RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Plane leaves from Chelsea every 25 minutes from West Ham airport. Air hostess told Frank Lampard that the plane had left 25 minutes ago and the next plane for Chelsea will leave at 7:00 p.m. At what time air hostess convey this information to Frank Lampard?
A.5:35 p.m
B.6:00 p.m
C.7:00 p.m
D.8:35 p.m
Answer: C.7:00 p.m
Explanation: Explanation:
Time of Frank Lampard last missed plane = 7:00 p.m - 25 min = 6:35 p.m
As this information has been given to Frank Lampard 25 minutes after the plane has already left, the air hostess gave the information at 6:35 p.m + 25 min = 7:00 p.m
Answer C
Question: By travelling at 40 kmph, a person reaches his destination on time. He covered two-third the total distance in one-third of the total time. What speed should he maintain for the remaining distance to reach his destination on time?
A.20 kmph
B.24 kmph
C.22 kmph
D.28 kmph
Answer: A.20 kmph
Explanation: A
20 kmph
Let the time taken to reach the destination be 3x hours. Total distance = 40 * 3x = 120x km
He covered 2/3 * 120x = 80x km in 1/3 * 3x = x hours So, the remaining 40x km, he has to cover in 2x hours. Required speed = 40x/2x = 20 kmph.
Question: The value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 24,000 is made?
A.328897
B.120000
C.877888
D.277768
Answer: B.120000
Explanation: The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000
SP such that a profit of Rs. 24,000 is made = 96,000 + 24,000 = Rs. 1,20,000
Answer: B
Question: K = wxyz, where w, x, y, z are prime numbers. Not including 1 and K, how many factors does K have?
A.7
B.14
C.21
D.28
Answer: B.14
Explanation: Suppose w = 2, x = 3, y = 5 and z = 7. Then wxyz = 210.
To find out how many factors 210 has, go through different combinations of the prime factors as follows. You don't even need to calculate the answers but I have done so here:
(factor #1) 2
(factor #2) 3
(factor #3) 5
(factor #4) 7
(factor #5) 2 x 3 = 6
(factor #6) 2 x 5 = 10
(factor #7) 2 x 7 = 14
(factor #8) 2 x 3 x 5= 30
(factor #9) 2 x 3 x 7 = 42
(factor #10) 2 x 5 x 7 = 70
(factor #11) 3 x 5 = 15
(factor #12) 3 x 7 = 21
(factor #13) 3 x 5 x 7 = 105
(factor #14) 5 x 7 = 35
Since we are not including 1 and 210, answer = 14
ANSWER:B
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is?
A.3/5
B.3/2
C.3/8
D.3/9
Answer: B.3/2
Explanation: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 23 ==> 27 x + 17 y = 23 x + 23 y ==> 4 x = 6 y ==> x/y = 3/2.
Answer: B
Question: A man purchases 8 pens for Rs.9 and sells 9 pens for Rs.8, how much profit or loss does he make?
A.20.98
B.20.93
C.20.95
D.20.92
Answer: A.20.98
Explanation: 81 ---- 17
100 ----- ? è 20.98%los
Answer: A
Question: By selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 9 p.c?
A.38028
B.36400
C.32977
D.38128
Answer: B.36400
Explanation: CP + CP/8 = 45000
CP = 40000
SP = 40000*(95/100)
= 36400
Answer:B
Question: In how many ways can three boys can be seated on five chairs?
A.60
B.15
C.30
D.10
Answer: A.60
Explanation: There are three boys.
The first boy can sit in any of the five chairs (5 ways).
5
Now there are 4 chairs remaining. The second boy can sit in any of the four chairs (4 ways).
5	4
Now there are 3 chairs remaining. The third boy can sit in any of the three chairs (3 ways).
5	4	3
Hence, total number of ways in which 3 boys can be seated on 5 chairs
=5×4×3=60
Ans: A
Question: A basket has 4 apples and 3 oranges. Two fruits are picked at random. The probability that at least 2 apples are picked is
A.2/7
B.2/9
C.3/7
D.3/10
Answer: A.2/7
Explanation: Total fruits = 7Since there must be at least two apples,4C2/7C2=2/7Answer:A
Question: Find a sum for first 11 prime numbers?
A.122
B.160
C.129
D.132
Answer: B.160
Explanation: Required sum = (2 + 3 + 5 + 7 + 11+13+17+19+23+29+31) = 160
Note: 1 is not a prime number
Option B
Question: Find the 18th term of an arithmetic progression whose first term is 4 and the common difference is 5.
A.45
B.38
C.72
D.74
Answer: C.72
Explanation: n th term of A.P = a +(n-1) *d
= 4+(18-1)*4 , = 4 + 68 = 72.
ANSWER:C
Question: The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 km in 4 hours, then the speed of the first train is:
A.70 km/hr
B.75 km/hr
C.84 km/hr
D.87.5 km/hr
Answer: D.87.5 km/hr
Explanation: Let the speed of two trains be 7x and 8x km/hr.
Then, 8x = 400/4 = 100
x = 100/8 = 12.5
Speed of first train = (7 x 12.5) km/hr = 87.5 km/hr.
Answer:D
Question: If in k+1 years from now John will be m years old, then how old was John t-1 years ago?
A.m-k-t
B.m+k-t+2
C.m+k-t+1
D.k-m-t+2
Answer: A.m-k-t
Explanation: Age t-1 years ago is m - k - 1 - ( t - 1 )
Or, Age t-1 years ago is m - k - 1 - t + 1
Or, Age t-1 years ago is m - k - t
Hence, Answer will definitely be (A) m - k - t
Question: On average, Machine A will produce a completed item once every four minutes, and Machine B will produce a completed item once every five minutes. The number of items Machine A produces in a 24-hour period is approximately what percent greater than the number of items Machine B would produce in that same period?
A.25%
B.15%
C.45%
D.33%
Answer: A.25%
Explanation: Machine A: 1 item in 4 minutes --> 1/4 items in 1 minute;
Machine B: 1 item in 5 minutes --> 1/5 items in 1 minute.
In the same time period, Machine A produces (1/4-1/5)/(1/5)*100=~25% more items than machine B.
Answer: A.
Question: A company organized a recruiting process for 3 vacant positions of assistant manager for its product launches. The company's efforts yielded 14 eligible candidates. How many sets of 3 candidates can the company choose to fill the 3 assistant manager positions?
A. 2,060
B. 1,320
C. 545
D. 364
Answer: D. 364
Explanation: 14*13*12/3*2*1 = 364
D
Question: Three 6 faced dice are thrown together. The probability that all the three show the same number on them is?
A.1/38
B.1/32
C.1/39
D.1/36
Answer: D.1/36
Explanation: It all 3 numbers have to be same basically we want triplets. 111, 222, 333, 444, 555 and 666. Those are six in number. Further the three dice can fall in 6 * 6 * 6
= 216 ways.
Hence the probability is 6/216
= 1/36
Answer:D
Question: Which of the following numbers is divisible by 5?
A.3221
B.6175
C.6231
D.5813
Answer: B.6175
Explanation: 6175. This is the only option with last two digits divisible by 5
Answer:B
Question: In how many ways 4 boys and 2 girls can be seated in a row so that they are alternate.
A.48
B.288
C.12
D.256
Answer: A.48
Explanation: Solution: Let the Arrangement be,
B G B G B B
4 boys can be seated in 4! Ways.
Girl can be seated in 2! Ways.
Required number of ways,
= 4!*2! = 48
Answer: Option A
Question: If Sn is the sum of the first n terms of a certain sequence and if Sn = n(n+2) for all positive integers n, what is the third term of the sequence?
A.3
B.4
C.6
D.8
Answer: B.4
Explanation: Tn = nth term
T1 = 1st term
T2 = 2nd term
and so on...
Sn = Sum of first n terms of the sequence
Sn = 1st term + 2nd term + 3rd term + ... + nth term
Sn = T1 + T2 + T3 + ....Tn
You are given here thatSn is the SUM of first n terms...So you have
Sn = T1 + T2 + T3 + ....Tn = n(n+1)
So S1 = T1
S2 = T1 + T2
S3 = T1 + T2 + T3
and so on
S1 = T1 = 1*(1+1) = 2
S2 = T1 + T2 = 2 + T2 = 2*(2+1) = 6
So T2 = 4
S3 = T1 + T2 + T3 = 2 + 4 + T3 = 3*(3+1) = 12
So T3 = 6
(This is what we wanted)
The third term is 4.
B
Question: If the height of a triangle is decreased by 40%, land its base is increased by 40%, what will be the effect on its area?
A.No change
B.16% increase
C.8% decrease
D.16% decrease
Answer: D.16% decrease
Explanation: Regd effect = ∣∣40−40−40×40100∣∣%=−16%|40−40−40×40100|%=−16%
i.e., the area will decrease by 16%
Answer D
Question: 2 log10 5 + log10 8 – ½ log10 4 = ?
A.2
B.4
C.2 + 2 log10 2
D.4 - 4 log10 2
Answer: A.2
Explanation: 2 log10 5 + log10 8 – ½ log10 4
= log10 (52) + log10 8 - log10 (41/2)
= log10 25 + log10 8 - log10 2 = log10 (25*8)/2
= log10 100 = 2
ANSWER:A
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%?
A.20%
B.25%
C.13 1/30%
D.12%
Answer: A.20%
Explanation: SP2 = 2/3 SP1
CP = 100
SP2 = 80
2/3 SP1 = 80
SP1 = 120
100 --- 20 => 20%
ANSWER:A
Question: The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 867 sq m, then what is the breadth of the rectangular plot?
A.15
B.17
C.12
D.16
Answer: B.17
Explanation: Let the breadth of the plot be b m.
Length of the plot = 3 b m
(3b)(b) = 867
3b2 = 867
b2 = 289 = 172 (b > 0)
b = 17 m.
Answer: Option B
Question: The ratio of boys and girls in a college is 5:6.if 25% of boys and 25%of girls are scholarship holders.then what percentage of students does not get the scholarship?
A.89%
B.78%
C.85%
D.65%
Answer: A.89%
Explanation: Ratio of boys : girls => 5x : 6x
Total no. of students including boys nd girls = 5x+6x = 11x
25% of boys => 5x*25/100 = 5x/4
25% of girls => 6x*25/100 =3x/2
No. of students getting scholorship => 5x/4 + 3x/2 = 11x/4
No. of students does not get the scholorship = 11x - 11x/4 = 33x/4
% of students not getting scolorship => 33x/4/11x * 100
=> 100*33x/44x
= 75%
ANSWER:A
Question: A is faster than B. A and B each walk 24 km. The sum of their speeds is 7 km/hr and the sum of times taken by them is 14 hours. Then, A's speed is equal to?
A.2
B.3
C.4
D.5
Answer: B.3
Explanation: Let A's speed = x km/hr. Then, B's speed = (7 - x) km/ hr.
So, 24/x + 24/(7 - x) = 14
x2 - 98x + 168 = 0
(x - 3)(x - 4) = 0 => x = 3 or 4.
Since, A is faster than B, so A's speed = 4 km/hr and B's speed = 3 km/hr.
Answer:B
Question: If population of certain city increases at the rate of 4%. If population in 1981 was 138910, then population in 1979 was?
A.12,0000
B.130000
C.128130
D.627000
Answer: C.128130
Explanation: Explanation:
X * (104/100) * (104/100) = 138915
X = 138910/1.0816
X = 128130
Answer: Option C
Question: Silk is purchased for $250 per square yard at the Silk Market. The silk is cut into patterns and made into s-size shirts - the excess silk is discarded (1/5 of the silk material). The area is 2 square yards in the pattern that makes 1 side of an s-size shirt. If 2 sides make one shirt, how much money is needed to buy silk to make x number of s-size shirts, in dollars?
A.2x
B.15x/8
C.850x
D.1,250x
Answer: D.1,250x
Explanation: The initial cost for a square yard of silk is = $250.
It takes 2 square yards of silk to make one side of an s-size shirt, but 1/5 of the material is wasted in cutting the material into patterns. The cost is; therefore, (1 square yard)(1 - 1/5) = $250, and so, 1 square yard = $250(5/4) for useful silk.
Because it takes 2 square yards to make one side, and 2 sides to make one shirt:
(2)(2)($250(5/4) = $1,250 = cost 1 shirt.
So, x number of shirts cost $1,250x
Answer is D
Question: Two cars cover the same distance at the speed of 56 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car.
A.373
B.338
C.448
D.838
Answer: C.448
Explanation: Explanation:
56(x + 1) = 64x
X = 7
56 * 8 = 448 km
Answer: Option C
Question: Insert the missing number. 12, 25, 49, 99, 197, 395, (...)
A.789
B.722
C.812
D.779
Answer: A.789
Explanation: Each number is twice the previous one with 1 added or subtracted alternatively.
Answer is A.
Question: A certain board game is played by rolling a pair of fair six-sided dice and then moving one's piece forward the number of spaces indicated by the sum showing on the dice. A player is frozen if her opponent's piece comes to rest in the space already occupied by her piece. If player A is about to roll and is currently five spaces behind player B, what is the probability that player B will be frozen after player A rolls?
A.1/12
B.5/36
C.1/9
D.1/3
Answer: C.1/9
Explanation: no. of possible outcomes = 6*6 = 36
no. of outcomes that result a total of 5 (as A is 5 spaces behind B) = 4 ( (1,4), (2,3), (3,2), (4,1) )
So, the probability = 1/9 (Option C)
Question: Rs.2500 is divided into two parts such that if one part be put out at 5% simple interest and the other at 6%, the yearly annual income may be Rs.140. How much was lent at 5%?
A.1500
B.1000
C.2000
D.3000
Answer: B.1000
Explanation: (x*5*1)/100 + [(2500 - x)*6*1]/100 = 140
X = 1000
ANSWER B
Question: A number is missing from the number series below.
Can you find it ?
84, 155, ?, 399 , 584, 819.
A.275
B.350
C.399
D.258
Answer: D.258
Explanation: D
The missing number is 258.
84 = 4^3 + 3^2 + 4
155 = 5^3 + 5^2 + 5
399 = 7^3 + 7^2 + 7
584 = 8^3 + 8^2 + 8
819 = 9^3 + 9^2 + 9
Thus,
258 = 6^3 + 6^2 + 6
Question: Total dinning bill for 7 people was $211.00.If they add 15% tip and divided the bill evenly ,
approximate.What was each persons find share$
A.30.14
B.34.66
C.32.4
D.32.29
Answer: B.34.66
Explanation: (211*15/100)=31.65
(211+31.65)/7=34.66
ANSWER:B
Question: sushi decided to save a certain amount of her monthly salary each month and her salary was unchanged from month to month. If sushi 's savings by the end of the year from these monthly savings were seven times the amount she spent per month, what should be the fraction of her salary that she spent each month?
A.12/19
B.12/20
C.19/12
D.12/17
Answer: A.12/19
Explanation: Let sushi's monthly savings = S
sushi's monthly pay = P
sushi's monthly expenditure = P-S
sushi's savings by the end of the year from these monthly savings were seven times the amount she spent per month
12S = 7*(P-S)
=>12/7 S = P-S
=> P = 19/7 S
sushi's monthly expenditure = P-S = 19/7S-S = 12/7S
fraction of her salary that sushi spent each month = 12/7S / 19/7S=P-S/P = 12/19. Answer is A
Question: In an election between the two candidates, the candidates who gets 70% of votes polled is winned by 160 vote’s majority. What is the total number of votes polled?
A.750
B.400
C.800
D.850
Answer: B.400
Explanation: Explanation:
Note: majority (40 %) = difference in votes polled to win (70 %) & defeated candidates (30 %)
40 % = 70 % - 30 %
40% -----> 160 (40*4 = 160)
100% -----> 400 (100*4 = 400)
Answer: Option B
Question: Prints a page 30 pg per min .If the printed for 2 hours except 10 min.Where there
was an paper jam,how many page did it print
A.10,880
B.3,300
C.14,880
D.8,880
Answer: B.3,300
Explanation: 30 pages ------->1 min
2 hrs except 10 mints means=2*60=120-10=110 mints
i.e.,110*30=3300 pages printed.
ANSWER:B
Question: solve this logic number sequence( based on circles in digits) puzzle by the correct digit?
8080=6
1357=0
2022=1
1999=3
6666=?
A.6
B.4
C.8
D.2
Answer: B.4
Explanation: Correct Answer : B
No. of circles in the number
Question: A and B invests Rs.8000 and Rs.9000 in a business. After 4 months, A withdraws half of his capital and 2 months later, B withdraws one-third of his capital. In what ratio should they share the profits at the end of the year?
A.32:48
B.32:40
C.32:45
D.32:46
Answer: C.32:45
Explanation: A : B
(8000*4)+(4000*8) : (9000*6)+(6000*6)
64000 : 90000
32 : 45
Answer: C
Question: A sum fetched total simple interest of 4016.25 at the rate of 11 p.c.p.a. in 5 years. What is the sum?
A.8925
B.8032.5
C.7302.3
D.8900
Answer: C.7302.3
Explanation: Let the sums be P.
Now, 55% of P = 4016.25
or, P = 7302.3
Answer C
Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 190 m long?
A.40 sec
B.42 sec
C.44 sec
D.48 sec
Answer: C.44 sec
Explanation: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 190 = 550 m
Required time = 550 * 2/25 = 44 sec
ANSWER:C
Question: An aeroplane covers a certain distance at a speed of 120 kmph in 4 hours. To cover the same distance in 1 2/3 hours, it must travel at a speed of:
A.520
B.288
C.820
D.740
Answer: B.288
Explanation: Distance = (240 x 5) = 480 km.
Speed = Distance/Time
Speed = 480/(5/3) km/hr. [We can write 1 2/3 hours as 5/3 hours]
Required speed = (480 x 3/5) km/hr = 288 km/hr
Answer B) 288 Km/hr
Question: The present worth of Rs.1183 due in 2 years at 4% per annum compound interest is
A.Rs.150.50
B.Rs.154.75
C.Rs.156.25
D.Rs.1093.75
Answer: D.Rs.1093.75
Explanation: Solution
Present Worth	= Rs.[1183/(1+4/100)²]
= Rs.(1183x25/26x25/26)
= Rs.1093.75
Answer D
Question: A father said his son , " I was as old as you are at present at the time of your birth. " If the father age is 40 now, the son age 5 years back was
A.14
B.17
C.15
D.19
Answer: C.15
Explanation: Let the son's present age be x years .Then, (40 - x) = x x= 20.
Son's age 5 years back = (20 - 5) = 15 years
Answer: C
Question: A rectangular field has to be fenced on three sides leaving a side of 25 feet uncovered. If the area of the field is 880 sq. feet, how many feet of fencing will be required?
A.75.4 feet
B.98.4 feet
C.95.4 feet
D.85.4 feet
Answer: C.95.4 feet
Explanation: Area of the field =880 sq. feet.
Length of the adjacent sides are
25 feet and 880/25=35.2 feet.
Required length of the fencing=25+35.2+35.2=95.4 feet
ANSWER:C
Question: At a dinner party 7 people are to be seated around a circular table. Two sitting arrangements are considered different only when the positions of the people are different relative to each other.What is the total number of possible sitting arrangements or the group?
A.5
B.10
C.5000
D.5040
Answer: D.5040
Explanation: Hi there,
You can treat this as an ordering question except thatfor a circular arrangement you need to divide by the number of spaces.So in this case:
7!/7=5040
If you spin the circle to right, that doesn't count as a new arrangement. Dividing by the number of spaces takes that into consideration.
Happy Studies,
HG.
D
Question: In a convention where they distributes prizes. In how many ways can 3 prizes be distributed among 4 boys when a boy gets any number of prizes?
A.58
B.60
C.64
D.68
Answer: C.64
Explanation: In this case, repetitions are allowed, so all the three prizes can be given in 4 ways, i.e. (4 x 4 x 4) ways = 4*3 ways = 64 ways
Question: Find the area of trapezium whose parallel sides are 30 cm and 18 cm long, and the distance between them is 15 cm.
A.227
B.299
C.360
D.161
Answer: C.360
Explanation: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (30 + 18) * (15)
= 360 cm2
Answer: C
Question: A store sells women purses for $50 each and men's wallets for $40 each. On every women purse, the store makes a profit of $10 while on every men's wallet it makes a profit of $6. If on a given day the store's sales amounted to $1000, which of the following cannot be the profit made on that day?
A.140
B.150
C.160
D.200
Answer: A.140
Explanation: $140 is the only option that does not satisfy a combination of integer number sales of women's purses and men's wallets. Answer: A
Question: A man invested Rs. 4455 in Rs. 10 shares quoted at Rs. 8.25. If the rate of dividend be 12%,his annual income is :
A.Rs. 207.40
B.Rs. 534.60
C.Rs. 648
D.Rs. 655.60
Answer: C.Rs. 648
Explanation: Solution
Numbers of shares =(4455/825)=540
Face value = Rs. (540X10)=Rs.5400
Annual income = Rs.(12/10x5400) = Rs. 648.
Answer C
Question: Thomas's age and Matt's age are in the ratio 3:5. Two years ago the ratio of their ages was 5:9. Find the ratio of their ages four years hence?
A.1:2
B.2:3
C.3:4
D.4:5
Answer: B.2:3
Explanation: Let ages of Thomas and Matt be x and y respectively.
x/y = 3/5 => x = 3/5 y
(x- 2)/(y - 2) = 5/9
=> 9x - 18 = 5y - 10 => 9x = 5y + 8
But x = 3/5 y
9 * 3/5 y = 5y + 8
27y = 25y + 40 => y = 20 years
=> x = 3*20/5 => 12 years
Ratio of their ages four years hence, (12 +4)/(20+ 4) = 16/24. => 2:3
Answer:B
Question: The average score of a cricketer for ten matches is 38.9 runs. If the average for first six matches is 42, then average for last four matches is
A.33.25
B.32.25
C.34.25
D.34.5
Answer: C.34.25
Explanation: Explanation:
=(38.9×10)−(42×6) / 4
=(1216−750) / 4=34.25
Option C
Question: The number N is 5,2H1, where H represents the ten's digit. If N is divisible by 3, what is the value of H?
A.1
B.3
C.5
D.6
Answer: A.1
Explanation: Integer is divisible by 3 - Sum of digits is divisible by 3
Answer: A
Question: In how many ways can a committee of 5 people comprising at least 3 boys be formed using a group of 5 boys and 6 girls?
A.67
B.64
C.65
D.66
Answer: D.66
Explanation: There are 2 options: the selected groups have no girls or one girls.
-First case: 1 girl + 3 boys: 6C1 * 5C3 = 6*10 = 60
-Second case: 4 boys: 5C4 = 5
So there are 60 + 5 = 66 ways in total.
D
Question: 5216 × 51 = ?
A.266015
B.266014
C.266016
D.266116
Answer: C.266016
Explanation: Normal way of multiplication may take time. Here is one alternative.
5216×51=(5216×50)+5216=(5216×1002)+5216=5216002+5216=260800+5216=266016
Answer is C.
Question: The division of a whole number N by 13 gives a quotient of 28 and a remainder of 2. Find N.
A.797
B.197
C.582
D.366
Answer: D.366
Explanation: According to the division process of whole numbers, N can be written, using multiplication, as follows
N = quotient *divisor + remainder = 28* 13 + 2 = 366 correc answer D
Question: S is a set containing 6 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.
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.
Answer: D. The sum of the terms in S is prime.
Explanation: 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.
D