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### 24 Cards in this Set

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 A and B are both two digit numbers. If A and B contain the same digits but in reverse order, what integer must be a factor of (A + B)? A + B = 10 x + y + 10y + x = 11x + 11y = 11(x+y) So, 11 must be a factor of A + B. When a question asks you about "digits", think 100h + 10t + u etc…. What is the Last Digit Shortcut? What is the units digit of 4^2 * 9^2 * 4^3? Only pay attention to the last digit of every intermediat product. 0. What is the Heavy Division Shortcut? Only pay attention to first few digits…and divide. For proper fractions between 0 and 1:As the NUMERATOR goes up, the fraction __ INCREASES For proper fractions between 0 and 1:As the DENOMINATOR goes up, the fraction __ DECREASES Increasing BOTH the numerator and the denominator by THE SAME VALUE brings the fraction_________ closer to 1… When you have complex ractions, you can NEVER split the ______ DENOMINATOR What is a Benchmark Value? Simple fractions with which you are already familiar. Percent change _____ Change / Original * 100. Simple Interest equation: Principle * Rate * Time Compound Interest Equation: P(1 + r/n) ^ (nt) P = Principle. R = rate. N - number of times per year. T = # of yrs Chemical Mixture Problems: 500 ml solution is 20% alcohol. If 100 ml of water is added, what is the new concentration of alcohol? Alcohol 100 ml 20% Alcohol 100 ml Water 400 ml 80% Water 500 ml Total 500 ml 100% Total 600 ml 100% 100 / 600 => 16.6% 1/100 => Decimal, Percent .01, 1% 1/50 => Decimal, Percent .02, 2% 1/25 => Decimal, Percent .04, 4% 1/20 => Decimal, Percent .05, 5% 1/10 => Decimal, Percent .1, 10% 1/8 => Decimal, Percent 0.125, 12.5% 1/6 => Decimal, Percent .1666, 16.6% 1/5 => Decimal, Percent .2, 20% 1/4 => Decimal, Percent 0.25, 25% The key to DS problems dealing with FDP's is to rephrase questions / statements into equations in order to keep track of what you know and what you need to know… DS: If a brokerage firm charged a commission of 2% of the total dollar amount of a certain trade, what was the total dollar amount of that trade? I. The dollar amount of the trade minus the brokerage firm's commission was \$88,000. II. The brokerage firm's commission decreased the profit earned on the trade by 20%. d = total dollar amount of trade. Let c - brokerage firm's commission -> c = .02d Test each statement, writing equations to represent information. If the info in the statement can be combined w/ the info in the question to ield a single equationwith the single variable d, then the statement is sufficient: I.: d - c = \$88,000 Rephrase: d - .02d = 88,000. Sufficient. II. P = profit before commission. p - c = .80p. We do not know p, the amount of profit before commission, so you cannot solve for c, the brokerage firm's commission. Not Sufficient.