EA Math Practice

Question 1

If Randy has twice as many coins as Alice, and if Maria has 7 times as many coins as Alice, what is the combined number of coins that all three of them have?

(1) Alice has 4 fewer coins than Randy.

(2) Maria has 20 more coins than Randy.

Answer 1

R = 2A
M = 7A
—
A + 4 = R
R + 20 = M

Question 2

Answer 2

Question 3

Answer 3

Question 4

Answer 4

Remember to make equations where possible

Question 5

Answer 5

Question 6

Simplify 14.25 / 91.25

Answer 6

(a) Find a simple fraction that is closest, e.g. in this case 1/6. Know that 1/6 is 0.1666. Adjust for actual numbers slightly if possible.
(b) Simplify (in this case divide by 25). Then do the above. The smaller numbers will make adjusting easier

Question 7

Last year, all registered voters in Kumannia voted for the Revolutionary Party or for the Status Quo Party. This year, the number of Revolutionary voters increased 10%, while the number of Status Quo voters increased 5%. No other votes were cast. If the number of total voters increased 8%, what fraction of voters voted Revolutionary this year?

Answer 7

Two tricks:
- Watch for x + y = 100%
- Sub in an easy number

Here make the total for last year 100. So T = R + (100-R).

This year 1.1R + 1.05(100-R) = 108.

Question 8

A grocery store sells two varieties of jellybean jars, and each type of jellybean jar contains only red and yellow jellybeans. If Jar B contains 20% more red jellybeans than Jar A, but 10% fewer yellow jellybeans, and Jar A contains twice as many red jellybeans as yellow jellybeans, by what percent is the number of jellybeans in Jar B larger than the number of jelly beans in Jar A?

Answer 8

Very simple if:
- Assume some number (e.g. here Jar A has 100 red)
- Make a simple table

Question 9

A feed store sells two varieties of birdseed: Brand A, which is 40% millet and 60% sunflower, and Brand B, which is 65% millet and 35% sunflower. If a customer purchases a mix of the two types of birdseed that is 50% millet, what percent of the mix is Brand A?

Answer 9

Here assume some number (100) for the amount of Brand B.

0.4(x) + 0.65(100) = 0.5 (x + 100)

Question 10

A string of 10 lightbulbs is wired in such a way that if any individual lightbulb fails, the entire string fails. If for each individual lightbulb the probability of failing during time period T is 0.06, what is the probability that the string of lightbulbs will fail during time period T ?

Answer 10

This is tricky. I initially answered 0.6^10. However, this is the probability that all fail. (Logically, I should have known this was incorrect as the probability gets smaller as the number of bulbs increases).

Instead the answer is 1 − (0.94)^10

Question 11

If a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many such committees are possible?

Answer 11

This was hard.

Easies solution might be more manual. (1086) to reflect the total number of options divided by 3! because the order does not matter.

Note I tried using the standard equation for a combination (3 of 5 spots) but this fails to fully account for 2 options per seat. The result 10 must be multipled by 2 for each seat (i.e. 3 times)