Q: A Math quiz has  multiple-choice questions, each with  choices. A student passes the quiz with  or more correct questions. If the student randomly picks their answers, what is the probability of passing the quiz?

A: 7/27  = 1/27 + 6/27
Scenario 1: The student gets all 3 correct (1/3) x (1/3) x (1/3) = 1/27
Scenario 2: The student gets 2 correct.  1/3 x 1/3 x 2/3 but this can happen 3 different ways as the student could get the 1st one incorrect or the 2nd or the 3rd.
so (1/3)x (1/3) x (2/3) x 3 = 6/27
1/27 + 6/27 = 7/27.

Q: If you only have 4s and 5s to make other numbers (such as 4 + 4 + 5 = 13 and 5 + 5 + 5 + 5 + 5 = 25),  how many numbers from 1 to 1000 have this property ?

A: 994
Which #s cannot be made?  There are 6 numbers that cannot be made:1 2 3 6 7  or 11.
That leaves 994 numbers.
All others can be made from 4s and 5s as 8 is 2 4s and 9 is 4 and 5 and 10 is 5 and 5.
After 12 which is 3 x 4, all other numbers can be made.
See above for 13, 14 is 9+5, 15 is 3 5s, 16 is 4 4 s 17 is 12 +5, 18 is 14 + 4, 19 is 15 +4 and so on and so on…

Q: Sabina’s car has 50% better fuel efficiency (miles per gallon) than her old car.  The new car uses diesel which is 20% more costly than the gas in her old car.  On a percent basis, how much will she save on a long trip?

A:  20%
For this problem, we made up numbers to make the Math easier :)
We can use 10 miles per gallon for Sabina’s old car which would make the new one 15 mpg.
We can pick an easy number that plays nice with 10 and 15 like 30.
If she goes 30 miles on a trip, she will need 3 gallons with the old car but only 2 gallons with the new car.
Now we need a price for gas so we assumed $4.
If gas is $4/gallon but diesel is 20% more at $4.80 per gallon, she would have spent 3 x $4 = $12 with the old car but now spends only $9.60 for the new car (2 x $4.80).
She saved $2.40 on $12 which is a 20% savings.