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5 Cards in this Set
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In a certain population, there are 3 times as many people aged 21 or under as there are people over 21. The ratio of those 21 or under to the total population is
A. 1 to 2 B. 1 to 3 C. 1 to 4 D. 2 to 3 E. 3 to 4 
Let x represent the people over 21. Then 3x represents the number of people 21 or under, and x+3x=4x represents the total population. Thus, the ratio of those 21 or under to the total population is 3x/4x or 3 to 4.
E 

Shipments Defects Total chips
S1 2 50000 S2 5 12000 S3 6 18000 S4 4 16000 A computer chip manufacturer expects the ratio of the number of defective chips to the total number of chips in all future shipments to equal the corresponding ratio for shipments S1, S2, S3 and S4 combined, as shown in the table above. What is the expected number of defective chips in a shipment of 60,000 chips? A. 14 B. 20 C. 22 D. 24 E. 25 
Let n be the expected number of defective chips in a shipment of 60,000 chips. The proportion comparing the number of defective chips to the total number of chips shipped can be expressed in
(2+5+6+4)/(5000+12000+18000+16000)=n/60000 17/51000=n/60000 n = 20 B 

The present ratio of students to teachers at a certain school is 30 to 1. If the student enrollment were to increase by 50 students and the number of teachers were to increase by 5, the ratio of students to teachers would then be 25 to 1. What is the present number of teachers?
A. 5 B. 8 C. 10 D. 12 E. 15 
Let s be the present number of students, and let t be the present number of teachers. According to the problem, the following two equations apply:
30/1=s/t (s+50)/(t+5)=25/1 Solving for t yields 15. E 

The ratio of two quantities is 3 to 4. If each of the quantities is increased by 5, what is the ratio of these two new quantities?
A. 3/4 B. 8/9 C. 18/19 D. 23/24 E. It cannot be determined from the information given. 
Let x and y be the two quantities such that x/y=3/4. There is no algebraic operation that can be used to increase x and y each by 5 and determine what happens to the ratio 3/4.
For example, if x=3 and y=4, then (x+5)/(y+5)=8/9. But if x=6 and y=8 which would still set x/y=3/4, then (x+5)/(y+5)=(6+5)/(8+5)=11/13. E 

The ratio, by volume, of soap to alcohol to water in a certain solution is 2:50:100. The solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved. If the altered solution will contain 100 cubic centimeters of alchol, how many cubic centimetes of water will it contain?
A. 50 B. 200 C. 400 D. 625 E. 800 
When a ratio is doubled or halved, it mean he first value of the ratio si doubled or halved. Thus, when the soap to alcholhol ratio is 2:50 is doubled, the new ratio fo soap to alchol is 4:50. When th soap to water ratio of 2:100 is halved, the new ratio of soap to water is 1:100.
Originally the ratio of soap to alchol to water was 2:50:100. Since soap is now represented by 4, it is necessary to change 1:100 to 4:400 to incorporate all the ratios together. The new solution ratio of soap to alcohol to water is thus 4:50:400. Since 100 cubic centimeters represents the 50 parts of alchol in the new solution, 600 cubic centimeters will represent the 400 parts of water in the solution. E 