MU-NLPC/Calc-aqua_rat huggingface dataset:
On a 26 question test, five points were deducted for each wrong answer and eight points were added for each correct answer. If all the questions were answered, how many were correct, if the score was zero ? Answers:  A) 10  B) 12  C) 11  D) 13  E) 16

Solution: Explanation :   Let the correct answer be : x   Therefore wrong answers = (26 - x)   Total socre = 8x - 5(26-x) = 0   or, 13x = 130   Therefore x = 10   10nswer : 10
Answer: A
Ramu bought an old car for Rs. 36000. He spent Rs. 15000 on repairs and sold it for Rs. 62900. What is his profit percent?  Select the correct option
A) 16%  B) 17%  C) 18%  D) 58%  E) 23%

Solution: Total CP = Rs. 36000 + Rs. 15000   = Rs. 51000 and SP = Rs. 62900   Profit(%)   = (62900 - 51000)/51000 * 100   = 23%   Answer: 23%
Answer: E
A thief is noticed by a policeman from a distance of 450 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes?
Choose the most appropriate option:
A) 150 m B) 200 m C) 170 m D) 100 m E) 350 m

Solution: Relative speed of the thief and policeman = 11 - 10= 
11 - 10 = 1
1 km/hr.   Distance covered in 6 minutes= 1/60 * 6 = 1/10 km = 100 m.   Distance between the thief and policeman = 450 - 100= 
450 - 100 = 350
350 m   350 m
Answer: E
Dan’s car gets 32 miles per gallon. If gas costs $4/gallon, then how many miles can Dan’s car go on $46 of gas?	Choose the correct option: A) 124 B) 256 C) 368 D) 424 E) 512

Solution: 46/4= 
46/4 = 23/2 = around 11.5
11.5 gallons     11.5*32= 
  11.5*32 = 368
368 miles   The answer is 368.
Answer: C
R is the set of positive even integers less than 101, and S is the set of the squares of the integers in R. How many elements does the intersection of R and S contain ? Choose the correct answer.
A) None B) Two C) Four D) Five E) Seven

Solution: R is the set of positive even integers less than 101, and S is the set of the squares of the integers in R.   How many elements does the intersection of R and S contain?   R=2,4,6,8,10,12...   S=4,16,36,64...   Numbers: 4, 16, 36, 64, and 100 are even integers (less than 101) that are in both sets.   Solution: Five   Answer: Five
Answer: D
If Z is a positive integer greater than 1, what is the sum of the multiples of Z from Z to Z^2, inclusive?	Pick one:
A) Z(Z + 1)(Z-1) B) Z^2(Z + 1)/2 C) Z^2(Z-1) D) (x^3 + 2x)/2 E) x(x-1)^2

Solution: Ans :- B=Z^2(Z + 1)/2   I substituted 3 in all answer choices.   Option B and C were both satisfying the condition.   So i substituted 4 instead of 3 in all answer choices,   Only Z^2(Z + 1)/2 option satisfied.
Answer: B
Out of eight crew members three particular members can sit only on the left side. Another two particular members can sit only on the right side. Find the number of ways in which the crew can be arranged so that four men can sit on each side.  Choose the correct choice from the following answers:  A) 864  B) 863  C) 865  D) 1728  E) None

Solution: Solution:   Required number of ways, = 3C2 *4! *4! = 1728.   Answer: Option 1728
Answer: D
A 14% stock yields 8%.The market value of the stock is :	Pick:
A) Rs. 175
B) Rs. 92
C) Rs. 112.50
D) Rs. 116.50
E) None of these

Solution: solution   To obtain Rs. 8, investment = Rs. 100.   To obtain Rs. 14, investment = Rs.(100/8X14)= Rs. 175   ∴ Market value of Rs. 100 stock = Rs.175   Rs. 175nswer Rs. 175
Answer: A
If the digits 27 in the decimal 0.00027 repeat indefinitely, what is the value of (10^5-10^3)(0.00027)?	Choose the most appropriate option
A) 0.27
B) 0.027
C) 27
D) 0.0027
E) 2.7e-06

Solution: 99*0.27= 
99*0.27 = 26.73
26.73 approx. 27   Answer : 27
Answer: C
What is the remainder when 7^74 - 5^74 is divided by 2?
Choose one
A) 5 B) 1 C) 2 D) 3 E) None of these

Solution: easiest way for me: 7^74 - 5^74 = (49)^37-25^37 = (24*2+1)^37 - (24+1)^37 -> remainder is 1^37 - 1^37 = 0   Ans :None of these
Answer: E
In a 1000 m race, A beats B by 50 m and B beats C by 100 m. In the same race, by how many meters does A beat C?
Pick one
A) 145 m B) 176 m C) 268 m D) 129 m E) 218 m

Solution: By the time A covers 1000 m, B covers  (1000 - 50)= 
 (1000 - 50) = 950
950 m.   By the time B covers 1000 m, C covers  (1000 - 100)= 
 (1000 - 100) = 900
900 m.   So, the ratio of speeds of A and C=   1000/950 * 1000/900 = 1000/855 So, by the time A covers 1000 m, C covers 855 m.   So in 1000 m race A beats C by 1000 - 855= 
1000 - 855 = 145
145 m.   145 mnswer:145 m
Answer: A
If a 4-member subcommittee is to be formed from a certain 6-member committee, how many different such subcommittee are possible?
Options
A) 6 B) 15 C) 20 D) 60 E) 216

Solution: Another way:   1st member can be selected in 6 ways   2nd can be selected in 5 ways   3rd can be selected in 4 ways   4th can be selected in 3 ways   So total ways : 360   15ut to avoid the similar scenarios 360/4!=15   15
Answer: B
In a function they are distributing noble prize. In how many ways can 4 prizes be distributed among 5 boys when a boy gets any no. of prizes?
Choose the correct choice from the following answers.
A) 48
B) 50
C) 625
D) 602
E) 525

Solution: Ans.(C)   Sol. In this case, repetitions are allowed, so all the four prizes can be given in 5 ways, i.e. (5*5*5*5) ways = 54 ways = 625 ways Or nr ways = 54 ways = 625 ways
Answer: C
If an object travels 90 feet in 3 seconds, what is the object’s approximate speed in miles per hour? (Note: 1 mile = 5280 feet)	Select:  A) 17.36  B) 20.45  C) 23.87  D) 26.92  E) 29.56

Solution: 90 feet/3 seconds = 30 feet/second   (30 feet/second)*(3600 seconds/hour)*(1 mile/5280 feet) = 20.45 miles/hour (approximately)   The answer is 20.45.
Answer: B
Rs.8000 become Rs.8652.8 in a certain interval of time at the rate of 4% per annum of C.I. Find the time? Choose the correct answer:	A) 6 years	B) 8 years	C) 9 years	D) 3 years	E) 2 years

Solution: 8652.8 = 8000(26/25)N   (26/25)^2 = (26/25)N => N = 2   At the end of two years what will be the comp.Answer: 2 years
Answer: E
The mean of 50 observations was 36. It was found later that an observation 34 was wrongly taken as 23. The corrected new mean is :  Pick.
A) 36.0	B) 36.5	C) 36.24	D) 36.12	E) 36.22

Solution: Explanation:   Correct Sum = (36 * 50 + 434 - 23) = 1825.   Correct mean = = 1811/50 = 36.5   Answer: 36.22) 36.22
Answer: E
On a ranch, a rancher can place a loop of rope, called a lasso, once in every 3 throws around a cow’s neck. What is the probability that the rancher will be able to place a lasso around a cow’s neck at least once in 3 attempts?	Select:
A) 1/3	B) 5/9	C) 7/9	D) 19/27	E) 23/27

Solution: P(missing all 3)=(2/3)^3=8/27   P(success on at least one attempt)=1-8/27=19/27   The answer is 19/27.
Answer: D
Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 10 cm? Pick one
A) 827 cm2
B) 216 cm2
C) 285 cm2
D) 178 cm2
E) 190 cm2

Solution: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)   = 1/2 (20 + 18) * (10)   = 190cm2   Answer:190 cm2
Answer: E
A committee is reviewing a total of 20x black-and-white films and 6y color films for a festival. If the committee selects y/x% of the black-and-white films and all of the color films, what fraction Q of the selected films are in color?	Choose the most appropriate option
A) 1/130  B) 1/5  C) 3/13  D) 10/13  E) 30/31

Solution: It's y/xpercentnot y/x.   If x=20 and y=10. Then:   20x=400 black-and-white films;   6y=60 color films.   y/x%=10/20= 
10/20 = 1/2 = around 0.5
0.5% of the black-and-white films, so 2 black-and-white films and all 60 color films, thus total of 62 films were selected.   Color films thus compose Q=60/62=30/31 of the selected films.   Answer: 30/31.
Answer: E
If the price has fallen by 14% what percent of its consumption be: increased so that the expenditure may be the same as before? Choose one.
A) 11 1/8% B) 11 1/5% C) 16 12/43% D) 17 7/9% E) 21 1/9%

Solution: 100 â€“ 14 = 86   86------14   100------? => 16 12/43%   Answer: 16 12/43%
Answer: C
If the ratio of boys to girls in a class is B and the ratio of girls to boys is G; then 10(B + G) is ?
Choose the most appropriate option:  A) Equal to 3  B) Less than 3  C) More than 10  D) Less than 10  E) none of these

Solution: Let number of boys = x   Let number of girls = y   Therefore x/y = B and y/x = G   10(B + G) = 10[(x/y) + (y/x)] = 10[(x2 + y2)/xy] > 10   ANSWER:More than 10
Answer: C
A train 345 m long passed a pole in 15 sec. How long will it take to pass a platform 760 m long?  Choose the correct choice
A) 76 sec  B) 43 sec  C) 45 sec  D) 15 sec  E) 16 sec

Solution: Speed = 345/15= 
345/15 = 23
23 m/sec.   Required time= (345 + 760)/23   = 48 sec.   Answer:43 sec
Answer: B
In a series of four football matches between Germany and Argentina , the probability of Germany winning a match is 1/3 and the probability that the match ends in a draw is 1/4. If a win gets the team 2 points, a draw 1 point and a loss 0 Points, What is the probability that Germany will end up in 4 draws in the series?	Choose the correct choice from the following answers.
A) 24/576  B) 125/864  C) 1/25  D) 1/256  E) 1/5

Solution: Since the probability of a draw is 1/4, then the probability of 4 draws in 4 matches is (1/4)^4=1/256.   Answer: 1/256.
Answer: D
A flight takes off at 2.00 a.m. from a place at 18N 10E and landed 10 hours later at a place with co-ordinates 36N 70W. What is the local time when the plane landed?
Answers.
A) 6.00 a.m. B) 6.40 a.m. C) 7.00 a.m. D) 7.40 a.m. E) 8.00 a.m.

Solution: Time difference between places will be 4*(70+10)= 
4*(70+10) = 320
320 min=   5 hrs 20 min   as change of 1 degree in longitude cause change of 4 minutes in time.   and that change is 80 degrees here.   so when plane land. time will be = 2.00 + 10.00 -5.20 = 6.40 a.m.   ANSWER:6.40 a.m.
Answer: B
If log 27 = 1.401, then the value of log 9 is:  Choose the correct choice from the following options: A) 0.934 B) 0.945 C) 0.954 D) 0.958 E) 0.998

Solution: log 27 = 1.401   log (3cube ) = 1.401   3 log 3 = 1.401   log 3 = 0.467   log 9 = log(3square ) = 2 log 3 = (2 x 0.467) = 0.934.   0.934nswer: Option 0.934
Answer: A
A, B, C subscribe Rs. 50,000 for a business. If A subscribes Rs. 4000 more than B and B Rs. 5000 more than C, out of a total profit of Rs. 35,000, what will be the amount A receives? Choose the correct choice:
A) 14700  B) 15700  C) 16700  D) 18700  E) 24700

Solution: Total amount invested = 50000   Assume that investment of C = x.   Then investment of B = 5000 + x ,   Investment of 14700 = 4000+5000+x = 9000+x   x + 5000+x + 9000+x = 50000   => 3x + 14000 = 50000   => 3x = 50000 – 14000 = 36000   => x = 36000/3= 
36000/3 = 12_000
12000=> Investment of C = x = 12000 ,   Investment of B = 5000 + x = 17000,   Investment of 14700 = 9000+x = 21000   Ratio of the investment of 14700 : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12   Share of 14700 = Total Profit * 21/50 = 35000 * 21/50 = 700*21= 
700*21 = 14_700
14700   14700nswer is 14700
Answer: A
Suppose f(x) is an odd function for which f(x + 2) = f(x) for all x, and
f(x) = x2nd for xε2 (0,1). Compute f(-3/2) + f(1). Select the correct option.
A) -1 B) -1/2 C) -1/4 D) 1/4 E) 1/2

Solution: Because f is periodic, we know that f(-3/2) = f(1/2) = (1/2)2 = 1/4. Because f   is odd, we know that f(1) = -f(-1), but because f is periodic, f(1) = f(-1). Therefore,   f(1) = 0 and the answer is 1/4.   correct answer 1/4
Answer: D
Six men and six women have to sit around a circular table so that no 2 women are together. In how many ways can that be done?	Options
A) 5!*6!
B) 6!*6!
C) 5!*7!
D) 6!*7!
E) 7!*7!

Solution: The number of arrangements of n distinct objects in a row is given by n!.   The number of arrangements of n distinct objects in a circle is given by (n-1)!.   The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have: n!/n=(n-1)!   Now, 6 men in a circle can be arranged in (6-1)! ways and if we place 6 women in empty slots between them then no two women will be together. The # of arrangement of these 6 women will be 6! and not 5! because if we shift them by one position we'll get different arrangement because of the neighboring men.   So the answer is indeed 5!*6!.   5!*6!
Answer: A
A man saves Rs 250 at the end of each year and lends the money at 5% compound interest. How much will it become at the end of 3 years.  Choose the correct choice from the following
A) Rs 827.53  B) Rs 862.01  C) Rs 822.02  D) Rs 862.03  E) None of these

Solution: Explanation:   =[250(21/20Ã—21/20Ã—21/20)+250(21/20Ã—21/20)+250(21/20)]=827.53   Option Rs 827.53
Answer: A
A certain candy manufacturer reduced the weight of Candy Bar M by 40 percent buy left the price unchanged. What was the resulting percent increase in the price per ounce of Candy Bar M?
Pick:  A) 66.66  B) 62.5  C) 58  D) 60  E) 62

Solution: assume 1oz candy cost $1 before.   now price remain same $1 but weight of candy reduces to 0.6 oz   new price of candy = 1/0.6 =1.6666   price increase 66.66 %   66.66
Answer: A
What are the maximum value and minimum values of f(x) = |2sin(2x - pi/3) - 5| + 3	Choose the correct choice: A) max10-min6 B) max11-min7 C) max12-min8 D) max13-min9 E) max14-min10

Solution: -1 <= sin(2x - pi/3) <= 1 : range of a sine function   -2 <= 2sin(2x - pi/3) <= 2 : mulitply all terms of the double inequality by 2   -2 - 5 <= 2sin(2x - pi/3) - 5 <= 2 - 5 : add -5 to all terms of the inequality.   -7 <= 2sin(2x - pi/3) - 5 <= -3   3 <= |2sin(2x - pi/3) - 5| <= 7 : change the above using absolute value.   3 + 3 <= |2sin(2x - pi/3) - 5| + 3 <= 7 + 3 : add 3 to all terms of the double inequality.   The maximum value of f(x) is equal to 10 and the minimum value of f(x) is equal to 6.   correct answer is max10-min6)max10-min6
Answer: A
A train 125 m long passes a man, running at 8 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:  Choose the correct choice from the following options.
A) 53	B) 50	C) 99	D) 288	E) 12

Solution: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 8) km/hr. x - 8 = 45 ==> x = 53 km/hr.53nswer: 53
Answer: A
Of the 5 numbers, whose average is 100, the first is one-fourth of the sum of the last 4. The first number is?
Choose the correct choice from the following answers.
A) 83.3
B) 80
C) 78.63
D) 56.98
E) 67.85

Solution: Let the first number be x   sum of the 5 numbers = x+5x = 6x   6x/5 = 100   x = 100*5/6 = 83.3   83.3nswer is 83.3
Answer: A
In how many different number of ways 4 men and 3 women can sit on a bench such that girls always sit together.
Choose the correct choice from the following choices:
A) 720 B) 740 C) 750 D) 770 E) 780

Solution: 720   720)
Answer: A
A division of a company consists of four men and six women. If two of these ten employees are randomly selected as representatives of the division, what is the probability that both representatives will be female?  Choose the correct choice from the following choices:  A) 1/6  B) 1/5  C) 1/4  D) 1/3  E) 1/2

Solution: The total number of ways to choose two representatives is 10C2=45.   The number of ways to choose two females is 6C2=15.   P(choosing two female representatives)=15/45=1/3   The answer is 1/3.
Answer: D
If an item that originally sold for A dollars was marked up by x percent and then discounted by L percent, which of the following expressions represents the final price of the item?
Select:
A) (10,000z + 100z(x – y) – xyz)/10,000  B) (10,000z + 100z(y – x) – xyz)/10,000  C) (100z(x – y) – xyz)/10000  D) (100z(y – x) – xyz)/10000  E) 10000 /(x – y)

Solution: value of item =A ..marked up by x% = Ax/100   total value = A +ax/100 .discounted by L% on Total L/100 * ( A+Ax/100)   Final price =(A+ Ax/100) - L/100 ( A +Ax/100)   (100z(x – y) – xyz)/10000
Answer: C
The sum of the non-prime numbers between 40 and 50, non-inclusive, is
Pick:
A) 131	B) 176	C) 274	D) 405	E) 495

Solution: The sum of the non-prime numbers between 40 and 50, non-inclusive, are {42, 44, 45, 46, 48, 49}.   6 times 40 something is approx north of 240   Hence the answer is (274) 274
Answer: C
If 75 percent of a class answered the first question on a certain test correctly, 35 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percent answered both correctly? Choose one:	A) 10%	B) (8) 20%	C) 30%	D) 50%	E) 65%

Solution: I didn't understand how to connect 20 percent with the whole equation.   Why 20 is out of the percentile diagram (circles) but inside of 100?   20% appeared in the exam; however did not answer Question AQuestion B correctly   So they are out of the two circles, however as they have appeared in the exam, they have to be taken into consideration for calculation purpose   I am doing it this way:   Suppose the total class size is 100, then 20 percent of the class answered incorrectly and rest 80 percent answered correctly in question 1 or 2 or both.   Now,   100 - [(75 - x) + x + (35 - x)] = 20 .......... values are in percent   x = 20 - 100 + 110= 
20 - 100 + 110 = 30
30   Ans: 30%
Answer: C
A bag contains 3 red, 2 green balls. 3 balls are drawn randomly. What is the probability that balls drawn contain exactly two green balls?  Choose one.
A) 1/7	B) 2/9	C) 3/11	D) 4/17	E) 3/10

Solution: Total number of balls = 3+2= 
3+2 = 5
5   n(S)= 5C3 = 5*4*3 / 3*2 = 10   n(3/10) = 2C2* 3C1 = 3   Probability = 3/10   Answer is 3/10
Answer: E
If all of the telephone extensions in a certain company must be even numbers, and if each of the extensions uses all four of the digits 1, 2, 3, and 6, what is the greatest number of four-digit extensions that the company can have?	Choose the correct option:
A) 4
B) 6
C) 12
D) 16
E) 24

Solution: The four digits available are 1,2,3 and 6   as the extensions can only be even numbers, the last digit has to be either 2 or 6   If it is 2...it leaves 1,3 and 6 for the first three digits...these can be arranged in 3! ways   If the last digit is 6...it leaves 1,2 and 3 for the first three digits...these can be arranged in 3! ways   Thus answer is 2*3! = 12 12
Answer: C
We have 10 people and 3 chairs. In how many ways chairs can be occupy? Choices.
A) 650 B) 720 C) 810 D) 790 E) 915

Solution: no. of ways they can be occupy = 10*9*8= 
10*9*8 = 720
720   Answer is 720
Answer: B
In a certain appliance store, each model of television is uniquely designated by a code made up of a particular ordered pair of letters. If the store has 80 different models of televisions, what is the minimum number of letters that must be used to make the codes?	Answers
A) 6  B) 7  C) 9  D) 8  E) 10

Solution: If n is the number of distinct letters used to create the two lettered codes, then a total of n∗n=n^2 different codes can be created. We need n2≥80. The smallest n which fulfills this condition is n = 9.   Answer 9
Answer: C
A taxi leaves Point A 2 hours after a bus left the same spot. The bus is traveling 20 mph slower than the taxi. Find the speed of the taxi, if it overtakes the bus in two hours. Choose one:	A) 42	B) 48	C) 44	D) 50	E) 40

Solution: Let the speed of bus be v - 20, speed of taxi be v   The bus travelled a total of 4 hrs and taxi a total of 2 hrs.   Hence 4 * (v-20) = 2v   4v - 80 = 2v   2v = 80   v = 40 mph   40
Answer: E
X, Y, and Z are different prime numbers. The product X^2*Y^2*Z^2 is divisible by how many different positive numbers?  Choose the correct choice from the following options:	A) 9	B) 18	C) 27	D) 36	E) 45

Solution: The exponents of X^2*Y^2*Z^2 are 2, 2, and 2.   The number of factors is (2+1)(2+1)(2+1) = 27   The answer is 27.
Answer: C
75% of the guestrooms at the Stagecoach Inn have a queen-sized bed, and each of the remaining rooms has a king-sized bed. Of the non-smoking rooms, 60% have a queen-sized bed. If 20% of the rooms at the Stagecoach Inn are non-smoking rooms with king-sized beds, what percentage of the rooms permit smoking?
Pick
A) 25%	B) 30%	C) 50%	D) 55%	E) 75%

Solution: Let x be the number of non-smoking rooms.   Let N be the total number of rooms at the inn.   40% of non-smoking rooms have a king-sized bed.   0.4x = 0.2N   x = 0.5N   The percentage of rooms which permit smoking is 1 - 0.5 = 50%   The answer is 50%.
Answer: C
Right triangle ABC is the base of the prism in the figure above. If AB=AC=âˆš10 and the height of the prism is 4, what is the volume of the prism?
Pick:  A) 40  B) 85  C) 20  D) 60  E) 45

Solution: Volume of prism = Area of base * height = 1/2* (square root of 10) * (square root of 10)*4= 20   Answer: 20
Answer: C
Jacob bought a scooter for a certain sum of money.He spent 10% of the cost on repairs and sold the scooter for a profit of Rs.1100. How much did he spend on repairs if he made a profit of 20% ?  Choose the correct choice from the following choices
A) Rs.400  B) Rs.440  C) Rs.500  D) Rs.550  E) Rs.650

Solution: Total Profit = Rs. 1100.   %Profit = 20.   20% = 1100,   So,   100% = 5500.   Rs. 5500 would be the cost price for Jacob.   He spends 10% on repairing. So,   Initial Cost + Repair Cost = 5500.   Let Initial Cost was X. then   X + 10% of X = 5500   1.1X = 5500   X = 5500/1.1= 
5500/1.1 = 5_000
5000.   The initial cost price was Rs. 5000. Thus, he spends Rs. 500 on repairing.   ANSWER : OPTION Rs.500
Answer: C
Two trains running in opposite directions cross a man standing on the platform in 25 seconds and 18 seconds respectively and they cross each other in 20 seconds. The ratio of their speeds is: Answers: A) 3 : 1 B) 3 : 2 C) 3 : 8 D) 2 : 5 E) 3 : 4

Solution: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 25 x meters, and length of the second train = 18 y meters. (25 x + 18 y) / (x + y) = 20 ==>   25 x + 18 y = 20 x + 20 y ==> 5 x = 2 y ==> x/y = 2/5   Answer: Option 2 : 5
Answer: D
How many 3 digit positive integers Q exist that when divided by 7 leave a remainder of 5? Choose the correct choice from the following choices:	A) 128	B) 142	C) 143	D) 141	E) 129

Solution: Minimum three digit number is 100 and maximum three digit number is 999.   The first three digit number that leaves remainder 5 when divided by 7 is 103.   14 * 7= 
14 * 7 = 98
98 +5= 
98 +5 = 103
103   The second three digit number that leaves remainder 5 when divided by 7 is 110.   15 * 7= 
15 * 7 = 105
105 +5= 
105 +5 = 110
110   The third three digit number that leaves remainder 5 when divided by 7 is 117   and so on   The last three digit number that leaves remainder 5 when divided by 7 is 999   142 * 7= 
142 * 7 = 994
994 + 5= 
994 + 5 = 999
999   Therefore, we identify the sequence   103,110,117.....999   use the formula of last term   Last term= first term + (n - 1) * common difference   you will get the answer 129 that is definitely 129.
Answer: E
A man invests Rs. 4,000 at the rate of 5% per annum. How much more should he invest at the rate of 8%, so that he can earn a total of 6% per annum? Answers
A) Rs. 1200
B) Rs. 1300
C) Rs. 1500
D) Rs. 2000
E) None of these

Solution: Explanation :   Interest on Rs.4000 at 5% per annum = ( 4000 × 5 × 1) / 100 = Rs. 200   Let his additional investment at 8% = x   Interest on Rs.x at 8% per annum = ( x × 8 × 1 ) / 100 = 2x/25.   To earn 6% per annum for the total, interest = (4000 + x) × 6 × 1/100.   => 200 + 2x/25 = (4000 + x) × 6 × 1/100.   => 20000 + 8x = (4000 + x) × 6.   => 20000 + 8x = 24000 + 6x.   => 2x=4000.   => x=2000.   Answer : Rs. 2000
Answer: D
A man travelled from the village to the post office at the rate of 10kmph and walked backed at the rate of 5 kmph. If the whole journey took 3hours, find the distance of the post office from the village? Select the correct option:	A) 10km	B) 15km	C) 20km	D) 25km	E) 30km

Solution: 10kmverage speed = 2xy/x+y = 2*10*5/10+5 = 20/3km/hr   Distance travelled in 3hours = 20/3 * 3= 
20/3 * 3 = 20
20km   Distance of the post office from the village= 20/2= 
20/2 = 10
10km   10kmnswer is 10km
Answer: A