MU-NLPC/Calc-aqua_rat huggingface dataset:
Let x be a positive integer, what is the remainder when 5^(3x+1)+5 is divided by 5?
Answers:
A) 0
B) 1
C) 2
D) 3
E) 4

Solution: For: (5^(3x+1)+5)/3   Let n = 3x + 1   5^n   5^1 = 5   5^2 = 25   5^3 = 125, ... last digit is always 5.   Rule: x^(m+n) = (x^m)(x^n)   (5^(3x))(5^1)   Rule: x^(mn) = (x^m)^n   ((5^3)^x)(5) => Now, (5)(125^x) + 5 = (5)(5) + 5 => Finally, 30/5 divides evenly with 0 remainder.   0nswer: 0
Answer: A
(x —1)(x + 3) > 0
(x +5)(x—4) < 0
Which of the following values of x satisfy both inequalities shown?
I. 3
II. -4
III. 2
IV. 5  Choose the most appropriate option:
A) I and II only	B) I and III only	C) II and III only	D) II and IV only	E) I, II, III,

Solution: (x - 1)(x + 3) > 0 --> x<-3 or x>1.   (x + 5)(x - 4) < 0 --> -5<x<4.   Among choices only -4 and 2 and 3 satisfy both inequalities.   Answer: II and IV only.
Answer: D
A car traveled 462 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city. If the car traveled 15 fewer miles per gallon in the city than on the highway, how many miles per gallon did the car travel in the city?	Pick one.
A) 14  B) 16  C) 21  D) 22  E) 40

Solution: I treat such problems as work ones.   Work=Rate*Time   Mileage(m)=Rate(mpg)*Gallons(g)   X gallons is a full tank   {462=RX   {336=(R-15)X solve for R, R=55   55-15= 
55-15 = 40
40 mpg   40
Answer: E
Anintegratedteam consists of 2 members from the engineering team and 2 members from the design team. If the engineering team has 7 members and the design team has 3 members, how manyintegratedteam formations are possible? Choose the correct answer:
A) 36
B) 54
C) 63
D) 90
E) 112

Solution: 2 out of 7 times 2 out of 3 => 7*6/2*1 * 3*2/2*1= 
7*6/2*1 * 3*2/2*1 = 63
63   63
Answer: C
A box contains seven bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that at least one bulb is good? Pick:
A) 2045/2401
B) 2121/2401
C) 2145/2401
D) 2345/2401
E) 2245/2401

Solution: Required probability   = 1 - 256/2401   = 2145/2401   Answer: 2145/2401
Answer: C
On the shelf, there are four books of poetry, four novels, and five reference works. Suppose we picked two books at random. What is the probability that we pick one novel and one reference work?
Choose the most appropriate option
A) 4/25 B) 6/31 C) 8/35 D) 10/39 E) 12/41

Solution: We could pick one novel and then one reference work, or, we could choose one reference work and then one novel.   P(one novel and one reference work) = 4/13*5/12 + 5/13*4/12 = 10/39   The answer is 10/39.
Answer: D
The standard deviation of a normal distribution of data is 2, and 3 standard deviations below the mean is greater than 48. What is a possible value for the mean of the distribution? Choose the correct choice from the following answers.
A) 46  B) 47  C) 48  D) 55  E) 50

Solution: The standard deviation ({SD}) = 2;   3 standard deviations below the mean is greater than 48:   {Mean} - 3*{SD} > 48;   {Mean} - 6 > 48;   {Mean} > 54.   Answer: 55.
Answer: D
Magnabulk Corp sells boxes holding n magnets each. The boxes are shipped in crates, each holding b boxes. What is the price charged per magnet, in cents, if Magnabulk charges m dollars for each crate?
Options
A) 100bn/m	B) 100m/(bn)	C) bn/(100m)	D) m/(bn)	E) bn/m

Solution: crate has = bn magnates   C crate cost = m dollars = 100 m cents   each magnate cost for each crate = 100 m / bn   Ans; 100m/(bn)
Answer: B
What is the length of a bridge (in meters), which a train 148 meters long and travelling at 45 km/h can cross in 30 seconds? Select the correct option.
A) 211
B) 219
C) 227
D) 235
E) 243

Solution: speed = 45 km/h = 45000 m / 3600 s = 25/2 m/s   In 30 seconds, the train can travel  25/2 * 30= 
 25/2 * 30 = 375
375 meters   375= length of train + length of bridge   length of bridge = 375 - 148= 
375 - 148 = 227
227 meters   The answer is 227.
Answer: C
How many seconds will a train 100 meters long take to cross a bridge 180 meters long if the speed of the train is 36 kmph? Choose the correct choice from the following answers
A) 26	B) 72	C) 28	D) 82	E) 27

Solution: Explanation:   D = 100 + 180= 
100 + 180 = 280
280   S= 36 * 5/18= 
36 * 5/18 = 10
10 mps   T= 280/10= 
280/10 = 28
28 sec   Answer: Option 28
Answer: C
Calculate how many men are needed to finish a specific task in 5 days if it will take 15 men to complete the same task in 10 days. ?	Choose the correct choice from the following options.
A) 13
B) 16
C) 35
D) 25
E) 15

Solution: men required to finish the work in 5 days = 5*15/5= 
5*15/5 = 15
15   Answer is 15
Answer: E
The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 9 years ago was 20 years. The present age of the husband is:  Choose one.
A) 20 years  B) 30 years  C) 60 years  D) 32 years  E) 35 years

Solution: D   32 years   Sum of the present ages of husband, wife and child = (27 x 3 + 3 x 3) years = 90 years.   Sum of the present ages of wife and child = (20 x 2 + 9 x 2) years = 58 years.   Husband's present age = (90 - 58)= 
(90 - 58) = 32
32 years.
Answer: D
Find the average of x and y if the average (arithmetic mean) of x, y, and 30 is 10 greater than the average of x, y, 20, and 30.
Choose the correct choice from the following choices:  A) 50  B) 75  C) 100  D) 125  E) 150

Solution: consider 30 is 10 greater than 20: 30 = 20+10   similarly   (x+y+30)/3 = (x+y+20+30)/4 + 10   get a like denominator on the right side   (x+y+30)/3 = (x+y+50)/4 + 40/4   (x+y+30)/3 = (x+y+50+40)/4   (x+y+30)/3 = (x+y+90)/4   cross multiply   4(x+y+30) = 3(x+y+90)   4x+4y+120 = 3x+3y+270   collect like terms   4x-3x + 4y-3y = 270 - 120   x + y = 150   thus (x+y)/2 = 150/2   (x+y)/2 = 75   the average of x and y is 75   75
Answer: B
Insert the missing number
6, 7, 9, 13, 21, ... Select the correct option.
A) 25  B) 29  C) 37  D) 32  E) 30

Solution: Difference between two numbers in the series is multiplied by 2 to get the next number   6,7 ...Difference is 1   7,9 Difference is 2   9,13 difference is 4   13,21 Difference is 8   21, 37 Difference is 16   ANSWER:37
Answer: C
M = {9.4, 9.9, 9.9, 9.9, 10.0, 10.2, 10.2, 10.5}
The mean and standard deviation of the 8 numbers in M are 10.0 and 0.3 respectively. What percent of the 8 numbers are within 1 standard deviation of the mean?	Choose the most appropriate option
A) 70%	B) 75%	C) 80%	D) 85%	E) 90%

Solution: If mean of the 8 numbers in M is 10.0 & standard deviation 0.3,   the number that lie within the 1st standard deviation (M - SD to M + SD)   range from 9.7 to 10.3 (both inclusive)   The numbers in this set in that range are 6/8 or 75%   Ans : (Option 75%)
Answer: B
The total circumference of two circles is 88. If the first circle has a circumference that is exactly twice the circumference of the second circle, then what is the approximate sum of their two radii?	Pick one:
A) 5.7  B) 6.0  C) 6.7  D) 9.7  E) 14.0

Solution: Let r= Radius of smaller circle. Let R = Radius of larger circle   Therefore:   2πr + 2πR = 88   where 2r = R   Thus:   2πr + 4πr = 88   6πr = 88   r = approx 4.7   πR + 2Rπ = 88   3πR = 88   R = approx 9.3   r + R = approx 14.0   Answer : 14.0
Answer: E
A and B invests Rs.10000 each, A investing for 8 months and B investing for all the 12 months in the year. If the total profit at the end of the year is Rs.25000, find their shares? Choose the correct choice from the following:
A) Rs.8000, Rs.17000  B) Rs.9000, Rs.16000  C) Rs.18000, Rs.7000  D) Rs.10000, Rs.15000  E) Rs.20000, Rs.15000

Solution: The ratio of their profits A:B = 8:12 = 2:3   Share of A in the total profit = 2/5 * 25000 = Rs.10000 Share of A in the total profit = 3/5 * 25000 = Rs.15000   ANSWER:Rs.10000, Rs.15000
Answer: D
A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 2000. The difference between the profit shares of A and C is?	Choose the correct answer.
A) 621  B) 276  C) 236  D) 800  E) 211

Solution: Explanation:   Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6   And also given that, profit share of B is Rs. 2000   => 5 parts out of 15 parts is Rs. 2000   Now, required difference is 6 - 4= 
6 - 4 = 2
2 parts   Required difference= 2/5 (2000) = Rs. 800   Answer: 800
Answer: D
How many four digit even numbers can be formed using the digits {2, 3, 5, 1, 7, 9}	Choose the correct choice from the following choices:
A) 65
B) 77
C) 32
D) 32
E) 60

Solution: The given digits are 1, 2, 3, 5, 7, 9   A number is even when its units digit is even. Of the given digits, two is the only even digit.   Units place is filled with only '2' and the remaining three places can be filled in ⁵P₃ ways.   Number of even numbers = 5P3 = 60.   Answer:60
Answer: E
What is the length of the longest pole which can be kept in a room 9 m long, 4 m broad and 3 m high?	Choose the correct answer.
A) 10.29  B) 9  C) 11  D) 13  E) None

Solution: Explanation:   d2 = 92 + 42 + 32 = 10.29   10.29)
Answer: A
A retailer sells 7 shirts. The first 2 he sells for $38 and $42. If the retailer wishes to sell the 7 shirts for an overall average price of over $50, what must be the minimum average price of the remaining 5 shirts?
Select:  A) $54.00  B) $57.00  C) $58.00  D) $60.50  E) $63.00

Solution: First 2 shirts are sold for $38 and $42=$80.   To get average price of $50,total sale should be 7*$50=$350   So remaining 5 shirts to be sold for $350-$807* 50= 
7* 50 = 350
$350   So remaining 5 shirts to be sold for $350-$80=$270   $54.00nswer should be 270/5350- 80= 
350- 80 = 270
$270   $54.00nswer should be  270/5= 
 270/5 = 54
$54.00 that is $54.00
Answer: A
What is the product of all the prime factors of 15? Pick.
A) 12 B) 3 C) 4 D) 15 E) 20

Solution: factors : 3,5   3*5= 
3*5 = 15
15   Answer : 15
Answer: D
Each digit 1 through 5 is used exactly once to create a 5-digit integer. If the 1 and the 2 cannot be adjacent digits in the integer, how many 5-digit integers are possible?
Select the correct option:
A) 72  B) 66  C) 76  D) 78  E) 90

Solution: Number of arrangements using 5 distinct digits = 5!   Number of arrangements in which 1 and 2 are adjacent - consider 1 and 2 together as one group. Now you have 4 numbers/groups to arrange which can be done in 4! ways. In each of these arrangements, 1 and 2 can be arranged as 12 or 21.   Number of arrangements in which 3 and 4 are not adjacent = 5! - 2*4! = 72   72nswer : 72
Answer: A
Linda spent 3/4 of her savings on furniture and the rest on a TV. If the TV cost her $400, what were her original savings? Choices:
A) $1500 B) $1600 C) $1700 D) $1800 E) $1900

Solution: If Linda spent 3/4 of her savings on furnitute, the rest   4 / 4 - 3 / 4 = 1 / 4 on a TV   But the TV cost her $400. So 1 / 4 of her savings is $400. So her original savings are 4 times $400 = $1600   correct answer $1600
Answer: B
At what time between 3 and 4 o'clock the hands are in opposite direction?
Choose the most appropriate option.
A) 49 1/11 min past 3 B) 16 min past 3 C) 2 min past 4 D) 3 2/11 min past 3 E) 4 2/11 min past 3

Solution: at 3'0 clock the minutes hand will be 15 min away from hours hand   both hands are opposite when they are 30 minutes away from each other   so,min hand has to gain 45 mins   to gain 1 min minute hand 12/11minutes=45*12/11=49 1/11   ans:49 1/11   49 1/11 min past 3NSWER:49 1/11 min past 3
Answer: A
If the average of ten numbers is 40, then which of the following could be the standard deviation of the ten numbers?
I. 0
II. 10
III. 40 Choose one
A) I B) II C) all three options D) III E) I&II

Solution: We know that we have 10 numbers (and they could be ANY values - including negatives and non-integers) and we know that the average of those numbers is 10. This is meant to say that there are an INFINITE number of possible sets of 10 numbers that fit this prompt.   IF all ten numbers were the same (meaning that we had ten 10s), then the SD would be 0. The more 'spread out' those ten numbers get, the higher the SD becomes. Since there's no limit to the 'spread', then there's no limit to what the SD could be either. Thus, it could be 10 or 20 or any other number.   all three options
Answer: C
If all the sides of a right triangle increase in length by 30%, then by what percentage does the area of the triangle increase?	Choices
A) 69%	B) 81%	C) 85%	D) 96%	E) 120%

Solution: Let B be the base and H be the height of the original triangle.   The original area is (1/2)BH.   The area of the expanded triangle is (1/2)(1.3B)(1.3H) = (1.3)(1.3)(1/2)BH = 1.69(1/2)BH   The answer is 69%.
Answer: A
In a contest, a bowl contains 12 keys, only one of which will open a treasure chest. If a contestant selects the key that opens the treasure chest, she wins the contents of that chest. If Anna is allowed to draw two keys, simultaneously and at random, from the bowl as the first contestant, what is the probability that she wins the prize?	Choose the correct option:
A) 1/11 B) 1/12 C) 1/6 D) 11/120 E) 2/11

Solution: P(not winning) = 11/12*10/11 = 5/6   P(winning) = 1 - 5/6 = 1/6   The answer is 1/6.
Answer: C
One-fifth of the cost price, one-seventh of the marked price and one-sixth of the selling price are all equal. What is the gain or loss to the trader?	Options.
A) 120 %
B) 140 %
C) 162/3 %
D) 20 %
E) None

Solution: Sol.   CP/5 = SP/6 ⇒ SP/CP = 1.2 ⇒ 20% gain.   Answer 20 %
Answer: D
For every $20 that a billionaire spends, a millionaire spends the equivalent of 10 cents. For every $4 that a millionaire spends, a yuppie spends the equivalent of $1. The ratio of money spent by a yuppie, millionaire, and billionaire can be expressed as	Choose the correct choice from the following options:
A) 1 : 2 : 400 B) 1 : 4 : 100 C) 20 : 4 : 1 D) 100 : 4 : 1 E) 400 : 4 : 1

Solution: B.........M........Y   20.....0,10......Y   B.........4........1   What I did first was to turn 0.20 to 2 (by multiplying by 10), so that it is easy to find the LCM. This led me to this:   B.........M........Y   200.....1.........Y   B........20......10   Then I multiplied every row by 20 (the LCM of 1 and 40), which led me to this:   B.........M........Y   4000...20.......10   Then I got rid of the extra zero, and in the correct order this is Y:M:B=1:2:40   1 : 2 : 400NS 1 : 2 : 400
Answer: A
P and Q started a business with respective investments of Rs. 4 lakhs and Rs. 10 lakhs. As P runs the business, his salary is Rs. 5000 per month. If they earned a profit of Rs. 2 lakhs at the end of the year, then find the ratio of their earnings?	Choose the most appropriate option:
A) 2:1	B) 1:8	C) 8:1	D) 1:1	E) 1:5

Solution: Ratio of investments of P and Q is 2 : 5   Total salary claimed by P = 12 * 5000 = Rs. 60000   Total profit = Rs. 2 lakhs.   Profit is to be shared = Rs. 140000   Share of P = (2/7) * 140000 = Rs. 400000   Share of Q = Rs. 100000   Total earnings of P = (60000 + 40000) = Rs. 100000   Ratio of their earnings = 1 : 1   Answer: 1:1
Answer: D
A group of tourists wants to visit only an even number of the four cities A, B, C, and D. How many travel itineraries can they make? All cities are connected to one another and please note that visiting the same cities in a different order counts as a different itinerary.
Choose the most appropriate option:
A) 20 B) 24 C) 28 D) 32 E) 36

Solution: The number of ways to choose two cities is 4C2=6.   The number of itineraries for each pair of 2 cities is 2!.   So the number of itineraries to two cities is  6*2= 
 6*2 = 12
12.   The number of ways to choose four cities is 4C4=1.   The number of itineraries for the group of 4 cities is 4!.   So the number of itineraries to four cities is 4!=24.   The total number of itineraries is   12+24= 
  12+24 = 36
36.   The answer is 36.
Answer: E
In a kilometer race, A beats B by 50 meters or 10 seconds. What time does A take to complete the race?	Choose the most appropriate option.
A) 190 sec
B) 120 sec
C) 130 sec
D) 210 sec
E) 220 sec

Solution: A   190 sec   Time taken by B run 1000 meters = (1000 * 10)/50= 
(1000 * 10)/50 = 200
200 sec.   Time taken by 190 sec= 200 - 10= 
200 - 10 = 190
190 sec.
Answer: A
A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent?	Choose the correct choice from the following options: A) 28% B) 20% C) 29% D) 27% E) 10%

Solution: 900 ---- 180   100 ---- ? => 20%   Answer:20%
Answer: B
A certain university will select 1 of 4 candidates eligible to fill a position in the mathematics department and 2 of 7 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions? Choose the correct choice from the following:
A) 81  B) 82  C) 84  D) 86  E) 88

Solution: 1844*2847 = 4*21= 
4*21 = 84
84   the answer is (84)
Answer: C
Two pipes A and B can fill a cistern in 37 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the B is turned off after:  Choose the correct option:
A) 9
B) 7
C) 6
D) 5
E) 4

Solution: Let B be turned off after x minutes. Then, Part filled by (A + B) in x min. + Part filled by A in (30 -x) min. = 1. x(2/75 + 1/45) + (30 - x). 2/75 = 1 11x/225 + (60 - 2x)/75 = 1 11x + 180 - 6x = 225. x = 9.   9nswer:9
Answer: A
If e is an even integer and q is an odd integer, which of the following must be an odd integer?	Choose the correct choice from the following options: A) e/q B) eq C) 2e+q D) 2(e+q) E) 3e/q

Solution: this is a must question:   A. e/q   can be a non-integer   B. eq   always even   C. 2e+q   e = even -> even+odd = odd   D. 2(e+q)   always even - e+q = odd *2 -> even   E. e/q   might be a non integer.   2e+q
Answer: C
Of the 90 people in a room, 2/5 are women. If 2/3 of the people are married, what is the maximum number of women in the room who could be unmarried? Choose the correct choice from the following answers:	A) 26	B) 30	C) 32	D) 34	E) 36

Solution: women = 2/5 * 90= 
2/5 * 90 = 36
36   married= 2/3 * 90= 
2/3 * 90 = 60
60   unmarried= 30   max(un-married women) = 30   30
Answer: B
Matt buys a roses for his wife for rs.64.99 and then they get into a fight, so he decides to sell them for rs.74.99. Find his gain %.	Choose the correct choice.
A) 17.92%	B) 12.46%	C) 2%	D) 15.39%	E) 16.88%

Solution: sol. cp=rs64.99, sp=rs 74.99   gain=rs(74.99 –64.99)=rs10.00   so gain%={(10.00/64.99)*100}=15.39%   Answer is 15.39%.
Answer: D
How many five-digit numbers are there, if the two leftmost digits are even, the other digits are odd and the digit 8 cannot appear more than once in the number.	Pick one
A) 2200
B) 2290
C) 2280
D) 2300
E) 2375

Solution: N=(4*5-1)*5*5*5= 
(4*5-1)*5*5*5 = 2_375
2375   where   4 cases of first digit {2,4,6,8}   5 cases of second digit {0,2,4,6,8}   1 case of 88 for two leftmost digit   5 cases of third digit {1,3,5,7,9}   5 cases of fourth digit {1,3,5,7,9}   5 cases of fifth digit {1,3,5,7,9}   2375
Answer: E
In a graduating class of 232 students, 144 took geometry and 119 took biology. What is the difference between the greatest possible number I and the smallest possible number of students that could have taken both geometry and biology? Choose the correct choice
A) 144  B) 119  C) 113  D) 88  E) 31

Solution: OFFICIAL SOLUTION:   First of all, notice that since 144 took geometry and 119 took biology, then the number of students who took both geometry and biology cannot be greater than 119.   {Total} = {geometry} + {biology} - {both} + {neither};   232 = 144 + 119 - {both} + {neither};   {both} = 31 + {neither}.   {both} is minimized when {neither} is 0. In this case {both} = 31.   The greatest possible number I of students that could have taken both geometry and biology, is 119.   Thus, the answer is 119 - 31= 
119 - 31 = 88
88.   Answer: 88.
Answer: D
Dhoni is 25 years older than his daughter Mary. In 10 years Ross will be twice as old as Mary. What is Mary current age.	Choose the correct choice from the following choices.
A) 14 B) 16 C) 17 D) 18 E) 15

Solution: Now: Mary = x, Dhoni =x+25   In 10 years Mary = x+10, Dhoni= x+25+10 or 2(x+10)   x+25+10 = 2(x+10)   x+35=2x+20   35-20=2x-x   15=x   Mary is 15 years old   Answer : 15
Answer: E
The mean of 50 observations was 36. It was found later that an observation 90 was wrongly taken as 23. The corrected new mean is?
Choose one.
A) 37.3 B) 36.1 C) 36.5 D) 36.9 E) 36.3

Solution: Correct sum   = (36 * 50 + 90 - 23)= 
(36 * 50 + 90 - 23) = 1_867
1867.   Correct mean= 1825/50   = 37.3   37.3nswer:37.3
Answer: A
80 white and black tiles will be used to form a 10x10 square pattern. If there must be at least one black tile in every row and at least one white tile in every column, what is the maximum difference between the number of black and white tiles that can be used? Choose the correct choice: A) 75 B) 80 C) 85 D) 90 E) 60

Solution: Answer = 60   Please refer diagram below     70 - 10= 
  70 - 10 = 60
60
Answer: E
An object thrown directly upward is at a height of h feet after t seconds, where h = -14 (t-3)^2 + 140. At what height, in feet, is the object 2 seconds after it reaches its maximum height?	Choose the correct choice from the following options
A) 62
B) 68
C) 76
D) 84
E) 96

Solution: We see that h will be a maximum h=140 when t-3=0, that is when t=3.   At t=5, h = -14(5-3)^2 + 140 = -14(4) + 140 = 84   The answer is 84.
Answer: D
A policeman noticed a criminal from a distance of 180 km. The criminal starts running and the policeman chases him. The criminal and the policeman run at the rate of 8 km and 10 km per hour respectively. What is the distance between them after 3 minutes ?	Select the correct option:	A) 100 m	B) 80 m	C) 130 m	D) 150 m	E) None of these

Solution: Explanation :   Solution: Relative speed = (10 - 8)= 
(10 - 8) = 2
2 km/hr.   Distance covered in 3 minutes= (2 * 3/60) km = 1/10 km = 100 m.   .'. Distance between the criminal and policeman = (180 - 100)= 
(180 - 100) = 80
80 m.   Answer : 80 m
Answer: B
A transport company’s 120 buses running 20 hrs a day consume 360 of fuel in a day. In the next 3 days, the company will invest in 30 more green buses that use 30% less fuel. How many lts of fuel will be consumed in a five day week after the new buses are added to the fleet?	Choose the correct answer
A) 3,060
B) 1, 512
C) 1,800
D) 1,260
E) 3,312

Solution: old buses use 360* 5 days = 1,800 lts   New buses use (0.70* 360)/120* 5 days * 30 buses = 1,512 lts   Total fuel is 3,312 lts   Answer is 3,312
Answer: E
Evaluate 28% of 450 + 45% of 280  Pick one: A) 232 B) 242 C) 252 D) 262 E) 272

Solution: Explanation:   = (28/100) * 450 + (45/100) * 280   = 126 + 126= 
126 + 126 = 252
252   Option 252
Answer: C
If the mean of a, b, c is M and ab + bc + ca = 0, then the mean of a2, b2, c2 is:
Choose the most appropriate option.
A) M2  B) 3M2  C) 6M2  D) 9M2  E) None of these

Solution: Explanation :   We have : (a + b + c)/3 = M or (a + b + c) = 3M.   Now, (a + b + c)*(a + b + c) = (3M)^2 = 9M^2   a2 + b2 + c2 + 2 (ab + bc + ca) = 9M^2   a2 + b2 + c2 = 9M^2   Required mean = (a2 + b2 + c2)/3 = 9M^2/3 = 3M2   Answer : 3M2
Answer: B
Two boats are heading towards each other at constant speeds of 5 miles/hr and 25 miles/hr respectively. They begin at a distance 20 miles from each other. How far are they (in miles) one minute before they collide ?
Select the correct option
A) 1/12 B) 5/12 C) 1/6 D) 1/2 E) 1/5

Solution: The question asks: how far apart will they be 1 minute=1/60 hours before they collide?   Since the combined rate of the boats is  5+25= 
 5+25 = 30
30 mph then 1/60 hours before they collide they'll be rate*time=distance --> 30*1/60=1/2 miles apart.   Answer: 1/2.
Answer: D
The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 35 kg. What is the weight of the new person?	Options:
A) 75  B) 65  C) 55  D) 95  E) 80

Solution: Total increase in weight = 8 × 2.5 = 20   If x is the weight of the new person, total increase in weight = x−35   => 20 = x - 35   => x = 20 + 35= 
20 + 35 = 55
55   Answer is 55.
Answer: C
The number of arrangements that can be made with the letters of the word MAETHS so that the word starts with M and ends with S Select the correct option:
A) A)2!	B) B)3!	C) C)4!	D) D)6!	E) E)7!

Solution: M _ _ _ _ S   the remaining 4 places can be filled by 4!   4!
Answer: C