MU-NLPC/Calc-aqua_rat huggingface dataset:
A certain number when divided by 45 leaves a remainder 31, what is the remainder if the same number be divided by 15?
Options:
A) 2
B) 7
C) 6
D) 1
E) 9

Solution: Explanation:   45 + 31= 
45 + 31 = 76
76/15= 1 (Remainder)   Answer: 1
Answer: D
A test has 180 questions. Each question has 5 options, but only 1 option is correct. If test-takers mark the correct option, they are awarded 1 point. However, if an answer is incorrectly marked, the test-taker loses 0.25 points. No points are awarded or deducted if a question is not attempted. A certain group of test-takers attempted different numbers of questions, but each test-taker still received the same net score of 40. What is the maximum possible number of such test-takers?  Choose the correct choice from the following options
A) 29
B) 33
C) 35
D) 40
E) 42

Solution: A correct answers get you 1 point, an incorrect answer gets you MINUS 1/4 point and a skipped question gets you 0 points. Since there are 200 total questions, there are a variety of ways to get a total of 40 points.   Let C be the number of correct answers and let I be the number of incorrect answers.   To get 40 points, a test taker must have at least 40 correct answers. Then C=> 40.   For every correct question above 40, the test taker has 4 incorrect answers.   Then, the I = 4*(C - 40).   Also, I + C <= 180. Thus 5C <= 340 and so C <= 68.   Then 40 <= C <= 68 and C can have 29 possible values.   The answer is 29.
Answer: A
A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 650 m long?  Pick
A) 870
B) 89
C) 90
D) 97
E) 98

Solution: Speed = 240/24= 
240/24 = 10
10 m/sec.   Required time= (240 + 650)/10= 
(240 + 650)/10 = 89
89 sec.   Answer: Option 89
Answer: B
For a light that has an intensity of 60 candles at its source, the intensity in candles, S, of the light at a point d d feet from the source is given by the formula S=60k/d^2 60, where k is a constant. If the intensity of the light is 20 candles at a distance of 3 feet from the source, what is the intensity of the light at a distance of 30 feet from the source?
Choose the correct choice from the following answers.
A) 3/10 candles
B) 1/2 candles
C) 1 1/3 candles
D) 1/5 candles
E) 3 candles

Solution: ANS = 3/10   S= 60k/d^2   At 3 feet   20 = 60k/9 so k = 3   At 20 feet   S = 60 *3/30^2 = 1/5   1/5 candles
Answer: D
The areas, in kilometers squared, of some countries are given below. USA: 9,629,091, Russia: 20,098,242, China: 9,598,094, Canada: 9,984,670, the UK: 242,400 and India: 3,287,263.
What is the difference between the areas of Russia and China? Choose the correct choice from the following.
A) 5,476,811 kilometers squared B) 10,500,148 kilometers squared C) 9,843,123 kilometers squared D) 1,878,965 kilometers squared E) 4,787,900 kilometers squared

Solution: he difference between the areas of Russia and China is given by   20,098,242 - 9,598,094 = 10,500,148 kilometers squared   correct answer 10,500,148 kilometers squared
Answer: B
The true discount on Rs. 1760 due after a certain time at 12% per annum is Rs. 160. The time after which it is due is :
Choose the correct choice from the following choices:
A) 6 months B) 8 months C) 9 months D) 10 months E) None of these

Solution: Solution   P.W = Rs. (1760 - 160) = Rs. 1600.   ∴ S.I on Rs.1600 ar 12% is Rs. 160.   ∴ Time = ( 100 x160/1600 x 12) = 5/6 = ( 5/6x12 ) months = 10 months.   Answer 10 months
Answer: D
Two trains 140 m and 200 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
Pick one:  A) 10.9 sec  B) 8.64 sec  C) 53.8 sec  D) 10.8 sec  E) 10.4 sec

Solution: Relative speed = 60 + 40= 
60 + 40 = 100
100 km/hr.= 100 * 5/18 = 250/9 m/sec.   Distance covered in crossing each other = 140 + 200 = 240 m.   Required time = 240 * 9/250= 
240 * 9/250 = 216/25 = around 8.64
8.64 sec.   Answer: 8.64 sec:
Answer: B
The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number?  Choose the correct choice from the following answers.
A) 79 B) 56 C) 81 D) Cannot be determined E) None of these

Solution: Let the ten's digit be x and unit's digit be y.   Then, x + y = 15 and x - y = 3 or y - x = 3.   Solving x + y = 15 and x - y = 3, we get: x = 9, y = 6.   Solving x + y = 15 and y - x = 3, we get: x = 6, y = 9.   So, the number is either 96 or 69.   Hence, the number cannot be determined.   Answer:Cannot be determined
Answer: D
A candidate got 32% of the votes polled and he lost to his rival by 1908 votes. How many votes were cast? Choose the correct option: A) 5100 B) 5200 C) 5300 D) 5400 E) 5500

Solution: Let x be the total number of votes.   0.32x + 1908 = 0.68x   0.36x = 1908   x = 1908/0.36= 
1908/0.36 = 5_300
5300   The answer is 5300.
Answer: C
A certain car can travel 64 kilometers on a liter of fuel. If the fuel tank’s contents decrease by 3.9 gallons over a period of 5.7 hours as the car moves at a constant speed, how fast is the car moving, in miles per hour? (1 gallon = 3.8 liters; 1 mile = 1.6 kilometers) Options:  A) 52  B) 65  C) 78  D) 91  E) 104

Solution: Fuel used 3.9 gallons ;convert to liters--> 3.9 x 3.8 liters   Time = 5.7 hours   1 mile = 1.6 kilometers ;convert to miles--> 1km = 1/1.6 mile   Speed (km/hour)  --  1= 
  --  1 = 1
1/1.6 mile   Speed (km/hour)= D/T = 64 (km*) x 3.9 x 3.8 / 5.7   replace (km*) to miles ; multiply by 1/1.6 mile   Speed (miles/hour)= 64 x 3.9 x 3.8 / 5.7 x 1.6 = 78 miles/hour   Ans :104   PS :i felt the factors were easy to cancel out ,so didn't require much rounding off   = 64 x 3.9 x 3.8 / 5.7 x 1.6   = 104 104
Answer: E
A can do a job in 15days and B in 20days. If they work on it together for 5 days, then the fraction of the work that is left is?
Choose the correct option
A) 2/15  B) 8/15  C) 3/11  D) 5/12  E) 6/13

Solution: A's 1 day work = 1/15   B's 1day work = 1/20   A+B 1day work = 1/15 + 1/20  +  1= 
 +  1 = 1
1/15 + 1/20= 7/60   A+B 5days work = 7/60*5 = 7/12   Remaining work = 1 - 7/12 = 5/12   Answer is 5/12
Answer: D
A and B walk around a circular track. They start at 9 a.m. from the same point in the opposite directions. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other before 10.30 a.m.?  Choose the correct choice from the following answers
A) 8
B) 7
C) 12
D) 5
E) 3

Solution: Sol.   Relative speed = (2 + 3)= 
(2 + 3) = 5
5 rounds per hour.   So, they cross each other 5 times in an hour and 2 times in half an hour.   Hence, they cross each other 12 times before 10.30 a.m.   Answer 12
Answer: C
What amount does Kiran get if he invests Rs.8000 at 10% p.a. compound interest for two years, compounding done annually?
Choose one:  A) Rs.9630  B) Rs.9680  C) Rs.9610  D) Rs.9650  E) None of these

Solution: A= P{1 + R/100}n   => 8000{1 + 10/100}2 = Rs.9680   ANSWNone of theseR:None of these
Answer: E
A can do a job in 20 days and B can do it in 30 days. A and B working together will finish twice the amount of work in ------- days? Choose the correct choice.
A) 24 days  B) 22 ½ days  C) 23 ½ days  D) 12 ½ days  E) None of these

Solution: Explanation:   1/20 + 1/30 = 5/60 = 1/12   12 = 12 *2= 
12 *2 = 24
24 days   24 daysnswer: 24 days
Answer: A
Which of the following inequalities has a solution set, when graphed on the number line, is a single line segment of finite length? Options: A) 2 <= 5x+6 <= 6 B) 2 <= 3x+4 <= 6 C) 2 <= 5x+4 <= 6 D) 2 <= 3x+7 <= 6 E) 2 <= 3x+8 <= 6

Solution: The key words in the stem are:a singleline segment offinite length   Now, answer choices A, B, and C can not be correct answers as solutions sets for these exponential functions are not limited at all (>= for even powers and <= for odd power) and thus can not be finite (x can go to + or -infinity for A and C and x can got to -infinity for B). As for D: we have thatabsolute valueof x is between two positive values, thus the solution set for x (because of absolute value) will be two line segments which will be mirror images of each other.   Answer: 2 <= 3x+4 <= 6.
Answer: B
U(x, y) is the intersection point between the circle (x^2 + y^2 = 4) and the line (y = x +2). Which of the following can be the point U?  Select the correct option:
A) (1, 2).  B) (2, 0).  C) (0, -2).  D) (-2, 0).  E) (2, 2).

Solution: A quick glance at the options,U(x, y) and we can see that A and E do not satisfy the circle equation. Now we are left with B, C and D. Now B and C do not satisfy the line equation. So we are just left with D. And thats the answer=(-2, 0).
Answer: D
If a man lost 8% by selling oranges at the rate of 25 a rupee at how many a rupee must he sell them to gain 25%?
Choose the correct choice from the following choices.
A) 20  B) 15  C) 18.4  D) 20  E) 12.8

Solution: 92% ---- 25   125% ---- ?     92/125* 25= 
  92/125* 25 = 92/5 = around 18.4
18.4   Answer: 18.4
Answer: C
There are 2 bars of gold-silver alloy; one piece has 2 parts of gold to 3 parts of silver and another has 3 parts of gold to 7 parts of silver. If both bars are melted into 8 kg bar with the final gold to silver ratio of 5:11. What was the weight of the first bar?  Choose the correct choice
A) 1 kg
B) 3 kg
C) 5 kg
D) 6 kg
E) 7 kg

Solution: irst bar is x kg, then second bar is (8-x)kg   First bar:   1 kgmt of gold = 2x/5kg   1 kgmt of silver = 3x/5 kg   Second bar:   1 kgmt of gold = 3(8-x)/10 kg   1 kgmt of silver = 7(8-x)/10 kg   Total amt of gold = 2x/5 + 3(8-x)/10 = (4x+24-3x)/10 = (x+24)/10 kg   Total amt of silver = 3x/5 + 7(8-x)/10 = (6x+56-7x)/10 = (56-x)/10 kg   Ratio of gold/silver = 5/11 = (x+24)/10 * 10/(56-x)   5/11 = (x+24)/(56-x)   5(56-x) = (x+24)(11)   x = 1kg   1 kgNSWER:1 kg
Answer: A
Watermelon Computer Company began production in 2001 with a total of only 10 employees. From 2001 to 2006, the total number of employees increased to 500. From 2001 to 2016, the total number of employees increased to 5,000. What was the percentage increase of employees from 2006 to 2016? Choices
A) 10,000%	B) 6,700%	C) 2,000%	D) 3,000%	E) 5,000%

Solution: The percentage increase of employees 2006-16 is calculated by;   (100)[(total employees 2001-16) - (total employees 2001-06)]/(total employees 2006) percent.   Solution:(100) [(5,000-500)/150]% = 3,000%   Answer is 3,000%
Answer: D
If 75 % of a boys answered the first question on a certain test correctly, 55 % answered the second question on the test correctly, and 20 % answered neither of the questions correctly, what % answered both correctly?	Choose the correct option
A) 10%	B) (8) 20%	C) 50%	D) 60%	E) 65%

Solution: {Total} = {First} + {Second} - {Both} + {Neither}   100% = 75% + 55% - {Both} + 20% --> {Both} = 50%.   Answer: 50%
Answer: C
What least number should be subtracted from 13601 such that the remainder is divisible by 87 ? Choose the correct answer
A) 27  B) 29  C) 28  D) 30  E) 31

Solution: 13601 ÷ 87 = 156, remainder = 29   Hence 29 is the least number which can be subtracted from 13601 such that the remainder   is divisible by 87   Answer is 29
Answer: B
If 3 persons can do 3 times of a particular work in 3 days, then, 7 persons can do 7 times of that work in?
Choose the correct choice from the following answers
A) 3 days  B) 5 days  C) 7 days  D) 11 days  E) 12 days

Solution: That is, 1 person can do one time of the work in 3 days.   Therefore, 7 persons can do 7 times work in the same 3 days itself.   3 days)
Answer: A
The average weight of 20 persons sitting in a boat had some value. A new person added to them whose weight was 45 kg only. Due to his arrival, the average weight of all the persons decreased by 5 kg. Find the average weight of first 20 persons?	Choose the correct choice from the following answers:  A) 55  B) 56  C) 57  D) 58  E) 60

Solution: 20x + 45 = 21(x – 5)   X=60   ANSW60R:60
Answer: E
A can do a half of certain work in 60 days and B one third of the same in 35 days. They together will do the whole work in.  Choose one.
A) 56 days  B) 420 days  C) 46 days  D) 560 days  E) 96 days

Solution: 56 days = 120 days   B = 105 days   1/120 + 1/105 = 45/2520 = 1/56   =>56 days   56 daysNSWER:56 days
Answer: A
A does half as much work as Band C does half as much work as A and B together. If C alone can finish the work in 20 days, then together ,all will finish the work in :
Choose the correct option:	A) 13 1/3 days	B) 12 1/3 days	C) 15 days	D) 20 days	E) 10 days

Solution: C alone can finish the work in 20 days.   (A + B)can do it in 20 days   (A + B)s 1 days wok = 1/20.   As 1 days work : Bs 1 days Work = 1/2 : 1 = 1:2.   Aâ€™s 1 dayâ€™s work = (1/20) * (1/3) = (1/60). [Divide 1/20 in the raio 1:2] Bs 1 days work = (1/20) * (2/3) = 1/30   (A+B+c)S 1 dayâ€™s work = (1/60) + (1/30) + (1/20) = 1/10   All the three together will finish it in = 10days.   ANSW10 daysR:10 days
Answer: E
The ratio of number of ladies to gents at a party was 1 : 2, but when 2 ladies and 2 gents left, the ratio became 1 : 3. How many people were originally present at the party? Choose the correct choice from the following answers
A) 6 B) 9 C) 12 D) 10 E) None of these

Solution: Let number of ladies = x   then, number of gents = 2x   Now, x−2/2x−2=13⇒ 3x - 6 = 2x - 2   ⇒ x = 4   ∴ Total number of people originally present = 4 + 8= 
4 + 8 = 12
12   Answer 12
Answer: C
The number which exceeds 12% of it by 52.8 is:
Choose the correct choice from the following answers:
A) 50
B) 52
C) 58
D) 60
E) None of these

Solution: Explanation:   Let the number be x. Then, x – 12% of x = 52.8   x – (12/100)x = 52.8   x (1– 12/100) = 52.8   (88/100)x = 52.8   x = (100 X 52.8) / 88 = 60   ANSWER 60
Answer: D
Baney covered a distance of 340 miles between city A and city B taking a total of 5 hours. If part of the distance was covered at 60 miles per hour speed and the balance at 80 miles per hour speed, how many hours did she travel at 60 miles per hour?	Choose the correct choice from the following options:
A) 1 hour 45 minutes	B) 2 hours	C) 2 hours 30 minutes	D) 3 hours	E) None of these

Solution: Baney covered a distance of 340 miles between city A and city B taking a total of 5 hours.time taken at 60:time taken at 80::(greater speed-average speed):(average speed-lower speed)   average speed is   340/5= 
  340/5 = 68
68   That gives the answer 3:2=3 hours
Answer: D
An exam consists of 200 questions to be solved in 3 hours, out of which 50 are maths questions. It is suggested that twice as much time be spent on each math question as for each other question. How many minutes should be spent on maths problems? Choose the correct answer
A) 36/25 minutes  B) 36/24 minutes  C) 36/26 minutes  D) 35/25 minutes  E) 34/25 minutes

Solution: x=time for each math problem   y= time for every other problem   50x+150y=180 minutes   x=2y because spent twic as much time on the math problems as the other   50(2y)+150y=180   100y+150y=180   250y=180   y= 180/250=18/25 of a minute per problem on the other questions   x=2(18/25)   x=36/25 minutes   36/25 minutesNSWER:36/25 minutes
Answer: A
I am five letter word. if you remove one, only two letters remain.
What word am I  Choose the correct choice from the following choices:
A) I am phone B) I am table C) I am Water D) I am Stone E) None

Solution: Correct Answer : D   Stone is five letter word. If your remove one from stone(not 1letter) we will get St
Answer: D
Which of the following describes all values of x for which 16–x^2 >= 0? Choose one.
A) x >= 1 B) x <= –1 C) 0 <= x <= 1 D) x <= –1 or x >= 1 E) –4 <= x <= 4

Solution: 16 - x^2 >=0   means x^2 - 16 <=0   => (x-4)(x+4) <= 0   => -4 <= x <= 4   Answer - –4 <= x <= 4
Answer: E
In a caravan, in addition to 50 hens there are 45 goats and 8 camels with some keepers. If the total number of feet be 224 more than the number of heads, find the number of keepers.  Choose the correct choice from the following choices.
A) 11  B) 12  C) 13  D) 14  E) 15

Solution: Let the number of keepers be x.   Then, total number of feet = 2*50+4*45+4*8+2x   = 2x + 312   Total number of heads = 50+45+8+x = 103 + x   Now, (2x+312) = (103+x)+224   => x = 15   ANSW15R:15
Answer: E
Albert completes a piece of work in 20 days, Rose completes the same work in 30 days. If both of them work together, then the number of days required to complete the work is?  Choose one.
A) 10 B) 12 C) 15 D) 20 E) 18

Solution: If A can complete a work in x days and B can complete the same work in y days, then, both   of them together can complete the work in x y/ x+ y days.   That is, the required No. of days = 20 × 30/50 = 12 days   Answer is 12
Answer: B
Ernie invested Rs. 2000, with compounded interest annually. After 3 and half years the investment doubled. How many more years will it take before he earns another Rs. 4000 compound interest? Choose the correct choice from the following choices: A) 3.5 years B) 1.5 years C) 2.5 years D) 3 years E) 5 years

Solution: Explanatory Answer   Rs.2000 invested in compound interest becomes Rs.4000 in 3.5 years.   The amount will double again in another 3.5 years.   i.e., the amount will become Rs.4000 in another 3.5 years.   So, to earn another Rs.4000 interest, it will take another 3.5 years.   3.5 yearsnswer 3.5 years
Answer: A
Ratio between Rahul and Deepak is 4:3, After 6 Years Rahul age will be 30 years. What is Deepak present age?	Choose the correct answer:  A) 18  B) 15  C) 77  D) 266  E) 182

Solution: Present age is 4x and 3x,   => 4x + 6 = 30 => x = 6   So Deepak age is = 3(6) = 18   18nswer: 18
Answer: A
A wheel that has 14cogs is meshed with a larger wheel of 28cogs. When the smaller wheel has made 20evolutions, then the number of revolutions mad by the larger wheel is: Select.
A) 20
B) 11
C) 12
D) 10
E) 15

Solution: D   10   Let the required number of revolutions made by larger wheel be x.   Then, More cogs, Less revolutions (Indirect Proportion)   28 : 14 :: 20 : x <-> 28 x x = 14 x 20   x = (14 x 20)/28   x =10
Answer: D
A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
Answers
A) 5.79
B) 5.71
C) 5.76
D) 5.79
E) 5.73

Solution: M = 6   S = 1.2   DS = 7.2   US = 4.8   x/7.2 + x/4.8 = 1   x = 2.88   D = 2.88 * 2= 
2.88 * 2 = 5.76
5.76   Answer: 5.76
Answer: C
√5 percent of 5√5 =  Choose one:
A) 0.05
B) 0.25
C) 0.5
D) 2.5
E) 25

Solution: √/1005/100* 55√5   = (5*5∗5− − √5∗5 )/100   = (5*5) /100   = 25/100= 
25/100 = 1/4 = around 0.25
.25   ANSWER:0.25
Answer: B
A and B started a partnership business investing some amount in the ratio of 3 : 5. C joined then after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C?
Pick one
A) 4 : 9 : 8	B) 5 : 7 : 4	C) 6 : 10 : 5	D) 7 : 9: 4	E) 5 : 4 : 8

Solution: Let the initial investments of A and B be 3x and 5x.   A : B : C = (3x x 12) : (5x x 12) : (5x x 6) = 36 : 60 : 30   = 6 : 10 : 5.   ANSWER :6 : 10 : 5
Answer: C
Out of 450 students of a school, 325 play football, 175 play cricket and 50 neither play football nor cricket. How many students play both football and cricket ?  Choose the correct option.
A) 75
B) 100
C) 125
D) 150
E) 175

Solution: Explanation:   Students who play cricket, n(A) = 325   Students who play football, n(100) = 175   Total students who play either or both games,   =n(Aâˆª100)=450âˆ’50=400Required Number,n(Aâˆ©100)=n(A)+n(100)âˆ’n(Aâˆª100)=325+175âˆ’400=100   ANSWER IS 100
Answer: B
If a boat goes 6 km upstream in 90 minutes and the speed of the stream is 3 kmph, then the speed of
the boat in still water is	Options:
A) 12 kmph
B) 7 kmph
C) 14 kmph
D) 15 kmph
E) None of these

Solution: Explanation:   Rate upstream = (6/90)*60= 
(6/90)*60 = 4
4 kmph.   Speed of stream= 3 kmph.   Let speed in still water is x km/hr   Then, speed upstream = (x ï¿½3) km/hr.   x-3 = 4 or x = 7 kmph   Answer: 7 kmph
Answer: B
What is the greatest prime factor of 9!8! + 8!7! ?
Choose the correct choice: A) 23 B) 43 C) 53 D) 73 E) 83

Solution: 9!8! + 8!7! = 8!7!(9*8+1) = 8!*7!*73   The answer is 73.
Answer: D
The owner of a cell phone shop charges his customer 23% more than the cost price. If a customer paid Rs.7,190 for a cell phone, then what was the cost price of the cell phone? Choose the correct choice from the following answers:  A) Rs.5,845  B) Rs.6,750  C) Rs.5,700  D) Rs.6,925  E) None of these

Solution: Explanation:   123% of CP =SP   Therefore, CP = Rs.7,190x100/123 = Rs.5845   Rs.5,845nswer: Option Rs.5,845
Answer: A
The maximum numbers of students among them 891 pens and 810 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is	Choose the most appropriate option:
A) 91  B) 81  C) 1001  D) 1911  E) None

Solution: olution   Required number of students.   = H.C.F of 891 and 810.   â€¹=â€º 81.   Answer 81
Answer: B
If the two hands in a clock are 3 minutes divisions apart,then the angle between them is	Select the correct option.
A) 3°	B) 18°	C) 24°	D) 60°	E) None of these

Solution: In a clock, each minute makes 6°   ∴ 3 minutes will make 6 × 3 = 18°   Answer 18°
Answer: B
A drove of sheep and chickens have a total of 99 heads and feet. There are twice as many chickens as sheep. How many of each are there? Choose the correct choice from the following answers: A) 18,9 B) 17,9 C) 1,9 D) 16,9 E) 18,8

Solution: let chicken be x and sheep be y   x=2y (given)   3x+5y=99 (chicken has two legs and one head i.e 3 likewise sheep=5   y=9   x=18   18,9NSWER:18,9
Answer: A
A gambler has won 40% of his 40 poker games for the week so far. If, all of a sudden, his luck changes and he begins winning 80% of the time, how many more games must he play to end up winning 60% of all his games for the week? Choose one:
A) 20	B) 25	C) 30	D) 35	E) 40

Solution: Let x be the number of additional games the gambler needs to play.   0.4(40) + 0.8x = 0.6(x+40)   0.2x = 8   x = 40   The answer is 40.
Answer: E
The probability that a man will be alive for 10more yrs is 1/2 & the probability that his wife will alive for 10 more yrs is 1/3. The probability that none of them will be alive for 10 more yrs, is Choose the correct choice from the following options
A) 1/2	B) 1	C) 1/3	D) 3/4	E) 2

Solution: Sol. Required probability = Pg.) x P(B) = (1— D x(1 —I) =: x 1=1/3   Ans.(1/3)
Answer: C
A set of numbers has an average of 20. If the largest element is 4 greater than 3 times the smallest element, which of the following values cannot be in the set? Choose one.
A) 55	B) 90	C) 23	D) 50	E) 55

Solution: Ans: B   Solution: we are given the relation between smallest and the largest term. so let the smallest a and largest be 3a+4   so the avg = 50   which tells us that any value of a must be less than 20   so a<50 means, largest value 3a+4 <(3*20)+4   =largest value must be <64   so 64 can not be the value in the set.
Answer: B
A shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 3 a rupee. Find his net profit or loss percent?  Choose the correct choice from the following answers:
A) 33 1/8 % B) 33 8/3 % C) 33 1/3 % D) 93 1/3 % E) 43 1/3 %

Solution: The total number of mangoes bought by the shopkeeper be 12.   If he buys 4 a rupee, his 33 1/3 %P = 3   He selling at 3 a rupee, his SP = 4   Profit = SP - 33 1/3 %P = 4 - 3= 
4 - 3 = 1
1   Profit Percent= 1/3 * 100 = 33 1/3 %   Answer:33 1/3 %
Answer: C
Kim bought a total of $2.65 worth of postage stamps in four denominations. If she bought an equal number of 5-cent and 25-cent stamps and twice as many 10-cent stamps as 5-cent stamps, what is the least number of 6-cent stamps she could have bought ? Choose the correct choice:
A) 5
B) 10
C) 15
D) 20
E) 2.5

Solution: 2.65 = 0.05x + 0.25x + 2 * 0.10x + 0.06y   => 2.65 = 0.30x + 0.20x + 0.06y   => 265 = 50x + 6y   So Max value of 50x < 265 = 250   Hence y = 2.5   Answer - 2.5
Answer: E