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11. The water from one outlet, flowing at a constant rate, can fill the swimming pool in 9 hours. The water from second outlet, flowing at a constant rate can fill up the same pool in approximately in 5 hours. If both the outlets are used at the same time, approximately what is the number of hours required to fill the pool?
Let the first outlet be A
Let the second outlet be B
One hour work of A is 1/A i.e., 1/9
One hour work of B is 1/B i.e., 1/5
One hour work of Both A and B is 1/A + 1/B = 1/9 + 1/5 = 14/45.
So Time taken to fill the swimming pool is 45/14 hours i.e., 3hrs 3/14 mins
12. If 75 % of a class answered the first question on a certain test correctly, 55 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percentage answered both correctly?
P(A) = answered the first question correctly
P(B) = answered the second question correctly
P(A v B) =answered neither of the questions correctly
P(A U B) = answered first and second questions correctly
P(A U B) = 1 -P(A v B) = 80 %
P(A ^ B) = answered both the questions correctly
P(A ^ B) =P(A)+P(B)-P(A U B)
= 75 + 55 - 80
= 50 %
13. A student's average (arithmetic mean) test score on 4 tests is 78. What must be the students score on a 5th test for the student’s average score on the 5th test to be 80?
Sum of 4 tests score is 78*4 = 312
Sum of 5 tests score is 80*5 =400.
Students score on fifth test is 400 - 312 =88.
14. Rural households have more purchasing power than do urban households at the same income level, since some of the income urban and suburban households use for food and shelter can be used by the rural households for other needs. Which of the following inferences is best supported by the statement made above?
(A) The average rural household includes more people than does the average urban or suburban household.
(B) Rural households have lower food and housing costs than do either urban or suburban households.
(C) Suburban households generally have more purchasing power than do either rural or urban households.
(D) The median income of urban and suburban households is generally higher than that of rural households.
(E) All three types of households spend more of their income on housing than on all other purchases combined.
Answer : B
15.Jose is a student of horticulture in the University of Hose. In a horticultural experiment in his final year, 200 seeds were planted in plot I and 300 were planted in plot II. If 57% of the seeds in plot I germinated and 42% of the seeds in plot II germinated, what percent of the total number of planted seeds germinated?
57 % of 200 seeds is 114 seeds.
42 % of 300 seeds is 126 seeds.
240 seeds are germinated.
(x/100) * 500 = 240
16.A closed cylindrical tank contains 36 pie cubic feet of water and it’s filled to half its capacity. When the tank is placed upright on its circular base on level ground, the height of water in the tank is 4 feet. When the tank is placed on its side on level ground, what is the height, in feet, of the surface of the water above the ground?
Volume = ∏* r² * h
36 ∏ = ∏*r²*4
r = 3 ft, So the Height (diameter) is 6 ft.
17.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 the teachers would then be 25 to 1 What is the present number of teachers?
Present student to teacher ratio is S/T = 30/1
Future student to teacher ratio is S+50/T+5 = 25/1
solving the first equation first equation for S gives, S = 30T.
Substitute the S value into the second equation, and solve for T.
S+50/T+5 = 25/1
30T + 50 = 25T + 125
T = 15
18. College T has 1000 students. Of the 200 students majoring in one or more of the sciences,130 are majoring in Chemistry and 150 are majoring in Biology. If at least 30 of the students are not majoring in either Chemistry or Biology, then the number of students majoring in both Chemistry and Biology could be any no. from ?
Total number of students in Science department =200
No of students in chemistry=130
No of students in Biology=150
No of students no majoring in Both chemistry and biology is >=30
Max. students majoring in both the subjects=Min. students of the two subjects=130
P(A ^ B) =P(A)+P(B)-P(A U B)
= 130 + 150 -(200 - 30 )
= 280 -170 =110
So the range is from 110-130
19. Kelly and Chris are moving into a new city. Both of them love books and thus packed several boxes with books. If Chris packed 60% of the total number of boxes, what was the ratio of the number of boxes Kelly packed to the number of boxes Chris packed?
Kelly packed = 100-60=40%
So the ratio of Kelly to Chris is 40:60=2:3
20. A drug that is highly effective in treating many types of infection can, at present, be obtained only from the bark of the ibora, a tree that is quite rare in the wild. It takes the bark of 5,000 trees to make one kilogram of the drug. It follows, therefore, that continued production of the drug must inevitably lead to the ibora's extinction. Which of the following, if true, most seriously weakens the argument above?
Answer: The ibora can be propagated from cuttings and grown under cultivation.
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