MU-NLPC/Calc-aqua_rat huggingface dataset:
x, a, z, and b are single digit positive integers. x = ¼ a. z = ¼ b. (10a + b) – (10x + z) could NOT equal	Choose the correct choice:
A) 33  B) 36  C) 44  D) 63  E) 66

Solution: From the given equations, a = 4x, b = 4z   (10a+b) - (10x+z) = 40x+4z - 10x-z = 30x +3z = 3(10x+z)   Therefore the resultant should be divisible by 3 which isn't possible only in the case of C.   Hence 44 is the answer
Answer: C
If a wholesaler distributes items to several outlets (A, B, C and D) in the ratio of 1/12 : 1/13 : 1/15 : 1/2, then find the total number of items the wholesaler distributes?	Options:
A) 567
B) 167
C) 267
D) 467
E) 667

Solution: Here, A : B : C : D = 1/12 : 1/13 : 1/15 : 1/2   1) L.C.M of 12 : 13 : 15 : 2 is 780   2) Find the number of books each friend received --------- (To find no. of books each friend has, multiply the ratio with the L.C.M. calculated)   A = (1/12) x 780 = 65   B = (1/13) x 780 = 60   C = (1/15) x 780 = 52   D = (1/2) x 780 = 390   3) Total number of toys = (65 x + 60 x + 52 x + 390 x) = 567 x   Minimum number of pens (x) = 1   Therefore, total number of items = 567 items.   Correct option :567
Answer: A
Rs.560 is divided amongst A, B, C so that 5 times A's share, six times B's share and eight times C's share are all equal. Find C's share?  Choose the correct choice from the following options.
A) Rs.142.37 B) Rs.152.37 C) Rs.242.37 D) Rs.210 E) Rs.142

Solution: Rs.142.37+B+C = 560   5Rs.142.37 = 6B = 8C = x   Rs.142.37:B:C = 1/5:1/6:1/8   = 24:20:15   15/59 * 560 = Rs.142.37   Rs.142.37NSWER:Rs.142.37
Answer: A
The table below shows the enrollment in various classes at a certain college.
Class | Number of Students
Biology | 65
Physics | 35
Calculus | 40
Although no student is enrolled in all three classes, 15 are enrolled in both Biology and Physics, 10 are enrolled in both Biology and Calculus, and 12 are enrolled in both Physics and Calculus. How many different students are in the three classes?
Answers:  A) 51  B) 88  C) 90  D) 103  E) 162

Solution: No. of total students = no of students of biology + no of students of physics but not biology + no of students of calculus but not biology and physics   No. of total students = 65 + (35-15) + (40-10-12) = 65+20+18= 
65+20+18 = 103
103   Hence, Answer will be 103.
Answer: D
Find the odd man out. 3, 5, 15, 75, 1120, 84375  Choose one: A) 15, B) 84375 C) 1120 D) 75 E) 3

Solution: 3   5   3 × 5 = 15   5 × 15 = 75   15 × 75 = 1125   75 × 1125 = 84375   Hence, 1120 is wrong. 1125 should have come in place of 1120   Answer is 1120
Answer: C
When positive integer n is divided by 3, the remainder is 2. When n is divided by 7, the remainder is 6. How many values less than 100 can n take?	Pick one.
A) 0	B) 2	C) 3	D) 6	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 6.. 6
Answer: D
A large field of 700 hectares is divided into two parts. The difference of the areas of the two parts is one–fifth of the average o fthe two areas. What is the area of the smaller part in hectares?  Choose the correct choice from the following
A) 225
B) 280
C) 300
D) 385
E) None

Solution: Solution   Let the areas of the two parts be   x and (700 - x)hectares	= [x - (700 - x)]   = 1 / 5 x [x + (700 - x)/ 2]   = 2x - 700= 70   x = 385.   Answer 385
Answer: D
In a stack of boards at a lumber yard, the 20th board counting from the top of the stack is immediately below the 19th board counting from the bottom of the stack. How many boards are in the stack?	Options:
A) 37 B) 36 C) 35 D) 34 E) 32

Solution: Counting from the top, after the 20th board, there are 17 boards left to count.   The answer is 37.
Answer: A
A man counted his animals, 80 heads and 270 legs (ducks and goats). how many goats are there?	Pick:
A) 30 B) 40 C) 50 D) 60 E) 55

Solution: let no of ducks=d and no of goat=g   d+g=80(heads)----------> eq 1   each duck has 2 legs and goat has 4 legs   2d+4g=270 and divide 2d+4g=270 by 2 we get d+2g=135 -----------> eq2   subtract eq1 from eq2   we get no of goats=55   ANSW55R:55
Answer: E
A tourist purchased a total of $4,500 worth of traveler’s checks in $10 and $50 denominations, During the trip the tourist cashed 7 checks and then lost all of the rest. If the number of $10 checks cashed was one more or one less than the number of $50 checks cashed, what is the minimum possible value of the checks that were lost?	Choose the correct choice from the following:  A) $1,430  B) $2,310  C) $3,290  D) $4,270  E) $5,150

Solution: Let the number of $10 checks cashed beT   Let the number of $50 checks cashed beF   7 checks cashed;   T+F=7   Now; T can be F+1 OR T can be F-1   Let's check both conditions;   T=F+1   T+F=7   F+1+F=7   2F=6   F=3   T=4   Value cashed = 3*50+4*10=150+40= 
150+40 = 190
$190   Let's check the other condition as well;   T=F-1   T+F=7   F-1+F=7   2F=8   F=4   T=3   Value cashed = 4*50+3*10=200+30= 
200+30 = 230
$230   The more money he cashes, the less loss he incurs. Thus, we must consider the latter case.   Value cashed= $230   Value lost = 4500-230= 
4500-230 = 4_270
$4270   Ans:$4,270
Answer: D
Train A left Centerville Station, heading toward Dale City Station, at 3: 00 p.m. Train B left Dale City Station, heading toward Centerville Station, at 0: 20 p.m. on the same day. The trains rode on straight tracks that were parallel to each other. If Train A traveled at a constant speed of 30 miles per hour and Train B traveled at a constant speed of 10 miles per hour, and the distance between the Centerville Station and Dale City Station is 90 miles, when did the trains pass each other?	Choose the correct choice:  A) 4: 45 p.m.  B) 2: 20 p.m.  C) 5: 20 p.m.  D) 5: 35 p.m.  E) 6: 00 p.m.

Solution: the distance travelled by the train A in first 20 minutes will be 10.   The distance which will be remaining is 80.   Now both trains are running in opposite direction.Their speed will be added so 40.   Time at which they will meet =80/40= 
80/40 = 2
2   time of train 2: 20 p.m. will be 0:20 +2=2:20   Hence answer is 2: 20 p.m..Hope i am correct
Answer: B
A string of length 40 metres is divided into three parts of different lengths. The first part is three times the second part, and the last part is 23 metres smaller than the first part.
Find the length of the largest part.  Choose one.
A) 27 B) 4 C) 5 D) 9 E) 8

Solution: Explanation :   Let the 2nd piece length be x.   1st piece length is 3x.   3rd piece length is 3x – 23.   Sum of all the pieces is 40.   3x + x + 3x – 23 = 40.   7x = 63.   x = 9.   Lengths of the pieces are 27, 9, 4.   27nswer : 27
Answer: A
A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is?  Choose the correct choice from the following answers
A) 22
B) 88
C) 12
D) 77
E) 87

Solution: S.I. for 3 years = (12005 - 9800) = Rs. 2205   S.I. for 5 years = Rs. 2205/3 * 5 = Rs. 3675.   Principal = (9800 - 3675) = Rs. 6125   Hence, rate = (100 * 3675) / (6125 * 5)= 
(100 * 3675) / (6125 * 5) = 12
12%   Answer: 12
Answer: C
If 6 (A's capital) = 8 (B's capital) = 10 (C's capital). Then the ratio of their capitals is?	Select the correct option:
A) 20:15:16
B) 20:15:18
C) 20:15:12
D) 20:15:11
E) 20:15:13

Solution: 6A = 8B = 10 20:15:12   A:B:20:15:12 = 1/6:1/8:1/10   = 20:15:12   Answer: 20:15:12
Answer: C
A recipe for a large batch of fruit juice at a factory calls for 10% oranges, 20% lemons, and 70% limes. if 200 oranges are used, how many lemons are needed?	Choose one.
A) 50	B) 100	C) 200	D) 400	E) 700

Solution: 10%= 200 fruit   100%=2000 fruit   20% of 2000 fruit=400 fruit   400 lemons   ANSWER:400
Answer: D
An article is bought for Rs.500 and sold for Rs.400, find the loss percent?	Choose the most appropriate option
A) 18 2/3% B) 16 7/3% C) 20% D) 16 2/3% E) 76 2/3%

Solution: 500 ---- 100   100 ---- ? => 20%   Answer:20%
Answer: C
A can do a piece of work in 10 days and B can do the same work in 12 days. A and B worked together for 2 days. How many more days are required to complete the remaining work if they work together?
Choose the correct choice from the following:
A) 2(5/11)days
B) 3(5/11)days
C) 4(5/11)days
D) 6(5/11)days
E) 8(5/11)days

Solution: B   3(5/11)days   A can do 1/10 of the work in a day.   B can do 1/12 of the work in a 1 day.   Both of them together can do (1/10 + 1/12) part of work in 1 day = (6 + 5)/60 = 11/60   They take 60/11 days to complete the work together.   Given that they already worked for 2 days.   The number of days required to complete remaining work => 60/11 - 2 = 38/11 = 3 (5/11) days.
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 most appropriate option:
A) 8 min	B) 7 min	C) 5 min	D) 9 min	E) 4 min

Solution: 1/10 + 1/15 - 1/x   = 1/18   x = 9   Answer: 9 min
Answer: D
Ravi and Kavi start a business by investing â‚¹ 2000 and â‚¹ 72000, respectively. Find the ratio of their profits at the end of year. Choose the correct option:
A) 2 : 36	B) 5 : 36	C) 7 : 36	D) 1 : 36	E) 3 : 36

Solution: Ratio of profit = Ratio of investments   = 2000 : 72000 = 1 : 36   Answer : 1 : 36
Answer: D
On the average Mr.Jackson has 2 hours to plan for an long hour meeting he talk to his assistant 7 hours to prepare the paper work needed.How much hours should jackson and assistant has t plan for 30 min meeting? Choose one
A) 4.5 hr B) 4.8 hr C) 4.9 hr D) 5.5 hr E) 6.5 hr

Solution: for a 1 hour talk he took total of 9 hr time   1hr=9hr(2+7)   30 min=1/2hr =?   so 9*1/2 div by 1   4.5 hr   4.5 hrNSWER:4.5 hr
Answer: A
An engineer undertakes a project to build a road 15 km long in 300 days and employs 30 men for the purpose. After 100 days, he finds only 2.5 km of the road has been completed. Find the (approximate) number of extra men he must employ to finish the work in time.	Choose the correct choice from the following answers.
A) a. 43	B) b. 45	C) c. 55	D) d. 68	E) e. 60

Solution: 30 workers working already   Let x be the total men required to finish the task in next 200 days   2.5 km done hence remaining is 12.5 km   Also, work has to be completed in next 200 days (300 - 100 = 200)   We know that, proportion of men to distance is direct proportion   and, proportion of men to days is inverse proportion   Hence, X = (30 * 12.5 * 100) / (2.5 * 200)   thus, X = 75   Thus, more men needed to finish the task = 75-30= 
75-30 = 45
45   hence Answer is b. 45
Answer: B
A farmer has an apple orchard consisting of Fuji and Gala apple trees. Due to high winds this year 10% of his trees cross pollinated. The number of his trees that are pure Fuji plus the cross-pollinated ones totals 180, while 3/4 of all his trees are pure Fuji. How many of his trees are pure Gala?  Choose the correct choice from the following:  A) 31  B) 33  C) 55  D) 77  E) 88

Solution: Let f = pure fuji , g = pure gala and c - cross pollinated.   c = 10% of x where x is total trees.   c = .1x   also 3x/4 = f and c+f = 180 => .1x + 3/4x = 180 => x = 211   211 - 180 = pure gala = 31.   31
Answer: A
Alice, Benjamin, and Carol each try independently to win a carnival game. If their individual probabilities for success are 1/5, 3/8, and 3/7, respectively, what is the probability that exactly two of the three players will win but one will lose?	Pick:  A) 63/280  B) 1/280  C) 3/56  D) 3/35  E) 7/40

Solution: P = P(A wins, B wins, C loses) + P(A wins, B loses, C wins) + P(A loses, B wins, C wins) = 1/5*3/8*4/7 + 1/5*5/8*3/7 + 4/5*3/8*3/7 = 63/280.   63/280nswer: 63/280
Answer: A
Using all the letters of the word "NOKIA", how many words can be formed, which begin with N and end with A?
Pick.
A) 7
B) 6
C) 2
D) 8
E) 4

Solution: There are five letters in the given word.   Consider 5 blanks ....   The first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 3! ways.   The number of words = 3! = 6.   Answer: 6
Answer: B
A sum of money at simple interest amounts to Rs.720 after 2 years and to Rs.1020 after a further period of 5 years. The sum is :  Select the correct option:
A) 400
B) 500
C) 600
D) 700
E) 800

Solution: SI of 5 year = (1020-720)= 
(1020-720) = 300
300   so, SI of 1 year=300/5= 
300/5 = 60
60   so, SI of 2 year=60*2= 
60*2 = 120
120   so, sum is=(720-120)= 
(720-120) = 600
600   ANSWER:600
Answer: C
Jack and Jill are marathon runners. Jack can finish a marathon (43 km) in 4.5 hours and Jill can run a marathon in 4.3 hours.What is the ratio of their average running speed? (Jack: Jill)  Choose the correct option:
A) 14/15
B) 43/45
C) 4/5
D) 5/4
E) Cannot be determined

Solution: Average Speed of Jack =Distance/ Time   = 43 /(9/2) = 86/9   Average Speed of Jill = 43/(4.2) = 10   Ratio of Average speed of Jack to Jill = (86/9)/10 = 86/90 = 43/45   Answer 43/45
Answer: B
The owner of a furniture shop charges his customer 10% more than the cost price. If a customer paid Rs. 7350 for a computer table, then what was the cost price of the computer table?	Options:  A) Rs.6289  B) Rs.6298  C) Rs.6681  D) Rs.6725  E) Rs.6708

Solution: CP = SP * (100/(100 + profit%))   = 7350(100/110) = Rs.6681.   Answer: Rs.6681
Answer: C
Find the number of zero’s in 173! (173 Factorial)?  Choose the correct choice from the following choices.
A) 38	B) 39	C) 40	D) 41	E) 42

Solution: no of zeroes in 173! is   173/5=34(quotient)   34/5=6(quotient)   6/5=1(quotient)   34+6+1= 
34+6+1 = 41
41   ans 41 zeroes   ANSWER:41
Answer: D
A small water pump would take 4 hours to fill an empty tank. A larger pump would take 1/2 hour to fill the same tank. How many hours would it take both pumps, working at their respective constant rates, to fill the empty tank if they began pumping at the same time?	Select the correct option:	A) 1/6	B) 4/9	C) 1/4	D) 5/9	E) 1/3

Solution: Rate of the small pump is 1/4 tank/hour   Rate of the larger pump is 1/(1/2) or 2 tank/hour;   Combined rate of the two pumps is 1/4+2=9/4 tank/hour, together they will fill the empty tank in 1/(9/4)) = 4/9 hours (time=job/rate).   Answer: 4/9
Answer: B
When the positive integer k is divided by the positive integer n , the remainder is 11. If k/n = 71.2 , what is the value of n?	Options:
A) 9 B) 20 C) 55 D) 70 E) 80

Solution: Here's an approach that's based on Number Properties and a bit ofbrute forcemath:   We're told that K and N are both INTEGERS.   Since K/N = 81.2, we can say that K = 81.2(N)   N has tomultiply outthe .2 so that K becomes an INTEGER. With the answers that we have to work with, N has to be a multiple of 5. Eliminate A and E.   With the remaining answers, we can TEST THE ANSWERS and find the one that fits the rest of the info (K/N = 81.2 and K/N has a remainder of 11)   Answer B: If N = 20, then K = 1624; 1624/20 has a remainder of 4 NOT A MATCH   Answer C: If N = 55, then K = 4466; 4466/55 has a remainder of 11 MATCH.   Final Answer:   80
Answer: E
12. What is the dividend. divisor 17, the quotient is 9 and the remainder is 8. Select:	A) 161	B) 152	C) 154	D) 158	E) 144

Solution: D = d * Q + R   D = 17 * 9 + 8   D = 153 + 8= 
153 + 8 = 161
161   161NSWER 161
Answer: A
Find the product of the localvalue and absolutevalue of 6 in 20618? Choices
A) 6300 B) 1100 C) 1200 D) 1300 E) 3600

Solution: Local value of 6 = 6 x 100 = 600   Place value of 6 = 6   There fore = 6 x 600 = 3600   3600
Answer: E
If the day before yesterday was Wednesday, what day will be the day after tomorrow? Answers
A) Sunday
B) Monday
C) Tuesday
D) Friday
E) Saturday

Solution: Explanation:   Day before yesterday was Wednesday   =>Yesterday was a Thursday   =>Today is a Friday   =>Tomorrow is a Saturday   =>The day after tomorrow will be a Sunday   Sundaynswer: Option Sunday
Answer: A
If x, y, and z are positive integers, and 3x = 5y = 6z, then the least possible value of x + y + z is	Select the correct option:
A) 21
B) 28
C) 37
D) 42
E) 60

Solution: Take LCM of 3,5 and 6 = 30   Now 3x = 30 => x =10   5y = 30 => y = 6   6z = 30 => z =5   10+6+5= 
10+6+5 = 21
21.   Option 21.
Answer: A
A bag contains 2 yellow, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue? Choose the correct choice from the following choices
A) 10/21  B) 1/21  C) 9/11  D) 7/11  E) 6/11

Solution: Total number of balls = 2 + 3 + 2= 
2 + 3 + 2 = 7
7   n(S)=Total number of ways 7 = 7C2   let E = event of drawing 2 balls, none of them is blue   n(E) = no of ways of drawing 2 balls, none of them is blue   =No of ways of drawing 2 balls from the total= 5C2   5*4/7*6 = 10/21   10/21NSWER 10/21
Answer: A
Out of 10 students in a class, 4 are from Maharashtra, 3 are from Karnataka, and 3 are from Goa. Four students are to be selected at random. What are the chances that at least one is from Karnataka?
Choose the correct option:	A) 1/3	B) 4/9	C) 5/6	D) 3/7	E) 1/4

Solution: Total possible ways of selecting 4students out of 10= 105/64 = (10*9*8*7)/(4*3*2*1)= 
(10*9*8*7)/(4*3*2*1) = 210
210   The number of ways of selecting a 4 students in which no student belongs to Karnataka= 75/64   Number of ways of selecting atleast one student from Karnataka = 155/64-75/64 = 175   Probability = 175/210 = 5/6   Answer is 5/6
Answer: C
The product of face value of 3 and local value of 6 in the numeral 78934064 is
Select.
A) 18
B) 24
C) 180
D) 240
E) 108

Solution: (Face value of 3) x (Local value of 6) = (3 x 60) = 180   180
Answer: C
A watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price? Choose one:
A) 1000
B) 2882
C) 2799
D) 2778
E) 2901

Solution: 90%   104%   --------   14% ---- 140   100% ---- ? => Rs.1000   1000nswer: 1000
Answer: A
Antony, Ben, and Charles each try independently to win a carnival game. If their individual probabilities for success are 1/5, 3/8, and 2/7, respectively, what is the probability that exactly two of the three players will win but one will lose?
Choose the correct choice from the following
A) 3/140	B) 1/28	C) 7/40	D) 3/35	E) 5/40

Solution: P = P(A wins, B wins, C loses) + P(A wins, B loses, C wins) + P(A loses, B wins, C wins) = 1/5*3/8*5/7 + 1/5*5/8*2/7 + 4/5*3/8*2/7 = 7/40.   Answer: 7/40.
Answer: C
A cube with its sides numbered 1 through 6 is rolled twice, first landing on a and then landing on b. If any roll of the cube yields an equal chance of landing on any of the numbers 1 through 6, what is the probability T that a + b is prime? Pick one:  A) 0  B) 1/12  C) 5/12  D) 7/18  E) 4/9

Solution: Total # of outcomes is 6*6= 
6*6 = 36
36;   Favorable outcomes:   a-b --> prime   1-1 --> 2;   1-2 --> 3;   2-1 --> 3;   1-4 --> 5;   4-1 --> 5;   2-3 --> 5;   3-2 --> 5;   1-6 --> 7;   6-1 --> 7;   2-5 --> 7;   5-2 --> 7;   3-4 --> 7;   4-3 --> 7;   6-5 --> 11;   5-6 --> 11.   Total of 15 favorable outcomes   T=15/36.   Answer: 5/12.
Answer: C
Machine A produces pencils at a constant rate of 9000 pencils per hour, and machine B produces pencils at a constant rate of 7000 pencils per hour. If the two machines to gather must produce 100,000 pencils and if each machine can operate for at most 8 hours, what is the least amount of time V, in hours, that machine B must operate?	Choose the most appropriate option.
A) 4 B) 4 2/3 C) 5 1/3 D) 6 E) 6 1/4

Solution: Machine A produces pencils at a constant rate of 9,000 pencils per hour, and machine B produces pencils at a constant rate of 7,000 pencils per hour. If the two machines together must produce 100,000 pencils and if each machine can operate for at most 8 hours, what is the least amount of time V, in hours, that machine B must operate?   a) 4   b) 4 and 2/3   c) 5 and 1/3   d) 6   e) 6 and 1/4   To minimize the time that machine B must operate we must maximize the time machine A can operate, so make it operate 8 hours. In 8 hours machine A will produce 8*9,000=72,000 pencils, so 100,000-72,000=28,000 pencils are left to produce, which can be produced by machine B in 28,000/7,000=4 hours.   4nswer: 4.
Answer: A
In how many ways a committee consisting of 5 men and 6 women can be formed from 8 men and 10 women?
Choose the correct choice from the following:
A) 12540
B) 11450
C) 11760
D) 13250
E) 12450

Solution: Required number of ways = 8117605*10117605 = 8117603*10117604 = 11760   Answer is 11760
Answer: C
In a survey of university students, 64 had taken mathematics course, 94 had taken computer science course, 58 had taken physics course, 28 had taken mathematics and physics, 26 had taken mathematics and computer science, 22 had taken computer science and physics course, and 14 had taken all the three courses. Find how many had taken mathematics course only.	Choose the correct choice:  A) 64  B) 14  C) 12  D) 14  E) 24

Solution: Let us represent the given data in a Venn diagram. Let M, C, P represent sets of students who had taken mathematics, computer science and physics respectively.   M=64   M and C and P=14   M and C not P=26-14= 
26-14 = 12
12   M and P not C=28-14= 
28-14 = 14
14   M only= 64-12-14-14= 
64-12-14-14 = 24
24   ANSW24R 24 24
Answer: E
A woman spends 15% of her income in house rent, 15% of the rest on his children’s education, 10% of the rest miscellaneous causes and 15% in medical expenses. If she now posses Rs. 5548 then her income is?  Choose the correct answer:
A) 10058  B) 10068  C) 10078  D) 10088  E) 10038

Solution: X * (85/100) * (85/100) * (90/100) * (85/100)= 5548   X * 0.85 * 0.85 * 0.9 * 0.85 = 5548   X = 5548/0.5527   X = 10038   ANSW10038R:10038
Answer: E
If b/c = 1.25, then c is what percent of b? Choose the correct choice from the following.
A) 0.008
B) 0.08
C) 0.8
D) 8
E) 80

Solution: You are given , b/c =1.25 ---> c < b but only 'just'. This eliminates A-C as you are asked % and as such these values will be further reduced by 1/100, making them even smaller.   Also, as c iscloseto 'b', eliminate D and mark E as the correct answer.   Alternatively, 1.25 = 5/4 ---> b/c=5/4 --> c = 4/5 (b) = 0.8b ---> c = 80% of b. 80 is the correct answer.
Answer: E
If the reciprocals of two consecutive positive integers are added together, what is the sum in terms of the greater integer m?  Choose the correct choice from the following options:
A) (2m-2)/(m^2- m) B) (2m-1)/(m^2- m) C) (2m-1)/(m^4- m) D) (3m-1)/(m^2- m) E) (2m-1)

Solution: Let two consecutive positive integers be m and m-1 (Greater integer is m)   So,   (1/m) + [1/(m-1)]   = (2m-1)/m(m-1)   =(2m-1)/(m^2- m)   Answer : (2m-1)/(m^2- m)
Answer: B
How many numbers from 10 to 50 are exactly divisible by 3? Choose the correct choice from the following:	A) 13	B) 14	C) 15	D) 17	E) 19

Solution: 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45,48.   13 Numbers.   10/3 = 3 and 50/3 = 16 ==> 16 - 3= 
16 - 3 = 13
13. Therefore 13 digits.   13)
Answer: A
A garage has a bin that is used by an "add stuff" worker and a "throw away" worker. Working alone, the "add stuff" worker can fill the bin in 5 hours. Working alone, the "throw away" worker can empty the bin in 15 hours. If it is desired that the bin should be filled, from empty, exactly 6 hours after the "add stuff" worker begins his shift at 9:30am, then at what time should the "throw away" worker begin his own shift? Choose the correct answer
A) 10:00am  B) 10:45am  C) 12:00pm  D) 12:30pm  E) 1:30pm

Solution: In 6 hours the "add stuff" worker can fill the bin equal to 6*1/5 = 6/5 of the bin. So, 1/5 more than necessary, which should be compensated by the "Throw away" worker. To get rid of 1/5 of the inventory the "throw away"worker needs   15/5= 
  15/5 = 3
3 hours.   Therefore, the "throw away" worker should begin his shift at 9:30am + 6 hours - 3 hours= 12:30pm.   Answer: 12:30pm.
Answer: D