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1.A drawer holds 4 red hats and 4 blue hats.What is the probability of getting exactly 3

red hats or exactly 3 blue hats when taking out 4 hats randomly out of the drawer and

immediately returning every hat to the drawer before taking out the next?

(a)1/8

(b)1/4(c)1/2

(d)3/8

(e)7/12i go for C 1/2

probability of taking a particular hat is 1/2 ( 4/8)

Now assume we have 2 take 3 blues and 1 red

P(BBBR) = (1/2)^4

P(BBRB) = (1/2)^4P(BRBB) = (1/2)^4

P(RBBB) = (1/2)^4total = 4 * (1/2)^4

similarly with red

thus the total is 2*4*1/16 = 8/16 =

2.A boat travelled upstream a distance of 90 miles at an average speed of (v-3) miles perhour and then travelled downstream at an average speed of (V+3) miles per hour. If the

trip upstream took half an hour longer than the trip downstream, how many hours did ittake the boat to travel downstream?

Speed = distance/time

use this and set up the 2 equations

For going up the river :

90 = t * (v - 3)

For going down the river :

90 = (t - 0.5) * (v + 3)

solve for the equations.to get = 2.5

hence 2.5 for downstream and 3 hrs for upstream..

hope it helps..

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PS: be careful while solving the equation...

3.If the perimeter of a rectangular flower bed is 30 feet, and its area is 44 square feet,

what is the length of each of its shorter sides?

find that solution unnecessarily complicated. From the above, we know

lw = 44

l + w = 15

That is, we are looking for two numbers that multiply to 44 and add to 15. We look for

pairs of numbers like this every time we factor a quadratic, and in this case the numbers

must be 4 and 11.

4.At a loading dock,each worker on the night crew loaded 3/4 as many boxes as each

worker on the day crew.If the night crew has 4/5 as many workers as the day crew,what

fraction of all the boxes loaded by the two crews did the day crew load?

A. 1/2B.2/5

C.3/5

D.4/5

E.5/8

OA is E

I picked numbers.

Lets say Day crew loads 20 boxes per 1 worker.

Then the night crew loads 3/4 * 20 = 15 boxes per worker.Lets say day crew has total 20 workers.

Then the night crew has total 4/5 * 20 = 16 workers.

Important to know what the question is asking.

"what fraction of all the boxes loaded by the two crews"

total boxes loaded by the two crews isDay Crew = 20*20= 400 boxes

Night crew = 15 * 16 = 240 , Total is 640

"did the day crew load"?

which is 400

Ans: 400 / 640 = 5/8

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5.If 37 teachers are to be assigned to 64 classes in such a way that each of teacher teaches

at least one class and at most three classes. What are the greatest possible number and the

least possible number of the teachers who teach three classes?(A) 14,0

(B) 13, 1

(C) 13, 0(D) 12, 2

(E) 12, 1

OA is c.

At least the teachers must teach one class. The number of unassigned classes after

fulfilling this requirement is 64 - 37 = 27.

For the maximum number of teachers who teach 3 classes:

27/2 = 13 with remainder of 1.

This means that there's going to be one teacher who teaches two classes.

For the minimum number of teachers who teach 3 classes:Out of those 27 classes we can assign it evenly to the 37 teachers, so the minimum

number of teachers who teach 3 classes is zero. There are going to be 10 teachers who

only teach 1 class in this case.

6.What is the sum of all possible 3 digit numbersthat can be constructed using

3,4,5.If each digit can be used only once in the number.

There are no options.

A = 2664

Can somebody please explain how to solve above question.yeah the answer shud be 2664

(sum of the numbers)*(n-1)!* (111.........n times)

(3+4+5) *(3-1)!*(111)

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12*2*111= 2664

hope that helps..

7.A certain farmer pays $30 per acre per month to rent farmland. How much does

thefarmer pay per month to rent a rectangular plot of farmland that is 360 feet by 605feet?(3,560 square feet = 1 acre)A. $5,330B. $3,360C. $1,350D. $360E. $150

its 43,560 = 1 acreans 150

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8. A cube of white chalk is painted red, and then cut parallel to the sides to form two

rectangular solids of equal volume. What percent of the surface area of each of the

new solids is not painted red?

Picking numbers is a great way to solve.

We could also reason it out:

If we cut the cube down the middle, our new shape will also have 6 sides, 5 of which

will be red (only the exposed middle will be white).

Two of the 6 sides will be full-sized (the white side and the side opposite) and 4 will

be half-sized (the 4 sides "ringing" the white side). Let's call the area of a full side x

and the area of a half side .5x; so, the entire surface area will be:

2(x) + 4(.5x) = 2x + 2x = 4x.

The white side has area x, so the proportion of the shape that's white is x/4x = 1/4.

_________________

9.Mr. Kramer, the losing candidate in a two-candidate election, received 942,568

votes, which was exactly 40 percent of all the votes cast. Approximately what

percent of the remaining votes would he need to have received in order to have won

at least 50 percent of all the votes cast?

(A) 10%

(B) 12%

(C) 15%

(D) 17%

(E) 20%

Is there any short method to do it instead of doing all calculationsYes, there is a simple method. Kramer got 40%. He need 10% more to win atleast50% of the total vote. What % is this 10% vote of the remaining 60%?

10/60*100= 16.666~17. You do not have to use 942,568 at all here. It does notmatter if the # of votes is 123456789.

10. The price of microchip declines by 67% every 6 months.At this rate approx. how

many years will it take for $81 microchip to reach to $1?

A.1.5B.2

C.3

D.13

E.13.5Decline of 67% ~ 1/3 the price

81/(3^4) = 1 => 4*6 months = 2 years.

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IMO B.

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11.A certain manufacturer of cake, muffin, and bread mixes has 100 buyers, of whom50 purchase cake mix, 40 purchase muffin mix, and 20 purchase both cake mix andmuffin mix. If a buyer is to be selected at random from 100 buyers, what is theprobability that the buyer selected will be one who purchases neither cake mix normuffin mix?

A.1/10B.3/10C.1/2D.7/10E.9/100a b100=50+40-20+x

100-70 = x

30=x

probability = 30/100=3/10

12.I've got 10 balls with numbers from 1 to 10 on them. I lost balls 3 and 7. From theballs left, how many ways are there to choose 4 elements in an increasing order?

A 336B 840C 70D 210E 1680

Yes, order is important here, but you need to consider it correctly. There are 8C4

ways of choosing four balls. Once those four balls are chosen, there are 4! ways to

put them in order. That is, there are

4!*8C4 (which is equal to 8P4)

ways of both choosing four balls *and* putting them in order. *But* only one of these

4! orders is increasing; the remaining 23 orders we might choose are not increasing.

There is 8C4 ways of choosing four balls, and only 1 way to put them in increasing

order, so the answer, as pointed out above, is 8C4.

12.Bag A contains red, white and blue marbles such that the red to white marble

ratio is 1:3 and the white to blue marble ratio is 2:3. Bag B contains red and white

marbles in the ratio of 1:4. Together, the two bags contain 30 white marbles. How

many red marbles could be in bag A?1

3

4

6

8

OA 6

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We known that in bag a, the ratio r:w:b =2:6:9

Whereas in bag B r:w = 1:4

Use answer choices: 4 reds in A would be accompanied by 12 whites. This would

mean that there are 18 whites in b (impossible). 6 reds in A would be accompaniedby 18 whites, meaning that there would be 12 whites in B (possible)

Let x machines are needed to complete the job in 8 days.

Machines...Days

6... 12x ... 8

Please note here that more machines would complete a job in fewer number of days, so

there will an inverse relationship.

6 * 12 = x * 8

x = 9 implies no. of additional machines required = 9 - 6 = 3