MU-NLPC/Calc-aqua_rat huggingface dataset:
Which of the following is closest to (9!-8!)/(9!+8!)?
Choose one:
A) 0.01
B) 0.8
C) 0.2
D) 1
E) 10

Solution: (9!-8!)/(9!+8!)   8! (9-1)/8! (9+1)   8/9 = 0.8   0.8 is the answer
Answer: B
If each term in the sum a1+a2+a3+.....+an is either 7 or 77 and the sum equals 364, which of the following could be equal to n?	Choices:	A) 38	B) 39	C) 40	D) 41	E) 42

Solution: Since, there is no 52 in the answer choices (364/7 = 52), we know there is at least one 77.   364 - 77= 
364 - 77 = 287
287   287/7= 
287/7 = 41
41   41+1= 
41+1 = 42
42.   If 42 wasn't there, I would have subtracted 77 from 287 and continued in a similar way.   Ans. 42
Answer: E
How many digits are there in the integer 8^7 × 25^12? Choose the correct choice from the following answers:
A) 27	B) 24	C) 21	D) 19	E) 15

Solution: 8^7 × 25^12   This can be simplified to   2^21 × 5^24 (since 2^3 = 8 and 5^2 = 25)   Now 2 x 5 =10   So, simplifying further   (2^21 × 5^21) x 5^3   = 10^21 x 5^3   = 125 x 10^21   10^21 has 1 one and 21 zeros which when multiplied with 125 gives 125 followed by 21 zeros   So, in total, 24 digits   Correct Option: 24
Answer: B
Tickets numbered from 1 to 21 are mixed and then a ticket is selected randomly. What is the probability that the selected ticket bears a number which is a multiple of 3?  Select the correct option:
A) 1/3
B) 2/5
C) 3/10
D) 3/7
E) 1/7

Solution: Here, S = [1, 2, 3, 4, …., 19, 20, 21]   Let E = event of getting a multiple of 3 = [3, 6, 9, 12, 15, 18, 21]   P (E) = n (E) / n (S) = 7 / 21 = 1/3   The answer is 1/3.
Answer: A
The average of 11numbers is 60. Out of 11numbers the average of first 6no. is 78, and last 6numbers is 75 then find 6th number?	Choose one.
A) A)258  B) B)65  C) C)58  D) D)62  E) E)48

Solution: 6th number = sum of 1st 6no.s + sum of last 6no.s - sum of 11no.s   answer = 6*78+6*75-11*60= 
6*78+6*75-11*60 = 258
258   258nswer is 258
Answer: A
A, B and C invests Rs.4000, Rs.3000 and Rs.2000 in a business. After one year B removed his money; A and C continued the business for one more year. If the net profit after 2 years be Rs.2400, then B's share in the profit is? Choose the correct choice from the following options.
A) 276	B) 289	C) 480	D) 400	E) 278

Solution: 4*24 : 3*12 : 2*24   8: 3: 4   3/15 * 2400= 
3/15 * 2400 = 480
480   Answer: 480
Answer: C
Which of the following numbers is the biggest => [-5/7 , -7/8 , -9/10 , -12/13 , -34/35] Choose the correct choice: A) A)-5/7 B) B)-7/8 C) C)-9/10 D) D)-12/13 E) E)-34/35

Solution: If we observe all the fractions just differ by one i.e denominator vs numerate.. in such case the biggest will be with large values... here all values are with -ve value...the least value is biggest. i.e. -5/7..   Hence -5/7 is correct answer...
Answer: A
What is the difference between 38% of 80 nd 12% of 160. Pick one:  A) 11.3  B) 12.4  C) 12.7  D) 11.2  E) 10.3

Solution: (38/100) * 80 â€“ (12/100) * 160   30.4 - 19.2= 
30.4 - 19.2 = 11.2
11.2   Answer: 11.2
Answer: D
Linda bought 3 notebooks at $1.20 each; a box of pencils at $1.50 and a box of pens at $1.70. How much did Linda spend?	Choose the correct choice from the following options:	A) $6.80	B) $2.80	C) $4.80	D) $7.80	E) $8.80

Solution: Linda spent   1.20 ? 3 = $3.60 on notebooks   The total amount of money that Linda spent is equal to    3.60 + 1.50 + 1.70= 
 3.60 + 1.50 + 1.70 = 6.8
$6.80   correct answer $6.80
Answer: A
If x is an odd negative integer and y is an even integer, which of the following statements must be true? I. (3x + 2y) is positive integer II. (xy)^2 is positive integer III. (y^2 - x) is even integer	Choose the correct choice from the following answers:  A) I only  B) III only  C) II only  D) I,III only  E) none of these

Solution: I. It is true if 3x < 2y   II. It is always positive   III. It is not always true   Answer : II only
Answer: C
Pary,INC recently conducted a survey and found that 75,000 of its customers live in rural areas. if the number of it customers who live in urban areas is 200 percents grater than the numbers of customers who live in rural areas, how many of Pary,INC customers live in urban areas ?	Choices
A) 200,000	B) 216,000	C) 225,000	D) 480,000	E) 540.0

Solution: Let's say that we have a starting value of X...   100% of X = X   100% MORE than X = X + X = 2X   200% MORE than X = X + 2X = 3X   300% MORE than X = X + 3X = 4X   Etc.   Here, we're told that 75,000 customers live in rural areas and the number who live in urban areas is 200% GREATER than the number who live in rural areas. That means that the number who are in urban areas is 3 times the number in rural areas...   3(75,000) = 225,000   Final Answer:225,000
Answer: C
A sum of Rs. 427 is to be divided among A, B and C in such a way that 3 times A’s share, 4 times B’s share and 7 times C’s share are all equal. The share of C is  Choose the correct choice from the following choices:	A) 82	B) 83	C) 84	D) 85	E) 86

Solution: A + B + 84 = 427   3A = 4B = 784   => (784/3) + (784/4) + 84 = 427   => 84 = 84   ANSWER:84
Answer: C
A number consists of two digits. If the digits interchange places and the new number is added to the original number, then the resulting number will be divisible by: Options.
A) 3  B) 5  C) 9  D) 11  E) 12

Solution: Explanation:   Let the ten's digit be x and unit's digit be y.   Then, number 10x + y.   Number obtained by interchanging the digits = 10y + x.   (10x + y) + (10y + x) = 11(x + y)   which is divisible by 11.   ANSWER IS 11
Answer: D
What amount does Kiran get if he invests Rs. 18000 at 15% p.a. simple interest for four years?	Choose the most appropriate option.
A) 29893 B) 27773 C) 29989 D) 28800 E) 29883

Solution: Simple interest = (18000 * 4 * 15)/100 = Rs. 10800   Amount = P + I = 18000 + 10800 = Rs. 28800   Answer: 28800
Answer: D
How many positive integers less than 100 are there such that they are multiples of 8 or multiples of 7 but not both?
Choose the correct choice from the following answers:
A) 21	B) 22	C) 25	D) 24	E) 31

Solution: for 8: 8...100=8*12   for 7: 7...98=7*14   but there is one integer 8*7. so   N=(12-1)+(14-1)= 
(12-1)+(14-1) = 24
24   24
Answer: D
There are 11 dozen mangoes in a box. If there are 39
such boxes, how many mangoes are there in all the
boxes together?  Choose the correct option.
A) 516  B) 5148  C) 6192  D) 628  E) None

Solution: Number of mangoes = 11 dozens   = 12 × 11 = 132   ∴ Number of mangoes in 39 boxes   = 39 × 132 = 5148   Answer 5148
Answer: B
In an examination 35% of the students passed and 455 failed. How many students appeared for the examination?	Choose the correct choice from the following choices
A) 540 B) 400 C) 700 D) 650 E) 840

Solution: Let the number of students appeared be x   then, 65% of x = 455   65x/100 = 455   x = 455*100/65= 
455*100/65 = 700
700   Answer is 700
Answer: C
14, 28, 20, 40, 32, 64, ?	Choices.
A) 43 B) 25 C) 58 D) 47 E) 56

Solution: 56   56   This is an alternating multiplication and subtracting series with a pattern x2, -8, x2, -8.
Answer: E
If cement, gravel and sand are to be mixed in 7:10:13 and 5 tons of cement is available how many tons of mixture can be produced assuming that sufficient gravel and sand is readily available.	Select the correct option.
A) 35 7/8 B) 36 C) 21 3/7 D) 34 5/7 E) 34 6/7

Solution: Cement:Gravel:Sand = 7:10:13 --> total of   7+10+13= 
  7+10+13 = 30
30 parts.   If we use 8 tons of cement, then we'll get 5/7*30= 21 3/7 tons of mixture.   Answer: 21 3/7.
Answer: C
A person crosses a 1000 m long street in 10 minutes. What is his speed in km per hour?
Pick one.
A) 7.1	B) 8.2	C) 4.6	D) 6.0	E) 12.8

Solution: distance = 1000 meter   time = 10 minutes = 10 x 60 seconds = 600 seconds   Speed = distance/time=1000/600=1.67m/s=1.67Ã—18/5 km/hr=6.0 km/hr   Answer :6.0
Answer: D
If f(y)=y^2 and y is a positive integer, which of the following CANNOT be the value of f(f(y))? Choose the correct choice from the following answers:
A) 1	B) 144	C) 81	D) 16	E) 256

Solution: f(y)=y^2   f(f(y)) = (y^2)^2   =y^4   A. 1 , y=1   D. 16 , y=2   C. 81 , y=3   B. 144   f(y)=12   Square root of 12 is not a positive integer . Hence 144 can not be the value of f(f(y)) .   E. 256 , y=4   Answer 144
Answer: B
The sum of two numbers is twice their difference. If one of the numbers is 10, the other number is Pick one
A) 3 1/3  B) 30  C) −3 1/3  D) a or b  E) None

Solution: Explanation:   Let the other number be a.   Given that, 10+a=2(a−10)⇒a=30   or if the other number is less than 10, 10+a=2(10−a)⇒a=10/3=3 1/3   Correct Option: a or b
Answer: D
If the positive integer x is a multiple of 9/15 and the positive integer y is a multiple of 5/3, then xy must be a multiple of which of the following?
I. 5
II. 3
III. 1
Choose the most appropriate option.
A) II only  B) I and II only  C) I only  D) III only  E) I, II, and III

Solution: x=9/15a   y=5/3b   xy=3/3ab=ab   where a,b are integers   Hence , xy will always be divisible by 1.   III only is the answer.
Answer: D
A girl scout was selling boxes of cookies. In a month, she sold both boxes of chocolate chip cookies ($1.25 each) and boxes of plain cookies ($0.75 each). Altogether, she sold 1,585 boxes for a combined value of $1,588.25. How many boxes of plain cookies did she sell?	Select:
A) 0	B) 233	C) 500	D) 695	E) 786

Solution: Let #plain cookies sold be X then #chocolate cookies = (total cookies-X)   Equating for X   (0.75)*X +(1.25)*(1585-X)=1588.25   =>x=786   First get the difference of the revenue to the number of boxes.   1588.25-1585= 
1588.25-1585 = 3.25
3.25   Now you know that the difference between plain cookies boxes and chocolate cookies boxes is small.   We now divide the revenue by two.   1588.25/2=~794   Because the difference between the possible answers is big, this leaves us with choice 786.
Answer: E
A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 500 m long? Choose the correct choice from the following answers:	A) 176 Sec	B) 190 Sec	C) 170 Sec	D) 267 Sec	E) 276 Sec

Solution: L = S*T   S= 1200/120= 
1200/120 = 10
10 m/Sec.   Total length (D)= 1700 m   T = D/S   T = 1700/10= 
1700/10 = 170
170 Sec   Answer:170 Sec
Answer: C
A scale 7 ft. 6 inches long is divided into 5 equal parts. Find the length of each part.  Choices.
A) 20 inches  B) 77 inches  C) 66 inches  D) 18 inches  E) 66 inches

Solution: Explanation:   Total length of scale in inches = (7*12) + 6= 
(7*12) + 6 = 90
90 inches   Length of each of the 5 parts= 90/5= 
90/5 = 18
18 inches   ANSWER:18 inches
Answer: D
The average weight of 10 person's increases by 4 kg when a new person comes in place of one of them weighing 70kg. What is the weight of the new person?
Choices:
A) 85
B) 86.5
C) 90
D) 88.5
E) 110

Solution: Total increase in weight =10 x 4 = 40   If x is the weight of the new person, total increase in weight = x−70   => 40= x - 70   => x = 40+70= 
40+70 = 110
110   ANSW110R:110
Answer: E
A man goes from A to B at a speed of 20 kmph and comes back to A at a speed of 30 kmph. Find his average speed for the entire journey?  Choose the correct choice from the following answers
A) 17 kmph  B) 24 kmph  C) 16 kmph  D) 19 kmph  E) 11 kmph

Solution: Distance from A and B be 'd'   Average Speed = total distance/total time   Average Speed = (2d)/[(d/20) + (d/30)]   = (2d)/[5d/60) => 24 kmph.   Answer:24 kmph
Answer: B
The ratio of money with Ram and Gopal is 7 : 17 and that with Gopal and Krishan is 7: 17. If Ram has Rs. 588, Krishan has ?  Choose the correct choice from the following answers.
A) s. 2890
B) s. 2330
C) s. 1190
D) s. 3468
E) s. 2680

Solution: Ram : Gopal = 7 : 17 = 49 : 119   Gopal : Krishan = 7 : 17 = 119 : 289   Ram : Gopal : Krishan = 49 : 119 : 289   Ram : Krishan = 49 : 289   Thus, 49 : 289 = 588 : N   &there N = 289 x 588 / 49   = Rs. 3468   Answer :s. 3468
Answer: D
A waiter's salary consists of his salary and tips. During one week his tips were 9/4 of his salary. What fraction of his income came from tips ?	Select:	A) 4/9	B) 5/4	C) 9/13	D) 5/9	E) 6/9

Solution: Income = salary (s) +tips = s + s*9/4 = s*13/4   Tips = s*9/4   fraction of his income came from tips = (s*9/4)/(s*13/4)= 9/13   ANSWER:9/13
Answer: C
A trumpet section includes seven musicians. If they hold an audition to determine chair order within the section, and there are to be no ties, how many distinct chair orders can result?	Choose the most appropriate option
A) 240 B) 125 C) 5040 D) 100 E) 25

Solution: We have a word problem using permutations. We must identify the number of total items in the group. There are seven possible musicians who could be placed in the first chair, six possible musicians for the second, five for the third, four for the fourth, and three for the fifth, and two for the sixth and one for the seventh. To determine the number of possible orderings, we multiply these numbers, which we can express as 7!. Now 7! = (7)(6)(5)(4)(3)(2)(1) = 5040=5040
Answer: C
Which of the following numbers is two more than the square of an odd integer?
Choose the correct choice from the following answers
A) 14,115
B) 14,163
C) 14,577
D) 14,737
E) 14,981

Solution: If a square has an odd unit's digit, then its ten's digit must be even.   Only 14,163-2 = 14,161 satisfies this condition.   The answer is 14,163.
Answer: B
A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 600 m long?  Choose the correct choice from the following options.
A) 80sec	B) 84sec	C) 90sec	D) 94sec	E) 100sec

Solution: Speed = 240/24= 
240/24 = 10
10 m/sec.   Required time= (240 + 600)/10= 
(240 + 600)/10 = 84
84 sec.   Answer:84sec
Answer: B
A certain company consists of 3 managers and 8 non-managers. How many different teams of 3 employees can be formed in which at least one member of the team is a manager and at least one member of the team is not a manager? (Two groups are considered different if at least one group member is different)	Choose one: A) 84 B) 108 C) 135 D) 270 E) 990

Solution: Total # of teams of 3 possible is C311=165   # of teams with only managers or only non-managers is: C33+C38=1+56= 
1+56 = 57
57;   # of teams of 3 with at least one manager or at least one non-manager is: 165-57= 
165-57 = 108
108.   ANSWER:108
Answer: B
A certain amount earns simple interest of Rs. 1750 after 7 years. Had the interest been 2% more, how much more interest would it have earned? Pick one:
A) 33
B) 38
C) 87
D) cannot be determined
E) 282

Solution: Explanation:   We need to know the S.I, principal and time to find the rate. Since the principal is not given, so data is inadequate.   Answer: cannot be determined)
Answer: D
The bankerâ€™s discount on Rs. 1600 at 6% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. The time is : Choose the correct choice from the following answers: A) 2 months B) 4 months C) 6 months D) 10 months E) None

Solution: Sol.   S.I. on Rs. 1600 = R.D. on Rs. 1680.   âˆ´ Rs. 1600 is the P.W. of Rs. 1680, i.e., Rs. 80 is S.I. on Rs. 1600 at 6%.   âˆ´ Time = [100 * 80 / 1600 * 6] year = 5/6 year = 10 months.   Answer 10 months
Answer: D
One vessel contains a mixture of 5 parts pure wine and 3 parts soda, whereas the other vessel contains a mixture of 9 parts pure wine and 5 parts soda. Compare the strength of the wine.
Pick one:
A) 35;36 B) 7 : 8 C) 7 : 4 D) 14 : 5 E) None of these

Solution: 5/8 : 9/14   LCM of 8,14 = 56   (5/8)*56 : (9/14)*56   35:36   35;36nswer is 35;36
Answer: A
Currently, y percent of the members on the finance committee are women and next month, z percent of the men on the finance committee will resign. If no other personnel changes occur, then after the resignations next month, the men who remain on the finance committee will represent what percent of the total finance committee members?	Choose the correct answer
A) (100)(100 - z)(100 - y)/(100^2 - z(100 - y)) B) (100 - z)(100 - y)/100 C) (100 - z)(100 - y) D) zy/100 - z E) z(100 - y)/100

Solution: Let's say that there are a total of 100 members   Let's also say that y = 50   So there are 50 men   Now z = 10 so 45 men are left   (45/95)*100 = 9/19 *100 = 900/19   Now let's plug answer choices   Target 900/19   Inputs   y=50   z=10   Only (100)(100 - z)(100 - y)/(100^2 - z(100 - y)) gives the correct answer
Answer: A
Carina has 55 ounces of coffee divided into 5- and 10-ounce packages. If she has 2 more 5-ounce packages than 10-ounce packages, how many 10-ounce packages does she have?	Pick:
A) 7
B) 6
C) 5
D) 4
E) 3

Solution: Lets say 5 and 10 ounce packages be x and y respectively.   Given that, 5x+10y=55 and x=y+2. What is the value of y.   Substituting the x in first equation, 5y+10+10y=55 ->y=45/15.= 
45/15. = 3
3   3
Answer: E
A wooden box of dimensions 8 m x 7 m x 6 m is to carry rectangularboxes of dimensions 2 cm x 7 cm x 3 cm. The maximum number ofboxes that can be carried in the wooden box, is  Choices:
A) 8000000  B) 1000000  C) 7500000  D) 1200000  E) None of these

Solution: Explanation: Number = (800*700*600)/2*7*3 = 8000000 8000000nswer: 8000000
Answer: A
Bruce purchased 8kg of grapes at the rate of 70 per kg and 11 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?
Select the correct option.
A) A)1040	B) B)1165	C) C)1055	D) D)1065	E) E)1075

Solution: Cost of 8 kg grapes = 70 × 8 = 560.   Cost of 11 kg of mangoes = 55 × 11 = 605.   Total cost he has to pay = 560 + 605= 
560 + 605 = 1_165
1165   1165
Answer: B
As a treat for her two crying children, a mother runs to the freezer in which she has two cherry ice pops, three orange ice pops, and five lemon-lime ice pops. If she chooses two at random to bring outside to the children, but realizes as she runs out the door that she cannot bring them different flavors without one invariably being jealous of the other and getting even more upset, what is the probability that she has to return to the freezer to make sure that they each receive the same flavor? Choose the correct option.
A) 1/9
B) 1/6
C) 5/18
D) 31/360
E) 5/6

Solution: Probability of not getting the same flavor ->   Favorable -> Cherry - orange [ 2C1 * 3C1 [or simply 2*3 ] or Cherry - lemon [ 2*5] or orange - lemon [3*5]   Prob = (2*3 + 2*5 + 3*5 ) / 9C2 = 31/360   Answer -> 31/360
Answer: D
Find the number of subsets of the set {1,2,3,4,5,6,7,8,9,10,11} having 4 elements.?	Select the correct option.
A) 1320
B) 660
C) 165
D) 330
E) None of these

Solution: Explanation :   Here the order of choosing the elements doesn’t matter and this is a problem in combinations.We have to find the number of ways of choosing 4 elements of this set which has 11 elements.This can be done in:11C4=11*10*9*81*2*3*4= 330 ways   Answer : 330
Answer: D
In the rectangular coordinate system Point O has coordinates (0,0) and Point B has coordinates (3,3) and if point A is equidistant from points O and B and the area of the triangle OAB is 16, which of the following are the possible coordinates of point A.	Choose one
A) (-2,6)	B) (0,4)	C) (2,-6)	D) (2,6)	E) (4,0)

Solution: Area.pngSince A is equidistant from points O and B, then it must be somewhere on the green line (perpendicular bisector of OB).   (2,-6) and (2,6) are not on that line. If A is at (0,3) or (3,0), then the area is 1/2*3*3=9/2. Thus A must be at (2,6).   Answer: (2,6).
Answer: D
In 1990 the budgets for projects Q and V were $660,000 and $860,000, respectively. In each of the next 10 years, the budget for Q was increased by $30,000 and the budget for V was decreased by $10,000. In which year was the budget for Q equal to the budget for V ?	Choose the most appropriate option:
A) 1992 B) 1993 C) 1994 D) 1995 E) 1996

Solution: Let the no of years it takes is x.   660+30x = 860-10x --> 40x = 200 and x=5.   Thus, it happens in 1995.   1995.
Answer: D
The sum of one-half, one-third and one-fourth of a number exceeds the number by 12. The number is	Options
A) 144  B) 154  C) 90  D) 174  E) 184

Solution: x/2+x/3+x/4=x+12   13x/12=x+12   x=144   144NSWER:144
Answer: A
12 spheres of the same size are made from melting a solid cylinder of 8 cm diameter and 27 cm height. What is the diameter of each sphere?  Choose the correct choice from the following answers
A) 2 cm B) 4 cm C) 6 cm D) 8 cm E) 10 cm

Solution: Volume of cylinder = pi*r^2*h   Volume of a sphere = 4*pi*R^3 / 3   12*4*pi*R^3 / 3 = pi*r^2*h   R^3 = r^2*h / 16 = 27 cm^3   R = 3 cm   D = 6 cm   The answer is 6 cm.
Answer: C
If x*y = xy – 2(x + y) for all integers x and y, then 5* (–3) = Select:
A) –19
B) –11
C) –4
D) 4
E) 16

Solution: 5*(-3) = 5*(-3) - 2 (5 + (-3) ) = -15 -4 = -19   Option (–19)
Answer: A
How many numbers from 10 to 100 are exactly divisible by 9?	Choose the correct choice.
A) 9 B) 10 C) 11 D) 12 E) 14

Solution: 10/9 = 1 and 100/9 = 11 ==> 11 - 1= 
11 - 1 = 10
10. Therefore 10 digits   10)
Answer: B
If sum of the first 11 terms of arithmetic progression equals that of the first 19 terms, then what is the sum of the first 30 terms?
Choose the correct choice from the following options:
A) 0  B) -1  C) 1  D) Not unique  E) None of these

Solution: Explanation :   Given,   t1 + t2 + ........t11 = t1 + t2 + ........t19 (for an AP)   => (11/2) [ 2a + (11-1)d = (19/2) [ 2a + (19-1)d ]   => 22 a + 110d = 28 a + 342 d   => 16 a + 232 d = 0   => 2a + 29 d = 0   => (30/2)[ 2a + (30-1)d = 0.   S30 terms = 0.   0nswer : 0
Answer: A
There are two sections B and C of a class, consisting of 46 and 54 students respectively. If the average weight of sections B is 50 kg and that of sections C is 45 kg. Find the average weight of the whole class Select the correct option:
A) 47.3  B) 48.3  C) 49.3  D) 50.3  E) None

Solution: Solution   Total weight of(46+54)Students	= (46x50+54x45)Kg   = 4730 kg.   Average weight of the whole class	= (4730 / 100)   = 47.30.   47.3nswer 47.3
Answer: A
If 8000 books need to be placed in boxes and each box can contain at most 9 books. How many books will be in the last unfilled box?
Choose the correct choice from the following answers:
A) 8 books
B) 9 books
C) 1 book
D) 5 books
E) 4 books

Solution: The number of books that can be placed in boxes of 9 books is the first number that is divisible by 9 that occurs before 8000.   In order to divide the sum in 9 parts, the amount must be divisible by 9   Divisibility rule of 9: The sum of the digits must be divisible by 9   Sum of digits of 8000 = 8 and 0 is divisible by 9.   Hence, we need to remove 8 to this number for it to be divisible by 9   Correct Option:8 books
Answer: A
There are 193 items that are members of set U. Of these items, 41 are members of set B, 59 are not members of either of set A or set B, and 23 are members of both sets A and B. How many of the members of set U are members of set A ?	Pick one:
A) 116  B) 85  C) 94  D) 98  E) 108

Solution: You had the answer almost right. The x = 93 refers to ONLY set A.   However what's being asked is how many members are part of set A. This will include:   1. Only Set A   2. Set 116 and Set B   So the answer is Set 116 = 93 + Set 116B = 93+23= 
93+23 = 116
116   116
Answer: A
Sand is poured into a box so that the box is being filled at the rate of 4 cubic feet per hour. If the empty rectangular box is 7 feet long, 6 feet wide, and 2 feet deep, approximately how many hours does it take to fill the box?
Choose the most appropriate option.
A) 20 B) 21 C) 22 D) 23 E) 24

Solution: The volume the box is: length*width*depth = 7*6*2= 
7*6*2 = 84
84 cubic feet.   84 cubic feet / 4 cubic feet per hour= 21 hours.   It will take 21 hours to fill the box.   The answer is 21.
Answer: B
While working alone at their respective constant rates, server M uploads 480 files in 4 hours and server Y uploads 480 files in 8 hours. If all files uploaded by these servers are the same size, how long would it take the two servers, working at the same time and at their respective constant rates, to process a total of 480 files?  Choose the correct choice from the following choices
A) 2 hr B) 2hr 20 min C) 2hr 40 min D) 5 hr 40 min E) 6hr

Solution: Server M processes 480/4= 
480/4 = 120
120 per hour   Server Y processes 180/8 files per hour= 60 per hour   Total files processed per hour when M and Y work together = 120+60= 
120+60 = 180
180 files per hour   480/180= 2 2/3 hours=2hr 40 min
Answer: C