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GMAT (Subject) / Economist Prep - Quant (Lesson)
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- Percentage translation English word --> Math translation what --> x, y... (any variable you like) percent --> % of --> * (times) is, are, were --> =
- Simple Interest Formula Simple Interest formula = Principal × Rate × Time Use simple interest in the following cases: The question explicitly uses the phrase "simple interest" The calculation time for the interest is shorter than the stated interest period. e.g. 12% annual interest calculated after a 6-month time period.
- Compound interest Example:John takes out a $10,000 loan at an annual interest of 12%, compounded semiannually. what will be the balance of the loan at the end of the year? Notice the following: 1) Interest rate = 12% annual 2) Time - 1 year 3) Compound - semiannually. Interest is calculated after six months, then again at the end of the year. Balance = P (1+r/n)n*t P = Principal, r = Interest rate (in %), n = number of times per year, t = number of years. In the case of the above example, the balance of the loan will be 10,000 (1+12% / 2)2 = 10,000 (1+6%)2 =$11,236.
- How to calculate compound interest Ballpark! Calculate simple interest under the same conditions Add a little => choose an answer choice that is a slightly higher!! OR: Model over a timeline
- Argument Flaw Questions We identify this question type through one of the following phrasings: 1. A major flaw in the argument above is that 2. The argument is flawed primarily because the author 3. Which of the following indicates a flaw in the reasoning above? 4. Which of the following points to the most serious logical flaw in the argument? 5. The argument is flawed because it fails to consider that...
- Geometry: Lines A line has no width and extends infinitely in either side. A line segment is determined by 2 points, and denoted by capital letters or a single lower case letter. (i.e. line AB, line m) If a line or a line segment seems straight, you may assume it is straight. If a line or a line segment passes through a point, you may assume it does.
- If b is the hypotenuse of the triangle, the sides opposite the angles are.. 45c : 45° : 90° b √2/2 : b √2/2 : b
- If a is an integer such that a2/123 is odd, which of the following must be an odd integer? Think about what value a could be. There are two things we know about a2, which we can use to infer about a: 1) a2 is divisible by 123, so it must contain all of the prime factors of 123 (at least) in order to be able to reduce the top of the fraction with the bottom and come up with an odd integer result. 2) a2 must be a perfect square, that is, it must have an integer square root. Break down 123 : (4⋅3)3 = 43⋅33 = (22)3⋅33 = 26⋅33. So a2 should at least equal 26⋅33. Can we take the square root of 26⋅33 and get an integer result? Taking the square root is the equivalent of multiplying the powers by 1/2, so if we take the square root of a2 = 26⋅33 we get a=23⋅33/2, which is not an integer.
- Sequences 1) Place dependent - The value of a term An is determined solely by its place in the sequence n. e.g. An = n+2 2) Term dependent - The value of a term An is determined by the value of the some other term, such as the preceding term An-1. e.g. An = An-1+4 3) Combination - The value of a term An is determined both by the value of the preceding term An-1 AND by its place n in the sequence - both are needed to calculate the value of An. e.g. An=An-1 - n + 2
- Formula of the nth term in a sequence Arithmetic sequence is an example of a sequence with a constant difference between every two terms. An = A1+(n-1)d - the nth term can be calculated by taking the 1st term and adding (n-1) "jumps" of d.
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- Arithmetic Sequence Formula The formula for the nth term is (the difference is labeled d): An = A1+(n-1)d
- Pattern for Remainder for Divisor 3 => What is the remainder when dividing 2^21 by 3? PATTERNS: Find a repeating pattern. remainder of 23 / 3? 8 / 3 is two with a remainder of 2. remainder of 24 / 3? 16 / 3 is five with a remainder of 1. remainder of 25 / 3? 32 / 3 is ten with a remainder of 2. It seems that when dividing 2n by 3, the remainder is 2 when n is odd and 1 when n is even. =>> Since 21 is odd, it follows that the remainder of 221 divided by 3 is 2.
- What is the Average in Arithmetic sequences? Average = Median. This includes, but is not limited to, consecutive integers
- If M is a sequence of consecutive integers which contains more than 11 terms, what is the average of M? (1) In M, the number of terms that are less than 10 is equal to the number of terms greater than 21. (2) There are 20 terms in M. statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked; (1) In M, the number of terms that are less than 10 is equal to the number of terms greater than 21.
- The Average of a Set of consecutive integers The Average of a Set of consecutive integers = Average of any equidistant pair of integers around the median. For any set of integers with a constant difference between any two consecutive terms (such as consecutive integers): The Average of the set = Average of any equidistant pair of terms around the median. => From this insight, remember this simpler rule: The Average of a Set of consecutive integers = Average of the first and last terms of the set.
- The product of 3 consecutive integers must be divisible by 3! = 3·2·1. Any set of 3 consecutive integers must contain one multiple of 3. The product of 3 consecutive integers must be divisible by 3. If x, y and z are consecutive integers, then one of them is divisible by 3, and therefore x·y·z will also be divisible by 3. Also, x, y and z must also include AT LEAST one even integer So the product x·y·z must be divisible by 2 AND 3 so it must be divisible by 6. We can state that the product of 3 consecutive integers must be divisible by 3! = 3·2·1.
- How many integers are there between 21 and 87, inclusive? The rule to remember here is this - remember that if both extremes should be counted, add one.
- How many multiples of 7 are there between 15 to 77, inclusive? The process of answering is as follows: 1) Find the extremes - the nearest multiples of 7 within the specified range. 15 is not a multiple of 7 - the nearest multiple of 7 within the range is 21. 77 is a multiple of 7, so we leave it as the higher extreme of our range. 2) Subtract the extremes, and divide by 7. (77 - 21) / 7 = 56 / 7 = 8 3) Add one. 8+1 = 9.
- What is the sum of the integers between 30 and 70, inclusive? Follow these 3 simple steps: 1) Find the average -> 100 / 2 = 50 2) Count the number of terms in the set: subtract the extremes, add one. -> 70-30, plus 1 = 40 +1 = 41. 3) Multiply the "middle" number -> 50·41 = 2050.
- If n is an integer between 1 and 96 (inclusive), what is the probability that n×(n+1)×(n+2) is divisible by 8? Plug in a few numbers for n to see what's going on: n=1 --> n×(n+1)×(n+2) = 1·2·3 = 6 --> not a multiple of 8. n=2 --> n×(n+1)×(n+2) = 2·3·4 --> a multiple of 8, since it has a 2 and a 4. n=3 --> n×(n+1)×(n+2) = 3·4·5 --> not a multiple of 8. n=4 --> n×(n+1)×(n+2) = 4·5·6 --> a multiple of 8, since it contains one multiple of 4 and one more even number. Some experimentation reveals that there are two scenarios in which n×(n+1)×(n+2) is divisible by 8: Scenario I) When n AND n+2 are even (thus one is a multiple of 2 and the other a multiple of 4), or Scenario II) When n and n+2 are odd, but n+1 is a multiple of 8. Calculate the probability of each scenario using the probability formula. Then add the probabilities of all scenarios since they are connected by an "OR" relationship. Scenario I) Between 1 and 96 half of the numbers are even and half are odd, thus the probability that n is even (which will make n+1 odd and n+2 even) is 1/2.