MU-NLPC/Calc-aqua_rat huggingface dataset:
15 lts are taken of from a container full of liquid A and replaced with Liquid B. Again 15 more lts of the mixture is taken and replaced with liquid B. After this process, if the container contains Liquid A and B in the ratio 9:16,What is the capacity of the container S?  Choose the correct option
A) A:45	B) B:25	C) C:37.5	D) D:36	E) E:42

Solution: If you have a 37.5 liter capacity, you start with 37.5 L of A and 0 L of B.   1st Replacement   After the first replacement you have 37.5-15= 
37.5-15 = 22.5
22.5 L of A and 15 L of B. The key is figuring out how many liters of A and B, respectively, are contained in the next 15 liters of mixture to be removed.   The current ratio of A to total mixture is 22.5/37.5; expressed as a fraction this becomes (45/2) / (75/2), or 45/2 * 2/75. Canceling the 2s and factoring out a 5 leaves the ratio as 9/15. Note, no need to reduce further as we're trying to figure out the amount of A and B in 15 L of solution. 9/15 of A means there must be 6/15 of B.   Multiply each respective ratio by 15 to get 9 L of A and 6 L of B in the next 15L removal.   Final Replacement   The next 15L removal means 9 liters of A and 6 liters of B are removed and replaced with 15 liters of B. 22.5-9=13.5 liters of A. 15 liters of B - 6 liters + 15 more liters = 24 liters of B.   Test to the see if the final ratio = 9/16; 13.5/24 = (27/2) * (1/24) = 9/16. C:37.5hoice C:37.5 is correct.
Answer: C
When 1/20% of 4,000 is subtracted from 1/10 of 4,000, the difference is
Select the correct option.
A) 50  B) 200  C) 380  D) 398  E) 400

Solution: (1/10)*4000 - (1/20*100)*4000   =400 - 2= 
400 - 2 = 398
398   Answer 398
Answer: D
Which of the following are/is prime?
I. 143
II. 147
III. 157 Pick one.
A) II only  B) III only  C) III  D) IIII  E) I, II,III

Solution: 1) 143 = 13*11 so we know it is not prime quickly eliminate all options having 1 as a choice   which leaves us with 2 ) and 3) as possible answers   From here on we find 147 = 3* 49 so we eliminate 147 which leaves us with 149 as the only possible solution   IIII
Answer: D
A committee of 5 is to be selected from among 3 boys and 6 girls. I how many ways can this be done if the committee is to consist of at-least one Girl?
what is the answer choice and how?
Pick one
A) 105 B) 225 C) 230 D) 350 E) 55

Solution: I'm sure there is some problem with the question.   R U sure its atleast one boy and not atleast 1 boy and 1 girl?   if its 1 boy and 1 girl   3C1*5C4 + 3C2*5C3 + 3C3*5C2   3*5 + 3*10 + 1*10   15 + 30 + 10   55   55
Answer: E
If the number 90x8 is divisible by 8,then what will be the value of x?  Choose the correct choice from the following answers.
A) 0 B) 4 C) A and B D) None E) 1

Solution: If Last three number are divisible by 8,then the number is divisible by 8.   So,X is replaced by either 0 or 4   Answer is A and b   Option A and B
Answer: C
A boy has nine trousers and 12 shirts. In how many different ways can he select a trouser and a shirt?  Choose the correct choice from the following options.
A) 277  B) 2678  C) 287  D) 108  E) 277

Solution: The boy can select one trouser in nine ways.   The boy can select one shirt in 12 ways.   The number of ways in which he can select one trouser and one shirt is   9 * 12= 
  9 * 12 = 108
108 ways.   Answer: 108
Answer: D
If Jake loses 20 pounds, he will weigh twice as much as his sister. Together they now weigh 224 pounds. What is Jake’s present weight, in pounds? Choose the correct choice: A) 131 B) 135 C) 156 D) 177 E) 188

Solution: Lets say J is the weight of Jack and S is the wt of his sister.   If he loses 20 pounds, he s twice as heavy as his sister.   J-20=2*S   Also, together they weight 224 pounds   J+S=224   solvong the 2 equation ,we get J=156 pounds !   156
Answer: C
An gun can take a maximum of four shots at an enemy plane moving away from it. The probability of hitting the plane at the 1st, 2nd, third & 4th shots are 1.4, 1.3, 1.2 & 1.1 respectively. What is the probability that the plane is hit when all the four shots are fired?
Choices
A) 0.6976  B) 0.7543  C) 0.8753  D) 0.9864  E) 1.2245

Solution: Required probability:   =(0.4×0.7×0.8×0.9)+(0.6×0.3×0.8×0.9)+(0.6×0.7×0.2×0.9)+(0.6×0.7×0.8×0.1)+(0.4×0.3×0.8×0.9)+(0.4×0.7×0.2×0.9)+(0.4×0.7×0.8×0.1)+(0.6×0.3×0.2×0.9)+(0.6×0.3×0.8×0.1)+(0.6×0.7×0.2×0.1)+(0.4×0.3×0.2×0.9)+(0.6×0.3×0.2×0.1)+(0.4×0.3×0.8×0.1)+(0.4×0.7×0.2×0.1)+(0.4×0.3×0.2×0.1)=(0.4×0.7×0.8×0.9)+(0.6×0.3×0.8×0.9)+(0.6×0.7×0.2×0.9)+(0.6×0.7×0.8×0.1)+(0.4×0.3×0.8×0.9)+(0.4×0.7×0.2×0.9)+(0.4×0.7×0.8×0.1)+(0.6×0.3×0.2×0.9)+(0.6×0.3×0.8×0.1)+(0.6×0.7×0.2×0.1)+(0.4×0.3×0.2×0.9)+(0.6×0.3×0.2×0.1)+(0.4×0.3×0.8×0.1)+(0.4×0.7×0.2×0.1)+(0.4×0.3×0.2×0.1)   =0.2016+0.1296+0.756+0.336+0.864+0.504+0.224+0.324+0.144+0.0084+0.0216+0.0036+0.0096+0.0056+0.002=0.2016+0.1296+0.756+0.336+0.864+0.504+0.224+0.324+0.144+0.0084+0.0216+0.0036+0.0096+0.0056+0.002   =0.6976=0.6976   Edit: Thank you Vaibhav for providing an alternative method.   0.6976lternate Method:   probability that the plane is hit when all the four shots are fired,   P=1−probability of not hitting the targetP=1−probability of not hitting the target   =1−(0.6×0.7×0.8×0.9)=1−(0.6×0.7×0.8×0.9)   =1−0.3024=1−0.3024   =0.6976   0.6976
Answer: A
Calculate the circumference of a circular field whose radius is 5 centimeters.	Choose the correct choice from the following options: A) 30 π cm B) 80 π cm C) 70 π cm D) 50 π cm E) 10 π cm

Solution: Circumference C is given by   C = 2πr = 2π*5 = 10 π cm   correct answer 10 π cm2 *5= 
2 *5 = 10
10 π cm   correct answer 10 π cm
Answer: E
A bullet train 160 m long is running with a speed of 70 kmph. In what time will it pass a man who is running at 8 kmph in the direction opposite to that in which the bullet train is going?	Options:	A) 23 sec	B) 15 sec	C) 7.38 sec	D) 6.92 sec	E) 16 sec

Solution: C   7.38 sec   Speed of the bullet train relative to man = (70 + 8)= 
(70 + 8) = 78
78*5/18 m/sec= 65/3 m/sec.   Time taken by the bullet train to cross the man = Time taken by it to cover 160 m at (65/3) m / sec   = (160 *3/65) sec = 7.38 sec
Answer: C
A factory produces 3400 toys per week. If the workers at this factory work 5 days a week and if these workers make the same number of toys everyday, how many toys are produced each day?
Answers: A) 575 toys B) 375 toys C) 680 toys D) 475 toys E) 675 toys

Solution: To find the number of toys produced every day, we divide the total number of toys produced in one week (of 5 days) by 5.   3400 / 5= 
3400 / 5 = 680
680 toys   correct answer 680 toys
Answer: C
If the price of an article went up by 30%, then by what percent should it be brought down to bring it back to its original price? Pick one: A) 25% B) 23 1/13% C) 16 7/3% D) 16 6/3% E) 16 2/3%

Solution: Let the price of the article be Rs. 100.   30% of 100 = 30.   New price   = 100 + 30 = Rs. 130   Required percentage   = (130 - 100)/130 * 100   = 30/130 * 100   = 23 1/13%   Answer:23 1/13%
Answer: B
ASvennumber is defined as a five-digit number which goes according to the following rules: the leftmost digit is even, any digit to the right of an even digit must be an odd digit, and any digit to the right of an odd digit can only be one of the digits 1 or 8. How many different 5-digit numbers areSvennumbers?	Select the correct option.
A) 20
B) 80
C) 160
D) 220
E) 250

Solution: ASvennumber is defined as a five-digit number which goes according to the following rules: the leftmost digit is even, any digit to the right of an even digit must be an odd digit, and any digit to the right of an odd digit can only be one of the digits 1 or 7. How many different 5-digit numbers areSvennumbers?   4/9*5/10*2/10*2/10*2/10=160/9000   D. 220
Answer: D
5^20+5^7/7=? Reminder is…………	Choices:
A) 1  B) 2  C) 3  D) 4  E) 5

Solution: 5^20 mod 7 + 5^7 mod 7   Since 5 nd 7 are co-primes, we can use Euler's theorem   E(7) = 6   So 5^E(7) = 1   5^20 mod 7 => (5^6)^3 * 5^2 mod 7   1 * 25 mod 7 = 4   Similarly 5^7 mod 7 => 5^6 * 5 mod 7   1 * 5 mod 7 = 5   Now 4 + 5 mod 7   9 mod 7 = 2   ANSWER:2
Answer: B
A barrel contains 12 oranges, 8 grapefruit, and 5 apples for a total of 25 pieces of fruit. As a game, several friends took turns randomly extracting a single piece of fruit from the barrel blindfolded. If the extracted piece of fruit was not an apple, it was returned to the bin. This process was repeated until an apple was drawn. What is the probability that an apple will be extracted on the third extraction or later? Select the correct option: A) 5/25 B) 8/25 C) 12/25 D) 16/25 E) 4/5

Solution: Favorable case = an apple is picked in the third extraction or later.   Unfavorable case = an apple is picked in either the first or second extraction.   Probability = Favorable outcomes / Total out comes   Also probability = 1-(Unfavorable outcomes / Total out comes)   Unfavorable case 1: probability of apple picked in first extraction = 5/25   Unfavorable case 2: probability of apple picked in second extraction (i.e., 2nd extraction not an apple)= (20/25)*(5/25) =(4/5)*(1/5)= 4/25   Total Unfavorable Probability = (5/25)+(4/25) = 9/25   i.e., Favorable Probability = 1 - (9/25) = 16/25   Answer Option: 16/25
Answer: D
Walking 7/6 of his usual rate, a boy reaches his school 7 min early. Find his usual time to reach the school? Choose the correct choice from the following choices
A) 22  B) 28  C) 99  D) 49  E) 66

Solution: Speed Ratio = 1:7/6 = 6:7   Time Ratio = 7:6   1 -------- 7   7--------- ? 49 m   Answer:49
Answer: D
A group of 55 adults and 70 children go for trekking. If there is meal for either 70 adults or 90 children and if 42 adults have their meal, find the total number of children that can be catered with the remaining food.  Choose the correct choice from the following answers:
A) 33	B) 54	C) 36	D) 17	E) 01

Solution: Explanation:   As there is meal for 70 adults and 42 have their meal, the meal left can be catered to 28 adults.   Now, 70 adults = 90 children   7 adults = 9 children   Therefore, 28 adults = 36 children   Hence, the meal can be catered to 36 children.   ANSWER: 36
Answer: C
Four machines, each working at the same constant rate, together can complete a certain job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the Job in 8 days?
Pick:  A) 2  B) 3  C) 4  D) 6  E) 8

Solution: Another solution which is faster is Since each machine works at a constant rate. The time needs to bought down from 12 to 8. So the new time is 2/3 of the original time. Thus to achieve this we need the rate to be 3/2 of original.   So 3/2* 4= 
3/2* 4 = 6
6   So we need   6-4= 
  6-4 = 2
2 more machines.   2nswer : 2
Answer: A
Speed of a man with current measures 15 km/hr. Speed of current is 2.5 km/hr. What is the speed of man against the current?	Pick one
A) 20 kmph	B) 18 kmph	C) 10 kmph	D) 16 kmph	E) 13 kmph

Solution: Explanation:   Let the speed of man in still water be x km/hr   Now, speed with current=15 km/hr   Speed of current: 2.5 km/hr   Speed of man with current: Speed of man in still water+Speed of current   =>15=x+2.5   =>x=12.5   Speed of man against the current: Speed of man in still water-Speed of current   =>12.5-2.5= 
12.5-2.5 = 10
>10 km/hr   ANSWER:10 kmph
Answer: C
A man walks at a speed of 3 km/hr and runs at a speed of 7 km/hr. How much time will the man require to cover a distance of 10 1/2 km, if he completes half of the distance, i.e., (5 1/4) km on foot and the other half by running?  Pick one
A) 3 1/2 hours B) 4 1/3 hours C) 6 1/3 hours D) 9 3/5 hours E) 2 1/2 hours

Solution: Required time   = (5 1/4)/3 + (5 1/4)/7   = 2 1/2 hours.   Answer:2 1/2 hours
Answer: E
What is the remainder when 49^74 - 5^74 is divided by 24?	Choose the correct choice from the following answers
A) 2  B) 1  C) 0  D) 3  E) None of these

Solution: easiest way for me: 49^74 - 5^74 = (49)^37-25^37 = (24*2+1)^37 - (24+1)^37 -> remainder is 1^37 - 1^37 = 0   Ans : 0
Answer: C
For an employee to qualify for early retirement at a certain company, the sum of the employee’s age and years of service must be at least 72, If Sue was K years old when she was hired by the company, what is the minimum age at which she could possibly qualify for early retirement.	Answers:
A) K+36  B) 2K+36  C) (72+K)/2  D) (72-K)/2  E) 2(72-K)

Solution: Let y be the years of service at the company.   After y years of service, Sue's age will be K + y.   Sue can retire when (K+y) + y = 72   y = (72 - K)/2   Then Sue's age will be K + y = K + (72 - K)/2 = (72+K) / 2   The answer is (72+K)/2.
Answer: C
Reduce
368/575
to the lowest terms  Choose one:
A) 30/25  B) 16/25  C) 28/29  D) 28/19  E) None of these

Solution: Explanation:   We can do it easily by in two steps   Step1: We get the HCF of 368 and 575 which is 23   Step2: Divide both by 23, we will get the answer 16/25   Answer: Option 16/25
Answer: B
If the area of a square with sides of length 8 centimeters is equal to the area of a rectangle with a width of 4 centimeters, what is the length of the rectangle, in centimeters?
Select the correct option.
A) 4  B) 8  C) 12  D) 16  E) 18

Solution: Let length of rectangle = L   8^2 = L*4   => L = 64/4= 
64/4 = 16
16   Answer 16
Answer: D
When two coins are tossed, Find the probability of getting all tails?	Choose the most appropriate option:
A) 1/3	B) 3/4	C) 1/8	D) 3/8	E) P(E) =1/4

Solution: When two coins are tossed,   S = {HH, HT, TH, TT} where H = Head and T = Tail   Let P( =1/4 = event of getting all tails   Then P( =1/4 = {TT}   so, P(P( =1/4) = n(P( =1/4)/n(S) =1/4
Answer: E
The fourth proportional to 5, 8, 15 is:	Choices:  A) 20  B) 22  C) 24  D) 21  E) 23

Solution: Let the fourth proportional to 5, 8, 15 be x.   Then, 5 : 8 : 15 : x   = 5x = (8 x 15)   x = (8 x 15)/5= 24.   Answer is 24.
Answer: C
A committee of three people is to be chosen from four teams of two. What is the number of different committees that can be chosen if no two people from the same team can be selected for the committee?
Choose the correct choice from the following answers.
A) 20
B) 22
C) 26
D) 30
E) 32

Solution: the amount of combinations of 3 person teams from a pool of 8. C(3/8) = 8!/5!*3! = 56 ways   Next I find the number of ways we CAN make a 3 person team using two from the same group, so   We take 2 people from a 2 person group C(2/2) and mutiply that by taking any 1 person from the remaining 6 C(1/6)   C(2/2)*C(1/6) = 6   This is the number of combinations by taking both parties from pair A. As we have a four pairs we must multiply this by 4 (4x6 = 24)   So there are 24 ways in which two people from the same pair can work together.   Finally we subtract this from the total number of combinations to find the number of groups where pairs do NOT work together....   56 - 24= 
56 - 24 = 32
32!   ANSW32R:32
Answer: E
How many words can be formed by using all letters of the word 'SCOUNDREL' ? Choose the correct choice from the following answers
A) 192870  B) 324880  C) 462880  D) 362880  E) 123880

Solution: The word SCOUN362880REL contains 9 different letters   Required number of words = 9P9 = 9! = 5*4*3*2*1= 
5*4*3*2*1 = 120
120   Answer is 362880
Answer: D
A train running at the speed of 70 km/hr crosses a pole in 36 seconds. What is the length of the train?	Choices:	A) 700	B) 770	C) 707	D) 710	E) 720

Solution: Speed=(70 * 5/18) m/sec = (175/9) m/sec Length of the train = (Speed x Time) = (175/9 * 36)= 
(175/9 * 36) = 700
700 m.   700nswer: 700
Answer: A
Jim is twice as old as Stephanie, who, four years ago, was three times as old as Kate. If, five years from now, the sum Q of their ages will be 51, how old is Stephanie ?	Answers:
A) 6 B) 10 C) 14 D) 20 E) 24

Solution: 1) take C (14y.o.), so mean that S=14, J=28, their sum itself is 42+10 years from now is 52, it is over the 51,   so eliminate C,D,E   2) take B (10y.o.), Q=meaning S=10,J=20, so  20+10+10= 
 20+10+10 = 40
40 and for K=10-4/3=2+9= 
2+9 = 11
11, finally 40+11= 
40+11 = 51
51. It is correct   10
Answer: B
If t is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of t ?	Choose the correct choice from the following options.
A) 10 B) 12 C) 14 D) 16 E) 18

Solution: Answer is C.   numbers in format of 3^k in the series from 1 to 30 inclusive t are: 3*1, 3*2, 3*3, 3*4, 3*5, 3*3*2, 3*7, 3*8, 3*3*3, 3*10. Total number of 3 = 13. So k=14.
Answer: C
On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $0.90 per glass on the first day, what was the price per glass on the second day?  Choose the correct choice from the following choices:
A) $0.15 B) $0.20 C) $0.30 D) $0.40 E) $0.6

Solution: On the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade;   On the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade;   So, the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3. Naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3.   We are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day.   Say the price of the glass of the orangeade on the second day was $x then 2*0.9=3*x --> x=$0.6.   Answer: $0.6.
Answer: E
In a single throw of a die, what is the probability of getting a number greater than 4? Choose one
A) 1/2  B) 1/3  C) 2/3  D) 1/4  E) None

Solution: Solution   When a die is thrown, we have S= {1,2,3,4,5,6}.   Let E = event of getting a number greater than 4= {5, 6}.   •P(E)= n(E) / n(S)   = 2/6   = 1/3.   Answer 1/3
Answer: B
A data set with a mean of 60 has a standard deviation of 4.5. Which of the following is the smallest number that falls within one standard deviation of the mean? Choose the correct answer:
A) 55
B) 56
C) 59
D) 63.5
E) 65

Solution: One standard deviation of the mean is from{mean}-{deviation}=60-4.5= 
60-4.5 = 55.5
55.5 to{mean}+{deviation}=60+4.5=64.5. The smallest number within this range from the options is 55.   Answer: A.   Hope this helps.
Answer: A
If a, b are the two roots of a quadratic equation such that a + b = 24 and a – b = 8, then the quadratic equation having a and b as its roots is :  Choose the correct choice from the following choices.
A) x2 + 2x + 8 = 0
B) x2 - 4x + 8 = 0
C) x2 - 24x + 128 = 0
D) 2x2 + 8x + 9 = 0
E) None of these

Solution: Sol.(c) a + b = 24 and a – b = 8   => a = 16 and b = 8 => ab = 16 × 8 = 128   A quadratic equation with roots a and b is   x2 - (a + b)x + ab = 0 or x2 - 24x + 128 = 0   Answer x2 - 24x + 128 = 0
Answer: C
A warehouse is labeling computer inventory with 4-digit codes. Each code is to consist of four digits between the numbers 0 and 7. The manager is debating whether to allow any 4-digit codes to have leading zero's before a non-zero number is used. If not allowed, then numbers like0025cannot be used.
The manager wants to measure the magnitude of the number of 4-digit code possibilities that are lost if he disallows the use of leading zero's. How many such codes would be lost?
Choose one:	A) 7000	B) 1000	C) 1011	D) 1101	E) 1110

Solution: The number of codes possible if leading zero is allowed = 10*10*10*10=10^4   The number of codes possible if leading zero is NOT allowed = 7*10*10*10=9*10^3   The difference = 10^4 - 7*10^3 = 10^3(10-7) = 7*10^3.   Answer: A.   Similar questions to practice:   Hope it helps.
Answer: A
A certain class of students is being divided into teams. The class can either be divided into 10 teams with an equal number of players on each team or 24 teams with an equal number of players on each team. What is the lowest possible number of students in the class?
Options.
A) 6
B) 36
C) 120
D) 60
E) 72

Solution: Let total no of students in the class be N   So, we are told that N is divisible by both 10 24   So, Lets find the least common multiple of 10 24 , ie 120   So our answer is (120) 120
Answer: C
A bag contains 12 white &18 black balls. 2balls are drawn in succession. What is the probability that first is white and second is black?	Select the correct option
A) 31/113 B) 36/145 C) 30/117 D) 31/213 E) 1/412

Solution: The probability that first ball is white:   =12C130C1=12C130C1   =1230=1230   =25=25   Since, the ball is not replaced; hence the number of balls left in bag is 29.   Hence, the probability the second ball is black:   =18C129C1=18C129C1   =1829=1829   Required probability,   =(25)×(1829)=(25)×(1829)   =36/145   36/145
Answer: B
The cost price of 13 articles is equal to the selling price of 11 articles. Find the profit percent?  Choices:	A) 18 2/19%	B) 18 2/11%	C) 18 2/91%	D) 18 2/81%	E) 18 2/121%

Solution: 13 CP = 11 SP   11 --- 2 CP   100 --- ? =>18 2/11%   Answer: 18 2/11%
Answer: B
The price of 5 kilograms of premium fertilizer is the same as the price of 16 kilograms of regular fertilizer. If the price of premium fertilizer is y cents per kilogram more than the price of regular fertilizer, what is the price, in cents, per kilogram of premium fertilizer?  Choose one
A) y/30  B) 5/6*y  C) 6/5*y  D) 5y  E) 16y/11

Solution: Usingpfor premium andrfor regular, I got two equations from the question stem:   5p = 16r and p = r+y   Substitute for p: 5(r+y) = 16r   Distribute: 5r + 5y = 16r   Subtract 5r from both sides: 5y = 11r   Plug back into the first equation: 5p = 16(5y/11)   Distribute: 5p = 80y/11   Divide both sides by 5: p = 16y/11   The answer is 16y/11.
Answer: E
A train 110 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
Choose one:
A) 5	B) 6	C) 7	D) 9	E) 1

Solution: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr   [66 * 5/18] m/sec = [55/3] m/sec.   Time taken to pass the man = [110 * 3/55= 
110 * 3/55 = 6
6 sec.Answer: 6
Answer: B
Which of the following is greatest?	Pick.
A) 1/5	B) 2/5	C) 3/5	D) 4/5	E) 6/5

Solution: A,B,C,D if we divide by 5 , we get the value <1. If we divide 6 by 5 we get the value >1   Answer : 6/5
Answer: E
A certain debt will be paid in 65 installments from January 1 to December 31 of a certain year. Each of the first 20 payments is to be $410; each of the remaining payments is to be $65 more than each of the first 20 payments. What is the average (arithmetic mean) payment that will be made on the debt for the year?  Choose the correct answer
A) 443  B) 455  C) 465  D) 468  E) 475

Solution: Total number of installments = 65   Payment per installment for the first 20 installments = 410   Payment per installment for the remaining 45 installments = 410+65= 
410+65 = 475
475   Average= (20*410 + 45*475)/65= 
(20*410 + 45*475)/65 = 455
455   Answer 455
Answer: B
Circular gears L and R start to rotate at the same time at the same rate. Gear L makes 10 complete revolutions per minute and gear R makes 30 revolutions per minute. How many seconds after the gears start to rotate will gear R have made exactly 6 more revolutions than gear L?
Choose the correct choice from the following choices.
A) a) 6 B) b) 8 C) c) 10 D) d) 12 E) e) 18

Solution: Gear L -- 10 rotations per 60 seconds -- 1 rotation per 6 seconds.   Gear R -- 40 rotations per 60 seconds -- 3 rotations per 6 seconds.   First 6 seconds -- Gear L makes 1 rotation. -- Gear R makes 4 rotations -- Net difference --2 rotations   Hence every 6 seconds the difference between the number of rotations of R and L gear is 2 units.   Required net difference should be 6 rotations => 3 (6 seconds later) ==> 18 seconds.   Answer: e) 18
Answer: E