Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company

Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 2/3 were basic and the rest were deluxe. If it takes 7/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?
A.7/17
B.14/31
C. 7/15
D.17/35
E.1/2

let the total number of steros be x therefore we get 2x/3 (basic) and x/3 deluxe steros
lets assume that it takes y hours to produce one basic stero, accordingly it takes 7y/5 hours to produce one deluxe stereo.

Combining both together we get the following

hours to produce 2x/3 basic stereos = 2xy/3
and hours to produce x/3 deluxe stereos = 7xy/15

total hours =17xy/15

therefore we get

(7xy/15)/(17xy/15)

which derives to 7/17

One smurf and one elf can build a treehouse together in two hours, but the smurf would need the help of two

One smurf and one elf can build a treehouse together in two hours, but the smurf would need the help of two fairies in order to complete the same job in the same amount of time. If one elf and one fairy worked together, it would take them four hours to build the treehouse. Assuming that work rates for smurfs, elves, and fairies remain constant, how many hours would it take one smurf, one elf, and one fairy, working together, to build the treehouse?

(A) 5/7
(B) 1
(C) 10/7
(D) 12/7
(E) 22/7

One Elf's rate + One Smurf's rate = 2 Fairies' rate + One Smurf's rate

One Elf's rate , E = 2 Fairies' rate, F

E = 2F

(E+F)*4 = T (T= work required to finish tree house) ------- (1)
(E+S)*2 = T --------- (2)
(2F+S)*2 = T ------ (3)


Solving we get E=T/6, S=T/3 and F =T/12 now we have to find T/(E+S+F) = T/T (1/(1/3+1/6+1/12) = 1/(7/12) = 12/7
 

Machines X and Y produced identical bottles at different constant rates. Machine X, operating alone

Machines X and Y produced identical bottles at different constant rates. Machine X, operating alone  for 4 hours, filled part of a production lot; then machine Y, operating alone for 3 hours, filled the rest  of this lot. How many hours would it have taken machine X operating alone to fill the entire production lot?

(1) Machine X produced 30 bottles per minute.
(2) Machine X produced twice as many bottles in 4hours as machine Y produced in 3 hours.

Statement 1 is insufficient. We have no idea how much of the production lot was left after 4 hours, and we have no idea what speed Y produces at.

Statement 2:

Without any formal math, we see that in 2 hours, it can produce as many items as y did in the 3. So to fill the lot, we need the original 4 hours X worked, plus the 2 hours needed to fulfill y's part of the lot. Or 6 total hours.

Sufficient.

Ans : B 

Tom, working alone, can paint a room in 6 hours. Peter and John, working independently

Tom, working alone, can paint a room in 6 hours. Peter and John, working independently, can paint the same room in 3 hours and 2 hours, respectively. Tom starts painting the room and works on his own for one hour. He is then joined by Peter and they work together for an hour. Finally, John joins them and the three of them work together to finish the room, each one working at his respective rate. What fraction of the whole job was done by Peter?










let X = amount of time in hours for Tom, Peter, and John to complete the job

1/6 + (1/6 + 1/3) + (1/6 + 1/3 + 1/2)*X = 1

X = 1/3

Total work done by Peter:

1/3 + (1/3)*(1/3) = 4/9

ANSWER: 4/9

Working together, John and Jack can type 20 pages in one hour.

Working together, John and Jack can type 20 pages in one hour. They will be able to type 22 pages in one hour if Jack increases his typing speed by 25%. What is the ratio of Jack's normal typing speed to that of John?
1/3
2/5
1/2
2/3
3/5











let N = rate of John typing
let K = rate of Jack typing

N + K = 20
N + 1.25*K = 22

Solve the system of equations:
N = 12
K = 8

K/N = 8/12

ANSWER: D. 2/3

Micheal and Adam can do together a piece of work in 20 days

Micheal and Adam can do together a piece of work in 20 days. After they have worked together for 12 days Micheal stops and Adam completes the remaining work in 10 days. In how many days Micheal complete the work separately.

80 days
100 days
120 days
110 days
90 days

Ans : 100 days

Working alone at its own constant rate, a machine seals k cartons in 8 hours

Working alone at its own constant rate, a machine seals k cartons in 8 hours,
and working alone at its own constant rate, a second machine seals k cartons in
4 hours. If the two machines, each working at its own constant rate and for the
same period of time, together sealed a certain number of cartons, what percent
of the cartons were sealed by the machine working at the faster rate?

25%
33 1/3%
50%
66 2/3%
75%

Machine A---- 1hr---K/8 carton
Machine B-----1 hr--K/4

Together In 1 hr k/4+k/8 = 3k/8 cartons

% = k/4/3k/8 = 8/12 *100 = 200/3=66.67%(Ans)(D)

A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 36 hours and a machine of type S does the same job in 18 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?
a) 3
b) 4
c) 6
d) 9
e) 12















Rate of Type R * # of Machines + Rate of Type S * # of Machines = Rate Together
let M = # of machines
M/36 + M/18 = 1/2
M = 6
ANSWER: C. 6

Machince A and B are each used to manufacture 660 sprockets. It takes A 10 hours longer to produce 660

Machince A and B are each used to manufacture 660 sprockets. It takes A 10 hours longer to produce 660 sprockets than machine B. B produces 10 percent more sprockets per hour than A. How many sprockets per hours does machine A produce?
A. 6
B. 6.6
C. 60
D. 100
E 110











let B = amount of time B takes to produce 660 sprockets in hours
Rate of Machine A:
660 / (10 +B)
Rate of Machine B:
660 / B
B produces 10% more sprockets per hour than A:
(660 / B) / (660 / (10 +B)) = 1.1
B = 100
therefore,
660/(10+100) = 6
ANSWER: A. 6