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Quantitative Reasoning Test 1 (100 OUT OF 100)
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Definition of percentage Per 100, how many parts per 100 Hundredths 5 % 5/100 or .05 are all the same in hundredths Tenths 3/10 or .3 or 30% notice the decimal in in the tenth place 5% of a class of 40 students get an A equals how many students? 5/100 * 40/1= 200/100 or 2 (students) What if you have a % in your decimal like .003%? Take the number & write it over 100 to make a fraction- .003/ The Three basic uses of percentages
- A portion of something; to express a fraction of a total or a ratio. 2. How something, a value, has changed or is different. 3. A compared value or comparison of two different numbers.
(Percentages are always a comparison; either of the total, a previous value or 1 out of 2 values to some standard value which signifies 100% which is the standard value always goes in the denominator) Appropriate uses of percentages
- To describe change ie. population growth, rising price, pay comparisons. 2. To describe a fraction of the total (work force). 3. To compare the performance or cost of products. Common abuses of percentages
- Shifting reference values (percentages fail if you don't have a standard & that standard must be constant or already known) 2. less than nothing, 2. Don't average percentages unless both tests happen to have the exact same number of questions. Absolute Change Describing a Change in a value describes the actual increase or decrease from a reference value to a (new) smaller or larger value. Absolute change=NV - RV new value minus the reference value (reference value is always the previous value, or, the New value minus the old, or new value-reference value Absolute Change for Comparisons of two different vaues the actual difference between the compared value and the reference value. Absolute difference = compared value - reference value. AD=CV-RV Relative Change that Describes a Change is a fraction that describes the size of the absolute change in comparison to the reference value: Relative change = the absolute change divided by the reference value which = the new value minus the reference value divided by the reference value.
More than is P% more than the original value or Reference value which is stating the relative change in the value. Of is looking at the ratio of the new value to the original value; 3 to 1 or 300% of the original value. They are similar in that 300% = 100% + 200% (pg 134) If the compared value is P% more than the Reference Value it is (100+P)% of the reference value If the compared value is P% less than the reference value it is (100-P)% of the reference value (pg 134) Percentage points versus % Percentage points are an absolute change or difference. Percentage is a relative change or difference. pg 135 50 is what percent larger than 25? 50 is 100% MORE THAN 25, or, 50 is 200% OF 25 30% of versus 30% off; Which is a better savings? 30% of because that would mean 70% off as opposed to 30% off. 100% off anything would be? Zero, there would be nothing left, except in money where you could go into debt.
Percentages are often called Rates Translating a more than statement into an of statement Retail prices are 100% + 25% = 125% of wholesale prices. You replace the of with multiplication. The retail price =125% times the wholesale price. If the compared value is P% more than the reference value then the compared value = 100% + P% times the reference value and the reference value = the compared value divided by 100% +P% If the compared value is less than the reference value then Use 100-P instead of + (plus) Shifting Reference Values The reference value shifts during the problem; it can be higher or lower in the first calculation versus the second. Consider this statement, Your investment lost 60% the first year but gained 75% the second, so you're 15% ahead. An investment of $1,000 that lost 60% of its value would leave you with $400, in the second year your investment gained 75%, of $400, which would be $300, for a total of $700. This is less than your original investment not a gain of 15% overall. Don't average percentages; why? Unless both tests or averages have the exact same numbers they wouldn't be an accurate average. You should NEVER average percentages.
- True Positives 2. False Positives 3. True Negatives 4. False Negatives pg. 186 True Positive an actual positive, malignant, result for a malignant tumor False Positive A benign tumor gets a positive, malignant, result in which the results suggests their tumor is malignant. True Negative Identifies benign tumors as benign. False Negative The result is negative even though the women actually have cancer. pg. Ratio Dividing two values to find the ratio of the two quantities. The ratio of $80,000 and $20,000 is $80, divided by $20,000 which equals 4 to 1. Notice the units of dollars cancelled each other out so the ratio is just a number. Because comparisons only make sense when compared with quantities of the same units, they always end up without units. What does accuracy mean in terms of positive or negative test results?What does it mean when it says it has an accuracy of 95%? The True Positive & True Negative are only guaranteed to be correct 95% of the time- Of the people who actually do or don't have the condition.The accuracy of that test when they give it to you. Ex. You're actually are or are not tested correctly 95% of the time (true Positive or True Negative 95% correct)
Compare the graduation rate in NE to LA; which is the Relative value? The term that comes after to-LA Compare the graduation rate Between NE 65% & LA 90% Their asking the same thing. Absolute change divided by the Relative Value = 90-65 divided by 90 or 25 divided by 90 What is the ratio of the graduation rate in NE to LA? will be a fraction 90 divided by 65 reduced Simple Interest Interest paid on the principal, original, investment (each time) only & not on any interest added at a later date. The interest paid is the same every year. Simple Interest formula A= (P x APR) ^ Y Total amount would be principal times the APR times the number of years. Compound Interest Pays interest on the interest paid as well as on the original principal. The original principal plus added interest creates a new accumulated balance. Interest is paid on a higher principal balance each time it compounds (annually, monthly, daily, etc.).
Compound Interest formula for more than one time a year A= P (1+APR/n) ex (n*Y) Installment Loan A loan you pay off with equal regular payments. Also called an Amortized loan. The portions of installment loan payments going toward principal and toward interest vary as the loan is paid down. Early in the loan most of it goes towards interest & gradually decreases as the portion toward the principal gradually increases. Installment Loan formula PMT= P * (APR/n)
[1-(1+APR/n) ex (-nY)] To find payments on an installment loan
- Use the loan payment formula 2. Multiply the monthly payment by the loan term in months to find the total payments 3. Subtract the principal from the total payments to find the total interest. Credit cards interest charges operate like compound interest in reverse. Mortgage One of the most popular types of installment loans designed specifically to buy a home.
Down payment Amount of money you must pay up front to be given a mortgage, usually 10%-20% of the purchase price Closing costs Are fees you must pay in order to be given a loan. Two types: 1. Direct fees for appraisal, checking credit, etc. Usually a set dollar amount. 2. Fees charged as points where each point is 1% of the total loan amount. Many are divided into two categories of an "origination fee" and "discount points". per & 'to' = a fraction bar; compare LA population to NV population is LA:NV or LA/NV. Use this method for seemingly unrelated values only, not a changing value. Denominator of a ratio is always the Reference Value Periodic payment An agreement that calls for periodic payments on the loan amount until it's paid in full. What is a teaser rate? low interest rates that are offered for a short period, such as 6 months, after which the card reverts to a very high rates.
have multiple cards, financial troubles from compounding interest, interest charged on cash advances & late payments.
