SAT PROBLEM ( 2^{nd} problem in a 25 problem section )

2. The average (arithmetic mean) of 3 numbers is 60. If two of the numbers are 50 and 60, what is the third number?

50

55

60

65

70

(Sunday/5.1997 #2) p. 483

E. 70 3*60=180, which is the total number of points earned; the two numbers we do know are 50 and 60 which add up to 110
The third number is 180-110=70 since all three numbers must add up to 180

TEST METHOD: AVERAGE PIE

Use the average pie to chart out what you know and simplify this problem.

SAT PROBLEM
( 8^{th} problem in 25 problem section)

In the triangles below what is the average (arithmetic mean) of a , b, c, x, and y?

21

45

50

52

54

(Sunday/5.1997 #8) p. 450 *

E. 54 x+y=90 since the other angle is 90^{o} and a triangle has 180^{o} in total; a, b and c must total 180^{o}

TEST METHOD: AVERAGE PIE

Tip: Total --> degrees=180+180=360, the total number of degrees in two triangles.

SAT PROBLEM #5 in a 10 problem section

In a certain game, each of the 5 players received a score between 0 and 100 inclusive. If their average(arithmetic mean) score was 80, what is the greatest possible number of the 5 players who dould have received a score of 50?

None

One

Two

Three

Four

( Saturday/5.2002 #5) p.675 *

C)

METHOD: AVERAGE PIE. You know the total (5*80=400); you know the number (5), and you know the average(80). You also know the answer is between 0-4. By Trial and error you should be able to answer this one.

If you're clueless, NO MATTER what you should be able to elimante A and guess. If you couldn't eliminate A, review how to solve average problems.

MEDIUM-HARD SAT PROBLEM: (17th problem in 25 problem section )

17. The average (arithmetic mean) of a, b, and c is equal to the median of a, b, and c. If 0 < a < b < c, which of the following must be equal to b ?

(a+c)/2

(a+c)/3

(c-a)/2

(c-a)/3

(Saturday/1.2002 #17 ) p. 610

A. (a+c)/2

TEST KEYWORD: "MUST"

Plug in numbers for a,b,c and see which answer 'must' work.

MEDIUM SAT PROBLEM:

The average(arithmetic mean) of nine numbers is 9. When a tenth number is added the average of the ten numbers is also 9. What is the tenth number ?

0

9/10

10/9

9

10

A.
Eliminate some obvious wrong ones B. , C., E. Remember to always estimate and have a good rough estimate of where the answers should be which is right around the original average of 9; if you added a new number that was much higher or lower like say 0 or 1,000 the average could never remain 9.

TEST TRAP: D is atrap and since you're not dealing with the first few problems you should not have gone on without really thinking about his one

VERY HARD SAT PROBLEM ( This is the 25th problem in 25 problem section )

If the average (arithmetic mean) of x, 2x-8, 2x+2, 3x-1, and 4x+1 is 6, what is the value of the mode of these numbers?

(Student Generated Response)

(Saturday/1.2000 SAT) #25 p. 540

8
If you're not shooting for at least a 700, you should skip the most difficult ones in the seciton; however, for those truly bold standardized test takers, a helpful hint with this one is to always remember to substitute in real number for algebraic variables like x (avoid ugly numbers like 19), then proceed through the problem.

METHOD: PLUG IN ACTUAL NUMBERS

TRAP: This problem is a series of traps! Good luck!

HARD SAT PROBLEM
( 25 ^{th} problem in a 25 problem section )
The average (arithmetic mean) of the test scores of a class of p students is 70, and the average of the test scores of a class of n students is 92. When the scores of both classes are combined, the average is 86. What is the value of (p/n)?

(Student generated answer)

(Saturday/5.1997 SAT #25) p. 465 *

(3/8) or .375
This is a toughie Good Luck!
TEST METHOD: AVERAGE PIE

Create two average pies; one to find p and one to find n, then divide.

Note: ETS gives this a 5 difficulty rating, the rating for the toughest questions.

HARD SAT PROBLEM:
( 25 ^{th} problem in a 25 problem section )

If the average(arithmetic mean) of three different positive integers is 70, what is the greatest possible value of one of the integers?
(Student generated answer)

(Saturday/11.1996 SAT #25) p. 385 *

A. 207

METHOD: Average Pie
Find the total(3*70=210), recognize that the smallest numbers you can have are 1 and 2 (remember the numbers must be "different" and "postive" integers;
At this point, it's a much easier question. 210-(1+2)= Answer