winner receives
11 points, the second place winner receives 7 points, the third place finisher receives 5
points, and the fourth place finisher receives 2 points. No other prizes are awarded.
John competes in the skeet shooting competition several times and receives points
every time he competes. If the product of all of the paints he receives equals 84,700,
how many times does he participate in the competition?

[anuprajan5]

Q1.

1. This tells me that
j divisible by 12 - j has atleast 2^2*3
j divisble by 10 - j has has 2*5

For j to be divisible by 24, j has to have 2^3*3. My answer would be CANNOT BE DETERMINED because j just needs one more 2 to have the necessary factors to be divisible by 24. It can be a plausible situation.

2.If k is divisible by 6 and 3k is not divisible by 5, is k divisible by 10?

k has 2 factors - 2 and 3
3k not divisible by 5, which means that k does not have 5 as a prime factor.

Therefore k is not divisible by 10 as it needs 5 as a prime factor. Hence NO

[anuprajan5]

Q.2

A skeet shooting competition awards prizes as follows: the first place winner receives
11 points, the second place winner receives 7 points, the third place finisher receives 5
points, and the fourth place finisher receives 2 points. No other prizes are awarded.
John competes in the skeet shooting competition several times and receives points
every time he competes. If the product of all of the paints he receives equals 84,700,
how many times does he participate in the competition?


[spoiler]84700 - 2^2*5^2*7*11^2. Adding up the powers, John participated 7 times.[/spoiler]