HAIN MATH QUESTIONS

Word problems

-Pay attention to units -Units conversion -integer constraints --basic motion:RTD CHART -matching units in RTD Chart -multiple rates -relative rates -average rate: don't jus add and divide(less than avg) --basic work problem chart -working together : add the rates -population problems: population chart -standard deviation:

59. A glucose solution contains 15 grams of glucose per 100 cubic centimeters of solution. If 45 cubic centimeters of the solution were poured into an empty container, how many grams of glucose would be in the container? (A) 3.00 (B) 5.00 (C) 5.50 (D) 6.50 (E) 6.75

Algebra Applied problems Let x be the number of grams of glucose in the 45 cubic centimeters of solution. The proportion comparing the glucose in the 45 cubic centimeters to the given information about the 15 grams of glucose in the entire 100 cubic centimeters of solution can be expressed as , and thus or . The correct answer is E.

64. A certain fruit stand sold apples for $0.70 each and bananas for $0.50 each. If a customer purchased both apples and bananas from the stand for a total of $6.30, what total number of apples and bananas did the customer purchase? (A) 10 (B) 11 (C) 12 (D) 13 (E) 14

Algebra First-degree equations; Operations with integers The correct answer is B.

51. If y is an integer, then the least possible value of |23-5y|= (A)1 (B)2 (C)3 (D)4 (E)5

Arithmetic Absolute value; Operations with integers

60. On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $0.60 per glass on the first day, what was the price per glass on the second day? (A) $0.15 (B) $0.20 (C) $0.30 (D) $0.40 (E) $0.45

Arithmetic Applied problems The ratio of the amount of orangeade made and sold on the first day to amount of orangeade made and sold on the second day is 2:3, because the orangeade on the first day was 1 part orange juice and 1 part water, while on the second day it was 1 part orange juice and 2 parts water. Thus, the ratio of the number of glasses of orangeade made and sold on the first day to the number of glasses of orangeade made and sold on the second day is 2:3. Since the revenues for each day were equal and 2 glasses were sold on the first day for every 3 glasses that were sold on the second day, 2($0.60) = 3p, where p represents the price per glass at which the orangeade was sold on the second day. Therefore, . The correct answer is D.

108 . Each year for 4 years, a farmer increased the number of trees in a certain orchard by of the number of trees in the orchard the preceding year. If all of the trees thrived and there were 6,250 trees in the orchard at the end of the 4-year period, how many trees were in the orchard at the beginning of the 4-year period? (A) 1,250 (B) 1,563 (C) 2,250 (D) 2,560 (E) 2,752

Arithmetic Operations on rational numbers The correct answer is D.

39. John has 10 pairs of matched socks. If he loses 7 individual socks, what is the greatest number of pairs of matched socks he can have left? (A) 7 (B) 6 (C) 5 (D) 4 (E) 3

Arithmetic Operations on rational numbers Determine first the lowest number of pairs of matched socks that can be made from the 7 individual socks. The lowest number of pairs that 7 individual socks can come from is 3 full pairs plus one sock from a fourth pair. The greatest number of pairs of matched socks John can have left is therefore 10-4=6 fully matched pairs.

1. A project scheduled to be carried out over a single fiscal year has a budget of $12,600, divided into 12 equal monthly allocations. At the end of the fourth month of that fiscal year, the total amount actually spent on the project was $4,580. By how much was the project over its budget? (A) $ 380 (B) $ 540 (C) $1,050 (D) $1,380 (E) $1,430

Arithmetic Operations with rational numbers The budget for 4 months was $12,600/12∗4=$4,200. Thus, the project was $4,580−$4,200=$380 over budget for the first 4 months. Answer: A.

58. A glass was filled with 10 ounces of water, and 0.01 ounce of the water evaporated each day during a 20-day period. What percent of the original amount of water evaporated during this period? (A) 0.002% (B) 0.02% (C) 0.2% (D) 2% (E) 20%

Arithmetic Percents Since 0.01 ounce of water evaporated each day for 20 days, a total of ounce evaporated. Then, to find the percent of the original amount of water that evaporated, divide the amount that evaporated by the original amount and multiply by 100 to convert the decimal to a percent. Thus, or 2%. The correct answer is D.

25. Of the 50 researchers in a workgroup, 40 percent will be assigned to Team A and the remaining 60 percent to Team B. However, 70 percent of the researchers prefer Team A and 30 percent prefer Team B. What is the lowest possible number of researchers who will NOT be assigned to the team they prefer? (A) 15 (B) 17 (C) 20 (D) 25 (E) 30

Arithmetic Percents The number of researchers assigned to Team A will be (0.40)50=20 , and so 30 will be assigned to Team B. The number of researchers who prefer Team A is (0.70)(50)=35 , and the rest, 15, prefer Team B. If all 15 who prefer Team B are assigned to Team B, which is to have 30 researchers, then 15 who prefer Team A will need to be assigned to Team B. Alternatively, since there are only 20 spots on Team A, 35-20=15 who prefer Team A but will have to go to Team B instead. The correct answer is A.

10. Raffle tickets numbered consecutively from 101 through 350 are placed in a box. What is the probability that a ticket selected at random will have a number with a hundreds digit of 2 ? (A) 2/5 (B) 2/7 (C) 33/83 (D) 99/250 (E) 100/249

Arithmetic Probability There are 250 integers from 101 to 350 inclusive, 100 of which (that is, 200 through 299) have a hundreds digit of 2. Therefore, the probability that a ticket selected from the box at random will have a hundreds digit of 2 can be expressed as 100/250 = 2/5 .

56. Four staff members at a certain company worked on a project. The amounts of time that the four staff members worked on the project were in the ratio 2 to 3 to 5 to 6. If one of the four staff members worked on the project for 30 hours, which of the following CANNOT be the total number of hours that the four staff members worked on the project? (A) 80 (B) 96 (C) 160 (D) 192 (e)240

Arithmetic Ratio and proportion For a certain value of x, the numbers of hours worked on the project by the four staff members are 2x, 3x, 5x, and 6x, for a total of 16x. It is given that one of these four numbers is equal to 30. If 2x = 30, then x = 15 and 16x = 16(15) = 240, which is (E). If 3x = 30, then x = 10 and 16x = 16(10) = 160, which is (C). If 5x = 30, then x = 6 and 16x = 16(6) = 96, which is (B). If 6x = 30, then x = 5 and 16x = 16(5) = 80, which is (A). The correct answer is D.

67 If m is the average (arithmetic mean) of the first 10 positive multiples of 5 and if M is the median of the first 10 positive multiples of 5, what is the value of ? (A) -5 (B) 0 (C) 5 (D) 25 (E) 27.5

Arithmetic Statistics answer:b

18. A carpenter constructed a rectangular sandbox with a capacity of 10 cubic feet. If the carpenter were to make a similar sandbox twice as long, twice as wide, and twice as high as the first sandbox, what would be the capacity, in cubic feet, of the second sandbox? (A) 20 (B) 40 (C) 60 (D) 80 (E) 100

Geometry Volume When all the dimensions of a three-dimensional object are changed by a factor of 2, the capacity, or volume, changes by a factor of 2*2*2=2^3= 8. Thus the capacity of the second sandbox is 10(8)=80 CUBIC FEET

104. If a square mirror has a 20-inch diagonal, what is the approximate perimeter of the mirror, in inches? (A) 40 (B) 60 (C) 80 (D) 100 (E) 120

The correct answer is B.

49.Car X averages 25.0 miles per gallon of gasoline and Car Y averages 11.9 miles per gallon. If each car is driven 12,000 miles, approximately how many more gallons of gasoline will Car Y use than Car X ? (A) 320 (B) 480 (C) 520 (D) 730 (E) 920

The correct answer is C.

103. The water from one outlet, flowing at a constant rate, can fill a swimming pool in 9 hours. The water from a second outlet, flowing at a constant rate, can fill the same pool in 5 hours. If both outlets are used at the same time, approximately what is the number of hours required to fill the pool? (A) 0.22 (B) 0.31 (C) 2.50 (D) 3.21 (E) 4.56

The correct answer is D.