Help with some sat questions?

Question

If $156 is divided among three people in the ratio of 1/2: 1/3: 1/4, what is the difference between the greatest share received and the least share received?
A $34.67
B $36
C $39
D $48
E $72

Of the total number of days in a week, what fraction of them occur only 52 times in a leap year?

At a casino there are three tables. The payoff at the first table is 10:1, at the second 30:1, and at the third 40:1. If a woman bets $10.00 at each table and wins at two of the tables what is the difference between her maximum and minimum possible gross winnings?
A $200
B $300
C $400
D $500
E $600

Answer 1

(1) 1/2 + 1/3 + 1/4 = 13/12. Use the reciprocal of that number to divide up the loot:

The first person gets $156 * 1/2 * 12/13 = $72

The third person gets $156 * 1/4 * 12/13 = $36

The difference is $72 - $36 = $36.
That's answer (B).

(2) Two wins at the smallest-paying two tables (10:1 and 30:1) would net $100 + $300 = $400 on two $10 bets.

Two wins at the best-paying two tables (30:1 and 40:1) would net $300 + $400 = $700 on two $10 bets.

In both cases there are two $10 losses, so the difference between the two grosses doesn't change.

The difference is $700 - $400 = $300.
That's answer (B).

Answer 2

1) Change up the ratio, multiply each by 12.

6:4:3 (sum up to 13 shares total)

Divide 156 by 13 to get 12. So each share is 12.

The takes are 6*12, 4*12, and 3*12.

Simply: $72, $48, and $36.

2) A leap year has 366 days. 52 weeks has 7*52=364 days. So two of the days have to get used an extra time. 5/7 are used only 52 times.

3) Her best possible would be to lose at the least-stakes table. That means she'd lose 10 and win 300 at one and 400 at another, for a total of 690.

Her worst possible would be to lose at the highest-stakes table. That means she'd lose 10 and win 300 at one and 100 at the other, for a total of 390.

The difference is $300. You can figure this quicker if you realize that this is just the difference of the highest stakes winnings and the lowest stakes winnings.

Answer 3

There are 365 days in a leap year. 52x7 will tells you that there can be 52 full weeks in 364 days. The extra day is going to be your odd ball. so 6/7 days of the week occur 52 times in a leap year.

The least the woman can win is $400. $100 from the 10:1 table and $300 from the 30:1 table.
The most she can win is $700. $300 from the 30:1 table and $400 from the 40:1 table.
The difference is $300.