MU-NLPC/Calc-aqua_rat huggingface dataset:
Jerry went to a shop and bought things worth Rs. 35, out of which 30 % went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?	Choose one:
A) 19  B) 19.7  C) 21.3  D) 21.5  E) 29.7

Solution: Total cost of the items he purchased = Rs.35   Given that out of this Rs.35, 30 % is given as tax   => Total tax incurred = 30 % = Rs.30/100   Let the cost of the tax free items = x   Given that tax rate = 6%   ∴ (35−30/100−x)6/100 = 30/100   ⇒ 6(35 −0.3 −x) = 30   ⇒ (35 − 0.3 − x) = 5   ⇒ x = 35 − 0.3 − 5 = 29.7   29.7)
Answer: E
Of the 800 employees of Company P, 60 percent have been with the company for at least ten years. If q of theselong-termmembers were to retire and no other employee changes were to occur, what value of q would reduce the percent oflong-termemployees in the company to 50 percent ?
Choose the correct choice from the following
A) 200 B) 160 C) 112 D) 80 E) 56

Solution: The # oflong-termemployees is 60%*800=480.   After q of them retire new # oflong-termemployees would become 480-q.   Total # of employees would become 800-q.   We want 480-q to be 50% of 800-q --> 480-q=(800 -q)*50% --> q = 160.   Answer: 160.
Answer: B
Three cricket players -- Ramesh, Suresh and Ganesh play for three different cricket Teams Haryana, Delhi and Rajasthan respectively. Ramesh was born in Chennai but brought up in Karnal, Haryana. Suresh was born in Delhi and brought up in Delhi. Ganesh's fore-fathers were from Madurai but settled in Rajasthan. All the three participated in a cricket tournament. Ramesh's runs to Suresh's runs and Suresh's runs to Ganesh's runs are in the ratio 5:7. If the total runs scored by all the three players in the tournament is 327, find the total runs scored by Suresh in the tournament?	Choose the correct choice from the following
A) 95	B) 85	C) 65	D) 105	E) 115

Solution: Ramesh:suresh=5:7 and Suresh:Ganesh=5:7   By making suresh to be equal in two ratios, we get   R:S=25:35 and S:G=35:49   So, Total runs scored by them=109x=327   x=327/109= 
327/109 = 3
3   Total runs scored by suresh=35*x=35*3= 
35*3 = 105
105   ANSWER:105
Answer: D
Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is? Choose the correct choice from the following answers:
A) 40
B) 50
C) 60
D) 70
E) 80

Solution: Let the speed of the slower train be x m/sec.   Then, speed of the train = 2x m/sec.   Relative speed = ( x + 2x) = 3x m/sec.   (100 + 100)/8 = 3x => x = 25/3.   So, speed of the faster train = 50/3 = 50/3 * 18/5= 
50/3 * 18/5 = 60
60 km/hr.   Answer: Option 60
Answer: C
Sinha and Mitra started a business by investing Rs.52000 and Rs.55000 respectively, after three months Mitra invested Rs.5000 more in the business. What is the share of Mitra in the half year profit of Rs.26280
Choose one:
A) 13860  B) 12000  C) 14200  D) 13980  E) 13800

Solution: Sinha = 52000 x 6 = 312000.   Mitra = 55000 x 3 = 165000 + 60000 x 3 = 180000 = 345000.   Ratio of investments = Sinha : MItra = 312000 : 345000 = 104 : 115 => [219 units].   Mitra share in the profit = 25280 × 115 / 219 = Rs.13800   Option 13800
Answer: E
A collector collects stamps from foreign countries. In June, she gave 20 percent of her stamps to her friend. In July, she gave 10 percent of her remaining stamps to another friend. If these were the only changes in the number of stamps in the stamp collection during those two months, what percent of her collection at the beginning of June did she give to away in June and July?
Choose the most appropriate option
A) 20%
B) 24%
C) 28%
D) 32%
E) 36%

Solution: Let x be the number of stamps in the original collection.   The percentage of the collection given away is:   0.2x + 0.1(0.8x) = 0.2x + 0.08x = 0.28x 0.2  + 0.08= 
0.2  + 0.08 = 0.28
0.28x= 28%   The answer is 28%.
Answer: C
Carol and Jordan draw rectangles of equal area. If Carol's rectangle measures 8 inches by 15 inches and Jordan's rectangle is 4 inches long, how wide is Jordan's rectangle, in inches?
Choose one:
A) 24
B) 26
C) 28
D) 30
E) 32

Solution: Area of first rectangle is 8*15= 
8*15 = 120
120 hence area of second would be 4x=120x   x=30   answer is 30
Answer: D
Peter rolls two dice at the same time. What is the probability that the total sum of numbers on the dices is 3? Options:
A) a) 1/12  B) b) 1/36  C) c) 1/6  D) d) 1/18  E) e) 1/3

Solution: We can have 6 different outcomes on a dice.   Total outcomes on two dices = 6*6   We need only the cases where sum of the outcomes is 3,   They can be {1, 2}, {2, 1}   A total of 2 outcomes   Probability = favorable outcomes/ total outcomes = 2/36 = 1/18.   Option d) 1/18
Answer: D
Let A = {x: x is a natural number and a factor of 18}
B= {x: x is a natural number and less than 6}
Find A ∪ B and A ∩ B Choose the correct choice:
A) A ∩ B = {1,2,3} B) A ∩ B = {2,5,4} C) A ∪ B = {5,7,9} D) A ∪ B = {1,2,3} E) A ∪ B = {2,5,4}

Solution: A ∩ B = {1,2,3}= {1,2,3,6,9,18}   B= {1,2,3,4,5} Therefore , correct answer : A ∩ B = {1,2,3} ∩ B = {1,2,3} (A ∩ B = {1,2,3})
Answer: A
How much greater is the combined area in square inches of the front and back of a rectangular sheet of paper measuring 11 inches by 9 inches than that of a rectangular sheet of paper measuring 4.5 inches by 11 inches?  Choose the correct choice from the following:
A) 50%
B) 87%
C) 100%
D) 187%
E) 200%

Solution: Let's just look at the dimensions (no calculation needed).   With dimension 11 the same, the other dimension 9 is twice 4.5   Then the area will be double which means 100% greater.   The answer is 100%.
Answer: C
756 can be expressed as a product of primes as
Choose the correct choice from the following.
A) 2 × 2 × 3 × 3 × 7 × 7  B) 2 × 3 × 3 × 3 × 7 × 7  C) 2 × 2 × 2 × 3 × 3 × 7  D) 2 × 2 × 3 × 3 × 3 × 7  E) None of these

Solution: Explanation:   It is clear that 756 = 2 × 2 × 3 × 3 × 3 × 7   Answer: Option 2 × 2 × 3 × 3 × 3 × 7
Answer: D
The average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 24 years. Find the average age of the women?	Select the correct option.
A) 11 B) 12 C) 30 D) 98 E) 15

Solution: 20 + 24 + 8 * 2= 
20 + 24 + 8 * 2 = 60
60/2= 
60/2 = 30
30   Answer: 30
Answer: C
Look at this series: 1000, 200, 40, ... What number should come next?
Choices.
A) 17  B) 10  C) 15  D) 18  E) 8

Solution: E   8   This is a simple division series. 8ach number is divided by 5.
Answer: E
A box contains 4 yellow balls and 5 black balls. One by one, every ball is selected at random without replacement. What is the probability that the fourth ball selected is black?
Choose the correct choice from the following options:
A) 2/5
B) 3/7
C) 5/9
D) 2/3
E) 3/4

Solution: Each ball has an equal chance (1/9) of being selected fourth.   The probability that a black ball is selected fourth is 5/9.   The answer is 5/9.
Answer: C
A team has to design a flag. The team two yellow strips of cloth and four green strips of cloth that they must use as is to make the flag. How many different flags can the team design with the materials at hand? Choose the correct choice from the following answers.
A) 15  B) 48  C) 240  D) 288  E) 720

Solution: The # of permutations of total 2+4= 
2+4 = 6
6 strips where 2 are identical yellow and 4 are identical green is 6!/(2!*4!)=15 (note that they must use all the materials at hand, also I guess that the strips must be either only vertical or only horizontal).   15nswer: 15.
Answer: A
Due to construction, the speed limit along an 5-mile section of highway is reduced from 60 miles per hour to 40 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options.
A) A) 3.12 B) B) 2.5 C) C) 10 D) D) 15 E) E) 24

Solution: Old time in minutes to cross 5 miles stretch = 5*60/60= 
5*60/60 = 5
5*1/1= 
5*1/1 = 5
5   New time in minutes to cross 5 miles stretch= 5*60/40 = 5*3/2= 
5*3/2 = 15/2 = around 7.5
7.5   Time difference= 2.5   Ans:2.5
Answer: B
Two trains 140 m and 170 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?  Choose the correct choice from the following:  A) 10.9 sec  B) 11.16 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 + 170= 
140 + 170 = 310
310 m.   Required time= 310 * 9/250= 
310 * 9/250 = 279/25 = around 11.16
11.16 sec.   Answer: 11.16 sec:
Answer: B
If the perimeter of a rectangular garden is 600 m, its length when its breadth is 150 m is?	Answers:
A) 150 m
B) 899 m
C) 200 m
D) 166 m
E) 187 m

Solution: 2(l + 150) = 600 => l   = 150 m   150 mnswer: 150 m
Answer: A
What is the least number that should be added to 1053, so the sum of the number is divisible by 23?  Answers
A) 1
B) 2
C) 3
D) 4
E) 5

Solution: (1053 / 23) gives a remainder 18 so we need to add 5.   The answer is 5.
Answer: E
In a ranch, the total number of black horses is 18% more than the number of male black horses. The total number of female horses is 16 times the number of black female horses. What percentage of male horses are black if the total number of male horses is double the number of female horses? Choose the correct option:  A) 17.4  B) 18.6  C) 19.2  D) 22.9  E) 50.6

Solution: Since we are dealing in percentage let us pick 100 as the number of black male horses.   That means that the total number of black horse is= 110 (18% more),   therefore the number of black female horse is 18.   The total number of female horses is 16x the number of black female horses= 16*18= 
16*18 = 288
288 female horses.   Male horse total population is twice the population of the female horses= 288*2= 
288*2 = 576
576   Therefore percentage of male horses that are brown= 100/576*100=17.4   Correct option is 17.4
Answer: A
In a shop, the cost of 4 shirts, 4 pairs of trousers and 2 hats is $560. The cost of 9 shirts, 9 pairs of trousers and 6 hats is $1,290. What is the total cost of 1 shirt, 1 pair of trousers and 1 hat? Options
A) 110$  B) 120$  C) 130$  D) 140$  E) 150$

Solution: et x be the price of one shirt, y be the price of one pair of trousers and z be the price of one hat.   4x + 4y + 2z = 560 :   9x + 9y + 6z = 1,290   3x + 3y + 2z = 430 : divide all terms of equation C by 3   x + y = 130 : subtract equation D from equation B   3(x + y) + 2z = 430 : equation D with factored terms.   3*130 + 2z = 430   z = 20 : solve for z   x + y + z = 130 + 20= 
130 + 20 = 150
$150
Answer: E
49 x 49 x 49 x 49 = 7? Answers:  A) 4  B) 7  C) 8  D) 16  E) 20

Solution: Solution   49 * 49 * 49 * 49 = (72 * 72 * 72 * 72) = 7(2 + 2 + 2 + 2) = 78   so, the correct answer is 8   Answer 8
Answer: C
A bag consists of 60 marbles, of which 5 are blue, 9 are red, and the remainder are white. If Lisa is to select a marble from the bag at random, what is the probability that the marble will be red or white?
Choose the most appropriate option.
A) 11/12	B) 2/4	C) 1/4	D) 1/8	E) 1/16

Solution: bag consists of 60 marbles, of which 5 are blue, 9 are red   remainder are white. So, white = 60 - 5 - 9= 
60 - 5 - 9 = 46
46.   probability that the marble will be red or white= probability that the marble will be red + probability that the marble will be white   probability that the marble will be red or white = 9/60+46/60 = 55/60 = 11/12   Hence, answer will be 11/12.
Answer: A
Harriet planned to complete a certain task on Wednesday, January 1, but because of illness the completion date was postponed 43 days. On which day of the week in February was the task completed? Choose the correct choice from the following answers
A) Monday	B) Tuesday	C) Wednesday	D) Thursday	E) Friday

Solution: This type of story problem is essentially just about a repeating pattern and a 'remainder.'   We're told that Harriet planned to complete a certain task on WEDNESDAY, January 1, but because of illness the completion date was postponed 43 DAYS. We're asked on what day of the week the task was actually completed on.   Since the task was supposed to be completed on a Wednesday....   A 1 day postponement would be Thursday   A 2 day postponement would be Friday   A 3 day postponement would be Saturday   A 4 day postponement would be Sunday   A 5 day postponement would be Monday   A 6 day postponement would be Tuesday   A 7 day postponement would be Wednesday   A 8 day postponement would be Thursday   Etc.   So this question is ultimately asking how many 'groups of 7' are there, and how many 'leftover days' are there, when you postpone 43 days.   43/7 = 6 remainder 1   This means that there are 6 full weeks AND 1 extra day after a Wednesday....Thus, the task was completed on a Thursday.   Thursday
Answer: D
A cube of side 8 meter length is cut into small cubes of side 16 cm each. How many such small cubes can be obtained? Choose the correct choice from the following
A) 10780 B) 127600 C) 125000 D) 152000 E) 10000

Solution: Along one edge, the number of small cubes that can be cut   = 800/16= 
800/16 = 50
50   Along each edge 50 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut=50 * 50 * 50= 
50 * 50 * 50 = 125_000
125000   Answer:125000
Answer: C
Set X consists of the integers from 0 to 12, inclusive, while set Y consists of the integers from 6 to 10, inclusive. How many distinct integers do belong to the both sets at the same time? Choose the correct choice from the following answers.
A) 4	B) 10	C) 5	D) 9	E) 8

Solution: X= {0,1,2,3,4, 5,6, 7, 8, 9, 10, 11, 12}   Y = {6, 7, 8, 9, 10}   5ommon elements = {6, 7, 8, 9, 10} = 5 elements   Answer: Option 5.
Answer: C
Maxwell leaves his home and walks toward Brad's house at the same time that Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 110 kilometers, Maxwell's walking speed is 4 km/h, and Brad's running speed is 7 km/h, what is the distance traveled by Brad?  Select the correct option:  A) 16  B) 18  C) 20  D) 70  E) 30

Solution: Time taken = Total Distance / Relative Speed   Total Distance = 110 kms   Relative Speed (Opposite side) (As they are moving towards each other speed would be added ) = 7+ 4= 
7+ 4 = 11
11 kms/hr   Time taken= 110 / 11= 
110 / 11 = 10
10 hrs   Distance traveled by Brad= Brad's speed * time taken = 7 * 10= 
7 * 10 = 70
70 kms... Answer - 70
Answer: D
A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12500 after a year? Choose the correct answer:  A) 3630  B) 3637  C) 3630  D) 3750  E) 3635

Solution: 6300:4200:10500   3:2:5   3/10 * 12500= 
3/10 * 12500 = 3_750
3750   Answer: 3750
Answer: D
Mudit's age 30 years hence will be thrice his age four years ago. Find Mudit's present age?  Choose the correct choice.
A) 12
B) 19
C) 27
D) 21
E) 15

Solution: Explanation:   Let Mudit's present age be 'm' years.   m + 30 = 3(m - 4)   => 2m = 42 => m = 21 years.   Answer:21
Answer: D
Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit ?
Answers
A) 10,529  B) 10,512  C) 10,110  D) 10,500  E) 10,511

Solution: The ratio of their investments:   50000x36 : 80000x30 = 3 : 4   Simran's share of profit = (24500x3/7) = Rs.10,500.   Answer: 10,500
Answer: D
The probability that a man will be alive for 10more yrs is 1/4 & 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 answers:
A) 1/2
B) 1
C) 3/2
D) 3/5
E) 1/3

Solution: Sol. Required probability = Pg.) x P(B) = (1— D x(1 —I) =: x 1=1/2   1/2ns.(1/2)
Answer: A
If a number x is in octal form and having zero as unit place then if we change that number x in decimal form then what is the probability that number x having zero as unit place?
Options.
A) 11/64
B) 11/69
C) 11/66
D) 11/64
E) 11/61

Solution: example (8)10=(10)8(8)10=(10)8, (16)10=(20)8(16)10=(20)8, (24)10=(30)8(24)10=(30)8, (32)10=(40)8(32)10=(40)8, (40)10=(50)8(40)10=(50)8, . . .   So out of five numbers end with zero in octal form, only one (50)8=(40)10(50)8=(40)10 has zero in decimal format. So the required probability is 1/5   My initial thinking:   Let the number be "ab0" in octal form. Remember here a, b < 8. So total possibilities are 64.   If we convert the given number into decimal format, then (ab0)8 = 64a + 8b.   We will find for how many values of 64a + 8b ends in zero.   64a + 8b = 60a + (4a + 8b)   For (0,0), (1, 2), (1, 7), (2, 4), (3, 1), (3, 6), (4, 3), (5, 5), (6, 2), (6, 7), (7, 4), (0, 0) the above expression gives unit digit 0.   So required probability = 11/64   (Imp: Still I am not comfortable with the solution I have written as it is not specified whether the given number is 3 digit or not. Just learn how I tried to solve it. )   11/64nswer:11/64
Answer: A
If the average (arithmetic mean) of the four numbers K + 1, 2K + 3, 3K – 5 and 5K + 1 is 63, what is the value of K?
Pick one
A) 11	B) 15 3/4	C) 22	D) 23	E) 22 10/11

Solution: K +1 + 2K +3 + 3K - 5 + 5K +1 = 11K   (11K )/4 = 63   11K = 63 * 4= 
63 * 4 = 252
252   K= 252 / 11 = 22 10/11   Answer 22 10/11.
Answer: E
A small company employs 5 men and 3 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 women?	Choose one:  A) 1/14  B) 1/7  C) 2/7  D) 1/2  E) 3/7

Solution: Total ways to choose 4 employees from 8 employees = 8C4   Two women = 3C2   Two Men = 5C2   P = (5C2 * 3C2)/8C2 = 3/7 hence 3/7.
Answer: E
A wheel rotates 10 times every minute and moves 30 cm during each rotation. How many metres does
the wheel move in one hour?  Choose one:
A) 6 metre
B) 18 metre
C) 180 metre
D) 1800 metre
E) 2200 metre

Solution: Expl : Number of times wheel moves in 1 hour = 10 * 60= 
10 * 60 = 600
600   :. Distance moves= (600 *30)= 
(600 *30) = 18_000
18000 cm   In metres= 180 metre   Answer: 180 metre
Answer: C
A is a working partner and B is a sleeping partner in the business. A puts in Rs.15000 and B Rs.25000, A receives 10% of the profit for managing the business the rest being divided in proportion of their capitals. Out of a total profit of Rs.9600, money received by A is?  Choose the correct choice from the following.
A) 2726	B) 1827	C) 1199	D) 4200	E) 1781

Solution: Explanation:   15:25 => 3:5   9600*10/100= 
9600*10/100 = 960
960   9600 - 960= 
9600 - 960 = 8_640
8640   8640*3/8= 
8640*3/8 = 3_240
3240 + 960= 
3240 + 960 = 4_200
4200   Answer:4200
Answer: D
15 litres of mixture contains 20% alcohol and the rest water. If 2litres of water be mixed with it, the percentage of alcohol in the new mixture would be?	Pick:	A) 16.67%	B) 23%	C) 18.3%	D) 17.64%	E) 21.23%

Solution: Alcohol in the 15litres of mix. = 20% of 15litres = (20*15/100)= 
(20*15/100) = 3
3litres   water in it= 15-3= 
15-3 = 12
12litres   new quantity of mix.= 15+2= 
15+2 = 17
17 litres   Quantity of alcohol in it= 3litres   Percentage of alcohol in new mix. = 3*100/17 = 17.64%   Answer is 17.64%
Answer: D
A committee is composed of w women and m men. If 3 women and 2 men are added to the committee, and if one person is selected at random from the enlarged committee, then the probability that a woman is selected can be represented by  Options
A) w/m
B) w/(w+m)
C) (w+3)/(m+2)
D) (w+3)/(w+m+3)
E) (w+3)/(w+m+5)

Solution: The total number of members on the enlarged committee is (w+3)+(m+2)=w+m+5;   The total number of women on the enlarged committee is w+3.   Thus, the probability that a woman is selected is P=favorable/total=(w+3)/(w+m+5).   Answer: (w+3)/(w+m+5).
Answer: E
The output of a factory was increased by 10% to keep up with rising demand. To handle the holiday rush, this new output was increased by 30%. By approximately what percent would the output now have to be decreased in order to restore the original output?  Choose the correct choice from the following answers:  A) 20%  B) 24%  C) 30%  D) 32%  E) 79%

Solution: The original output increases by 10% and then 30%.   Total % change = a + b + ab/100   Total % change = 10 + 30 + 10*30/100= 
10 + 30 + 10*30/100 = 43
43%   Now, you want to change it to 0, so,   0= 43 + x + 43x/100   x = -43(100)/143 = 30% approximately   Answer is 30%
Answer: C
What is the product of all the possible values of x if x^2(x + 2) + 7x(x + 2) + 6(x + 2) = 0?  Pick:
A) –29
B) –12
C) 12
D) 29
E) 168

Solution: x^2(x + 2) + 7x(x + 2) + 6(x + 2) = 0   => (x+2)(x^2 + 7x + 6) = 0   =>(x+2)(x+1)(x+6)=0   => x= -1 or -2 or -6   product =-12   answer option -12   ANSWER:–12
Answer: B
A jogger running at 9 kmph alongside a railway track in 240 meters ahead of the engine of a 120 metres long train running at 45 kmph in the same direction . in how much time will the train pass the jogger ?	Select:	A) 18 seconds	B) 26 seconds	C) 36 seconds	D) 16 seconds	E) 46 seconds

Solution: Total Distance(d) = 240+120= 
240+120 = 360
360 meter   Relative speed (s)= 45 - 9= 
45 - 9 = 36
36 Kmph= 36*5/18= 
36*5/18 = 10
10mps   d= s* t   360 = 10*t   t = 36 seconds   ANSWER:36 seconds
Answer: C
The side of a square is increased by 15% then how much % does its area increases?	Pick.
A) 52.65  B) 56.25  C) 50.75  D) 32.25  E) 52.75

Solution: a = 100 a2 = 10000   a = 115 a2 = 13225   ----------------   10000 --------- 3225   100 -------? => 32.25 %   ANSWER: 32.25
Answer: D
A crate of apples contains 1 bruised apple for every 25 apples in the crate. Three out of every 4 bruised apples are considered not fit to sell, and every apple that is not fit to sell is bruised. If there are 12 apples not fit to sell in the crate, how many apples are there in the crate?
Choose the correct answer.
A) 270
B) 360
C) 480
D) 600
E) 400

Solution: as given 3 out of every 4 bruised apple is not fit to sell   or, 75% of the bruised apples are not fit to sell.   as per the question 12 are not fit to sell   or,   0.75x=12   x=1200/75= 
1200/75 = 16
16   thus total number of bruised apples=16   total number of apples =25*16= 
25*16 = 400
400   Answer: 400
Answer: E
set s contains the following numbers 10, 14, 19, 27, 36, 49, 67, 70,94. It was found that Mark had inadvertently interchanged the digits of one of the numbers. Steve, in charge of statistics, rectified this error, and as a result mean and median were changed and the shift in mean was of 5.
Whats the number that was incorrectly noted?  Choose the correct answer
A) 36
B) 49
C) 94
D) 27
E) 41

Solution: Firstly the NEW median will be 27 or 49...   secondly the change in SUM will be   9*5= 
  9*5 = 45
45, so the difference in number and in reversed order will be 45...   and the reversed NUMBER and actual number should be on either side of the MEDIAN 36..   lets see the choices on these points..   A. 36... reverse= 63 but 63−36≠4563−36≠45.... eliminate   B. 49... reverse = 94, and   94-49= 
  94-49 = 45
45, BUT both 49 and 94 lie on the SAME side of 36, so no effect on MEDIAN... ELIMINATE   C. 94... SAME as B.. eliminate   D. 27.... reverse= 72.. 72-27 = 45.. yes and 27 is lesser than 36 and 72 is >36 so median will shift to 49... CORRECT   E. 41.... reverse 14, but 41−14≠4541−14≠45.. eliminate   ANSWER:27
Answer: D
Let C be defined as the sum of all prime numbers between 0 and 28. What is C/3
Choose the correct choice from the following answers.
A) 155
B) 100/3
C) 61
D) 47
E) 43

Solution: Prime numbers between 0 and 30 - 2 , 3 , 5 , 7, 11 , 13 , 17 , 19 , 23   Sum,C = 100   C/3 = 11/3   Answer 100/3
Answer: B