GRE Math Concepts

If the average (arithmetic mean) of 24 consecutive odd integers is 48, what is the median of the 24 numbers?

an arithmetic sequence is a sequence where the same number is added to each element to get the next one. 2, 4, 6, 8 or 3, 6, 9, 12. ** for any arithmetic sequence, the mean and median are equal! so the answer here is 48

combination problems

combination problems is when a small group is drawn from a larger group

Percent increase/decrease: some problems give us the new and old values and ask to find the percent increas eof decrease. A multiplier is equal to new price/old. so we divide and then converth the multiplier back to a percent. The price of an item went from 60 to 102, what is the percent increase? the price of an item decreased from 250 to 200 dollars, what is percent decrease?

102/60=1.7 which is the multiplier for 70%. 200/250=0.8 which is the multiplier for a 20% decrease

If the mean of list A is 6.8 and the standard deviation is 3.6, then how many elements of list A are within 1 unit of standard deviation of the mean? A = {2, 9, 2, 6, 9, 10, 7, 4, 5, 14}

7

** The price of an item increased from 200 to 800. what is the percent increase. people often say 400% but thats incorrect

800 is 400% OF 200 but it is not the increase, here we use a mulitplier of 4. 4-1=3 so 800 is 300% greater than 200

Associative Law: If a, b, and c are real numbers, which of the following must be true? a + (b + c) = (a + b) + c a − (b − c) = (a − b) - c a*(b*c) = (a*b)* c a/(b/c) = (a/b)/c

A and C.The Associative Law says that, for addition or for multiplication, you can group the parts in any way. Statements (A) & (C) are bonafide statements of the Associative Law of Addition and of Multiplication, respectively. There is no "associative law" for either subtraction or division, because changing the grouping with those changes the numerical answer.

Charlene must buy a gift for each of her five grandchildren. She can buy each grandchild either a book or a board game, sold at a price of $7 and $13 respectively. Charlene pays the price of all five gifts, plus a 6% sales tax, with a $50 bill, and she receives the exact change.Which of the following statements could be true? Charlene spent more on board games than on books, Charlene purchased more board games than books, Charlene received less than 25 cents in change.

Answer A and C

Percent increase and decrease: a $170 item is discounted 30% whats the new price? The price of an item increased by 35% then decreased by 20%, this is equivalent ti what percent change?

Percent increase: if Y increased by 30%, we have the value of Y and 30% more. oUr multiplier would be 1.03 to represent both the Y we already have and the 30% increase. if we are disocunting Y by 30%, we multiply by 1-.30 so we'd multiple by .70. 170 dollar item discounted by 30% is 170*.7.

Product Law: If k ≠ 0, k ≠ ±1 (K^3 * K * K^4)^2 / K^n x K = K^14

Product Law: (X^a * X^b = X^a+b) and (X^a)^b = X^a*b (X^a/X^b = X^a-b) so first line would be (K^8)^2 and then K^16, and bottom would become K^n+1. So we have K^16/K^n+1 which becomes K^16-(n+1)= k^14 and since our bases match we set the exponents equal. 16-n+1=14 and then 15-n=14 so n = 1

In a two-week period, 5/6 of the knives produced at a certain factory are 8 inches long, and 1/20​​ of the knives produced are 6 inches long. Which of the following could be the number of knives that the factory produced during this two-week period? Select all that apply. 4,000 4,010 4,020 4,040 4,050 4,080

answers 4020 and 4080. we cant have anything but whole numbers of knives. so we can take each number and multiple it by the fraction to determine how much 5/6 and 1/20 of each of the answer choices would be, and if we get decimals for any we know thats not correct

The sum of 5 consecutive even integers is 0. what is larger, the product of the 5 integers or 0?

key words consecutive and even* if x is the smallest number, the second integer has t be x+2, then x+4 as the third, x+6 as the fourth, x+8 as the fifth. so our equation is x+(x+2)+(x+4)+(x+6)+(x+8)=0 now combine like terms 5x+20=0 5x=-20 x=-4. now we plug our x into our formula for each integer, first integer is -4, second is -2, the o, 2, 4. the sum of these all multiplied together is 0. so the answr is column a and b is equal

p^2 * sqrrt p^5 / p^-2 = p^n n>1, solve for n

n=6.5 move p^-2 to the top P^2 * p^2 * sqrrt p^5 = p^n which becomes p^4 * sqrrt p^5 = p^n sqrrt of p^5 can be rewritten as p^5 *1/2 5 * 1/2 becomes p^5/2 which in decimal form is p^2.5 so we have p^n=p^4 * p^2.5 multiply the ps to get p^n = p^6.5

For integers p and q, (2p)(5q) = 40000. Which of the following is the value of p + q?

p+q =10

Percent Change: Which of the following is percent increase in the number of TVs in Jenkinsville from 1955 to 1960? (number of Tvs went from 80 to 150)

percent change formula is final-initial/initial x100. so 150-80/80= 0.875 so 87.5%

review geometry, algebra, arithmetic and fractions

review

reviews finding areas of shaded regions, circle areas, etc.

review

30-60-90 triangle property and how do you find the area of a triangle and the angles

short leg : long leg : hypotenuse is x : x sqrrt of 3 : 2x, so we can find the lengths of a triangle if it has those angles and one length revealed. for example a triangle with hypotenuse of 8. hypotenuse is 2x so x is 4, which means short leg has a lenth of 4 and the long leg has a lenth of 4 sqrrt 3. area = 1/2 b x h. angles all angles should equal 180, so if two are revealed subtract from 180 to find the length of the third one

ab^2c^-5/a^-1/2b^3/2 rewrite and simplify

sqrrt of a^3b/c^5

after an item was discounted 80%, the new price is 150. what is original price?

use multiplier for an 80% decrease which is 0.2. 0.2x=150, 150/0.2 = 750

after a 30% increase, the price of something is $78. what is the original price?

use percent multipliers. if something increases by 30% we multiply original price by 1.3, so for this problem 1.3x-78, 78/1.3 gives us the answer at 60

​3^6 x 4^4 x 9^n / 6^8 = 81 what is the value of n

when we look at these numbers we can notice multiples of 3 and 2. we can rewrite the problem as 3^6 x 2^8 x 9^n/ 3^8 x 2^8. the 2s cancel leaving 3^6 x 9^n/3^8. the 6 3s at top cancel leaving 2 at the bottom. 9^n/3^2 = 81. multiple both sides by 3^2 to get 9^n=81 x 9. 81 x 9 is the same number as 9 x9 x9 so three 9s the answer is 3

If 16x = 8, what is the value of x?

write with same base 2^4x=2^3 set exponents equal since base is the same 4x=3 x=3/4