MU-NLPC/Calc-aqua_rat huggingface dataset:
Set X consists of 15 integers and has median of 20 and a range of 20. What is the value of the greatest possible integer that can be present in the set?
Choose the correct choice:
A) 32  B) 37  C) C.40  D) 60  E) 50

Solution: Note that both median and range do not restrict too many numbers in the set. Range is only concerned with the smallest and greatest. Median only cares about the middle.   Quick check of each option starting from the largest:   (E) 50   Range of 20 means the smallest integer will be 30. So 20 cannot lie in between and hence cannot be the median.   (D) 43   Range of 20 means the smallest integer will be 23. So 20 cannot lie in between and hence cannot be the median.   (C) 40   Range of 20 means the smallest integer will be 20. 20 can lie in between such as:   20, 20, 20, 20, 20, 20, 20, 20, 20, 40, 40, 40, 50, 60   This is possible. Hence it is the greatest such number.   Answer (60)
Answer: D
In a T.V. factory, an average of 60 TVs are produced per day for the fist 25 days of the months. A few workers fell ill for the next five days reducing the daily average for the month to 58 sets per day . The average production per day for day last 5 days is ? Select the correct option
A) 45
B) 48
C) 52
D) 58
E) None

Solution: Production during these 5 days = Total production in a month - production in first 25 days.   = 30 x 58 - 25 x 60   = 240   ∴ Average for last 5 days = 240 / 5= 
240 / 5 = 48
48   Correct Option: 48
Answer: B
The music class consists of 4 girls and 5 boys. How many ways can a group of 3 be formed if it has to include at least one boy?  Pick one.
A) 80  B) 158  C) 161  D) 165  E) 172

Solution: Reverse combinatorics approach is preferred method on this one   Note that at least 1 boy gives clue to using this method   80ll combinations - four girls = answer   80ll combinations is 9C3 = 84   80ll girls 4C3 = 4   So our answer is   84-4= 
  84-4 = 80
80   Hence, answer is (80)
Answer: A
The mean of 30 values was 140. It was detected on rechecking that one value 145 was wrongly copied as 135 for the computation of the mean. Find the correct mean. Choose the correct choice from the following options.
A) 151	B) 140.33	C) 152	D) 148	E) None of the above

Solution: Corrected mean = 140×30−135+145/30   = 4200−135+145/30   =4210/30=140.33   Answer 140.33
Answer: B
In a certain pond, 40 fish were caught, tagged, and returned to the pond. A few days later, 50 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond?	Choose the correct choice from the following options:  A) 400  B) 625  C) 1,250  D) 2,500  E) 1,000

Solution: This is a rather straight forward ratio problem.   1. 40 fish tagged   2. 2 out of the 50 fish caught were tagged thus 2/50   2/50=40/x   thus, x=1000   Think of the analogy: 2 fish is to 50 Fish as 50 fish is to ...?   You've tagged 50 fish and you need to find what that comprises as a percentage of the total fish population - we have that information with the ratio of the second catch.   1,000
Answer: E
11, 22, 14, 28, 20, 40, ?
Choose the correct option
A) 21	B) 25	C) 31	D) 31	E) 32

Solution: 32   32   This is an alternating multiplication and subtracting series with a pattern x2, -8, x2, -8.
Answer: E
A person took some amount with some interest for 2 years, but increase the interest for 1%, he paid Rs.120/- extra, then how much amount he took? Options:
A) Rs.5500/-	B) Rs.6000/-	C) Rs.4000/-	D) Rs.7000/-	E) Rs.8000/-

Solution: Explanation:   2 years = Rs.120/-   year = 120/2   Rate of Interest = 1%   100/1% × 120/2 = Rs.6000/-   P = Rs.6000/-   Answer: Option Rs.6000/-
Answer: B
The mantissa of log 3274 is 0.5150. The value of log(0.3274) is  Choose one.
A) 1.5150 B) 1.5150 C) 2.515 D) None of these E) Cannot be determined

Solution: Solution   Since, 0.3274 gives characteristic 1. Therefore value of log (0.3274) = 1.5150. 1.5150nswer 1.5150
Answer: A
Find the area of a parallelogram with base 18 cm and height 16 cm?  Select:
A) 423 cm2  B) 122 cm2  C) 420 cm2  D) 251 cm2  E) 288 cm2

Solution: Area of a parallelogram   = base * height   = 18 * 16= 
18 * 16 = 288
288 cm2   Answer: 288 cm2
Answer: E
A,B, and C are on a trip by a car. A drives during the 1st hour at an average speed of 50km/hr. B drives during the next 2 hours at an average speed of 48km/hr. C drives for the next 3 hours at an average speed of 52km/hr. They reached their destination exactly after 6 hours. Their mean speed is?
Choose the correct option
A) 45.5km/hr
B) 50.3km/hr
C) 56.9km/hr
D) 62.5km/hr
E) 38.9km/hr

Solution: Total distance traveled = 50*1 + 48*2 + 52*3= 
50*1 + 48*2 + 52*3 = 302
302km   Total time taken= 6hrs   Mean speed = 302/6 = 50.3km/hr   Answer is 50.3km/hr
Answer: B
The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
Pick one:
A) 140 sq.units	B) 170 sq.units	C) 190 sq.units	D) 940 sq.units	E) 149 sq.units

Solution: Explanation:   Given that the area of the square = 1225 sq.units   => Side of square = √1225 = 35 units   The radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35= 
2/5 * 35 = 14
14 units   Given that breadth= 10 units   140 sq.unitsrea of the rectangle = lb = 14 * 10= 
14 * 10 = 140
140 sq.units   140 sq.unitsnswer: Option 140 sq.units
Answer: A
The tax on a commodity is diminished by 20% but its consumption is increased by 10%. Find the decrease percent in the revenue derived from it?  Choose the correct choice from the following answers.
A) 18% B) 82% C) 72% D) 12% E) 11%

Solution: 100 * 100= 
100 * 100 = 10_000
10000   80 * 110= 
80 * 110 = 8_800
8800   10000------- 1200   100 ------- ?= 12%   Answer: 12%
Answer: D
You roll P (P > 1) number of Q (Q > 1) sided dice at once. What is the probability that at least two of the P dice will land on difference numbers. Choose the correct option
A) 1 - P/(Q^P)	B) 1 - Q/(P^Q)	C) 1 - 1/(P^(Q-1))	D) 1 - 1/(Q^(P-1))	E) 1 - 1/(Q-1)^P

Solution: This can be calculated by first finding the probability of all dice landing on the same number, and taking 1 - it:   The incorrect rolls are any Q-ples: 11...1, 22...2, ..., PP...P. This is makes Q possibilities. The P dice can roll Q*Q*...*Q (Q^P) number of ways. Thus the probability of landing on the same number is Q/(Q^P) = 1/(Q^(P-1)). Therefore, the probability of at least two of the P dice landing on different numbers is:   1 - 1/(Q^(P-1))   Answer: 1 - 1/(Q^(P-1)).
Answer: D
The majority owner of a business received 25% of the profit, with each of 4 partners receiving 25% of the remaining profit. If the majority owner and two of the owners combined to receive $76,875, how much profit did the business make? Answers.
A) $98,000
B) $106,000
C) $112,000
D) $118,000
E) $123,000

Solution: Let P be the total profit.   P/4 + 1/2*(3P/4) = P/4 + 3P/8 = 5P/8 = $76,875   P = $123,000   The answer is $123,000.
Answer: E
Julie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest. After two years she earned $112 and $120 from the simple interest account and the compound interest account respectively. If the interest rates for both accounts were the same, what was the amount of Julie's initial savings?  Choose the correct choice from the following choices:  A) 600  B) 784  C) 1080  D) 1200  E) 1440

Solution: $112 for 2 years = $56 per year.   Extra $8 yearned with the compound interest is the percent yearned on percent. So, $8 is yearned on $56, which means that the interest = 7%.   This on the other hand means that half of the savings = 56*7= 
56*7 = 392
$392. Twice of that= $784.   Answer: 784.
Answer: B
Solution Y is 30 percent liquid A and 70 percent water. If 2 kilograms of water evaporate from 8 kilograms of solutions Y and 2 kilograms of solution Y are added to the remaining 6 kilograms of liquid, what percent of this new liquid solution is liquid A?	Choose the correct choice from the following answers.
A) 30% B) 33 1/3% C) 37 1/2% D) 40% E) 50%

Solution: Answer:C   Took time to solve this one, the statement2 kilograms of solution Y are added to the remaining 6 kilograms of liquidwas confusing to me. After thinking more deeply, it was clear to me that new 2 kg of solution Y will also be 30% liquid A and 70% water, and then I was able to get the answer. That was a bit tricky and nice question.=37 1/2%
Answer: C
Working together, Wayne and his son can shovel the entire driveway in three hours. If Wayne can shovel six times as fast as his son can, how many hours would it take for his son to shovel the entire driveway on his own? Choices
A) 4
B) 6
C) 8
D) 7
E) 12

Solution: W: the time for Wyane to do the job   S: the time for his son to do the job   We have 1/W + 1/S = 1/6 and W = 6S   Then we have 1/(6*S) + 1/S = 1/6 <=> 7/(6*S) = 1/6 <=> S = 7   ANS: 7
Answer: D
150 candies are distributed to children with the same number of candies for each child. What can’t be the range which includes the number of children? Choose the correct choice from the following:
A) 1~10
B) 10~20
C) 20~30
D) 45~55
E) 55~65

Solution: 150 = 2*3*5^2   There are factors in each range except for 55~65   The answer is 55~65.
Answer: E
Which of the following inequalities is equivalent to –2 < x < 4 ? Choose the correct choice from the following options:
A) | x – 2 | < 4
B) | x – 1 | < 3
C) | x + 1 | < 3
D) | x + 2 | < 4
E) None of the above

Solution: Soln:-   (A) | x – 2 | < 4 => -2<x<6: out   (| x – 1 | < 3) | x – 1 | < 3 => –2 < x < 4: yeah   (C) | x + 1 | < 3 => -4<x<2: out   (D) | x + 2 | < 4 => -6<x<2: out   (E) None of the above: out   Ans: | x – 1 | < 3
Answer: B
The volumes of two cones are in the ratio 1 : 10 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire?
Options:
A) 2 : 5
B) 2 : 8
C) 2 : 1
D) 2 : 0
E) 2 : 2

Solution: The volume of the cone = (1/3)πr2h   Only radius (r) and height (h) are varying.   Hence, (1/3)π may be ignored.   V1/V2 = r12h1/r22h2 => 1/10 = (1)2h1/(2)2h2   => h1/h2 = 2/5   i.e. h1 : h2 = 2 : 5   2 : 5nswer: 2 : 5
Answer: A
As part of a game, seven people each must secretly choose an integer between 1 and 7, inclusive. What is the approximate likelihood that all seven people will choose different numbers? Answers:
A) 1%
B) 12%
C) 16%
D) 20%
E) 25%

Solution: 1%ns:a)   1st person has option no's- (1,2,3,4,5,6,7) - there fore probability of getting a no =7c1/7c1 = 1   2nd person has option no's any six ,   he has to choose a no from six no's - there fore probability of getting a no = 6c1/7c1 = 6/7   3rd person has option no's any five,   he has to choose a no from five no's -there fore probability of getting a no = 5c1/7c1 =5/7   4th person has 4 options - there fore probability of getting a no= 4c1/7c1 =4/7   5th person has 3 options - there fore probability of getting a no= 3c1/7c1 = 3/7   6th person has 2 options - there fore probability of getting a no= 2c1/7c1 = 2/7   7th person has only one option - there fore probability of getting a no= 1c1/7c1 = 1/7   =1*6/7*5/7*4/7*3/7*2/7*1/7 = 1%
Answer: A
When positive integer N is divided by positive integer P, the quotient is 20, with a remainder of 7. When N is divided by (P + 2), the quotient is 15 and the remainder is 2. What is the value of N?
Choose the correct choice from the following answers
A) 107	B) 331	C) 511	D) 691	E) 871

Solution: N/P=10 7/P= 20P+7   N/(P+2)=15 2/(P+2)=15P+30+2   solving these two equations   we get P=5 N= 107 answer is 107.
Answer: A
The New York Classical Group is designing the liner notes for an upcoming CD release. There are 10 soloists featured on the album, but the liner notes are only 5 pages long, and therefore only have room for 5 of the soloists. The soloists are fighting over which of them will appear in the liner notes, though not about which page they appear on. How many different combinations T of soloists can appear in the liner notes? Choose the correct choice from the following options
A) 5!
B) 10!/(5!5!)
C) 10!/5!
D) 10!
E) 10!*5!

Solution: Total Soloists to choose from = 10   Soloist Required = 5   Question : How many different combinations T of soloists can appear in the liner notes?   The language of the question clearly mentions that only the combinations need to be calculated   i.e. Arrangement of the Soloists does NOT matter(Refer theHighlightedpart of the question)   Method-1:   Total Ways to Choose 5 out of 10 soloists = 10C5 = 10! / (5!*5!)   Method-2:   No. of ways to select and arrange 5 soloist on 5 Page = 10*9*8*7*6   Since the arrangement of 5 selected Notes (which can happen in 5! ways) doesn't NOT matter,   Therefore total ways to pick 5 out of 10 soloists = 10*9*8*7*6 / 5! = 10*9*8*7*6 *5! / (5!*5!) = 10! / (5!*5!)   Answer: Option 10!/(5!5!)
Answer: B
The average of first 18 natural numbers is? Choose one:  A) 9.6  B) 9.5  C) 9.9  D) 9.4  E) 9.1

Solution: Sum of 18 natural no. = 342/2= 
342/2 = 171
171   Average= 171/18= 
171/18 = 19/2 = around 9.5
9.5   Answer:9.5
Answer: B
In an effort to plan out expenses, the Roberts family is representing its annual budget as a circle graph. Each sector of the graph is proportional to the amount of the budget it represents. If “clothes and shoes” takes up 54° of the chart, how much of the Roberts’s $30,000 annual budget is dedicated to clothes and shoes?
Choose the correct choice from the following options.
A) $1,500	B) $3,000	C) $4,500	D) $5,000	E) $5,400

Solution: Given for clothes and shoes” takes up 54° of the circular chart.   Then clothes and shoes = 54/360 * 30000.= 
54/360 * 30000. = 4_500
> 4500.   IMO option $4,500 is correct answer...
Answer: C
The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8215 for a computer table, then what was the cost price of the computer table? Select the correct option:
A) 7297 B) 6625 C) 2871 D) 6725 E) 2981

Solution: Explanation:   CP = SP * (100/(100 + profit%))   = 8215(100/124) = Rs. 6625.   Answer: 6625
Answer: B
A rectangular table seats 2 people on each of two sides, with every person directly facing another person across the table. If four people choose their seats at random, what is probability that any two of them directly face other?
Choose the correct choice
A) 1/3  B) 1/8  C) 1/7  D) 15/56  E) 4/7

Solution: A B   ------------   | TABLE |   ------------   C D   A to D are 4 people.   Prob to select any 1 person = 1   Prob to select the person opposite to the chosen person = 1/3   For ex. If we select A as the person than prob of choosing C is 1/3.   Hence, answer will be 1/3.
Answer: A
A train A leaves Mysore at 6 a.m. and reaches Bangalore at 10 a.m. Another train leaves B Bangalore at 8 a.m. and reaches Mysore at 11.30 a.m. At what time do the two trains cross each other ?	Choose the correct choice from the following answers:
A) 8.30 a.m.  B) 8.45 a.m.  C) 8.56 a.m.  D) 9 a.m.  E) None of these

Solution: Explanation :   Solution: Let the distance between mysore and bangalore be x km and let the trains meet y hours after 8 a.m.   Clearly, A covers x km in 4 hours and B covers x km in 4.5 hrs = (7/2) hrs   .'. Speed of A = x/4 kmph, speed of B = 2x/7 kmph.   Distance covered by A in (y+2) hrs + distance covered by B in y hrs = x.   .'. x/4(y+2) + 2x/7 * y = x   => (y+2)/4 + 2y/7 = 1   => y = 14/15 hrs =14*60/15= 
14*60/15 = 56
56 min.   Hence, the trains meet at 8.56 a.m.   Answer : 8.56 a.m.
Answer: C
The smallest number when increased by "2 " is exactly divisible by 12, 30, 48, 74 and 100 is: Choose the most appropriate option:  A) 14439  B) 44398  C) 44400  D) 44402  E) 15005

Solution: LCM = 44400   44400 - 2= 
44400 - 2 = 44_398
44398   ANSWER:44398
Answer: B
Four different books (A, B, C and D) are to be arranged on a shelf. Books A and B are to be arranged first and second starting from the right of the shelf. The number of different orders in which books C and D may be arranged is
Select:  A) 16!  B) 12!  C) 8!  D) 11!  E) 2!

Solution: Solution   Since books A and B are arranged first and second, only books C and D will change order. Therefore it an arrangement problem involving 2 items and the number of different order is given by   2!   Answer 2!
Answer: E
The cost of a one-family home was $ 120,000 in 1980. In 1988, the price had increased to $ 174,000. What was the percent increase in the cost of the home?	Choose the correct choice from the following answers.
A) 60% B) 50% C) 55% D) 40% E) 45%

Solution: Increase = 174000-120000= 
174000-120000 = 54_000
54000   % increase= 54000*100/120000= 
54000*100/120000 = 45
45%   Answer: option 45%
Answer: E
Find the greatest number of four digits which is perfectly divisible by 3 and when divided by 5, 7 and 9 leaves a remainder 3 in each case.
Select the correct option:
A) 1128
B) 1659
C) 2687
D) 1667
E) 1891

Solution: LCM of 3, 5, 7, 9 = 315. Greatest number of four digits which is divisible by 315 is 9765. The required number = 9765 + 3= 
9765 + 3 = 9_768
9768. Ask doubt with Question Id: 1658 13) Find greatest number of four digits which when increased by 3568 is exactly divisible by 6, 8, 12, 20. a) 9992 b) 9785 c) 9840 d) None Explanation: Greatest number of 4 digits= 9999. 9999 + 3568 = 13567. LCM of 6, 8, 12 and 20 is 120.   ∴ Required number of 4 digits = 9999 – 7 = 9992 i.e. 9992 is the number to which if 3568 is added, then it is exactly divisible by 6, 8, 12, 20. Ask doubt with Question Id: 1659   Answer:1659
Answer: B
Three friends are buying a gift for a friend. Declan contributes 9 dollars more than 1/4 the cost of the gift, Ed contributes 1 dollar less than 1/3 the cost of the gift, and Frank contributes the remaining 22 dollars. What is the cost of the gift?
Select.
A) 48 B) 54 C) 60 D) 66 E) 72

Solution: Declan = D, 72d = 72, Frank = F   t = total   D + 72 + F = t   (t/4 + 9) + (t/3 - 1) + 22 = t   t = 30 + (7t/12)   12t = 30(12) + 7t   5t = 5*6(12)   t = 72   The correct answer is 72.
Answer: E
In the exam the average was found to be p mark. After deducting typographical error the average marks of 85 student reduced from 75 to 50 . Due to this the average came down by 25 marks. What was the number of students who took the exam? Pick one
A) 100	B) 85	C) 110	D) 130	E) 160

Solution: Explanation :   Number of student = (75-50) * 85/25= 
(75-50) * 85/25 = 85
85   Answer : 85
Answer: B
A coin has two sides. One side has the number 1 on it and the other side has the number 2 on it. If the coin is flipped three times what is the probability that the sum of the numbers on the landing side of the coin will be greater than 3?
Choose the correct choice from the following.
A) 3/8	B) 1/16	C) 7/8	D) 1/2	E) 1/4

Solution: One approach to solve the problem is to list the different possibilities for a toss of coin three times. Because there are two outcomes and the coin is tossed three times, the table will have 2*2*2 or 8 rows.   Next add the resulting rows together to find the sum (the fourth column in the table below).   Toss 1 | Toss 2 | Toss 3 | Sum   1 ---------- 1 -------- 1 ------ 3   1 ---------- 1 -------- 2 ------ 4   1 ---------- 2 -------- 1 ------ 4   1 ---------- 2 -------- 2 ------ 5   2 ---------- 1 -------- 1 ------ 4   2 ---------- 1 -------- 2 ------ 5   2 ---------- 2 -------- 1 ------ 5   2 ---------- 2 -------- 2 ------ 6   From the table we see that there are 7 situations where the sum of the tosses will be greater than 3. And there are 8 possible combinations resulting in a probability of   7/8 or a probability of 7/8.   SO the correct answer is 7/8.
Answer: C
Three partners A, B, C in a business invested money such that 4(Aâ€™s capital) = 2(Bâ€™s capital) = 12(Câ€™s capital) then, The ratio of their capitals is Select
A) 63 : 45 : 34	B) 63 : 54 : 34	C) 36 : 54 : 28	D) 3 : 6 : 1	E) None of these

Solution: Explanation:   Let 4(Aâ€™s capital) = 2(Bâ€™s capital) = 12(Câ€™s capital) = Rs.x   Then, Aâ€™s capital = Rs x/4, Bâ€™s capital = Rs. x/2 and Câ€™s capital = Rs. x/12   A : B : C = x/4 : x/2 : x/12   3 : 6 : 1   Answer: Option 3 : 6 : 1
Answer: D
A man saves 20% of his monthly salary. If an account of dearness of things he is to increase his monthly expenses by 20%, he is only able to save Rs. 230 per month. What is his monthly salary?
Select the correct option:  A) 5000  B) 5750  C) 2878  D) 2990  E) 2771

Solution: Income = Rs. 100   Expenditure = Rs. 80   Savings = Rs. 20   Present Expenditure 80*(20/100) = Rs. 96   Present Savings = 100 â€“ 96 =Rs. 4   100 ------ 4   ? --------- 230 => 5750   Answer: 5750
Answer: B
Find the average of the first 9 natural numbers? Choose the correct choice:
A) 8
B) 5
C) 10
D) 11
E) 12

Solution: Average of the first 'n' natural numbers = (n + 1)/2   We get  (9 + 1)/2= 
 (9 + 1)/2 = 5
5   ANSWER:5
Answer: B
If a and b are positive integers, which of the following cannot be an integer? Choose the correct choice:
A) (2b)/(4a+1)
B) (2b)/(3a+1)
C) (2a+1)/(4b)
D) (2a+1)/(4b+1)
E) (2a·b)/(4b+2)

Solution: I'd first look for an option which gives odd/even for any values of a and b, because odd/even is not an integer.   Option C fits: 2a+1/4b=even+odd/even=odd/even≠integer   To discard other A consider a=5 and b=1.   To discard other B consider a=2 and b=1.   To discard other D consider a=2 and b=1.   To discard other E consider a=3 and b=1.   Answer: (2a+1)/(4b).
Answer: C
Matt is touring a nation in which coins are issued in two amounts, 2¢ and 5¢, which are made of iron and copper, respectively. If Matt has ten iron coins and ten copper coins, how many different sums from 1¢ to 70¢ can he make with a combination of his coins?	Choose the correct choice.
A) 66  B) 67  C) 68  D) 69  E) 70

Solution: The total sum is 10*2 + 10*5= 
10*2 + 10*5 = 70
70¢. If you can make each sum from 1 to 70 (1¢, 2¢, 3¢, ..., 70¢), then the answer would be 70 (maximum possible).   Now, with 2¢ and 5¢ we cannot make 1¢ and 3¢. We also cannot make 69¢ and 67¢ (since total sum is 70¢ we cannot remove 1¢ or 3¢ to get 69¢ or 67¢).   So, out of 70 sums 4 are for sure not possible, so the answer must be   70 - 4= 
  70 - 4 = 66
66 sums or less. Only A fits.   66nswer: 66.
Answer: A
What is the greatest prime factor of 12!11! + 11!10!?	Choices:
A) 7 B) 11 C) 13 D) 17 E) 19

Solution: Soln:   12!11!+11!10!= 12*11*10!*11*10!+11*10!*10!=10!*10!*11(11*12+1)=10!*10!*11*133=10!*10!*11*19*7   greatest prime factor in 10! is 7 which is less than 19.   So Ans is 19
Answer: E
An empty wooden vessel weighs 12% of its total weight when filled with paint. If the weight of a partially filled vessel is one half that of a completely filled vessel, what fraction of the vessel is filled.	Choose the correct choice: A) 3/5 B) 5/11 C) 1/24 D) 4/9 E) 2/5

Solution: An empty wooden vessel weighs 12% of its total weight when filled with paint:   Vessel = 0.12(Vessel + Paint);   12V = V + P (so the weight of completely filled vessel is 12V)   P = 11V (so the weight of the paint when the vessels is completely filled is 11V).   The weight of a partially filled vessel is one half that of a completely filled vessel:   V + P' = 1/2*12V;   P' = 5V (so the weight of the paint when the vessels is partially filled is 5V).   What fraction of the vessel is filled?   So, we need to find the ratio of the weight of the paint when the vessel iscompletely filledto the weight of the paint when the vessel ispartially filled:   P'/P = 5V/11V = 5/11.   Answer: 5/11.
Answer: B
A sum fetched a total simple interest of Rs. 750 at the rate of 6 p.c.p.a. in 5 years. What is the sum?	Choose the correct choice from the following choices
A) 2600  B) 2500  C) 2900  D) 2800  E) 2700

Solution: Sol.   Principal = Rs. [100 * 750 / 6 * 5] = Rs. [75000 / 30] = Rs. 2500.   Answer 2500
Answer: B
A salesman sold twice as much pears in the afternoon than in the morning. If he sold $420 kilograms of pears that day, how many kilograms did he sell in the afternoon? Pick.
A) 120
B) 180
C) 240
D) 280
E) 320

Solution: 3x=420   x=140   Therefore, the salesman sold 140kg in the morning and 2⋅140=280 kg in the afternoon. So answer is 280.
Answer: D