MU-NLPC/Calc-aqua_rat huggingface dataset:
An assembly line produces 30 cogs per hour until an initial order of 60 cogs is completed. The speed of the assembly line is then immediately increased so that it can produce 60 cogs per hour until another 60 cogs are produced. What is the overall average output, in cogs per hour, for the assembly line during this whole time?
Choose the correct choice from the following answers:  A) 40  B) 44  C) 48  D) 52  E) 56

Solution: The time to produce the first 60 cogs is 60/30= 
60/30 = 2
2 hours.   The time to produce the next 60 cogs is 60/60= 
60/60 = 1
1 hour.   The average output is 120 cogs / 3 hours= 40 cogs per hour.   The answer is 40.
Answer: A
The average age of a group of 10 persons was decreased by 3 years when one person, whose age was 44 years, was replaced by a new person. Find the age of the new person?
Select
A) 18 B) 56 C) 12 D) 17 E) 14

Solution: Initial average age of the 10 persons be P.   Age of the new person Q.   Sum of the ages of the initial 10 persons = 10P   New average   = (P-3) 10(P-3)   = 10P - 44 + Q   => Q = 14   Answer:14
Answer: E
x is a set containing 8 different positive odd numbers. y is a set containing 7 different numbers, all of which are members of S. Which of the following statements CANNOT be true? Choose the correct answer.
A) The range of y is even.	B) The mean of x is even.	C) The mean of y is even.	D) The range of x is equal to the range of y.	E) The median of y is equal to the mean of y.

Solution: Given: x is a set containing 8 different positive odd numbers   Easily inferred: y is a set containing 7 differentoddnumbers   (A) The range of y is even. - Always even, since it is a difference of two odd numbers   (B) The mean of x is even. - can be. suppose 8 numbers consist of 4 pairs of (16n-1,16n+1) for different values of n. Adding these will give a multiple of 16, which when divided by 8 (to arrive at mean), will give an even number   (C) The mean of y is even. - Cannot be. Mean = (sum of 7 odd numbers)/7 = Odd number/odd number thus cannot be even.   (D) The range of x is equal to the range of y.   (E) The median of y is equal to the mean of y   Option The mean of y is even.
Answer: C
The H.C.F and L.C.M of two numbers are 84 and 21 respectively. If the ratio of the two numbers is 1 : 4 , then the larger of the two numbers is	Choose the correct choice from the following:
A) 32 B) 37 C) 84 D) 29 E) 21

Solution: Explanation:   Let the numbers be x and 4x. Then, \inline \fn_jvn x\times 4x =84\times 21\: \: \Leftrightarrow \: \: x^{2}=\frac{84\times 21}{4} \: \: \Leftrightarrow \: \: x=21   Hence Larger Number = 4x = 84   Answer: 84) 84
Answer: C
A horse is tethered to one corner of a rectangular grassy field 36 m by 20 m with a rope 18 m long. Over how much area of the field can it graze?  Choose the correct answer
A) 154 cm2 B) 308 m2 C) 254 m2 D) 260 m2 E) None of these

Solution: Area of the shaded portion   = 1⁄4 × π × (18)2 = 254 m2   Answer 254 m2
Answer: C
Jo's collection contains US, Indian and British stamps. If the ratio of US to Indian stamps is 5 to 2 and the ratio of Indian to British stamps is 5 to 1, what is the ratio of US to British stamps?
Choices.
A) 10 : 5	B) 15 : 2	C) 20 : 2	D) 25 : 2	E) None of these

Solution: Explanation:   Indian stamps are common to both ratios. Multiply both ratios by factors such that the Indian stamps are represented by the same number.   US : Indian = 5 : 2, and Indian : British = 5 : 1. Multiply the first by 5, and the second by 2.   Hence the two ratios can be combined and US : British = 25 : 2   Now US : Indian = 25 : 10, and Indian : British = 10 : 2 Answer: 25 : 2
Answer: D
The average weight of A, B and C is 43 kg. If the average weight of A and B be 48 kg and that of B and C be 42 kg, then the weight of B is:	Select the correct option.
A) 55 kg B) 53 kg C) 49 kg D) 52 kg E) 51 kg

Solution: EXPLANATION   Let A, B, C represent their respective weights. Then, we have:   A + B + C = (43 x 3) = 129 â€¦. (i)   A + B = (48 x 2) = 96 â€¦. (ii)   B + C = (42 x 2) = 84 â€¦.(iii)   Adding (ii) and (iii), we get: A + 2B + C = 180 â€¦. (iv)   Subtracting (i) from (iv), we get : B = 51.   Bâ€™s weight = 51 kg.   Answer 51 kg
Answer: E
The average of six numbers is 3.95. The average of two of them is 3.3, while the average of the other two is 3.85. What is the average of the remaining two numbers?  Choose the correct choice
A) 4.5 B) 4.6 C) 4.7 D) 4.8 E) 4.9

Solution: Sum of the remaining two numbers   = (3.95 × 6) – [(3.3 × 2) + (3.85 × 2)]   = 23.70 – (6.6 + 7.7)   = 23.70 – 14.3 = 9.40   ∴ Required average = (9.4⁄2) = 4.7   Answer 4.7
Answer: C
For the positive numbers, n+3, n + 4, n + 6, n + 8, and n + 9, the mean is how much greater than the median? Choose the correct option:
A) 0
B) 1
C) n+l
D) n+2
E) n+3

Solution: Let’s first calculate the mean (arithmetic average).   mean = sum/quantity   mean = (n + 3+n + 4 + n + 6 + n + 8 + n + 9)/5   mean = (5n + 30)/5   mean = n + 6   Next, we determine the median. The median is the middle value when the terms are ordered from least to greatest. The terms ordered from least to greatest are as follows:   n+3, n + 4, n + 6, n +8, n + 9   The median is n + 6   Finally we are asked how much greater the mean is than the median. To determine the difference we can subtract the smaller value (the median) from the larger value (the mean) and we get:   n + 6 – (n + 6) = n + 6 – n – 6 = 0   The answer is 0
Answer: A
The average of first six prime numbers which are odd is?  Select
A) 15.5  B) 15.7  C) 9.3  D) 15.8  E) 15.1

Solution: Sum of first 6 prime no. which are odd = 56   Average = 56/6 = 9.3   Answer:9.3
Answer: C
Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?  Options
A) 12  B) 13  C) 16  D) 10  E) 15

Solution: Suppose they meet x hours after 7 a.m.   Distance covered by A in x hours = 20x km.   Distance covered by B in (x - 1) hours = 25(x - 1) km.   Therefore 20x + 25(x - 1) = 110   45x = 135   x = 3.   So, they meet at 10 a.m.   Answer: 10
Answer: D
A can do a piece of work in 4 days. B can do it in 5 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it? Choose the correct option:
A) 23 days B) 18 days C) 20 days D) 22 days E) 28 days

Solution: 20 days   20 days   20 days = 1/2 - 1/4 - 1/5 = 1/20 => 20 days
Answer: C
A certain fruit stand sold apples for $0.70 each and bananas for $0.60 each. If a customer purchased both apples and bananas from the stand for a total of $6.30, what total number of apples and bananas did the customer purchase?	Answers:
A) 8
B) 9
C) 10
D) 11
E) 12

Solution: Let's start with 1 apple for $0.70.   Let's subtract $0.70 from $6.30 until we get a multiple of $0.60.   $6.30, $5.60, $4.90, $4.20 = 7*$0.60   The customer purchased 7 bananas and 3 apples.   The answer is 10.
Answer: C
Sagar purchased 10 kg of rice at the rate of Rs. 15 per kg and 25 kg of rice at the rate Rs. 14 per kg. He mixed the two and sold the mixture. Approximately at what rate per kg should he sell the mixture to make 40 % profit in the transaction?
Select the correct option:
A) Rs. 20.00
B) Rs. 19.50
C) Rs. 15
D) Rs. 17.5
E) None of these

Solution: By 40% profit on cost price,   Selling price of mixture = 140/100 * 500   = Rs. 700   Therefore, selling price per kg of mixture = 700/35 = Rs. 20   Rs. 20.00NSWER Rs. 20.00
Answer: A
The cost of 3 pens and 5 pencils is Rs.200. Also the cost of one pen and one pencil is in the ratio of 5:1 respectively. What is the cost of one dozen pens?
Choose the correct choice from the following.
A) Rs.200	B) Rs.250	C) Rs.300	D) Rs.150	E) Rs. 600

Solution: Explanation:   Let the cost of one pen is ‘5x’ and pencil is ‘x’   3 X 5x + 5x = Rs.200   15x + 5x = Rs.200   X = 200/20= 
200/20 = 10
10   :. Cost of 1 pen= 5x = 5 x 10 = 50   :. Cost of 12 pens, i.e. (one dozen) = 50 x 12 = Rs.600   Answer: Option Rs. 600
Answer: E
The sum of two numbers is 16. The difference is 4. What are the two numbers?Let x be the first number. Ley y be the second number
x + y = 16
x - y = 4 Choose the correct answer:	A) 10 and 6	B) 10 and 5	C) 10 and 4	D) 10 and 3	E) 10 and 2

Solution: Solution   Let x be the first number. Ley y be the second number   x + y = 16   x - y = 4   Solve the system of equations by elimination   10 and 6dding the left sides and the right sides gives:   x + x + y + -y = 16 + 4   2x = 20   x = 10   Since x + y = 16, 10 + y = 16   10 + y = 16   10 - 10 + y = 16 - 10= 
16 - 10 = 6
6   The numbers are 10 and 6   10 and 6nswer 10 and 6
Answer: A
There are 28 balls which are red, blue or green. If 12 balls are green and the sum of red balls and green balls is less than 24, at most how many red balls are there?
Pick one.
A) 10 B) 12 C) 11 D) 13 E) 14

Solution: r+g+b=28   g=12   r + g < 24   => r + 12 < 24   => r < 12   => at most 11 red balls   ANSWER:11
Answer: C
At a certain restaurant, 30 percent of the servers reported their tips, while 40 percent of the servers who were tipped didn't report their tips. What percent of the servers were tipped?
Choose the correct choice from the following answers:
A) 30% B) 60% C) 50% D) 70% E) 80%

Solution: Statement: 30% of Servers (S) Reported their Tips (RT). Of the servers who were tipped (T) 40% didn't report their tips (notRT). [Note: A Venn Diagram is useful to visualize the problem.]   Solution: Sample space is 100%.   S = 100%   RT/S = 30%   notRT/T = 40% => 100% - 40% => RT/T = 60%   T/S = (30)/(60)% = 50%   Answer: 50%
Answer: C
The value of a machine depreciates at the rate of 10% per year. If its present is Rs.1,62,000 what will be its worth after 2 years ? What was the value of the machine 2 years ago ?
Choose one
A) 50000  B) 100000  C) 150000  D) 200000  E) None of them

Solution: Value of the machine after 2 years   =Rs.[162000*(1-(10/100))^2] = Rs.[162000*(9/10)*(9/10)]   =Rs. 131220   Value of the machine 2 years ago   = Rs.[162000/(1-(10/100)^2)]=Rs.[162000*(10/9)*(10/9)]=Rs.200000   Answer is 200000.
Answer: D
In the first 10 overs of a cricket game, the run rate was only 4.6. What should be the run rate in the remaining 40 overs to reach the target of 282 runs? Choose one:  A) 4.25  B) 5.9  C) 6.25  D) 7  E) 7.5

Solution: Required run rate = 282 - (4.6x 10) =	236 236/40= 5.9   5.9)
Answer: B
A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 98.01, the number of the member is the group is:
Answers.
A) 57
B) 67
C) 77
D) 99
E) 97

Solution: Money collected = (98.01 x 100) paise = 9801 paise.   Number of members =Square root of 9801 = 99.   Answer: Option 99
Answer: D
A certain tire company can produce tires at a cost of $22,500 per batch plus $6 per tire. The company can sell tires to the wholesaler at a cost of $20 per tire. If a batch of 15,000
tires is produced and sold, what is the company’s profit per tire? Choose the correct option:
A) $9.00  B) $9.50  C) $11.00  D) $13.50  E) $12.50

Solution: CP(15000 tires) = $22500 +($6×15000) =$112500   SP (15000 tires) = $20×15000 = $300000   Profit = SP-CP   = $300000-$112500= $187500   PROFIT/TIR$12.50 300000- 112500= 
300000- 112500 = 187_500
$187500   PROFIT/TIR$12.50= $187500/15000= 
187500/15000 = 25/2 = around 12.5
$12.50   Answer $12.50
Answer: E
A rower can row 5 km/h in still water. When the river is running at 2 km/h, it takes the rower 1 hour to row to Big Rock and back. How many kilometers is it to Big Rock? Choices:
A) 1.5	B) 1.8	C) 2.1	D) 2.4	E) 2.7

Solution: Let x be the distance to Big Rock.   time = x/3 + x/7 = 1   x = 21/10= 
21/10 = 21/10 = around 2.1
2.1 km   The answer is 2.1.
Answer: C
A garrison of 3300 men has provisions for 32 days when supplied at the rate of 850 g per head. At the end of 7 days, a reinforcement arrives, and it is found that the provisions can last for 17 days more when supplied at the rate of 825 g per head. What is the strength of the reinforcement?  Select
A) 1700  B) 1000  C) 3000  D) 2700  E) 2600

Solution: 825*17*x=850*25*3300   => 5000   strength of reinforcement = (5000-1300)= 1700   final answer 1700.   1700NSWER:1700
Answer: A
Priya and her father differ in their ages by 31 years. After 8 years. if the sum of their ages will be 69, their present ages are  Pick one.
A) 11, 42 B) 12, 24 C) 15, 42 D) 16, 19 E) 33, 44

Solution: 11, 42   11, 42   Let the age of Priya = x years   Then, the age of her father = (x+ 31) years   11, 42TQ,   (x+ 8) + (x+ 31 + 8) = 69   2x+ 47 = 69   2x= 69 – 47 = 22   x= 11   The age of Priya = 11 years   The age of her father = 11 + 31= 
11 + 31 = 42
42 years
Answer: A
A reduction of 10% in the price of tea enables a dealer to purchase 25 kg more tea for Rs. 22500. What is the reduced price per kg of tea?  Select.
A) Rs. 70
B) Rs. 80
C) Rs. 90
D) Rs. 100
E) None

Solution: Solution: 1st Method:   Let the original price of tea be Rs. x/kg.   After reduction the price becomes = x -10% of x = 9x/10 per kg.   Now,   (22500/(9x/10))-22500/x = 25   Or, 22500[10/9x- 1/x] = 25   Or, 25*9x = 22500;   Or, x = (22500/2589) = Rs. 100.   Hence, new price = 90 per kg.   Thought process Method:   Let the original price be Rs. 100 per kg, he get tea = 22500/100= 
22500/100 = 225
225 kg.   After reduction the price becomes= 90 per kg, he get tea = 22500/90= 
22500/90 = 250
250 kg.   So, reduction price is Rs. 90 per kg as it enables him to buy 25 kg of more tea.   Answer: Option Rs. 90
Answer: C
Find (7x + 4y ) / (x-2y) if x/2y = 3/2 ? Pick:
A) 24
B) 25
C) 26
D) 27
E) 29

Solution: x/2y=3/2   =>x=6y/2=3y   6 /2= 
6 /2 = 3
3y=>(7x+4y)/(x-2y)=((7*(3y))+4y)/(3y-2y)   =>25y/y((7*(3 ))+4 )/(3 -2 )= 
((7*(3 ))+4 )/(3 -2 ) = 25
>25y/y=25   ANSWER:25
Answer: B
In how many ways can the letters of word IMAGINATION be arranged such that all the vowels as well as all the Consonants always appear together?
Select the correct option:
A) 9!
B) 5!*4!
C) 5!*5!
D) 5!*4!*2!
E) 6!*5!*2!

Solution: Since all the vowels and consonants have to be together there can only be there are 6! way to order the vowels and 5! to order the consonants. But they must be together either vowels come first or consonants so you multiply by 2.   So 6!5!2! (6!*5!*2!)
Answer: E
When positive integer N is divided by positive integer J, the remainder is 18. If N/J = 134.03, what is value of J? Choose the correct choice from the following answers:
A) 22	B) 56	C) 78	D) 112	E) 600

Solution: 1) We know that   decimal part of decimal quotient ={remainder/divisor}   So 0.03, the decimal part of the decimal quotient, must equal the remainder, 18, divided by the divisor J.   0.03 = 18/J   0.03*J = 18   J = 18/0.03 = 1800/3= 
1800/3 = 600
600   So J= 600, answer = 600.
Answer: E
The rate of spin of a certain gyroscope doubled every 15 seconds from the moment a particular stopwatch started. If after a minute and a half the gyroscope reached a speed of 400 meters per second, what was the speed, in meters per second, when the stopwatch was started? Options:
A) 25/2  B) 25/4  C) 25/8  D) 25/16  E) 25/32

Solution: Let x be the original speed when the stopwatch was started.   In 90 seconds, the speed doubled 6 times.   2^6 * x = 400   x = (2^4 * 25) / 2^6 = 25/4   The answer is 25/4.
Answer: B
A train covers a distance of 15 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?  Choose the most appropriate option:	A) m	B) m	C) m	D) m	E) m

Solution: Speed = (15/10 * 60) km/hr   = (90 * 5/18) m/sec = 25 m/sec.   Length of the train = 25 * 6= 
25 * 6 = 150
150 m.   Answer:m
Answer: C
A man purchases the milk at Rs. x/litre and sells it at Rs. 2x/liter stillhe mixes 2liters waterwith every 6liters of pure milk. What is the profit %?
Answers:
A) 123%  B) 134%  C) 145%  D) 166.66%  E) 186.66%

Solution: Let the cost price of 1 litre pure milk be Re.1, then   \inline{6litres(milk)→CP=Rs.62litres(water)→CP=Rs.0}{6litres(milk)→CP=Rs.62litres(water)→CP=Rs.0}\rightarrow CP=Rs.6 only   and 8 litre mixture \rightarrow SP \rightarrow 8 x 2 = Rs.16   Profit %= 166.66%   166.66%
Answer: D
In the xy-plane, line k passes through point (3,-2) and intersect perpendicularly with line n that passes through points (0,3) and (3,5). What is the equation of line k?  Pick one.
A) 3x+2y-5=0
B) 3x+2y+5=0
C) 2x-3y-12=0
D) 2x+3y=0
E) 4x+3y-6=0

Solution: If two lines intersect perpendicularly, we get -1 when we multiply two slopes together. The slope of a line n is (5-3)/(3-0)=2/3. Hence, the slope of a line k should be -3/2. Since it crosses (3,-2), if we calculate we get 3x+2y=5. Hence, the correct answer is 3x+2y-53 +2= 
3 +2 = 5
5. Hence, the correct answer is 3x+2y-5=0.  3 +2 -5= 
  3 +2 -5 = 0
0.
Answer: A
A can build up a wall in 8 days while B can break it in 3 days. A has worked for 4 days and then B joined to work with A for another 2 days only. In how many days will A alone build up the remaining part of wall?
Choose the correct answer:
A) 13 1⁄3 days
B) 7 1⁄3 days
C) 6 1⁄3 days
D) 7 days
E) None of these

Solution: A’s one day’s work = 1⁄8th work.   B’s one day’s work = 1⁄3rd work.   ∴ A’s 4 day’s work = 4 × 1⁄8 = 1⁄2nd work   ∴ In next two days, total wall = 1⁄2 + 2(1⁄8) - 2(1⁄3) = 1⁄12th wall   Remaining wall = 1 - 1⁄12 = 11⁄12th   Now, 1⁄8th wall is built up by A in one day.   ∴ 11⁄12th wall is built up by A in 8 × 11⁄12 = 71⁄3 days.   Answer 7 1⁄3 days
Answer: B
The probability that A speaks truth is 7/9 and that of B speaking truth is 9/13. What is the probability that they agree in stating the same fact? Pick.
A) 18/35
B) 111/117
C) 157/195
D) 192/235
E) None of these

Solution: If both agree stating the same fact, either both of them speak truth of both speak false.   Probability = 7/9 * 9/13 + 6/9 * 8/13   = 63/117 + 48/117 = 111/117   ANSWER:111/117
Answer: B
Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
Choose the correct choice from the following answers:
A) 60
B) 50
C) 48
D) 76
E) 34

Solution: Relative speed = 45 + 30= 
45 + 30 = 75
75 km/hr.   75 * 5/18= 125/6 m/sec.   Distance covered = 500 + 500= 
500 + 500 = 1_000
1000 m.   Required time= 1000 * 6/125= 
1000 * 6/125 = 48
48 sec.   Answer: Option 48
Answer: C
James have 10 parrots, 4 fishes, 9 rabbits and 6 dogs.How many pets does he have in all? Answers
A) 17
B) 11
C) 9
D) 15
E) 29

Solution: 10+4+9+6= 
10+4+9+6 = 29
29. Answer is 29
Answer: E
Scott's average (arithmetic mean) golf score on his first four rounds was 58.What score does he need on his fifth round to drop his average score by 2 points?
Options:
A) 48  B) 72  C) 78  D) 88  E) 312

Solution: 48verage score for first 4 rounds = 58   48verage score after 5 rounds = 56   Score Scott needs on his 5th round to drop average score by 2 points = 58 - (2*5)= 
58 - (2*5) = 48
48   48nswer 48
Answer: A
In what ratio must rice at Rs.7.10 be mixed with rice at Rs.9.20 so that the mixture may be worth
Rs.8 per Kg? Choose the correct option:
A) 5 : 4
B) 2 : 1
C) 3 : 2
D) 4 : 3
E) None of these

Solution: Explanation :   By the rule of alligation, we have   CP of 1 kg Rice of 1st kind CP of 1 kg Rice of 2nd kind   7.1 9.2   Mean Price   8   9.2 - 8= 
9.2 - 8 = 1.2
1.2 8 - 7.1= .9   Required ratio = 1.2 : .9 = 12 : 9 = 4 : 3   Answer : Option 4 : 3
Answer: D
A man buys Rs. 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value of each share is:	Select the correct option:
A) 12 B) 13 C) 14 D) 15 E) 18

Solution: 15ividend on Rs 20 = 9/100*20 = 9/5   is 12 income 100   9/5 is an income on Rs   (100/12*9/5)= 
  (100/12*9/5) = 15
Rs 15   ANSWER 15
Answer: D
Taps A and B can fill a bucket in 10 minutes and 15 minutes respectively. If both are opened and A is closed after 3 minutes, how much further time would it take for B to fill the bucket?	Choose the correct choice.
A) 7 min. 30 sec.	B) 8min. 20 sec.	C) 7min. 25 sec	D) 7 min.35 sec.	E) 8min. 20 sec.

Solution: Explanation:   Part filled in 3 minutes =   3∗(1/10+1/15)=3∗5/30=5/10   Remaining part =1−5/10=5/10   =>1/15:5/10=1:X   =>X=15/2   =>X=7.5mins.   So it will take further 7 mins 30 seconds to fill the bucket.   Option7 min. 30 sec.
Answer: A
For what value of â€œkâ€ will the equation (2kx2 + 4kx +2)=0 have equal roots?	Choose the correct answer:
A) 1
B) 9/4
C) 16/25
D) 7/1
E) 7/2

Solution: for a 2nd degree equation ax2+bx_c=0 has equal roots the condition is b2-4ac =0   in the given equation   (4k)^2-4*2k*2=0   by solving this equation   we get k=0, k=1   1NSWER:1
Answer: A
Which of the following numbers should not be included in the set?
331, 482, 551, 263, 386, 242, 111
Choices.
A) 263	B) 386	C) 242	D) 111	E) None of these

Solution: Solution   In each number except 386,the product of first and third digits is the middle one. Answer 386
Answer: B
If x is an integer such that 5 < x < 21, 7 < x < 18, 13 > x > 2, 12 > x > 9, and x + 1 < 13, then x is  Choose the correct choice from the following answers.
A) 3	B) 5	C) 7	D) 9	E) 11

Solution: 5 < x < 21,   7 < x < 18,   2 < x < 13   9 < x < 12   x<13   From above: 10< x < 12 --> x = 11.   Answer: 11.
Answer: E
How long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 170 m in length?	Choose one:
A) 16.8	B) 17.8	C) 15.9	D) 13.2	E) 12.4

Solution: D = 110 + 170= 
110 + 170 = 280
280 m   S= 60 * 5/18 = 50/3   T = 280 * 3/50= 
280 * 3/50 = 84/5 = around 16.8
16.8 sec   16.8NSWER 16.8
Answer: A
The average of first 11 prime numbers is? Choose one:
A) 14.55  B) 11.11  C) 12.11  D) 13.11  E) 14.11

Solution: Sum of 11 prime no. = 160   14.55verage = 160/11 = 14.55   14.55NSWER: 14.55
Answer: A
On flipping 3 coins together what is the outcomes for at least three TAILl?	Choose the correct choice from the following
A) 1/7	B) 3/8	C) 1/8	D) 4/13	E) 5/13

Solution: Sample space, S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}   Favorable outcomes for at least two heads   = favorable outcomes for exactly two heads and favorable outcomes for more than two heads   = {TTT}   1/8   1/8
Answer: C
If 12!/3^x is an integer, what is the greatest possible value of x? Choose the correct choice from the following options.
A) 3	B) 4	C) 5	D) 6	E) 7

Solution: This question is asking how many power of 3 exists in 12!   easiest way is to identify factor of three   12 -> 4*3 => 1 power of 3   9 -> 3*3=> 2 power of 3   6 -> 2*3=> 1 power of 3   3 -> 1*3=> 1 power of 3   Total equal 5   ANSWER:5
Answer: C
Number of prime numbers between 70 and 100 is	Choose the correct answer
A) 4 B) 5 C) 6 D) 7 E) 9

Solution: total 6=71, 73, 79, 83, 89, 97   ANSWER:6
Answer: C
Carl is facing very difficult financial times and can only pay the interest on a $10,000 loan he has taken. The bank charges him a quarterly compound rate of 4%. What is the approximate interest he pays annually? Choose the correct choice.
A) $1750	B) $2000	C) $2150	D) $2500	E) $12000

Solution: An easy way too attempt this is by approximation:   For the first quarter, he pays 4% of 10,000 which is $400.   So for the four quarters in the year, he will approximately play  400*4= 
 400*4 = 1_600
1600 over the entire year.   Because of compound interest it will be more than 1600. Approx. option A is correct.   $1750nswer : $1750
Answer: A
If x ≠ 0 and y/x=y+x, which of the following expressions is equal to its opposite?  Choose the correct choice from the following:
A) x^2	B) x^2 – y^2	C) y^2	D) x^2 + xy - y^2	E) (x – y)^2

Solution: y/x=(y+x)/y   => y^2 = xy +x^2   => x^2 + xy - y^2+  2= 
+  2 = 2
> x^2 + xy - y^2= 0   Answer x^2 + xy - y^2
Answer: D
In a renowned city, the average birth rate is 5 people every two seconds and the death rate is 3 people every two seconds. Estimate the size of the population net increase that occurs in one day. Choose the correct choice from the following answers: A) 85,400 B) 86,400 C) 87,400 D) 88,400 E) 89,400

Solution: This question can be modified so that the birth rate is given every m seconds and the death rate is given every n seconds.   For this particular question : Increase in the population every 2 seconds = 5-3= 
5-3 = 2
2 people.   Total 2 second interval in a day= 24*60*60/2 = 43,200   Population increase = 43,200 * 2 = 86,400. Hence 86,400.
Answer: B