Jack Z.

Graduating Industrial Engineer at Georgia Tech

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SSAT

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Question:

The price of a new computer is $1000. The company then decides to raise the price by 35 percent. Later on it then decides to cut this new price by 20 percent. What is the resulting price of the computer?

Jack Z.

Answer:

We first have $1000 as the price. Raising that by 35% means multiplying this by 1.35. 1000*1.35 = $1350 Then the company cuts the price by 20%. A quick rule of thumb for this percentage is to find 10% then double it. 10% can be found by simply sliding the decimal point one point to the left, so 10% of 1350 is 135. Double this to find 20% and we get 135*2 = 270. So cutting the price by 20% results in 1350-270 = 1080. So the final price is $1080.

SAT II Mathematics Level 1

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Question:

What is the probability that someone rolling 2 dice gets a combined total of 6?

Jack Z.

Answer:

First off their are 36 total outcomes, 6 possibilities of dice 1 combined with 6 possibilities of dice 2. 6*6=36 Dice 1 has possible outcomes of 1, 2, 3, 4, 5, and 6. Looking at these 6 options, we can pair together outcomes of dice 2 that create a sum of 6. So we have pairings: 1+5=6, 2+4=6, 3+3=6, 4+2=6, 5+1=6. If dice 1 is a 6 we have no feasible combination since the sum will always be higher than 6. So we have 5 options for summing to 6. The answer would be 5 out of the possible 36 options, so 5/36.

Statistics

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Question:

What is the probability of getting a full house in a game of 5-card poker? (3 of one number, 2 of another)

Jack Z.

Answer:

First the number types must be selected. There are 13 types of cards (Ace thround 10, Jack, Queen, King). For the first card, it is 13 choose 1. For the second card, because we have already selected one, it is 12 choose 1. Once we have that, we have 2 sets of 4 cards. One needs to have 3 of a kind; the other 2. So we have 4 choose 3 and 4 choose 2. The final solution for this problem is (13 choose 1)*(12 choose 1)*(4 choose 3)*(4 choose 2) which is approximately .0014, or .14%

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