SAT PROBLEM ( 2nd 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
( 8th 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 90o and a triangle has 180o in total; a, b and c must total 180o
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
