MU-NLPC/Calc-aqua_rat huggingface dataset:
Four car rental agencies A, B, C and D rented a plot for parking their cars during the night. A parked 15 cars for 12 days, B parked 12 cars for 20 days, C parked 18 cars for 18 days and D parked 16 cars for 15 days. If A paid Rs. 1125 as rent for parking his cars, what is the total rent paid by all the four agencies?
Choose the correct answer.
A) Rs.6158	B) Rs.6120	C) Rs.6119	D) Rs.6150	E) Rs.6151

Solution: The ratio in which the four agencies will be paying the rents = 15 * 12 : 12 * 20 : 18 * 18 : 16 * 15   = 180 : 240 : 324 : 240 = 45 : 60 : 81 : 60   Let us consider the four amounts to be 45k, 60k, 81k and 60k respectively.   The total rent paid by the four agencies = 45k + 60k + 81k + 60k= 246k   It is given that A paid Rs. 1125   45k 45  + 60  + 81  + 60= 
45  + 60  + 81  + 60 = 246
246k   It is given that A paid Rs. 1125   45k= 1125 => k = 25   246k = 246(25) = Rs. 6150   Thus the total rent paid by all the four agencies is Rs.6150.   Answer:Rs.6150
Answer: D
In a 1000 m race, A beats B by 100 meters or 25 seconds. Find the speed of B?
Pick:
A) 8  B) 9  C) 7  D) 5  E) 4

Solution: Since A beats B by 100 m or 25 seconds, i   t implies that B covers 100 m in 25 seconds.   Hence speed of B = 100/25= 
100/25 = 4
4 m/s.   Answer: 4
Answer: E
Two persons start from two places 160 km apart at the same time with velocities 50 km/hr and 30 km/hr. move in opposite direction. Where they meet ?  Choose one:
A) 90 km from A	B) 50 km from B	C) 100 km from A	D) 70 km from B	E) None of these

Solution: Explanation :   Solution: d = 160, v1 = 50, v2 = 30   relative speed vr = v1 + v2 = 50 + 30= 
50 + 30 = 80
80.   the distance covered by them will be indirectly proportional to their distance   of the persons of meeting from A= 160*50/(50+30) km   = 160*5/8= 
160*5/8 = 100
100 km.   Answer : 100 km from A
Answer: C
A rectangular tank needs to be coated with insulation. The tank has dimensions of 3 feet, 5 feet, and 2 feet. Each square foot of insulation costs $20. How much will it cost to cover the surface of the tank with insulation?
Choose the correct answer:
A) $1100 B) $1240 C) $1360 D) $1480 E) $1550

Solution: The total surface area is 2(2*3 + 3*5 + 2*5) = 62 square feet   The total cost is 62*$20 = $1240   The answer is $1240.62* 20= 
62* 20 = 1_240
$1240   The answer is $1240.
Answer: B
If A^2 + B^2 = 10 and AB = 10, what is the value of the expression (A - B)^2 + (A + B)^2?	Choose the correct choice from the following options
A) 10 B) 20 C) 30 D) 60 E) 70

Solution: (a-b)^2 = a^2 + b^2 - 2ab = 10-20= -10   (a+b)^2 = a^2 + b^2 + 2ab = 10+20= 
10+20 = 30
30   so (a+b)^2 + (a-b)^2= 30 - 10= 
30 - 10 = 20
20   20
Answer: B
The largest 4 digit number exactly divisible by 88 is:  Choose the correct choice from the following answers
A) 4252  B) 6287  C) 7631  D) 9944  E) 6736

Solution: D   Divide largest four digit number 9999 by 88. You get 113.625.   Obviously 113 would be exactly divisible so we want to know what that number is.   We get this by multiplying 113 with 88 = 9944
Answer: D
The average of runs of a cricket player of 10 innings was 30. How many runs must he make in his next innings so as to increase his average of runs by 4?	Answers:
A) 87
B) 74
C) 10
D) 76
E) 17

Solution: Average after 11 innings = 34   Required number of runs   = (34 * 11) - (30 * 10) = 374- 300= 
374- 300 = 74
74.   Answer: 74
Answer: B
Tough and Tricky questions: Combinations.
Six contestants representing four different countries advance to the finals of a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded? Pick
A) 6  B) 7  C) 12  D) 18  E) 24

Solution: Number of ways First-place medal can be awarded to four contestants = 6   Number of ways Second-place medal can be awarded to contestants after awarding First-place medal =3   Therefore number of possibilities = 6 *3= 
6 *3 = 18
18   Answer:18
Answer: D
A can build a wall in the same time in which B and C together can do it. If A and B together could do it in 25 days and C alone in 35 days, in what time could B alone do it?	Choose the correct choice from the following choices:	A) 275 days	B) 178 days	C) 185 days	D) 175 days	E) 675 days

Solution: Explanation:   No explanation is available for this question!   ANSWER: 175 days
Answer: D
When positive integer n is divided by 3, the remainder is 2. When n is divided by 5, the remainder is 5. How many values less than 100 can n take?	Choose the correct choice from the following choices.
A) 0
B) 2
C) 3
D) 4
E) 5

Solution: a quick approac to this Q is..   the equation we can form is.. 3x+2=7y+5..   3x-3=7y... 3(x-1)=7y...   so (x-1) has to be a multiple of 7 as y then will take values of multiple of 3..   here we can see x can be 1,8,15,22,29 so 5 values till 100 is reached   as   (29-1)*3= 
  (29-1)*3 = 84
84 and next multiple of 7 will be 84+21>100..   ans 0.. 0
Answer: A
the largest four-digit number which is a perfect cube, is	Select:
A) 8000	B) 9261	C) 9999	D) None of these	E) Cannot be determined

Solution: Solution   Clearly, 9261 is a perfect cube satisfying the given property.   Answer 9261
Answer: B
The end of a blade on an airplane propeller is 20 feet from the center. If the propeller spins at the rate of 1,320 revolutions per second, how many miles will the tip of the blade travel in one minute? (1 mile = 5,280 feet)
Choose the correct answer:	A) 200π	B) 240π	C) 600π	D) 480π	E) 1,200π

Solution: Distance traveled in 1 revolution = 2πr= 2π20/5280   Revolutions in one second= 1320   Revolutions in 60 seconds (one minute)= 1320*60   Total distance traveled= total revolutions *distance traveled in one revolution   1320*60 *2π20/5280= 600π   600π is the answer
Answer: C
A train which has 390 m long, is running 45 kmph. In what time will it cross a person moving at 9 kmph in same direction ? Pick one:
A) 26 sec B) 39 sec C) 36 sec D) 29 sec. E) 19 sec.

Solution: Time taken to cross a moving person = length of train/ relative speed   Time taken = 390/((45-9) (5/18)   = 390/ 36*(5/18)   = 390/10= 
390/10 = 39
39 sec   ANSWER:39 sec
Answer: B
In an engineering class that contained 25 students, the final exam consisted of 2 questions. Three fifths of the students answered the first question correctly. If four fifths of the remainder answered the second question correctly, how many students answered both questions incorrectly?	Pick.
A) 2 B) 6 C) 10 D) 12 E) 24

Solution: 1st Question : Three fifths of the students answered the first question correctly - so 3/5âˆ—25=15   2nd Question : four fifths of the remainder answered the second question correctly so 4/5âˆ—(25âˆ’15)=4/5âˆ—10=8   total students who answered at least one Q correct =15+8= 
15+8 = 23
23   so students who answered BOTH incorrectly= 25âˆ’23=2   2NSWER:2
Answer: A
If x*y = xy – 2(x + y) for all integers x and y, then 1* (–3) = Select
A) –16	B) –11	C) –4	D) 4	E) 1

Solution: 1*(-3) = 1*(-3) - 2 (1 + (-3) ) = -3 +4= 
-3 +4 = 1
1   Option (1)
Answer: E
Presently the ratio between the ages of Dan and James is 6:5. after 4 years Dan will be 28. What is the present age of James?	Answers:
A) 20	B) 19	C) 21	D) 18	E) 22

Solution: Let the present ages Dan and James be 6x years and 5x years respectively   6x+4 = 28   6x = 24   x = 4   Kim's age = 5x = 20 years   20nswer is 20
Answer: A
Of the 3,600 employees of Company X, 1/4 are clerical. If the clerical staff were to be reduced by 1/4, what percent of the total number of the remaining employees would then be clerical?	Choices:  A) 25%  B) 22.2%  C) 20%  D) 12.5%  E) 11.1%

Solution: Welcome, just post the question and the choices   Let's see, the way I did it was   1/4 are clerical out of 3600 so 900 are clerical   900 reduced by 1/3 is 900*1/3   so it reduced 300 people , so there is 600 clerical people left   but since 600 people left, it also reduced from the total of 3600 so there are 3000 people total   since 600 clerical left / 300 people total   you get (A) 20%   Answer : 20%
Answer: C
The banker's gain on a bill due due 1 year hence at 12% per annum is Rs.8.4. The true discount is	Answers.
A) Rs.70 B) Rs.36 C) Rs.54 D) Rs.50 E) none

Solution: Solution   T.D	= [B.G x 100 / R x T]   = Rs.(8.4 x 100 / 12 x 1)   = Rs.70.   Rs.70nswer Rs.70
Answer: A
Working individually, Allison can sew dresses for 9 hours and Al can sew dresses in 12 hours. If Allison and Al work together but independently at the task for 3 hours, at which point Al leaves, how many remaining hours will it take Allison to complete the task alone?
Answers:
A) 45/12
B) 23/12
C) 40/33
D) 34/12
E) 43/5

Solution: In first 3 hrs Al will finish 3/12 = 1/4 of work and Allison will finish 3/9=1/3 work so total 1/4 + 1/3 = 7/12 work is finished and 1-7/12 = 5/12 work remaining. Now Allison will take (5/12)*9 = 45/12 hrs to finish it.   So answer is 45/12.
Answer: A
What is the probability for a family with four children to have two boys and two girls (assuming the probability of having a boy or a girl is equal)?  Choose the correct option:
A) 1/2
B) 1/4
C) 1/8
D) 3/8
E) 5/16

Solution: One possible case is: girl - girl - boy - boy   The probability of this is 1/2*1/2*1/2*1/2 = 1/16   There are 4C2 = 6 such cases so we should multiply by 6.   P(two boys and two girls) = 6/16 = 3/8   The answer is 3/8.
Answer: D
Out of four numbers ,the average of first three is 16 and that of the last three is 15. If the last number is 20,the first number is :	Options:
A) 22  B) 23  C) 77  D) 99  E) 27

Solution: Explanation:   Let the numbers be a,b,c,d   Given, a + b + c = 48, b + c + d = 45   Now, d = 20   thus, b + c + 20 = 45 ⇒ b + c = 25   Putting the value of b + c in a + b + c = 48   a + 25 = 48 ⇒ a = 23   Answer: 23
Answer: B
6x – 5y + 3z = 26
4x + 8y – 11z = 7
5x – 6y + 2z = 12
Given the equations above, x + y + z = ?	Choose the correct choice:
A) 11
B) 12
C) 13
D) 14
E) 15

Solution: (6x – 5y + 3z) - (5x – 6y + 2z ) = 26-12   or, x+y+z = 14   Option 14 is the ans
Answer: D
Consider a lady took a loan from a bank at the rate of 12% p.a. simple interest. After 3 years she had to pay Rs. 9000
interest only for the period. The principal amount borrowed by her was	Choose the correct answer:
A) Rs. 25000  B) Rs. 10000  C) Rs. 15000  D) Rs. 20000  E) None of these

Solution: Explanation :   Principal = Rs. (100×9000 / 12×3)   => Rs. 25,000.   Rs. 25000nswer : Rs. 25000
Answer: A
In a certain city, 60 percent of the registered voters are Democrats and the rest are Republicans. In a mayoral race, if 75 percent of the registered voters who are Democrats and 20 percent of the registered voters who are Republicans are expected to vote for Candidate A, what percent of the registered voters are expected to vote for Candidate A ? Pick one:
A) 50%
B) 53%
C) 54%
D) 55%
E) 57%

Solution: Registered voters = 100   D = 60   R = 40   75% of D ( 60) = 45   20% of R ( 40 ) = 8   Total voter% of registered voters = 53 / 100   53%   Answer: 53%
Answer: B
On a scale of a map 0.6 cm represents 6.6km. If the distance between two points on the map is 80.5 cm , what is the the actual distance between these points?
Answers.
A) 885.5 km B) 860 km C) 892.5 km D) 825 km E) None of these

Solution: Explanation :   Let the required actual distance be x km   More scale distance, More actual distance(direct proportion)   Hence we can write as   scale distance.6:80.5}::6.6:x   ⇒.6x = 80.5 × 6.6   ⇒ .1x = 80.5 × 1.1   ⇒ x = 80.5 × 11 = 885.5. 885.5 kmnswer : Option 885.5 km
Answer: A
Calculate how much time could be saved if the train would run at its usual speed, given that it ran at 6/8 of its own speed and got to its destination in 11 hours?
Choose the correct choice:	A) 2.5 hrs	B) 2.9 hrs	C) 4.5 hrs	D) 3.5 hrs	E) 1.5 hrs

Solution: New speed = 6/8 of usual speed   New time = 6/8 of usual time   6/8 of usual time = 10 hrs   Usual time = 10*6/8= 
10*6/8 = 15/2 = around 7.5
7.5 hrs   Time saved= 10-7.5= 
10-7.5 = 2.5
2.5 hrs   2.5 hrsnswer is 2.5 hrs
Answer: A
How many two-digit numbers satisfy this property.: The last digit (unit's digit) of the square of the two-digit number is 3 ?
Choose the correct choice:
A) 4 B) 0 C) 3 D) 2 E) 1

Solution: A number ending with 3 can never be a perfect square.   Answer: 0
Answer: B
Today is Tuesday. After 75 days, it will be:	Choose the correct choice from the following options.
A) Saturday B) Sunday C) Friday D) Thursday E) Wednesday

Solution: Each day of the week is repeated after 7 days.   So, after 77 days, it will be Tuesday.   After 75 days, it will be Sunday.   Answer :Sunday
Answer: B
Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in?	Choose the correct answer:  A) 7 min  B) 13 min  C) 23 min  D) 9 min  E) 8 min

Solution: 1/10 + 1/15 - 1/x = 1/18   x = 9   ANSWER:9 min
Answer: D
What is the rate percent when the simple interest on Rs.2000 amount to Rs.500 in 2 Years?	Select the correct option:
A) 5%
B) 6%
C) 12.5%
D) 95%
E) 1%

Solution: Interest for 2yrs = 500   Interest for 1yr = 250   Interest rate = 250/2000 x 100 = 12.5%   Answer : 12.5%
Answer: C
Workers at a campaign office have 2000 fliers to send out. If they send out 1/10 of them in the morning and 1/4 of the remaining ones out during the afternoon, how many are left for the next day?	Answers:
A) 300
B) 1350
C) 1100
D) 1200
E) 1900

Solution: (1/10)*2000= 
(1/10)*2000 = 200
200   Remaining= 2000-200= 
2000-200 = 1_800
1800   (1/4) of remaining= (1/4)*1800= 
(1/4)*1800 = 450
450   Remaining now= 1800-450= 
1800-450 = 1_350
1350   Answer: Option 1350
Answer: B
The number 70 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers? Select.
A) 17  B) 16  C) 15  D) 14  E) 13

Solution: I think brute force with some common sense should be used to solve this problem.   Write down all perfect squares less than 70: 1, 4, 9, 16, 25, 36, 49, 64.   Now, 70 should be the sum of 3 of those 8 numbers. Also to simplify a little bit trial and error, we can notice that as 70 is an odd numbers then either all three numbers must be odd (odd+odd+odd=odd) OR two must be even and one odd (even+even+odd=odd).   We can find that 60 equals to 9+25+36=3^2+5^2+6^2=70 --> 3+5+6=14.   Answer: 14.
Answer: D
In what ratio must sugar at Rs.7.10 be mixed with sugar at Rs.9.20 so that the mixture may be worth Rs.8 per kg? Choose the correct choice from the following options:  A) 6:3  B) 7:3  C) 1:7  D) 4:3  E) 2:1

Solution: CP of 1 kg sugar of 1st kind =7.1   CP of 1 kg sugar of 2nd kind=9.2   Mean Price=8   CP of 1 kg sugar of 1st kind - Mean Price=8-7.1= 
8-7.1 = 0.9
0.9   CP of 1 kg sugar of 2nd kind - Mean Price=9.2-8= 
9.2-8 = 1.2
1.2   Required ratio= 1.2 : 0.9 = 12 : 9 = 4 : 3   Answer:4:3
Answer: D
A can complete a project in 20 days while B can complete same project in 30 days. If A and B start working together and A leaves the work 10 days before completion of project, then in how many days the project will be completed?	Choose one
A) 15 B) 16 C) 17 D) 18 E) 19

Solution: A's 1day work=1/20;   B's 1day work=1/30;   (A+B) 1day work=(1/20+1/30)=1/12;   It is given that A leaves the work 10 days before completion of the project..   Thus,B alone does the remaining job in 10 days.   So,In 10 days ,B can do 1/3 w ..   Thus,(A+B) have worked (1-1/3)=2/3 w..   (A+B)can do 1/12 work in 1 day...   They did 2/3 w in 8 days.   Total days=(8+10)= 
(8+10) = 18
18   ANSWER:18
Answer: D
There are 7 players in a bowling team with an average weight of 85 Kg. If two new players join the team, one weighs 110 Kg and the second weighs 60 Kg, what will be the new average weight?
.	Choose the correct choice from the following choices:
A) 75 Kg
B) 80 Kg
C) 85 Kg.
D) 90 Kg
E) 92 Kg

Solution: New average weight= 110+60/2= 85 kgs   Since avg weight of 85 is added to avg weight of 85, the average will remain the same, i.e 85   85 Kg. is the answer
Answer: C
A HEXAGON IS FORMED ABCDEF WHICH PERIMETER 36cm. A POLYGON IS FORMED BY JOINING THE POINTS AE &BD . FIND THE AREA OF THE POLYGON ABDE?
Choose the most appropriate option.
A) 34√3 cm2	B) 35√3 cm2	C) 36√3 cm2	D) 37√3 cm2	E) 38√3 cm2

Solution: A regular hexagon consist of 6 equilateral triangle. Each of side 6 cm.   So the area of 1 equilateral triangle is = ¼(√3 a2) = 9√3 cm2   The figure formed by joining polygon ABDE consist of 2 equilateral triangle and 4 half equilateral triangle   Which employs area of 4 equilateral triangle.   So, The area of polygon ABDE = 4*(area of equilateral traingle)   = 4* 9√3 = 36√3 cm2   ANSWER:36√3 cm2
Answer: C
The average marks of 10 students in a class is 100. But a student mark is wrongly noted as 90 instead of 10 then find the correct average marks? Choose the correct choice from the following:
A) A)78  B) B)82  C) C)92  D) D)91  E) E)85

Solution: correct avg marks = 100+(10-90)/10   avg = 100-8= 
100-8 = 92
92   Answer is 92
Answer: C
A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is  Choose the correct option.
A) 9	B) 10	C) 11	D) 12	E) 13

Solution: Man's rate in still water = (15 - 2.5) km/hr = 12.5 km/hr.   Man's rate against the current = (12.5 - 2.5) km/hr = 10 km/hr.   Answer:10
Answer: B
Tough and Tricky questions: Word Problems.
In a rare coin collection, one in six coins is gold, and all coins are either gold or silver. If 10 silver coins were to be subsequently traded for an additional 10 gold coins, the ratio of gold coins to silver coins would be 1 to 6. Based on this information, how many gold coins would there be in this collection after the proposed trade?  Choose the correct option.
A) 50  B) 60  C) 180  D) 200  E) 300

Solution: The correct answer is 180.
Answer: C
An athlete decides to run the same distance in 1/4th less time that she usually took. by how much percent will she have to increase her average speed?
Answers:	A) 40	B) 44.4	C) 33.3	D) 22.2	E) 12.2

Solution: simple logic (1-1/4)=3/4 then reverse it so 4/3=1.333   1.33-1=33.33   ANSWER:33.3
Answer: C
Suppose 3 monkeys take 3 minutes to eat 3 bananas. How many monkeys would it take to eat 6 bananas in 6 minutes?
Pick one:
A) 9	B) 10	C) 11	D) 3	E) 13

Solution: One monkey takes 3 min to eat 1 banana , so in 6 mins 1 monkey will eat 2 bananas , so for 6 bananas in 6 min we need  6/2= 
 6/2 = 3
3 monkeys   ANSWER:3
Answer: D
A car started running at a speed of 30 km/hr and the speed of the car was increased by 2 km/hr at the end of every hour. Find the total distance covered by the car in the first 10 hours of the journey.	Choose the correct choice from the following choices:
A) 278 km  B) 390 km  C) 267 km  D) 286 km  E) 296 km

Solution: The total distance covered by the car in the first 10 hours   = 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 + 48   = sum of 10 terms in AP whose first term is 30 and last term is 48   = 10/2 [30 + 48] = 390 km.   Answer: 390 km
Answer: B
The sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter?
Pick:
A) 91.5 cm
B) 93.5 cm
C) 94.5 cm
D) 92.5 cm
E) None of these

Solution: Explanation:   Perimeter of the sector = length of the arc + 2(radius)   = (135/360 * 2 * 22/7 * 21) + 2(21)   = 49.5 + 42= 
49.5 + 42 = 91.5
91.5 cm   91.5 cmNSWER IS 91.5 cm
Answer: A
A train running at the speed of 60 km/hr crosses a pole in 12 seconds. What is the length of the train?  Choose the correct choice from the following answers
A) 140
B) 130
C) 150
D) 200
E) 160

Solution: Speed=(60x5/8)m/sec = (50/3) m/sec.   Length of the train = (Speed x Time).   Length of the train = (50/3 x 12)m = 200 m.   Answer is 200.
Answer: D
You are a cashier at a grocery store. Your customer, David, buys a pound of bacon
$1.39, one dozen eggs for $1.29, and a pound of coffee for $2.79. What is the sum
total of his purchases?	Choose the correct choice from the following
A) $5.47	B) $6.47	C) $7.47	D) $8.47	E) $9.47

Solution: $5.47dd $1.39+ $1.29+$2.79   we have the sum $5.47   correct answer $5.47
Answer: A
The total marks obtained by a student in Mathematics and Physics is 32 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together.  Choose the correct choice:
A) 40
B) 26
C) 27
D) 28
E) 22

Solution: Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively.   Given , M + C = 32 and C - P = 20 M + C / 2 = [(M + P) + (C - P)] / 2 = (32 + 20) / 2= 
(32 + 20) / 2 = 26
26.Answer:26
Answer: B
A person is 80 years old in 490 and only 70 years old in 500 in which year is he born?
Choose one
A) 400
B) 550
C) 570
D) 440
E) 450

Solution: 490(80),500(70),510(60),520(50),530(40),540(30),550(20),560(10),570(0)   ANSWER:570
Answer: C
The areas of the two spheres are in the ratio 1: 4. The ratio of their volume is?	Choose the correct choice from the following:
A) 1:7
B) 1:3
C) 1:8
D) 1:9
E) 1:1

Solution: 4πr12 : 4πr22 = 1 : 4   r1 : r2 = 1 : 2   4/3 πr13 : 4/3 πr23   r13 : r23 = 1:8   Answer:1:8
Answer: C
A manufacturer of a certain product can expect that between 0.1 percent and 0.3 percent of the units manufactured will be defective. If the retail price is $2,500 per unit and the manufacturer offers a full refund for defective units, how much money can the manufacturer expect to need to cover the refunds on 20,000 units?  Answers: A) Between $15,000 and $25,000 B) Between $50,000 and $150,000 C) Between $60,000 and $100,000 D) Between $150,000 and $250,000 E) Between $300,000 and $500,000

Solution: Number of defective units is between = .1 % of 20000 and .3% of 20000   = 20 and 60   Retail Price per unit = 2500 $   Expected price of refund is between = 2500 x 20 and 2500 x 60   =50,000 and 1,50,000 dollars   Answer Between $50,000 and $150,000
Answer: B
An engagement team consists of a 2 project managers, 3 team leaders, and four consultants. There are 3 candidates for the position of project manager, 4 candidates for the position of team leader, and 7 candidates for the 4 consultant slots. If 2 out of 7 consultants refuse to be on the same team, how many different teams are possible?  Answers:
A) 25	B) 35	C) 150	D) 210	E) 300

Solution: Answer= Total number combinations - Total number of combinations with constraints   Total number of combinations = 3C2*4C3*7C4= 420   Total number of combinations with constraints = 3C2*4C3*5C2=120   Answer=420-120= 
420-120 = 300
300   ANSW300R: 300
Answer: E
A bookseller has two display windows. She plans to display 5 new fiction books in the left window, and 6 new non-fiction books in the right window. Assuming she can put the six fiction books in any order, and separately, the three non-fiction books in any order, how many total configurations will there be for the two display windows?	Choose the most appropriate option.
A) 86400  B) 65777  C) 89000  D) 34560  E) 12420

Solution: Two displays books could be arranged n! # of total arrangements are combinations multiplied together,   5!*6! =120*720= 
120*720 = 86_400
86400   86400nswer is 86400
Answer: A
Liam is pulled over for speeding just as he is arriving at work.He explains to the police officer that he could not afford to be late today, and has arrived at work only four minutes before he is to start. The officer explains that if Liam had driven 5mph slower for his whole commute, he would have arrived at work exactly on time. If Liam's commute is 20 miles long,how fast was he actually driving?(Assume that Liam drove at a constant speed for the duration of his commute.)  Choose the correct answer:
A) 40 mph
B) 45 mph
C) 48 mph
D) 52 mph
E) 60 mph

Solution: Let t be the number of hours he would need to reach office on time.   when he is driving with over speed, he reached office 4 min earlier! so the equation for this is s(t - 4/60) = 30   where s is the speed and 30 is the distance.   if he decreases his speed by 5mph then he would have reached his office on time: (s-5)t = 30   if you solve above equations, you will arrive at t = 2/3 hr and s = 40mph   therefore answer is 40 mph
Answer: A