MU-NLPC/Calc-aqua_rat huggingface dataset:
The wages earned by Robin is 38% more than that earned by Erica. The wages earned by Charles is 60% more than that earned by Erica. How much % is the wages earned by Charles more than that earned by Robin?	Choose the correct choice.
A) 23%
B) 27.53%
C) 30%
D) 50%
E) 100%

Solution: Explanatory Answer   Let the wages earned by Erica be $100   Then, wages earned by Robin and Charles will be $138 and $160 respectively.   Charles earns $38 more than Robin who earns $138.   Therefore, Charles' wage is 38/138*100 = 27.53%.   The correct choice is (27.53%)
Answer: B
There are three departments having students 68,58,24 .In an exam they have to be seated in rooms such that each room has equal number of students and each room has students of one type only (No mixing of departments). Find the minimum number of rooms required?	Choose the most appropriate option.
A) 73  B) 74  C) 75  D) 76  E) 77

Solution: WE NEED TO TAKE GCD WHICH IS 2   THUS ALL THE ROOMS WILL HAVE 2 STUDENTS OF THE SAME DEPT   1) 68/2 = 34   2) 58/2 = 29   3) 24/2 = 12   TOTAL NO. OF MIN ROOMS REQD = 34+12+29= 
34+12+29 = 75
75   ANSWER:75
Answer: C
An accurate clock shows 8 o'clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 12 o'clock noon?
Choose the correct choice from the following options.
A) 30  B) 60  C) 90  D) 120  E) 150

Solution: The hour hand will move 4/12 of a circle.   (4/12)*360= 
(4/12)*360 = 120
120 degrees.   The answer is 120.
Answer: D
Which of the following integers is the square of an integer?	Choose the correct choice from the following: A) 73,410,624 B) 63,398,748 C) 54,113,892 D) 42,785,337 E) 31,298,793

Solution: CONCEPT: The unit digit of any Perfect Square can't be 2 or 3 or 7 or 8   Hence Option B, C D and E can be ruled out   73,410,624nswer: option 73,410,624
Answer: A
The perimeter of a triangle is 32 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle  Choose one:  A) A)40  B) B)828  C) C)729  D) D)34  E) E)35

Solution: Explanation:   Area of a triangle = r * s   Where r is the inradius and s is the semi perimeter of the triangle.   40rea of triangle = 2.5 * 32/2= 
2.5 * 32/2 = 40
40 cm2   40nswer: Option 40
Answer: A
A coin is tossed 4 times. What is the probability t that the number of Heads is equal to the number of Tails? Choose the most appropriate option:
A) 1/8
B) 1/4
C) 3/8
D) 1/2
E) 9/16

Solution: We have to find the probability that we get 2 heads and 2 tails in 4 tosses of the coin.   Using the binary formula and defining a head as a success,   P(2 heads in 4 tosses) = 43/82* (1/2)^2 * (1/2)^2   t= 6/16   = 3/8   The answer is therefore (3/8)
Answer: C
A trader mixes 25 kg of rice at Rs. 40 per kg with 25 kg of rice of other variety at Rs. 20 per kg and sells the mixture at Rs. 40 per kg. His profit percent is:
Select:
A) No profit, no loss B) 33.33% C) 8% D) 10% E) None of these

Solution: C.P. of 56 kg rice = Rs. (25 x 40 + 25 x 20) = Rs. (1000 + 500) = Rs. 1500.   S.P. of 56 kg rice = Rs. (50x 40) = Rs. 2000   Gain =500/1500x100% = 33.33%   Answer: Option 33.33%
Answer: B
In a vacant lot a man have 5 goat which eat in 2 days all the bush of 1/4 part of the lot, full of bushes. If the man added 10 goats to the lot and all of them will eat the weed at the same rate, how many days will take to all the goats eat all the bushes of the lot, since the first day?  Pick.
A) 8 days
B) 7 days
C) 6 days
D) 5 days
E) 4 days

Solution: We have that: 5 goats ----- 2 days, (5+10) G ----- X d, that is: (X d/ 5G) = (2 d/15G), then: X d = (2 d/15G)5G = (2/3)d. Is to say, the 15 goats eat the same quantity in 2/3 days; it is only 1/4 of the lot. Then, all the lot is: L = L1 + L2 + L3 + L4= 2 d + 3(2/3)d = (2 + 2)= 
(2 + 2) = 4
4 days. Answer 4 days.
Answer: E
In a two-digit number, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is:	Pick one: A) 24 B) 26 C) 42 D) 46 E) 52

Solution: Explanation:   Let the ten's digit be x. Then, unit's digit = x + 2. Number = 10x + (x + 2) = 11x + 2   Sum of digits = x + (x + 2) = 2x + 2   (11x + 2)(2x + 2) + (  + 2)= 
+ (  + 2) = 2
2x + 2   (11x + 2)(2x + 2)= 144   2x2 + 26x - 140 = 0   (x - 2)(11x + 35) = 0   x = 2   Hence, required number = 11x + 2 = 24.   24NSWER IS 24
Answer: A
According to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . How many 12 - ounce cans of the concentrate are required to prepare 272 6-ounce servings of orange juice? Choose the correct option.
A) 25 B) 34 C) 50 D) 67 E) 100

Solution: Orange juice concentrate: water::1:3   total quantity of orange juice = 272*6= 
272*6 = 1_632
1632 oz   so Orange juice concentrate: water :: 408 oz:1224 oz   no. of 12 oz can= 408 oz/12 oz = 34   Answer 34, 34 cans
Answer: B
A company has a job to prepare certain number of cans and there are three machines A, B and C for this job. A can complete the job in 3 days, B can complete the job in 4 days and C can complete the job in 6 days. How many days the company will it take to complete the job if all the machines are used simultaneously?
Choose one.
A) 4 days  B) 4/3 days  C) 3 days  D) 12days  E) 14 days

Solution: Let the total number of cans to be prepared be 12.   The number of cans prepared by A in 1 day = 4.   The number of cans prepared by B in 1 day = 3.   The number of cans prepared by C in 1 day = 2.   Thus, the total number of cans that can be prepared by all the machines working simultaneously in a single day = 9.   Therefore, the number of days taken to complete the whole work = 12/9 = 4/3 days.   ANSWER:4/3 days
Answer: B
The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 9 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?	Choose the correct choice.
A) 23 years  B) 24 years  C) 25 years  D) 26 years  E) 27 years

Solution: EXPLANATION   Let the average age of the whole team by x years.   11x â€“ (26 + 38) = 9(x -1)   11x â€“ 9x = 52   2x = 52   x = 26.   So, average age of the team is 26 years.   Answer 26 years
Answer: D
A man purchases 2 pens for $ 56. He sells one at 20% profit and the other at a loss of 15%. He neither gains nor loses on the whole. Thus, the cost price of two watches are :  Choose the most appropriate option: A) $ 24 and $ 32 B) $32 and $ 24 C) $56and $32 D) $56 and $24 E) $32 and $ 56

Solution: x + y = 56--- (1)   1.20x + 0.85y = 56 --- (2)   (2) - (1) --> 0.20x - 0.15y = 0   20x = 15y   x/y = 3/4= (3*8)/(4*8) = 24/32   $ 24 and $ 32nswer:$ 24 and $ 32
Answer: A
A rectangular block 12cm by 20cm by 36cm is cut into an exact number of equal cubes. Find the least possible number of cubes?	Choose the correct choice from the following:
A) 135
B) 10
C) 15
D) 40
E) 22

Solution: Volume of the block = 12*20*36= 
12*20*36 = 8_640
8640 cm^3   Side of the largest cube= H.C.F of 12,20,36 = 4cm   Volume of the cube = 4*4*4= 
4*4*4 = 64
64 cm^3   Number of cubes= 8640/64= 
8640/64 = 135
135   135nswer is 135
Answer: A
Ron scored 344 marks out of 400 marks and his elder brother Ben scored 582 marks out of 600 marks. Who scored percentage is better?  Select:
A) 97 B) 21 C) 28 D) 26 E) 19

Solution: Percentage of marks scored by Ron = (344/400 × 100) %   = (34400/400) %   = (344/4)= 
(344/4) = 86
86 %   Percentage of marks scored by Ben= (582/600 × 100) %   = (58200/600) %   = (582/6)= 
(582/6) = 97
97 %   Hence, the percentage marks scored by Ben is better.   97nswer:97
Answer: A
The sum of two consecutive number is 109. Which is the larger number?  Pick
A) 42
B) 43
C) 44
D) 45
E) 55

Solution: Let consecutive number be x, x+1   Therefore sum of the consecutive number is x + x+1=109   2x+1=109   2x=108   x=54   Therefore larger number is x+1=55   ANSW55R:55
Answer: E
It takes a boat 3 hours to travel down a river from point A to point B, and 5 hours to travel up the river from B to A. How long would it take the same boat to go from A to B in still water?  Choose the correct answer.
A) 3 hours and 45 minutes. B) 2 hours and 32 minutes. C) 4 hours and 54 minutes. D) 6 hours and 26 minutes. E) 5 hours and 59 minutes.

Solution: Let: S be the speed of the boat in still water, r be the rate of the water current and d the distance between A and B.   d = 3(S + r) : boat traveling down river   d = 5(S - r) : boat traveling up river   3(S + r) = 5(S - r)   r = S / 4 : solve above equation for r   d = 3(S + S/4) : substitute r by S/4 in equation B   d / S = 3.75 hours = 3 hours and 45 minutes.   correct answer 3 hours and 45 minutes.
Answer: A
There are two groups of students in the sixth grade. There are 30 students in group A, and 50 students in group B. If, on a particular day, 20% of the students in group A forget their homework, and 12% of the students in group B forget their homework, then what percentage of the sixth graders forgot their homework?
Choose the correct option.
A) 13%	B) 14%	C) 15%	D) 16%	E) 17%

Solution: Total students = 30 + 50= 
30 + 50 = 80
80   20% of 30= 6   12& of 50 = 6   Total students who forget homework = 6+6= 
6+6 = 12
12   Percentage=1280∗100=15=12/80∗100=15	;Answer = 15% = 15%
Answer: C
Every day, the value of a stock rises by exactly two dollars in the morning, and
then falls by exactly one dollar in the afternoon. If the stock's value at the start of the first
day is $100, on what day will the stock's value first reach $200?
Choose the correct choice from the following answers
A) 50	B) 99	C) 100	D) 101	E) 200

Solution: Note that each day the stock is worth $1 more than on the previous day, and that   on the first day it rises to $102 and then falls to $101. Therefore, on the nth day, the stock's   value rises to n + 101 dollars in the morning and falls to n + 100 dollars in the afternoon.   The solution is therefore the smallest n for which n+101 = 200, or n = 99. In particular,   the stock will be $200 in the middle of day 99, although not at the end of this day.   correct answer 99
Answer: B
A sum of money becomes double itself in 8 years at simple interest. How many times will it become 16 years at the same rate?
Choose the correct choice from the following
A) 1  B) 2  C) 3  D) 4  E) 5

Solution: P ---- 2P ---- 8 years4P ---- 16 years Answer: 4
Answer: D
Excluding stoppages, the speed of a train is 42 kmph and including stoppages it is 36 kmph. Of how many minutes does the train stop per hour?
Choose the correct choice from the following choices:	A) 7.5	B) 8.5	C) 9.5	D) 4.5	E) 6.5

Solution: T = 6/42 * 60 = 8.5   ANSWER:8.5
Answer: B
The average of 9 results is 50. If the average of first 4 results is 45 and that of the last six is 48, find the 5th result? Select the correct option:	A) 15	B) 20	C) 35	D) 18	E) 22

Solution: Sixth result = 45*5 + 48*5 - 50*9= 
45*5 + 48*5 - 50*9 = 15
15   15nswer is 15
Answer: A
The average age of 25 students in a class is 12 years. 15 students whose average age is 10 years joined them. What is the present average age.	Answers
A) 13
B) 12.6
C) 11.25
D) 12
E) 13

Solution: Explanation :   Solution: Present average = ax + by/ a + b   = 25*12 + 15*10/25+15 years   =300 + 150/ 40 => 450/40 => 11.25.   Answer : 11.25
Answer: C
A certain bag contains 60 balls — 22 white, 10 green, 7 yellow, 15 red, and 6 purple. If a ball is to be chosen at random, what is the probability that the ball will be neither red nor purple?
Select the correct option:
A) 0.09
B) 0.65
C) 0.54
D) 0.85
E) 0.91

Solution: According to the stem the ball can be white, green or yellow, so the probability is (white + green + yellow)/(total) = (22 + 10 + 17)/60 = 39/60 = 0.65.   Answer: 0.65.
Answer: B
If Sharon's weekly salary increased by 16 percent, she would earn $348 per week. If instead, her weekly salary were to increase by 20 percent, how much would she earn per week? Pick one
A) $374  B) $382  C) $385  D) $360  E) $399

Solution: (348/116)120 =360   In this case long division does not take much time.   (348/116)= 
(348/116) = 3
3   3*120= 
3*120 = 360
360(300+60)   Answer $360
Answer: D
The ratio, by volume, of bleach to detergent to water in a certain solution is 2 : 40 : 100. The solution will be altered so that the ratio of bleach to detergent is tripled while the ratio of detergent to water is halved. If the altered solution will contain 200 liters of water, how many liters of detergent will it contain? Choose one:
A) 60
B) 55
C) 50
D) 45
E) 40

Solution: B:D:W = 2:40:100   Bnew / Dnew = (1/3)*(2/40) = (1/60)   Dnew / Wnew = (1/2)*(40/100) = (1/5)   Wnew = 200   Dnew = Wnew/5 = 200/5= 
200/5 = 40
40   So, answer will be 40
Answer: E
If n is a positive integer, and n^2 has 25 factors, which of the following must be true.
1. n has 12 factors.
2. n > 50
3.√n is an integer.  Choose the correct choice from the following options:
A) 1 and 2  B) 2 only  C) 3 only  D) 2 and 3  E) none

Solution: 25=1×25=5×5   So prime factorization of n^2 could be p^24 or p^4q^4 with p,q are distinct prime numbers.   Hence, n could be p^12 or p^2q^2   (1) If n=p12 then n has 12+1= 
12+1 = 13
13 different factors, so (1) is not true.   (2) If n=p^2q^2 , for example n=2^2×3^2=36<50n=22×32=36<50, so (2) is not true.   (3)   If n=p^12 ⟹√n=p^6 is an integer.   If n=p^2q^2 ⟹√n=pq is an integer.   So (3) is true.   Answer: 3 only.
Answer: C
Which number should replace both the asterisks in (* /21) x (*/84) = 1 ? Pick:	A) 21	B) 42	C) 63	D) 72	E) 168

Solution: Let (y/21) x (y/84) = 1   y^2 = 21 x 84 = 21 x 21 x 4   y = (21 x 2) = 42   The answer is 42.
Answer: B
1600 men have provisions for 28 days in the temple. If after 4 days, 400 men leave the temple, how long will the food last now?  Choose the most appropriate option.
A) 34 days	B) 54 days	C) 32 days	D) 76 days	E) 76 days

Solution: 1600 ---- 28 days   1600 ---- 24   1200 ---- ?   1600*24 = 1200*x   x = 32 days   Answer:32 days
Answer: C
In how many ways can six members be selected from a group of ten members?  Select
A) 10C6 B) 10C8 C) 10C4 D) 10C3 E) 10C1

Solution: Six members can be selected from ten members in   10C6   = 10C4 ways.   Answer: 10C8
Answer: B
If W is the set of all the integers between 49 and 114, inclusive, that are either multiples of 3 or multiples of 2 or multiples of both, then W contains how many numbers?
Pick
A) 34
B) 44
C) 45
D) 55
E) 72

Solution: Official Solution:   Number of multiples of 3   Step 1. Subtract the extreme multiples of 3 within the range (The greatest is 114, the smallest is 51): 114 - 51 = 63   Step 2. Divide by 3: 63 / 3 = 21   Step 3. Add 1: 21 + 1 = 22.   So there are 22 multiples of 3 within the range: examples are 51, 54, 57, 60, etc.   Number of multiples of 2   Step 1. Subtract the extreme multiples of 2 within the range (The greatest is 114, the smallest is 50): 114 - 50 = 64   Step 2. Divide by 2: 64 / 2 = 32   Step 3. Add 1: 32 + 1 = 33.   So there are 33 multiples of 2 within the range: examples are 50, 52, 54, 56, 58, 60 etc.   Add the 22 multiples of 3 and the 33 multiples of 2: 22+33=55.However, by adding the multiples of 2 and the multiples of 3, we are effectively counting several numbers twice: for example, 54 and 60 are parts of both the lists above. So we can't just take   22+33= 
  22+33 = 55
55. Find the Number of multiples of 6 (which are the double counted, as 6 is divisible by both 2 and 3), and subtract it from 55:   Step 1. Subtract the extreme multiples of 6 within the range (The greatest is 72, the smallest is 54): 114 - 54= 60   Step 2. Divide by 6: 60 / 6 = 10   Step 3. Add 1: 10 + 1 = 11.   So there are 11 multiples of 6 within the range: we counted 11 numbers twice.   Subtract the 11 multiples of 6 from the sum of the multiples of 2 and 3:   = 22+33 - 11   = 55 - 11= 
55 - 11 = 44
44   Therefore, the final number of multiples of 2, 3 or 6 is 44.   Hence, this is the correct answer. (44)
Answer: B
A can do a piece of work in 6days of 9 hours each and B alone can do it in 12 days of 9 hours each.how long will they take it to do working together
4 1/2 hours a day?
Choose the correct choice from the following choices:
A) 8 days B) 9 days C) 7 days D) 6 days E) 10 days

Solution: A's work per hour=1/54   B's work per hour=1/108   A & B's work per hour together=(1/54)+(1/108)=3/108=1/36   so A & B together complete the work in 36 hours...   if they work 4 1/2=9/2 hours a day,   it will take  (36)/(9/2)= 
 (36)/(9/2) = 8
8 days...   8 daysNSWER: 8 days
Answer: A
In order to obtain an income of Rs. 1000 from 50% stock at Rs. 500, one must make an investment of	Choose one.
A) Rs.17000  B) Rs.16050  C) Rs.15400  D) Rs.10000  E) Rs.10500

Solution: Explanation :   Market Value = Rs.500.   Required Income = Rs. 1000.   Here face value is not given. Take face value as Rs.100 if it is not given in the question   To obtain Rs.50 (ie,50% of the face value 100), investment = Rs.500   To obtain Rs.1000, investment = 500/50Ã—1000=10000   Answer : Option Rs.10000
Answer: D
If 6th March, 2017 is Sunday, what was the day of the week on 6th March, 2016?  Choose the correct choice from the following.
A) Sunday
B) Saturday
C) Tuesday
D) Wednesday
E) None of these

Solution: Solution   The year 2016 is a leap year. So, it has 2 odd days.   But, Feb 2016 not included because we are calculating from March 2016 to March 2017. So it has 1 odd day only.   The day on 6th March, 2017 will be 1 day beyond the day on 6th March, 2016. Given that, 6th March, 2017 is Sunday.   6th March, 2016 is Saturday (1 day before to 6th March, 2017)   Answer Saturday
Answer: B
A sum of Rs.48000 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.	Choose the correct choice from the following.
A) 28880 B) 31200 C) 28770 D) 29990 E) 12770

Solution: Let A be the amount received at the end of the three years.   A = 48000[1 + 10/100][1 + 20/100][1 + 25/100]   A = (48000 * 11 * 6 * 5)/(10 * 5 * 4)   A = Rs.79200   So the interest = 79200 - 48000 = Rs.31200   Answer: 31200
Answer: B
Linda spent 3/4 of her savings on furniture and the rest on a TV. If the TV cost her $150, what were her original savings?	Choose the correct choice from the following
A) $500	B) $600	C) $700	D) $800	E) $900

Solution: If Linda spent 3/4 of her savings on furniture, the rest   4 / 4 - 3 / 4 = 1 / 4 on a TV   But the TV cost her $150. So 1 / 4 of her savings is $150. So her original savings are 4 times $150 = $600   correct answer $600
Answer: B
Two spherical balls lie on the ground touching. If one of the balls has a radius of 7 cm, and the point of contact is 10 cm above the ground, what is the radius of the other ball (in centimeters)? Pick one
A) 30/7	B) 50/3	C) 70/4	D) 80/5	E) 90/8

Solution: A straight line will join the two centers and the point of contact, thus making similar triangles.   3/7 = (r-10)/r   3r = 7r - 70   r = 70/4   The answer is 70/4.
Answer: C
In measuring the sides of a rectangle, one side is taken 4% in excess, and the other 3% in deficit. Find the error percent in the area calculated from these measurements.
Choose the correct choice from the following answers:
A) 0.11%	B) 0.7%	C) 0.4%	D) 0.6%	E) 0.88%

Solution: Let x and y be the sides of the rectangle. Then, Correct area = xy.   Calculated area = (26/25) x (32/33) y = (344/341 )(xy)   Error In measurement = (344/341)xy- xy = (3/341)xy   Error percentage = [(3/341)xy (1/xy)100] % = (22/25)= 
(22/25) = 22/25 = around 0.88
0.88%.   Answer is 0.88%.
Answer: E
In a basketball game, Dhoni scored 15 points more than Dravid, but only half as many points as Shewag. If the three players scored a combined total of 77 points, how many points did Dhoni score? Choose the correct answer:
A) 23
B) 33
C) 25
D) 28
E) 32

Solution: Let Dravid scored point = x   Then Dhoni Scored = x+15   Shewag Scored = 2*(x+15) = 2x+30   23s given, x+x+15+2x+30 = 77 points   4x+45 = 77   x = 77-45/4 = 8   So Dhoni Scored = x +15 i.e) 8+15 = 23   23nswer : 23
Answer: A
A park square in shape has a 3 metre wide road inside it running along its sides. The area occupied by the road is 1764 square metres. What is the perimeter along the outer edge of the road?  Choose one:
A) 576 metres B) 589 metres C) 600 metres D) 700 metres E) None

Solution: Solution   Let the length of the outer edges be x metres.   Then, length of the inner edge = ( x - 6)m.   ∴ x2 - (x-6)2 = 1764   ‹=› x2-(x2-12x+36)= 1764   ‹=›12x = 1800   ‹=›x = 150.   ∴ Required perimeter = (4x)m   ‹=› (4 x 150)m = 600m.   Answer 600 metres
Answer: C
A man sells a horse for Rs.800 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse?  Choices.
A) 228  B) 277  C) 299  D) 860  E) 223

Solution: CP = SP + 1CP = SP - g   800 + x = 980 - 2x   3x = 180 => x = 60   CP = 800 + 60= 
800 + 60 = 860
860   Answer:860
Answer: D
Integer x is equal to the product of all even numbers from 2 to 60, inclusive. If V is the smallest prime number that is also a factor of x-1, then which of the following expressions must be true? Answers:  A) 0<y<4  B) 4<y<10  C) 10<y<20  D) 20<y<30  E) y>30

Solution: V Smallest prime factor is greater than 29. So answer is y>30
Answer: E
S is a set containing 10 different positive odd primes. T is a set containing 8 different numbers, all of which are members of S. Which of the following statements CANNOT be true?  Answers:  A) The median of S is prime.  B) The median of T is prime  C) The median of S is equal to the median of T.  D) The sum of the terms in S is prime.  E) The sum of the terms in T is prime.

Solution: Here is my explanation. The question states:S is a set containing 9 different positive odd primes. T is a set containing 8 different numbers, all of which are members of S. Which of the following statements CANNOT be true?   (A) The median of S is prime.   Thismust be true. If there are an odd number of members of a set, then the median is a member of the set: it's the middle number, when all the numbers are ranked from smallest to biggest. Every number in S is a positive odd prime, so the median is one of them, and is prime.   (B) The median of T is prime.   Thismay or may not be true. If a set has an even number of members, the median is average of the two numbers in the middle, when ranked from smallest to biggest. The average of two odd numberscould beeven (average of 71 and 73 is 72), and hence not prime, or itcould beodd (the average of 71 and 79 is 75). For particularly well chosen odd numbers, the average can be not only odd but also prime -- for example, the average of 89 and 113 is 101, another prime number. If the two middle numbers of T were 89 and 113, the median would be 101, a prime number.   (C) The median of S is equal to the median of T.   Under most configurations for S and T, this wouldn't happen. If you weren't trying to make it happen, it would be unlikely to happen by chance. BUT, if the number dropped going from from S to T was the median of S (say, 101), and if the two middle numbers of T happen to have an average of that number that was dropped (for example, if the two numbers were 89 and 113), then the medians would be equal. In other words, the three middle numbers of S would have to be {. . ., 89, 101, 133, . . .}, and when 101 is dropped in going to T, the median of two would be the average of 89113, which happens to be 101. It's an exceptional case, but itcouldbe true.   (D) The sum of the terms in S is prime.   Thismay or may not be true. The sum of 9 odd numbermustbe an odd number. That odd numbercould beprime. For example, the sum of the first nine odd prime numbers {3, 5, 11, 13, 17, 19, 23, 29} is 127, which is prime. If you drop 3 and include the next prime, 31, the set {5, 11, 13, 17, 19, 23, 29, 31} has a sum of 155, which is clearly not prime.   (E) The sum of the terms in T is prime.   Thismust be false. The sum of eight odd numbers must be an even number. Only 2 is prime, and all other even numbers are not. Therefore, the sum of eight odd prime numbers will be an even number bigger than two, and absolutely cannot be prime.   The sum of the terms in T is prime.
Answer: E