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Which of the following inequalities has a solution set that, [#permalink]
14 Mar 2007, 05:47
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1. Which of the following inequalities has a solution set that, when graphed on the number line, is a single line segment of finite length?
a. x^4 >= 1
b. x^3 <27>= 16
d. 2 <= |x| <= 5
e. 2 <= 3x + <= 6
2. Each employee on a certain task force is either a manager or a director. What percent of the employees on the task force are directors?
(1) The average (arithmetic mean) salary of the managers on the task force is $5,000 less than the average salary of all employees on the task force.
(2) The average (arithmetic mean) salary of the directors on the task force is $15,000 greater than the average salary of all employees on the task force.
3. Before being simplified, the instructions for computing income tax in Country R were to add 2% of one's annual income to the averge (arithmetic mean) of 100 units of Country R's currency and 1% of one's annual income. Which of the following represents the simplified formula for computing the income tax, in Country R's currency, for a person in that country whose annual income is i?
a. 50 + i/200
b. 50 + 3i/100
c. 50 + i/40
d. 100 + i/50
e. 100 + 3i/100
4. If p is a positive odd integer, what is the remainder when p is divided by 4?
(1) When p is divided by 8, the remainder is 5.
(2) p is the sum of the squares of two positive integers.
5.If x is positive, which of the following could be the corret ordering of 1/x, 2x, x^2?
I. x^2 < 2x < 1/x
II. x^2 < 1/x < 2x
III. 2x < x^2 < 1/x
b. I only
c. III only
d. I and II only
e. I, II, III
6. Last month 15 homes were sold in Town X. The average (arithmetic mean) sale price of the homes was $150,000, and the median sale price was #130,000. Which of the following statements must be true?
I. At least one of the homes was sold for more than $165,000.
II. At least one of the homes was sold for more than $130,000 and less than $150,000.
III. At least one of the homes was sold for less than $130,000.
a. I only
b. II only
c. III only
d. I and II
e. I and III
7. At least 100 students at a certain high school study Japanese. If 4 percent of the students at the school who study French also study Japanese, do more students at the school study French than Japanese?
(1) 16 students at the school study both French and Japanese
(2) 10% of the students at the school who study Japanese also study French.
8. Each employee of Company Z is an employee of either Division X or Division Y, but not both. If each dvision has some part-time employees, is the ratio of the number of full-time employees to the number of part-time employees greater for Division X than fr Company Z?
(1) The ration of the number of full-time employees to the number of part-time employees is less for Division Y than for Company Z.
(2) More than half of the full-time employees of Company Z are employees of Division X, and more than half of the part-time employees of company Z are employees of Division Y.
9. Machine X and Y work at their respective constant rates. How many more hourse does it take machine Y, working alone, to fill a production order of a certain size than it takes machine X, working alone?
(1) Machine X and Y, working together, fill a production order of this size in two-thirds the time that machine X, working alone, does.
(2) Machine Y, working alone, filles a production order of this size in twice the time that machine X, working alone, does.
10. Of the 60 animals on a certain farm, 2/3 are either pigs or cows. How many of the animals are cows?
(1) The farm has more than twice as many cows as it has pigs.
(2) The farm has more than 12 pigs.
11. A contractor combined x tons of a gravel mixture that contained 10% gravel G, by weight, with y tons of a mixture that contained 2% gravel G, by weight, to produce z tons of a mixture that was 5% gravel, by weight. What is the value of x?
(1) y = 10
(2) z = 16
explanation: let number of managers is M and number of director is D
we need to find out D/(M+D)
let avg salary of manager is X and avg salary of director is Y
from 1) we have MX+DY/(M+D) - X = 5000
solving this we will have D(Y-X)/ (M+D)= 5000 since we dont have value of y-x hence its insuff
from 2) we have Y- (MX+DY)/M+D = 15000 its also in sufficient
now solving for both 1) and 2) we will get Y-X=20K
putting this value in equation we will get the value of D/M+D hence answer is C.
Anser is E
explanation 2% of i = 2i/100, 1% of i = i/100 and avg of 100 units of currency = 100
adding all will give 3i/100 + 100
Answer is A
explanation.. for any odd number, which gives remainder 5 on dividing it by 8, will give remainder 1 on dividing it by 4. you may test by putting numbers such as 13, 21, 29 etc... or follow the simple rule of dividing the remainder by 4.
from 2) is no suff for e.e. 4+9 = 13 will give 1 as remainder while 4 + 16 will not give any remainder.
Answer is D (I and II) only...
explanation: X is positive means it can lie btw 0 and 1, can be equal to 1 or > than 1.
by putting the values you may find I and II are possible but not III.
Answer is A) I only
explanation: Avg price is USD 150K for 15 homes so total price for 15 homes is = 15x150K = USD 2250K
Now median is 130K, which means 8th house is for 130K.
suppose three is wrong and there is no house having prices more less than 130K, then total value of first 8 houses will be 8*130K = USD 1040K
value of rest of 7 houses will be 2250-1040 = 1210K, so the avg price of 7 houses will be more than 170K... this is possible so III is wrong
Now applying the same logic II is also wrong as rest of the 7 houses may cost more than 150K, while I will be write as the avg price of rest & houses is more than 170K, when we consider the max value of first 8 houses to be USD 130K.
rest of the answers will follow in subsequesnt mail
4% of french student study both french and Japanese.
from 1) 16 students at the school study both FnJ, which means total number of students who studied french are 400. but we dont have any idea about number of students who studied french, question says atleast 100. insuff
from 2) 10% of students who studied japanese has studied french. also we know that 4% of the students who studies french has studied japanese.
this means 10% of Japanese = 4% of french, which means F>J, sufficient.
Answe is B
1) its in sufficient as number or % of distribution of employee is not mentioned.
2) sufficient suppose 60% of full time employee of company Z are in X and 60% of the part time employee of Z is Y, putting in the equation u will get the result... sufficient.
Answer is E.. though both equation I and equation II will give the same results but the none will tell you the difference hours in absolute term. these two equation will only tell the relation between the hours taken by X and Y.
Answer is C
from the question we have P + C = 40
now both in I and II we have more than, which will not lead us to the specific number, so both I and II are insuff
now combining them will give pig to be more than 12, and cow to be more than twice of pigs... that means pig will be 13 and cow will be 27
Answer is D
from question we have 0.1X + 0.02Y = 0.05Z and X+Y = Z
now from I) we may put the value of Y and put Z=X+Y in equation one to get the value of X suff
from II) we may put the value of Z in both the equation I and II and solve them to get the value of X and Y. suff