MU-NLPC/Calc-aqua_rat huggingface dataset:
In the xy-plane, line h 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 h?	Choose the correct choice from the following options.
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 h 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
For which of the following functions does f(−z)=−f(z) for all real number values of x?	Choose the most appropriate option.
A) z^8−z^4
B) z^5/(z^2+1)
C) z^5/z^7
D) z^9/(z^5+1)
E) z^8

Solution: all even root cannot be matched eliminated   put z=2   f(−z)=(−2)^5/(−2^)2+1=−32/5, and   −f(z)=−2^5/2^2+1=−32/5, for a match.   ANSWER: z^5/(z^2+1)
Answer: B
111 = O,
222 = E,
333 = T,
444 = S,
Reading and analyzing the above, can you find out the following ?
555 = ?  Select the correct option:  A) 0  B) 1  C) 3  D) 2  E) 4

Solution: Solution:   0   Explanation:   1 * 1 * 1 = One   2 * 2 * 2 = Eight   3 * 3 * 3 = Twenty seven   4 * 4 * 4 = Sixty Four   For all the above, you can see that the first letter of the sum is the code.   Thus 5 * 5 * 5 = One twenty five   Thus 555 = O.   0nswer 0
Answer: A
Ten years ago, the age of Anand was one-third the age of Bala at that time. The present age of Bala is 8 years more than the present age of Anand. Find the present age of Anand?  Choose the most appropriate option.
A) 12	B) 14	C) 15	D) 16	E) 18

Solution: Explanation:   Let the present ages of Anand and Bala be 'a' and 'b' respectively.   a - 10 = 1/3 (b - 10) --- (1)   b = a + 8   Substituting b = a + 8 in first equation,   a - 10 = 1/3 (a -2) => 3a - 30 = a - 2   => 2a = 28 => a = 14.   Answer: 14
Answer: B
If 2994 ÷ 14.5 = 172, then 29.94 ÷ 1.45 = ? Pick one:
A) 17.2
B) 18.2
C) 19.2
D) 15.2
E) 16.2

Solution: 29.94/ 1.45 = 299.4/14.5   = (2994/14.5) x 1/10) [ Here, Substitute 172 in the place of 2994/14.5 ]   = 172/10= 
172/10 = 86/5 = around 17.2
17.2   17.2nswer is 17.2.
Answer: A
A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 18 hrs and a machine of type S does the same job in 9 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?  Choose the correct choice:
A) A)3
B) B)4
C) C)6
D) D)9
E) E)12

Solution: Rate of machine R =1/18   Rate of machine S =1/9   since same no of machines used for R and S to do the same work in 2 hrs   So collective rate needed to finish the work in 2 hrs= 1/2   Let the no of machine be x   So, x/18 +x/9 =1/2   3x/18=1/2   x=18/6= 
18/6 = 3
3   So no of machine R is 3   3nswer 3
Answer: A
A vessel of capacity 2 litre has 30% of alcohol and another vessel of capacity 6 litre had 40% alcohol. The total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water. What is the new concentration of Mixture?	Choose the correct choice from the following answers:	A) 30%.	B) 71%.	C) 49%.	D) 29%.	E) 51%.

Solution: 30% of 2 litres = 0.6 litres   40% of 6 litres = 2.4 litres   Therefore, total quantity of alcohol is 3.0 litres.   This mixture is in a 10 litre vessel. Hence, the concentration of alcohol in this 10 litre vessel is 30%   30%.NSWER:30%.
Answer: A
The sum of the fourth and twelfth term of an arithmetic progression is 20. What is the sum of the first 15 terms of the arithmetic progression? Choose the correct answer:
A) 3 B) 1/3 C) 2 D) 9 E) 1/9

Solution: The sum of the first n terms of a G.P. is given by , where 'a' is the first term of the G.P., 'r' is the common ratio and 'n' is the number of terms in the G.P.   Therefore, the sum of the first 6 terms of the G.P will be equal to   And sum of the first 3 terms of the G.P. will be equal to   Use the ratio between these two sums to find 'r'   The ratio of the sum of the first 6 terms : sum of first 3 terms = 9 : 1   i.e.   Or r3 + 1 = 9   r3 = 8   r = 2   The answer is 2
Answer: C
A tortoise was walking on a 700-feet circular path in a garden at a rate of 100 feet per hour. One hour after the tortoise started, a hare started running from the same starting point on the path at 200 feet per hour. What is the shortest time that the hare could need in order to catch up with the tortoise?	Choose the correct choice:
A) 1 hour  B) 2 hours  C) 2.5 hours  D) 3 hours  E) 4 hours

Solution: we don't need to assume here the direction.we need to find which will take less time   so there are 2 cases   1)both moving in same direction...then time would be 1 hour   2)both moving in opposite direction then time would be 2 hours   as we need the shortest time it would be the first case.   Correct answer is 1 hour
Answer: A
A man has 53 socks in his drawer: 21 identical blue, 15 identical black and 17 identical red. The lights are fused and he is completely in the dark. How many socks must he take out to make 100 per cent certain he has a pair of black socks? Choose the correct option.
A) 10 socks  B) 20 socks  C) 30 socks  D) 40 socks  E) 50 socks

Solution: D   40 socks.   If he takes out 38 socks, although it is very unlikely, it is possible they could all be blue and red. To make 100 percent certain that he also has a pair of black socks he must take out a further two socks.
Answer: D
A certain amount earns simple interest of Rs. 1750 after 7 years. Had the interest been 2% more, how much more interest would it have earned?
Choose the correct choice: A) Rs.35 B) Rs.245 C) Rs.350 D) cannot be determined E) None of these

Solution: Explanation:   We need to know the S.I, principal and time to find the rate. Since the principal is not given, so data is inadequate.   Answer: cannot be determined
Answer: D
In a class there are less than 500 students.When it is divided by 3 it gives a whole number. Similarly when it is divided by 4, 5 or 7 gives a whole number. Find the number of students in the class?
Answers
A) 410  B) 420  C) 430  D) 440  E) 450

Solution: L.C.M of 3,4,5,7 = 420   ANSWER:420
Answer: B
A milk man borrowed 2,500 from two money lenders. For one loan, he paid 5% p.a. and for the other, he paid 7% p.a.The total interest paid for two years was 275. How much did he borrow at 7% rate?  Pick: A) 600 B) 625 C) 650 D) 675 E) None of these

Solution: Let he borrowed at 5% = x   ∴ he borrowed at 7% = (2500 – x)   Now I1 + I2 = 275   x×5×2/100+(2500−x)×7×2/100=275   ⇒ 10x + 14(2500 – x) = 27500   ⇒ 4x = 35000 – 27500 = 7500   ⇒ x = Rs 1875   ∴ Sum borrowed at 7% rate = 2500 – 1875 = 625   Answer 625
Answer: B
Sequence G consists of 16 consecutive integers. If -6 is the least integer in sequence G, what is the range of the positive integers in sequence G?	Choose the most appropriate option.
A) 16
B) 15
C) 9
D) 8
E) 7

Solution: Since set G consists of 16 consecutive integers and -6 is the least integer then set G is consecutive integers from -6 to 9, inclusive: 9-(-6)+1= 
9-(-6)+1 = 16
16.   The range of positive integers in sequence G is 9-1= 
9-1 = 8
8.   Answer: 8.
Answer: D
Worldwide production of motor vehicles was 3.9 million vehicles in 1946 and 49 million in 1987. Of the following, which is closest to the average (arithmetic mean) annual increase, in millions, in worldwide production of motor vehicles during this period? Choose one.
A) 0.08 B) 1.0 C) 1.1 D) 10.5 E) 41.8

Solution: 1.1hange in production of motor vehicles = 49 - 3.9= 
49 - 3.9 = 45.1
45.1 million in 41 years (1987 - 1946)   average increase per year= 45.1/41= 
45.1/41 = 1.1
1.1 million (apporx.)   Answer (1.1)
Answer: C
When positive integer x is divided by positive integer y, the remainder is 9. If x/y = 86.12, what is the value of y?  Answers:
A) 96
B) 87
C) 75
D) 25
E) 12

Solution: by the definition of a remainder, the remainder here is equal to 9/y. the remainder in decimal form is given as .12   therefore, 9/y = .12   solve for y and get 75.   75
Answer: C
During the second quarter of 1984, a total of 2,976,000 domestic cars were sold. If this was 30% greater than the number sold during the first quarter of 1984, how many were sold during the first quarter ?  Choose the correct choice from the following options: A) 714,240 B) 2,289,230 C) 2,400,000 D) 3,690,240 E) 3,915,790

Solution: Let number of cars sold in 1st quarter = x   Number of cars sold in 2nd quarter = 30% greater than the number sold during the first quarter = (1 + 30/100)= 
(1 + 30/100) = 13/10 = around 1.3
1.3 x   1.3 x= 2,976,000   => x = 2,289,230   So, answer will be 2,289,230
Answer: B
A boat M leaves shore A and at the same time boat B leaves shore B. They move across the river. They met at 500 yards away from A and after that they met 300 yards away from shore B without halting at shores. Find the distance between the shore A & B. Choose the correct choice from the following answers:	A) 1100 yards	B) 1200 yards	C) 1300 yards	D) 1400 yards	E) 1000 yards

Solution: If X is the distance, a is speed of A and b is speed of 1200 yards, then ;   500/a= (x-500)/b and (x+300)/a = (2x-300)/b , solving it, we get x=1200 yards   ANSWER:1200 yards
Answer: B
Three numbers are in the ratio 3:4:5 and their L.C.M is 2400. Their H.C.F is? Select the correct option.
A) 40 B) 99 C) 88 D) 44 E) 11

Solution: Let the numbers be 3x, 4x and 5x.   Then, their L.C.M = 60x. So, 60x = 2400 or x = 40.   The numbers are (3 * 40), (4 * 40) and (5 * 40).   Hence, required H.C.F = 40.   40nswer: 40
Answer: A
On a certain road 10% of the motorists exceed the posted speed limit and receive speeding tickets, but 50% of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on the road exceed the posted speed limit? Pick.
A) 10.5%	B) 12.5%	C) 15%	D) 22%	E) 20%

Solution: 0.1 M = 0.50 E   => E/M = 1/5* 100= 
1/5* 100 = 20
20%   So answer is E.   M - # of Motorists   20% - # of Motorists exceeding speed
Answer: E
In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 46, the dividend is  Pick
A) 5200	B) 5226	C) 5286	D) 5330	E) 5336

Solution: Divisor = (5 * 46)= 
(5 * 46) = 230
230= 10 * Quotient = Divisor   => Quotient = 230/10= 
230/10 = 23
23   Dividend= (Divisor * Quotient) + Remainder   Dividend = (230 * 23) + 46= 
(230 * 23) + 46 = 5_336
5336.   5336
Answer: E
A, B and C can do a piece of work in 24, 30 and 40 days respectively. They start the work together but C leaves 4 days before the completion of the work. In how many days is the work done?
Choose the correct answer:  A) 22 days  B) 77 days  C) 88 days  D) 11 days  E) 18 days

Solution: x/24 + x/30 + x/40 = 1   x = 11 days   Answer:11 days
Answer: D
A vessel of capacity 90 litres is fully filled with pure milk. Nine litres of milk is removed from the vessel and replaced with water. Nine litres of the solution thus formed is removed and replaced with water. Find the quantity of pure milk in the final milk solution?  Choose the most appropriate option.
A) 73.9	B) 72.9	C) 73.0	D) 73.5	E) 92.2

Solution: Let the initial quantity of milk in vessel be T litres.   Let us say y litres of the mixture is taken out and replaced by water for n times, alternatively.   Quantity of milk finally in the vessel is then given by [(T - y)/T]n * T   For the given problem, T = 90, y = 9 and n = 2.   Hence, quantity of milk finally in the vessel   = [(90 - 9)/90]2 (90) = 72.9 litres.   Answer: Option 72.9
Answer: B
It takes 30 days to fill a laboratory dish with bacteria. If the size of the bacteria doubles each day, how long did it take for the bacteria to fill 1/64 of the dish?
Pick
A) 20
B) 22
C) 24
D) 26
E) 28

Solution: The bacteria doubles each day, so after 29 days, the dish was half full.   After 28 days, the dish was one quarter full.   After 27 days, the dish was one eighth full.   After 26 days, the dish was one sixteenth full.   After 25 days, the dish was 1/32 full.   After 24 days, the dish was 1/64 full.   The answer is 24.
Answer: C
If the average (arithmetic mean) of 5 positive temperatures is z degrees Fahrenheit, then the sum of the 3 greatest of these temperatures, in degrees Fahrenheit, could be:  Choose the correct choice from the following options
A) 6z	B) 4z	C) 5z/3	D) 3z/2	E) 3z/5

Solution: The sum of three greatest should be more than sum of two lowest.   The total sum is; 5z   A. 6z; 6z is more than 5z. Not possible.   B. 4z; 5z-4z=z(Possible)   C. 5z/3; 10z/3; 10z/3 > 5z/3. Not possible   D. 3z/2; 7z/2; 7z/2 > 3z/2. Not possible   E. 3z/5; 22z/5; 22z/5 > 3z/5. Not possible.   Ans:4z
Answer: B
Find number which is 60% less than 120.
Pick one
A) 18 B) 22 C) 28 D) 48 E) 98

Solution: Explanation:   60% less is 40% of the given number   Therefore, 40% of 120 is 48.   ANSWER: 48
Answer: D
A shopkeeper marks the price of his goods at 25% higher than the original price. After that, he allows a discount of 12%. What profit or loss does he get?  Choose the correct choice from the following options
A) 10% profit B) 15% profit C) 10% loss D) 15% loss E) 25% loss

Solution: Here, x = 25 and y = - 12   Therefore, the net % change in value   = ( x + y + xy/100) %   = [25 - 12 + ( -12 x 25)/100]% or 10%   Since the sign is positive , there is a profit of 10%   10% profitNSWER:10% profit
Answer: A
Sandy buys an old scooter for $800 and spends $200 on its repairs. If Sandy sells the scooter for $1400, what is the gain percent? Pick:	A) 20%	B) 30%	C) 40%	D) 50%	E) 60%

Solution: selling price / total cost = 1400/1000= 
1400/1000 = 7/5 = around 1.4
1.4   The gain percent is 40%.   The answer is 40%.
Answer: C
Sam bought a container of cashew for Rs.2200000 weighing 14 tons. Packed it in a package of 1 kg and sold the package for Rs. 200. What is the % of profit Sam has made? Options.
A) 20.3%
B) 24.2%
C) 29.5%
D) 27.2%
E) 30.1%

Solution: Cost of buying= Rs. 2200000   Cost of selling= Rs(14000x200)=Rs.2800000   Profit made by Sam=Rs.600000   Percentage of profit made by Sam=(600000/2200000)x100=27.2%   Answer:27.2%
Answer: D
Two tests had the same maximum mark. The pass percentages in the first and the second test were 40% and 45% respectively. A candidate scored 249 marks in the second test and failed by 66 marks in that test. Find the pass mark in the first test?
Choose the correct choice from the following answers
A) 768	B) 243	C) 246	D) 280	E) 224

Solution: Let the maximum mark in each test be M.   The candidate failed by 66 marks in the second test.   pass mark in the second test = 249 + 66= 
249 + 66 = 315
315   45/100 M= 315   Pass mark in the first test = 40/100 M = 40/45 * 315= 
40/45 * 315 = 280
280.   Answer:280
Answer: D
The quantities S and T are positive and are related by the equation S=K/T, where k is a constant. If the value of S increases by 70 percent, then the value of T decreases by what percent? Choose one:
A) 16 1/3%
B) 33 ¹/₃%
C) 50%
D) 66 ²/₃%
E) 75%

Solution: We can assign numbers:   lets say S = 2, K = 6 (constant) and T = 3 (so that S=K/T)   Now increasing S by 50% gives S=6, K remains constant, so T = 2 (6/2=3)   decrease in T= 1, percent decrease in T = (1/6)*100 = 16.33%   16 1/3%nswer 16 1/3%
Answer: A
John was 19 years old when he married Betty. They just celebrated their fifth wedding anniversary, and Betty's age is now 7/8 of John's. How old is Betty?
Choose the most appropriate option:
A) 21	B) 26	C) 28	D) 30	E) 32

Solution: Assume Betty's age on marriage = x years.   John's age on marriage = 19   John's age after 5 years = 24 years.   Betty's age after 5 years = x + 5   Given: x + 5 = 7/8 (24) = 21   Therefore Betty's current age = 21   Option 21
Answer: A
Find the area of a parallelogram with base 25 cm and height 15 cm? Choose the correct choice from the following answers:
A) 295 cm2
B) 385 cm2
C) 275 cm2
D) 375 cm2
E) 285 cm2

Solution: Area of a parallelogram = base * height = 25 * 15= 
25 * 15 = 375
375 cm2   Answer:375 cm2
Answer: D
If x, y and r are positive integers greater than 1, and x and y are factors of r, which of the following must be the factor of r^(xy)?
I. x+y
II. y^x
III. x^2 * y^2 Choices
A) I only  B) II only  C) III only  D) I and II  E) II and III

Solution: given that p and q are factors of r.   so we can picture it this way r=x*y*n (n-some another factor of r)   so, r^xy= (x*y*n)^xy   I. x+y .since the question is MUST BE TRUE, we eleminate this option   II. (x*y*n)^xy / y^x= integer YII and IIIS!   III.(x*y*n)^xy/ x^2 * y^2 YII and IIIs, since we are said that integer x>1 and integer y>1
Answer: E
If the number 5 * 2 is divisible by 6, then * = ?	Choices:
A) 2	B) 7	C) 3	D) 6	E) 5

Solution: Explanation :   Replacing * by x   5 x 2 is divisible by 2 (Reference : Divisibility by 2 rule)   For 5 x 2 to be divisible by 3, 5 + x + 2 shall be divisible by 3 (Reference : Divisibility by 3 rule)   => 7 + x shall be divisible by 3   => x can be 2 or 5 or 8   From the given choices, answer = 2. 2nswer : Option 2
Answer: A
What is the next number in the series?
2,4,7,10,15,18,.... Choose the correct choice from the following:
A) 23	B) 24	C) 25	D) 26	E) 27

Solution: Adding (0,1,2,3,4,5,6,7) to the prime numbers.   2+0= 
2+0 = 2
2   3+1= 
3+1 = 4
4   5+2= 
5+2 = 7
7   7+3= 
7+3 = 10
10   11+4= 
11+4 = 15
15   13+5= 
13+5 = 18
18   17+6= 
17+6 = 23
23   23NSWER:23
Answer: A
The tax on a commodity is diminished by 25% and its consumption increased by 15%. The effect on revenue is?  Select
A) 12% decrease	B) 18% decrease	C) 19% decrease	D) 13.75% decrease	E) 12.5% decrease

Solution: 100 * 100= 
100 * 100 = 10_000
10000   75 * 115= 9200   -----------   10000-----------1375   100-----------? => 13.75% decrease   Answer: 19% decrease
Answer: C
In a certain pond, 60 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? Select.
A) 400
B) 1,500
C) 1,250
D) 2,500
E) 10,000

Solution: This is a rather straight forward ratio problem.   1. 60 fish tagged   2. 2 out of the 50 fish caught were tagged thus 2/50   2/50=60/x   thus, x=1500   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.   1,500
Answer: B
A bank pays interest to its customers on the last day of the year. The interest paid to a customer
is calculated as 10% of the average monthly balance maintained by the customer. John is a
customer at the bank. On the last day, when the interest was accumulated into his account, his
bank balance doubled to $5620. What is the average monthly balance maintained by John in his
account during the year?	Choose the correct choice from the following options
A) 2840
B) 5680
C) 6840
D) 7540
E) 28100

Solution: bank balance is doubled with accumulation of interest tp 5620..   this means INTEREST is   5620/2= 
  5620/2 = 2_810
2810 for entire year..   although since interest is 10% of avg MONthly balance, it becomes 28100..
Answer: E
What sum of money will produce Rs.80 as simple interest in 4 years at 3 1/2 percent?  Choose the correct answer.
A) 263  B) 571.4  C) 367  D) 368  E) 339

Solution: 80 = (P*4*7/2)/100   P = 571.4   Answer: 571.4
Answer: B
If 0.75 of a number is equal to 0.025 of another number, the ratio of the numbers is :
Choose the most appropriate option: A) 2 :3 B) 3 :4 C) 1:30 D) 20 : 3 E) 30:7

Solution: 0.75A = 0.025B   -> A/B = 0.025/0.75 = 25/750 = 1/30   :. A : B = 1 : 30   ANSWER:1:30
Answer: C
The length of a rectangle is halved, while its breadth is tripled. Wat isthe % change in area? Choose the correct choice from the following:
A) 40%
B) 45%
C) 50%
D) 60%
E) 67%

Solution: Let original length = x and original breadth = y.   Original area = xy.   New length = x .   2   New breadth = 3y.   New area = x x 3y = 3 xy.   2 2   Increase % = 1 xy x 1 x 100 % = 50%.   2 xy   50%
Answer: C
If a pair of opposite sides of a square is increased by 5cm each, then the ratio of the sides of the new figure is 3 : 2. What is the original area of the square? Pick one:
A) 125 cm2 B) 225 cm2 C) 81 cm2 D) 100 cm2 E) None of these

Solution: Let the original side of the square = x cm   x+5/x=3/2 or 2x + 10 = 3x   \ x = 10 cm   \ original area = (10)2 = 100 cm2   Answer 100 cm2
Answer: D
There are 150 'zeroes' and 151 'ones' written on a black board. A step involves choosing three digits and replacing them with a single digit. If all the three digits are identical, they are replaced with the same digit. Otherwise, the digit that appears twice replaces the three chosen digits. What is the minimum number of steps after which there will be no zero written on the blackboard?
Pick:
A) 11
B) 37
C) 36
D) 76
E) 33

Solution: If we strike out 3 zeros, we are in effect reducing two zeroes. So we need 74 steps to reduce 148 zeroes. There are 2 zeroes and 151 ones left now. The remaining zeroes can be reduced in 2 steps. Hence the answer is 76.   Answer:76
Answer: D
A merchant gets a 5% discount on each meter of fabric he buys after the first 2,000 meters and a 7% discount on every meter after the next 1,500 meters. The price, before discount, of one meter of fabric is $2, what is the total amount of money the merchant spends on 6,000 meters of fabric?	Choose the correct choice.
A) $9,300	B) $10,400	C) $11,500	D) $12,600	E) $13,700

Solution: For first 2000 meters he does not get any discount.   The price is  2*2000= 
 2*2000 = 4_000
$4000   For next 1500 meters, he gets a 5% discount.   The price is  1.9*1500= 
 1.9*1500 = 2_850
$2850   For the next 1500 meters, he gets a 7% discount.   The price is  1.86*2500= 
 1.86*2500 = 4_650
$4650   The total price is $4000 + $2850 + $4650= $11,500   The answer is $11,500.
Answer: C
A man can hit a target once in 3 shots. If he fires 4 shots in succession, how many ways that he will hit his target?  Choose the correct choice from the following answers.
A) 71/234
B) 81/133
C) 81/343
D) 16/81
E) 91/324

Solution: The man will hit the target if he hits it once or twice or thrice or all four times in the four shots that he takes.   So, the only possibility when the man will not hit the target is when he fails to hit the target in even one of the four shots that he takes.   The event of not hitting the target even once is the complement of the event of hitting the target at least once.   The probability that he will not hit the target in any given shot = 1 - 1/3 = 2/3   Therefore, the probability that he will not hit the target in any of the four shots = 2/3 ^4 = 16/81   16/81
Answer: D
Identify the next two numbers in this Sequence ?
101, 112, 131, 415, 161, 718, ???, ???
Choose one:
A) 123005 B) 456804 C) 545788 D) 342678 E) 192021

Solution: 192021   192 021   If you look at it as two-digit numbers you'll see:10 11 12 13 14 15 16 17 18 19 20 21
Answer: E
How many diagonals does a 59-sided convex polygon have?	Choose one:
A) 1168
B) 1652
C) 2452
D) 3304
E) 4256

Solution: A 59-sided convex polygon has 59 vertices.   If we examine a single vertex, we can see that we can connect it with 56 other vertices to create a diagonal. Note that we can't connect the vertex to itself and we can't connect it to its adjacent vertices, since this would not create a diagonal.   If each of the 59 vertices can be connected with 56 vertices to create a diagonal then the total number of diagonals would be (59)(56) = 3304   However, we must recognize that we have counted every diagonal twice.   To account for counting each diagonal twice, we must divide 3304 by 2 to get 1652.   The answer is 1652.
Answer: B
An inspector rejects 0.04% of the meters as defective. How many will he examine to reject 2?	Answers:
A) A)1500
B) B)2000
C) C)2500
D) D)5000
E) E)3100

Solution: Let the number of meters to be examined be x   Then, 0.04% of x = 2   (4/100)*((1/100)*x = 2   x = 5000   Answer is 5000
Answer: D