MU-NLPC/Calc-aqua_rat huggingface dataset:
Nine men and nine women have to sit around a circular table so that no 2 women are together. In how many ways can that be done?
Choose the correct choice from the following choices:
A) 5!*6!  B) 6!*6!  C) 5!*7!  D) 6!*7!  E) 8!*9!

Solution: The number of arrangements of n distinct objects in a row is given by n!.   The number of arrangements of n distinct objects in a circle is given by (n-1)!.   The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have: n!/n=(n-1)!   Now, 9 men in a circle can be arranged in (9-1)! ways and if we place 9 women in empty slots between them then no two women will be together. The # of arrangement of these 9 women will be 9! and not 8! because if we shift them by one position we'll get different arrangement because of the neighboring men.   So the answer is indeed 8!*9!.   8!*9!
Answer: E
x =2.5 3.5 1.5
y= 25 49 9 then what is the relation between x and y	Choose one:
A) Y=(2*X)^2 B) Y=(2*X)^3 C) Y=(2*X)^4 D) Y=(3*X)^2 E) Y=(4*X)^2

Solution: Y=(2*X)^2   25=(2*2.5)^2   Y=(2*X)^2NSWER:Y=(2*X)^2
Answer: A
A question paper has 2parts, A & B, each containing 10 questions. If a student has to choose 8 from part A &5 from part B, in how many ways can he choose the questions?  Pick one:
A) 1020
B) 1100
C) 1140
D) 1150
E) 1140

Solution: There 10 questions in part A out of which 8 question can be chosen as = 10C8.   Similarly, 5 questions can be chosen from 10 questions of Part B as = 10C5.   Hence, total number of ways,   =10C8*10C5   =[10!/(2!8!)]*[10!/(5!*5)]   = {10*9/2}*{10*9*8*7*6/(5*4*3*2*1)}   = 1140.   1140
Answer: E
A certain manufacturer of cake, muffin, and bread mixes has 100 buyers, of whom 50 purchases cake mix, 40 purchase muffin mix, and 17 purchase both cake mix and muffin mix. If a buyer is to be selected at random from the 100 buyers, what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix?
Choose the correct choice from the following options.
A) 1/10	B) 3/10	C) 1/2	D) 27/100	E) 9/100

Solution: C+M+B-CM-MB-CB-2CMB = 100   C - cake buyers, M - muffin and B - Bread buyers. CM,MB,CB and CMB are intersecting regions.   the question asks for people who have bought only bread mixes = B-CB-MB-2CMB has to be found out.   50 + 40 + B-CB-MB-17-2CMB = 100   B-CB-MB-2CMB = 27   hence the probability = 27/100   27/100
Answer: D
How many paying stones, each measuring 2 1/2 m * 2 m are required to pave a rectangular court yard 30 m long and 16 1/2 m board?	Choices:
A) 99	B) 18	C) 16	D) 10	E) 15

Solution: 30 * 33/2 = 5/2 * 2 * x => x   = 99   99nswer:99
Answer: A
A toy store sells small, medium, large, and super-large toy trucks in each of the colors red, blue, black, green, orange, and yellow. The store has an equal number of trucks of each possible color-size combination. If Paul wants a medium, red truck and his mother will randomly select one the trucks in the store, what is the probability that the truck she selects will have at least one of the two features Paul wants?
Choose the most appropriate option:
A) 1/3  B) 2/5  C) 3/5  D) 3/8  E) 11/24

Solution: Probability of NOT selecting medium out of 4 sizes = 3/4   Probability of NOT selecting red out of 6 colours = 5/6   Total probability of NOT selecting red and medium = (3/4)*(5/6) = 5/8   Required probability = 1 - 5/8 (this will select at least one of red and medium)   = 3/8   The answer is 3/8.
Answer: D
In honor of the year 2012, a donor has purchased 2016 books to be distributed evenly among the elementary schools in a certain school district. If each school must receive the same number of books, and there are to be no books remaining, which of the following is NOT a number of books that each school could receive? Choose the correct choice from the following choices:
A) 18  B) 36  C) 42  D) 51  E) 56

Solution: All options other than 'D' are factors of 2012. Hence, '51' is the answer
Answer: D
Find the number of square tiles to cover the floor of a room measuring 3.5 m * 9 m leaving 0.25 m space around the room. A side of square tile is given to be 25 cms? Select the correct option.
A) 408	B) 476	C) 472	D) 471	E) 445

Solution: 3 * 8 1/2 = 1/4 * 1/4 * x => x   = 408   408nswer:408
Answer: A
7 people average age is 30. youngest person age is 3. find average of the people when youngest was born. Choose the correct choice from the following.
A) 23  B) 24  C) 25  D) 26  E) 27

Solution: average age of people =30   so have total age =210   before 7 years we have to deduct each person age by seven years   210-21= 
  210-21 = 189
189   so average age would be 189/7= 
189/7 = 27
27   ANSW27R:27
Answer: E
A man covered a certain distance at some speed. Had he moved 3 kmph faster, he would have taken 40 minutes less. If he had moved 2 kmph slower, he would have taken 40 minutes more. The distance (in km) is Choose the correct option
A) 27  B) 87  C) 40  D) 18  E) 17

Solution: Explanation:   Let distance = x km and usual rate = y kmph.   Then, x/y - x/(y+3) = 40/60 --> 2y (y+3) = 9x ----- (i)   Also, x/(y-2) - x/y = 40/60 --> y(y-2) = 3x -------- (ii)   On dividing (i) by (ii), we get:   x = 40 km.   Answer: 40
Answer: C
The function F(n) is defined as the product of all the consecutive positive integers between 3 and n^2, inclusive, whereas the function G(n) is defined as the product of the squares of all the consecutive positive integers between 1 and n, inclusive. The exponent on 2 in the prime factorization of F(3)/G(3) is Choices
A) 1	B) 2	C) 3	D) 4	E) 5

Solution: F(3)/G(3)   =product(1 to 3 ^2) / 1.2^2.3^2   =1.2.3.4.5.6.7.8.9/1.4.9   =1.2.3.(2^2).5.(2.3).7.(2^3).9/1.(2^2).9   =1.(2^7).3.5.7.9/1.(2^2).9   Loof for 2^7/2^2=2^5 ----Exponent 3   Answer: 3
Answer: C
The average of 7 consecutive numbers is 20. The largest of these numbers is	Choose the correct choice from the following answers:	A) 12	B) 27	C) 23	D) 28	E) 11

Solution: Let the numbers be x, x + 1, x + 2, x + 3, x + 4, x + 5 and x + 6,   Then (x + (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5) + (x + 6)) / 7 = 20.   or 7x + 21 = 140 or 7x = 119 or x =17.   Latest number = x + 6 = 23.   Answer: 23
Answer: C
On the xy co-ordinate plane, point C is (5,-1) and point D is (-1,2.5). The point on line segment CD that is twice as far from C as from D is:	Choose the correct choice:  A) (1,-1)  B) (1,1)  C) (2,0.25)  D) (3,0.5)  E) (3,1)

Solution: We want the point on the line that is twice as far from C as it is from D. We can examine the x and y coordinates separately since they are independent.   *It should be noted that there are two solutions to this problem, one point between C and D, and another point with D in the middle of C and the point. We can quickly look at the answer choices and see that all the points are between C and D, therefore we can search for that point using the following method:   Taking the x-coordinate first, the distance between C and D is |(x-coordinate of C) - (x-coordinate of D)|= |5 - (-1)= 
5 - (-1) = 6
6   The x-coordinate that is twice as far from C as it is from D (and in between C and D) will be 4 units from C and 2 units from D. So the x coordinate of the point we're looking for is  5-4= 
 5-4 = 1
1, or  (-1)+2= 
 (-1)+2 = 1
1.   Now looking at the y-coordinate, we do the same thing. The distance between C and D is |(-2) - 2.5|= 4.5   The y-coordinate that is twice as far from C as it is from D (and in between C and D) will be 3 units from C and 1.5 units from D. So the y coordinate of the point we're looking for is  (-2)+3= 
 (-2)+3 = 1
1, or  2.5-1.5= 
 2.5-1.5 = 1
1.   So now we have our coordinates of the point on the line that is twice as far from (2,0.25) as it is from D: (2,0.25)   Answer: (2,0.25)
Answer: C
A ladies hostel had provision of food for 120 women for 35 days. After 10 days, 25 women left the hostel. The number of days for which the remaining food will last is:
Choose the correct choice:
A) 39.47
B) 39
C) 39.23
D) 39.74
E) 39.64

Solution: Explanation :   After 10 days : 120 women had food for 25 days.   Suppose 95 women had food for x days.   Now, Less women, More days (Indirect Proportion)   95 : 150 :: 25 : x   => 95 x x = 150 x 25   => x = 150 x 25 / 95   => x = 39.47   39.47nswer : 39.47
Answer: A
A basket contains 10 bananas and 20 mangoes out of which 3 bananas and 5 mangoes are spoiled. If we choose two fruits at random, what is the probability that either both are mangoes or both are non spoiled?	Choices:
A) 309/435
B) 311/433
C) 316/401
D) 314/501
E) 316/435

Solution: Let A be the event of getting two oranges and   B be the event of getting two non-defective fruits.   and be the event of getting two non-defective oranges   = 316/435   316/435
Answer: E
With out any halt a train travels a certain distance with an average speed of 75 km ph , and with halts it covers the same distance at an average speed of 60 kmph. When it is traveling with halts, how many
minutes/per hour does the train halt on an average ?  Choose the most appropriate option.
A) 48 min B) 12min. C) 15min. D) 18min. E) 20min

Solution: With halt in 1 hour the train travels 60km   With out halt for traveling same distance it take 60/75 = 4/5 = 48 minutes   :. 12 minutes is the halting time per hour   Answer: 12min.
Answer: B
How many two-element subsets of {1,2,3,4} are there that do not contain the pair of elements 2 and 4?	Choose one
A) One  B) Two  C) Four  D) Five  E) Six

Solution: {1,2}, {1,3}, {1,4}, {2,3}, {3,4}.   Or: C24−1=5   Answer: Five.
Answer: D
8 man's increases average weight by 2.5 kg when a new man comes in place of one of them weighing 65 kg. What might be the weight of the new man?  Choose the correct choice from the following options:
A) 85 kg B) 70 kg C) 75 kg D) 90 kg E) 79 kg

Solution: Total weight = (8 x 2.5) kg = 20 kg.   Weight - new man = (65 + 20)= 
(65 + 20) = 85
85 kg   85 kgNSWER 85 kg
Answer: A
During 2001, a stock lost 60 percent of its value. During the following year, the stock's value increased by 200 percent. Which of the following is the percent change in the stock's value during those two years?	Select.
A) 60 percent decrease  B) 40 percent decrease  C) 20 percent increase  D) 60 percent increase  E) 140 percent increase

Solution: Let the value of the stock in 2000 be 100, then in 2001 its value would be 100*(1-60/100)=100*0.4= 
100*0.4 = 40
40 and in 2002 its value would be   40*(1+200/100)= 
  40*(1+200/100) = 120
120. Hence during those two years the value of the stock increased from 100 to 120, so by 20%.   Answer: 20 percent increase.
Answer: C
Two pipes can fill a tank in 18 minutes and 15 minutes. An outlet pipe can empty the tank in 45 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank?	Select:
A) 1/15  B) 1/16  C) 1/11  D) 1/10  E) 1/12

Solution: Part of the filled by all the three pipes in one minute   = 1/18 + 1/15 - 1/45 = (5 + 6 - 2)/90 = 9/90 = 1/10   So, the tank becomes full in 10 minutes.   Answer:1/10
Answer: D
6,61,212,507,_? Choose the correct option:
A) 974  B) 994  C) 954  D) 845  E) 754

Solution: (2)3-2=6   (4)^3-3=61   (6)^3-4=212   (8)^3-5=507   (10)^3-6=994   ANSWER:994
Answer: B
John bought a 1-year, $20,000 certificate of deposit that paid interest at an annual rate of 8 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity?	Choose the correct option.
A) $1650	B) $1660	C) $2632	D) $1632	E) $2750

Solution: 8 percent compounded semiannually --> 4% in 6 moths.   For the first 6 moths interest was 4% of $20,000, so $800;   For the next 6 moths interest was 4% of $20,800, so $832   Total interest for 1 year was $800+$832=$1632   Answer : $1632  800+ 832= 
  800+ 832 = 1_632
$1632   Answer : $1632
Answer: D
The average weight of a group of boys is 20 kg. After a boy of weight 35 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?	Options:
A) 12
B) 14
C) 18
D) 24
E) 10

Solution: Let the number off boys in the group originally be x.   Total weight of the boys = 20x   After the boy weighing 35 kg joins the group, total weight of boys = 20x + 35   So 20x + 35 = 21(x + 1) = > x = 14.   ANSWER:14
Answer: B
A wholeseller has $329,864 in her savings account. What is the least amount of money (in whole number of dollars) that he must add to his account if she wants to split this money evenly among his 9 debters?
Pick.
A) $1	B) $2	C) $3	D) $4	E) $6

Solution: To find the least amount the wholeseller should add to her saving account to split the money evenly among his 9 debtors,   he needs to make the total divisible by 9   Simply add the individual digits of the total = 3+2+9+8+6+4= 
3+2+9+8+6+4 = 32
32   If you add 4 , the number is divisible by 9 (32+ 4)   Correct Option : $4
Answer: D
The altitude drawn to the base of an isosceles triangle is 8 cm and the perimeter is 32 cm. The area of the triangle is
Choose the correct choice from the following answers:
A) 72 cm2 B) 60 cm2 C) 66 cm2 D) 65 cm2 E) None of these

Solution: Let ABC be the isosceles triangle and AD be the altitude.   Let AB = AC = x. Then, BC = (32 – 2x).   Since, in an isosceles triangle, the altitude bisects the base. So, BD = DC = (16 – x).   In ΔADC, AC2 = AD2 + DC2   ⇒ x2 = (8)2 + (16 – x)2   ⇒ 32x = 320 ⇒ x = 10.   ∴ BC = (32 – 2x) = (32 – 20) cm = 12 cm.   Hence, required area = (1⁄2 × 60 cm2C × AD)   = (1⁄2 × 12 × 10) cm2 = 60 cm2   Answer 60 cm2
Answer: B
A salt manufacturing company produced a total of 2500 tonnes of salt in January of a particular year. Starting from February its production increased by 100 tonnes every month over the previous months until the end of the year. Find its average monthly production for that year?	Choose the correct choice:
A) 2060
B) 3050
C) 5550
D) 2889
E) 2506

Solution: Total production of salt by the company in that year = 2500 + 2600 + 2700 + .... + 3600 = 36600.   Average monthly production of salt for that year = 36600/12= 
36600/12 = 3_050
3050.   Answer: 3050
Answer: B
A train 110 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?	Choose the correct answer:
A) 6  B) 7  C) 9  D) 5  E) 3

Solution: Speed of train relative to man = 60 + 6= 
60 + 6 = 66
66 km/hr.= 66 * 5/18 = 55/3 m/sec.   Time taken to pass the men = 110 * 3/55= 
110 * 3/55 = 6
6 sec.   6nswer: 6
Answer: A
A man can do a piece of work in 7days, but with the help of his son, he can finish it in 3days. In what time can the son do it alone? Choose the correct choice from the following choices
A) 5 B) 4 1/5 C) 7 1/2 D) 6 E) 9 1/2

Solution: Son's 1day work = 1/3 - 1/7 = 5/21   Son alone can do the work in 21/5days = 4 1/5 days   Answer is 4 1/5
Answer: B
A man can row downstream at 22 kmph and upstream at 14 kmph. Find the speed of the man in still water and the speed of stream respectively? Pick.
A) 13, 3  B) 18, 4  C) 15, 3  D) 14, 4  E) None of these

Solution: Explanation:   Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.   Given x + y = 22 --- (1)   and x - y = 14 --- (2)   From (1) & (2) 2x = 36 => x = 18, y = 4.   Answer: Option 18, 4
Answer: B
A circular path of 13 m radius has marginal walk 2 m wide all round it. Find the cost of leveling the walk at 25p per m2? Choose the correct choice from the following answers
A) 46  B) 47  C) 44  D) 42  E) 41

Solution: π (152 - 132) = 176   176 * 1/4 = Rs.44   Answer: 44
Answer: C
John has 6 friends who want to ride in his new car that can accommodate only 4 people at a time (John plus 3 passengers). How many different combinations of 3 passengers can be formed from John's 6 friends?	Select:
A) 3  B) 8  C) 10  D) 15  E) 20

Solution: 6C3 = 20   The answer is 20.
Answer: E
12 men work 8 hours per day to complete the work in 10 days. To complete the same work in 8 days, working 15 hours a day, the number of men required  Choices:
A) 8 days  B) 3 days  C) 7 days  D) 5 days  E) 6 days

Solution: That is, 1 work done = 12 × 8 × 10   Then, 12 8 × 10 = ? × 15 × 8   ? (i.e. No. of men required) = 12 × 8 × 10/15× 10 = 8 days.   8 days
Answer: A
A man can do a piece of work in 5days, but with the help of his son, he can do it in 3 days. In what time can the son do it alone? Choose the correct choice from the following answers:
A) 13/2
B) 7
C) 15/2
D) 8
E) 9

Solution: Son's 1day's work = (1/3)-(1/5) = 2/5   The son alone can do the work in 15/2 days   Answer is 15/2
Answer: C
If 60 men can do a piece of work in 25 hours, in how many hours will 15 men
do it ?  Pick.
A) 100 hours	B) 90 hours	C) 80 hours	D) 70 hours	E) 60 hours

Solution: Let the required number of hours be x. Then,   Less men, More hours	(Indirect Proportion)   15 : 60 : : 25 : x<=>(15 x x) =(60 x 25)<=>(60 x 25)/15 = 100   Hence, 15 men can do it in 60 hours   100 hoursnswer is 100 hours.
Answer: A
The length of the bridge, which a train 150 meters long and travelling at 45 km/hr can cross in 30 seconds, is:  Choose the correct option.
A) 239	B) 277	C) 225	D) 88	E) 232

Solution: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (150 + X)/30   = 25/2 ==> 2(150 + X) = 750 ==> X = 225 m.   Answer: 225
Answer: C
The sector of a circle has radius of 21 cm and central angle 144o. Find its perimeter?	Choices.
A) 80cm B) 82cm C) 90cm D) 94.8cm E) 95cm

Solution: Perimeter of the sector = length of the arc + 2(radius)   = (144/360 * 2 * 22/7 * 21) + 2(21)   = 52.8 + 42= 
52.8 + 42 = 94.8
94.8 cm   Answer:94.8cm
Answer: D
What is the ratio between perimeters of two squares one having 5 times the diagonal then the other? Choose one.
A) 5:1	B) 3: 1	C) 5: 8	D) 3: 2	E) 8: 3

Solution: d = 5d d = d   a√2 = 5d a√2 = d   a = 5d/√2 a = d/√2 => 5: 1   5:1nswer:5:1
Answer: A
A student multiplied a number by	3/5 instead of 5/3. What is the percentage error in the calculation?
Select:
A) 54
B) 48
C) 65
D) 25
E) 64

Solution: Let the number be x.   Then, error = 5/3 X - 3/5 X = 16/15 X.   64rror % = (16X/15 * 3/5X * 100)% = 64%   Answer 64) 64%(16 /15 * 3/5  * 100)= 
(16 /15 * 3/5  * 100) = 64
64%   Answer 64) 64%
Answer: E
The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team ?
Choose the correct choice
A) 17 years
B) 88 years
C) 23 years
D) 15 years
E) 12 years

Solution: Explanation:   Let the average age of the whole team be x years.   11x - (26 + 29) = 9 (x - 1)   => 11x - 9x = 46   => 2x = 46   => x = 23.   So, average age of the team is 23 years.   Answer: 23 years
Answer: C
Rob also compared the Empire State Building and the Petronas
Towers. What is the height difference between the two if the Empire
State Building is 464m tall and the Petronas Towers is 472m tall?	Choices
A) 9	B) 8	C) 23	D) 45	E) 12

Solution: 472-464= 
472-464 = 8
8.Answer is 8.
Answer: B
Three friends rani, Bond and gokul divide $1107 amongs them in such a way that if $4, $6 and $8 are removed from the sums that rani, Bond and gokul received respectively, then the share of the sums that they got will be in the ratio of 2 : 4 : 10. How much did gokul receive?  Choices:	A) $170	B) $130	C) $150	D) $180	E) $174

Solution: Explanatory Answer   Let the sums of money received by A, B and C be x, y and z respectively.   Then x - 4 : y - 6 : z -8 is 2a : 4a : 10a   When $4, $6 and $8 are removed, we are removing a total of $18 from $1107.   Therefore, 2a + 4a + 10a = 1107 - 18= 
1107 - 18 = 1_089
1089   i.e., 16a= 1089   or a = 68.   We know that z - 10 = 16a = 10 * 16= 
10 * 16 = 160
160   Therefore, z= 160 + 10= 
160 + 10 = 170
$170   The correct choice is ($170)
Answer: A
If 10 men working 6 hours a day can do a work in 88 days. Then 6 men working 8 hours a day can do it in how many days?
Choose the correct choice from the following
A) 78 days.  B) 110 days.  C) 49 days.  D) 48 days.  E) 67 days.

Solution: B   110 days.   From the above formula i.e (m1*t1/w1) = (m2*t2/w2)   so (10*6*88/1) = (6*8*d/1)   on solving, d = 110 days.
Answer: B
think you are driving the car
1 3 5
2 4 ?
Do you know what will come in place of?
hint is Not 6	Choices.
A) R
B) 6
C) 0
D) None of the Above
E) B

Solution: Correct Rnswer : R   It represents gear stick, the number 1-5 represents gears and the last one should be reverse gear R
Answer: A
If the value of a piece of house decreases by 10% while the new tax rate on the house represent 110% of the original tax rate, what is the effect on the taxes?  Choose the most appropriate option.
A) a - taxes increase by 10%	B) b- taxes increase by 1%	C) c- there is no change in taxes	D) d- taxes decrease by 1%	E) c- taxes decrease by 10%

Solution: Cansider the value of house = 100, Original tax rate 10%, hence tax value = 100*10% = 10.   Decreased value of house = 90, New tax rate = 110% of 10 = 11%, hence tax value = 90*11% = 9.9   10-9.9 = decrease by 1%.   Answer d- taxes decrease by 1%.
Answer: D
In a stockpile of products produced by three machines M1, M2 and M3, 40% and 30% were manufactured by M1 and M2 respectively. 3% of the products of M1 are defective, 1% of products of M2 defective, while 92% of the products of M3 III are not defective. What is the percentage of defective in the stockpile?
Choose the correct option
A) 3%  B) 5%  C) 3.9%  D) 4.9%  E) 6.5%

Solution: Explanation :   Let there be 100 products in the stockpile. 40% and 30% were manufactured by M1 and M2 respectively. So, 30% are manufactured by M3.   Products from M1 = 40, from M2 = 30 and from M3 = 30.   Number of defective products from M1 = 0.03 x 40 = 1.2, from M2 = 0.01 x 30 = 0.3 and from M3 = 0.08 x 30 = 2.4   Therefore, total number of defective products = 3.9   Answer : 3.9%
Answer: C
Angles AMB and CMD are right angles, ∠AMD is acute, and ∠BMC=y° is acute. What is ∠AMD ?  Choose the correct choice.
A) 90°−y
B) 180°−y
C) 90°+y
D) 2y
E) y

Solution: LAMB = 90   LCMB = y   so, LAMC = 90-y   and since LDMC = 90   LDMA = 90 - (90-y) = y   Answer: y
Answer: E
A larger cube has 216 cubic inch as a volume and in the cube there are 216 smaller cubes such that their volume is 1 cubic inch. What is the difference between the surface areas’ sum of the 216 smaller cubes and the surface area of the larger cube, in square inch?
Choose the correct choice from the following answers:
A) 54
B) 64
C) 81
D) 1080
E) 120

Solution: Volume of larger cube = 216 = 6^3   Side of larger cube = 6   Volume of smaller cube = 1 --> Side of smaller cube = 1   Surface area of larger cube = 6 * 6^2 = 216   Surface area of 27 smaller cubes = 216 * 6 * 1= 
216 * 6 * 1 = 1_296
1296   1080ifference= 1296 - 216= 
1296 - 216 = 1_080
1080   Answer: 1080
Answer: D
At a certain resort, each of the 39 food service employees is trained to work in a minimum of 1 restaurant and a maximum of 3 restaurants. The 3 restaurants are the family buffet, the dining room, and the snack bar. Exactly 15 employees are trained to work in the family buffet, 18 are trained to work in the dining room, and 12 are trained to work in the snack bar. If 4 employees are trained to work in exactly 2 restaurants, how many employees are trained to work in all 3 restaurants?  Choose the correct answer.
A) 2	B) 3	C) 4	D) 5	E) 1

Solution: 39 = 15+ 18 + 12 - 4 - 2x   2x = 15 + 18 + 12 - 4 - 39   = 41 - 39= 
41 - 39 = 2
2   x=1   1
Answer: E
A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 81 km/hr. What is the length of the platform?  Choose the most appropriate option: A) 240 B) 288 C) 277 D) 360 E) 422

Solution: Speed = 81 * 5/18= 
81 * 5/18 = 45/2 = around 22.5
22.5 m/sec.   Length of the train= 22.5 * 20= 
22.5 * 20 = 450
450 m.   Let the length of the platform be x m . Then,   (x + 450)/36= 22.5 => x = 360 m.   Answer: 360
Answer: D