RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A 250m long train is travelling at 30km/hr. Another 200m long train travelling at 40km/hr in the same direction overtakes it. How long would it take to pass the first train completely?
A.2min32secs.
B.1min32secs.
C.3min42secs.
D.2min42secs,
Answer: D.2min42secs,
Explanation: Relative speed =x-y x,y are their speeds. Distance =(250+200)m =450m Relative speed = (40-30)km/hr =450m =25/9 m/s Time taken to cover 450m = 450*9/25 secs. =162 secs. =2min.42sec. Answer : D
Question: A boy is traveling from his house to school at 3km/hr and reached school 9minutes late. Next day he traveled 4km/hr and reached 6minutes early. Then find the distance between house and school?
A.3km
B.4.5km
C.5km
D.2.5km
Answer: A.3km
Explanation: Let distance be x
S1 = 3km/hr
S2 = 4km/hr
T1 = x/3hr
T2 = x/4hr
Difference in time = 9+6 = 15m = 1/4hr
(x/3)-(x/4) = 1/4
x = 3km
Answer is A
Question: A, B, C, D and E play a game of cards. A says to B, "If you give me three cards, you will have as many as E has and if I give you three cards, you will have as many as D has." A and B together have 10 cards more than what D and E together have. If B has two cards more than what C has and the total number of cards be 133, how many cards does B have ?
A.37
B.23
C.25
D.29
Answer: C.25
Explanation: Clearly, we have :
B-3 = E ...(i)
B + 3 = D ...(ii)
A+B = D + E+10 ...(iii)
B = C + 2 ...(iv)
A+B + C + D + E= 133 ...(v)
From (i) and (ii), we have : 2 B = D + E ...(vi)
From (iii) and (vi), we have : A = B + 10 ...(vii)
Using (iv), (vi) and (vii) in (v), we get:
(B + 10) + B + (B - 2) + 2B = 133 5B = 125 B = 25.
Answer: C
Question: There are r red ball, b blue ball and w white ball in a bag. What is the ratio of the number of blue ball to the total no. of ball in terms of r, b and w.?
A.(r + b + w)
B.r / (r + b + w)
C.r * (r + b + w)
D.r / (r + b )
Answer: B.r / (r + b + w)
Explanation: The total number of marbles is
r + b + w
The total ratio of blue marbles to the total number of marbles is
r / (r + b + w)
B
Question: What is the total number of X integers between 100 and 200 that are divisible by 3?
A. 33
B. 32
C. 31
D. 30
Answer: A. 33
Explanation: yes there is a different way of arriving at that answer ....
u can also use airthmetic progression to get the answer
since the first term to be divisble by 3 is 102 ..take that as A .. the starting no
and since 198 is the last digit to be divisible by 3 take that as N ...
since the difference is 3 take that as D
no u have to find what term is 198 take that as nth term
the formula for that is N = A + (n-1) * d
198 = 102 +(n-1) * 3
from this u get n =33
Question: Half of the workers in Palabras bookstore have read the latest book by J. Saramago, and 1/6 of the workers have read the latest book by H. Kureishi. The number of workers that have read neither book is one less than the number of the workers that have read the latest Saramago book and have not read the latest Kureishi book. If there are 42 workers in the Palabras bookstore, how many of them have read both books?
A.3
B.12
C.9
D.8
Answer: A.3
Explanation: There are total 42 workers.
Half of the workers in Palabras bookstore have read the latest book by J. Saramago,
So 21 have read Saramago.
1/6 of the workers have read the latest book by H. Kureishi.
So (1/6) * 42 = 7 have read Kureishi
The number of workers that have read neither book is one less than the number of the workers that have read the latest Saramago book and have not read the latest Kureishi book
If B workers have read both books, 20 - B have read Saramago but not Kureishi.
So, (21 - B - 1) have read neither.
Total = n(A) + n(B) - Both + Neither
42 = 21 + 7 - B + (21 - B - 1)
B = 3
Answer (A)
Question: In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?
A.33
B.63
C.22
D.29
Answer: B.63
Explanation: Explanation:
Required number of ways = \inline {\color{Black}(7C_{5}\times 3C_{2})=(7C_{2}\times 3C_{1})=63}
Answer: B) 63
Question: The surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 12 cm each. The radius of the sphere is:
A.4cm
B.6cm
C.8cm
D.10cm
Answer: B.6cm
Explanation: Explanation:
Curved surface area of sphere =4/πr2Surface area of cylinder =2πrh
=>4/πr2=2πrh
=>r2=6∗12/2
=>r2=36
=>r=6
Note: Diameter of cylinder is 12 so radius is taken as 6.
Option B
Question: If cost of sugar increases by 52%. How much percent consumption of sugar should be decreased in order to keep expenditure fixed?
A.34.21
B.35.15
C.36.32
D.28.21
Answer: A.34.21
Explanation: 100
152
-----
152 ----- 52
100 ------ ? => 34.21%
Answer:A
Question: Three numbers are in the ratio 1:4:8 and their H.C.F is 3. The numbers are?
A.3, 15, 24
B.3, 12, 27
C.3, 12, 22
D.3, 12, 24
Answer: D.3, 12, 24
Explanation: Let the required numbers be x, 4x and 8x. Then, their H.C.F = x. So, x = 3.
The numbers are 3, 12, 24.
Answer: D
Question: Compound interest earned on a sum for the second and the third years are Rs.1200 and Rs.1440 respectively. Find the rate of interest?
A.80% p.a
B.10% p.a
C.20% p.a
D.28% p.a
Answer: C.20% p.a
Explanation: Rs.1440 - 1200 = Rs.240 is the interest on Rs.1200 for one year.
Rate of interest = (100 * 240) / (100 * 1) = 20% p.a
Answer:C
Question: In a class of 40 students 26 play football and play 20 long tennis, if 17 play above, many play neither?
A.6
B.8
C.10
D.11
Answer: D.11
Explanation: 26 + 20 - 17 = 29
40 - 29 = 11 play neither
Answer is D
Question: Express 20 mps in kmph?
A.23
B.88
C.90
D.72
Answer: D.72
Explanation: 20 * 18/5 = 72 kmph
Answer:D
Question: The length of a room is 5.5 m and width is 3.75 m. Find the cost of paving the floor by slabs at the rate of Rs. 1400 per sq. metre.
A.Rs. 15000
B.Rs. 15550
C.Rs. 15600
D.Rs. 28875
Answer: D.Rs. 28875
Explanation: Solution
Area of the floor = (5.5 × 3.75) m2 = 20.625 m2
∴ Cost of paving = Rs. (1400 × 20.625) = 28875. Answer D
Question: At the time of marriage, a man was 8 years elder to his wife. 15 years after their marriage, his age is 5/4 times the age of his wife. What was wife's age at the time of marriage ? Choose one answer.
A.15 years
B.30 years
C.18 years
D.17 years
Answer: D.17 years
Explanation: let wifes age= x
husband age = x+8
now after 15 years of mrg x+15 wifes age
x+8+15 husbands age
5/4(x+15)=x+8+15
after solving x=17
ANSWER:D
Question: List L: ABC, BCA, CAB
In list L above, there are 3 positive integers, where each of A, B, and C is a different nonzero digit. Which of the following is the sum of all the positive integers that MUST be factors of the sum of the integers in list L?
A.47
B.114
C.152
D.161
Answer: C.152
Explanation: Sum = (100A + 10B + C) + (100B + 10C + A) + (100C + 10A + B) = 111*(A + B + C).
So, we have that the sum will be a multiple of 111=3*37.
As for A + B + C: if A=1, B=2 and C=4, then A + B + C = 7, so the sum will also be divisible by 7 BUT if A=1, B=2 and C=8, then A + B + C = 11, so the sum will also be divisible by 11. This implies that A + B + C will not produce the same factors for all possible values of A, B and C.
Therefore, we can say that 111*(A + B + C) MUST be divisible only by 111 --> so, by 1, 3, 37, and 111 --> 1 + 3 + 37 + 111 = 152.
Answer: C.
Question: The ratio between the present age of P and Q is 6 : 7. if Q is 4 years old then P, what will be the ratio of the ages of P and Q after 4 year ?
A.3 : 4
B.3 : 5
C.7 : 8
D.4 : 3
Answer: C.7 : 8
Explanation: Solution
Let P's age and Q's age be 6x years and 7x years respectively.
Then, 7x - 6x = 4 ⇔ x = 4.
∴ Required ratio = (6 x + 4) : (7 x + 4) = 28 : 32 = 7 : 8 .Answer C
Question: A die is thrown twice and the sum of the numbers appearing is observed to be 6.
find the conditional probability that the number 4 has appeared at least once?
A.2/5
B.3/5
C.3/7
D.3/11
Answer: A.2/5
Explanation: Let E be the event that ‘number 4 appears at least once’ and F be
the event
that ‘the sum of the numbers appearing is 6’.
Then, E = {(4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (1,4), (2,4), (3,4),
(5,4), (6,4)}
and F = {(1,5), (2,4), (3,3), (4,2), (5,1)}
We have P(E) = 11/36
and P (F) = 5/36
Also EnF = {(2,4), (4,2)}
Therefore P(EnF) = 2/36
the required probability
P(E|F) = P(EnF)/P(F) = (2/36)/(5/36) = 2/5.
A)
Question: A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long?
A.333 Sec
B.190 Sec
C.176 Sec
D.2687 Sec
Answer: B.190 Sec
Explanation: L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (D)= 1900 m
T = D/S
T = 1900/10
T = 190 Sec
Answer:B
Question: A, B can Complete a work in 15 days &10 days respectively. They started doing thework together after 2 days B had to leave and A alone completed the remaining work.The whole work wascompleted in how many days?
A.8 days
B.10 days
C.12 days
D.14 days
Answer: C.12 days
Explanation: A and B can complete whole work in
30/(2+3)=6 days
Part of work completed together in
3 days =2/6=1/3 part
Now 2/3 part will be completed by A in
2/3*15=10 days
Hence, whole work will be completed in
2+10=12 days
C
Question: Baseball's World Series matches 2 teams against each other in a best-of-seven series. The first team to win four games wins the series and no subsequent games are played. If you have no special information about either of the teams, what is the probability E that the World Series will consist of fewer than 7 games?
A. 12.5%
B. 25%
C. 31.25%
D. 68.75%
Answer: D. 68.75%
Explanation: Your explanation is very close toManhattan GMAT's official answer - it's quite uncanny:
"There are many other ways this could happen. Using the permutation formula, there are 6!/(3!)(3!) = 20 ways for the two teams to split the first 6 games (3 wins for each).
There are then 2 possible outcomes to break the tie in Game 7. Thus, there are a total of 202 = 40 ways for the World Series to last the full 7 games.
The probability that any one of these 40 ways occurs can be calculated from the fact that the probability of a team winning a game equals the probability of a team losing a game = 1/2.
Given that 7 distinct events must happen in any 7 game series, and that each of these events has a probability of 1/2, the probability that any one particular 7 game series occurs is.
Since there are 40 possible different 7 game series, the probability that the World Series will last exactly 7 games is: (1/2)^7 = 1/128
40*1/128 = 40/128 = 31.25%
Thus the probability E that the World Series will last less than 7 games is 100% - 31.25% = 68.75%.
The correct answer is D."
Question: Find the sum of first 30 natural numbers
A.470
B.468
C.465
D.463
Answer: C.465
Explanation: Explanation:
Sum of n natural numbers
=n(n+1)2
=30(30+1)2=30(31)2=465
Answer: Option C
Question: What should come in place of the question mark(?) in the following equation?
4 1⁄2 × 4 1⁄3 - 8 1⁄3 ÷ 5 2⁄3 = ?
A.8
B.18 1⁄34
C.13 3⁄34
D.7⁄17
Answer: B.18 1⁄34
Explanation: ? = 9⁄2 × 13⁄3 - 25⁄3 × 3⁄17
= 39⁄2 - 25⁄17 = 663−50/34=613/34=18 1/34
Answer B
Question: A certain telephone company company charges 3.10 cents for the first 1/5 of a minute plus 0.40 cents for each additional 1/5 of a minute. What would this company charge for a talk time of 8 minutes long?
A.15.60
B.16.0
C.17.8
D.18.7
Answer: D.18.7
Explanation: first 1/5 minute charge = 3.10 cents
rest of the minute = 8 - (1/5) = 39/5
charge for the rest of the minute = 39 *0.4 = 15.6
total charge = 3.10+15.6 = 18.7 cents
Answer is D.
Question: How many numbers with 3 different digits can be formed using only the even-numbered digit?
A.10
B.24
C.40
D.60
Answer: B.24
Explanation: Odd digits are 2, 4, 6, 8.
We want 3 different digits.
First digit can be chosen in 4 ways.
Second digit can be chosen in 3 ways.
Third digit can be chosen in 2 ways.
Total ways = 4*3*2
= 24
Hence option (B).
Question: A list of measurements in increasing order is 4, 5, 6, 8, 15 and x. If the median of these measurements is 3/4 times their arithmetic mean, what is the value of x?
A.16
B.18
C.20
D.22
Answer: B.18
Explanation: The median is (6+8)/2 = 7
The mean is (4+5+6+8+15+x)/6 = (38+x)/6
(38+x) /6 * 3/4 = 7
x = 56-38 = 18
The answer is B.
Question: 4 friends went for a cinema, and everyone decided to contribute equally to the total bill of $60. If one of the friends had a coupon for 8% off the total bill, and if each friend still contributed equally after the coupon was applied to the bill, how much did each friend pay?
A.13
B.13.1
C.13.2
D.13.8
Answer: D.13.8
Explanation: At the non-discounted price, each friend would pay $15, as $60 divided by 4 friends is $15 per friend. But if the bill is 8% off, then each friend would pay 8% less. 8% of $15 is $1.2, so each friend saves $1.2 and pays the remaining 13.8
CORRECT OPTION:OPTION D
Question: A rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?
A.Rs.3990
B.Rs.3967
C.Rs.3927
D.Rs.3900
Answer: D.Rs.3900
Explanation: Area = (l + b – d) d
(80 + 60 – 10)10 => 1300 m2
1300 * 3 = Rs.3900
Answer: D
Question: Distance between two stations A and B is 778 km. A train covers the journey from A to B at 84 km per hour and returns back to A with a uniform speed of 56km per hour. Find the average speed of the train during the whole journey?
A.67.8
B.67.4
C.67.2
D.67.6
Answer: C.67.2
Explanation: If a car covers a certain distance at x kmph and an equal distance at y kmph. Then,
average speed of the whole journey = (2xy)/x+y kmph.
By using the same formula, we can find out the average speed quickly.
Average speed
=(2×84×56)/(84+56)
=(2×84×56)/140
=(2×21×56)/35
=(2×3×56)/5
=3365=67.2
Answer is C.
Question: A reduction of 40% in the price of bananas would enable a man to obtain 64 more for Rs.40. What is the reduced price/dozen?
A.3
B.4
C.5
D.6
Answer: A.3
Explanation: Sol. lie purchases 6a bananas mere for 4096 of Rs 40 or, Rs 16. Reduced price per do 3
A
Question: A soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price. During the annual summer sale, everything in the store is an additional 20 percent off the original list price. If a replica jersey's list price is $80, approximately what percent of the list price is the lowest possible sale price?
A.20
B.25
C.30
D.40
Answer: D.40
Explanation: Let the list price be 2x
for min sale price, the first discount given should be 50%, 2x becomes x here
now, during summer sale additional 20% off is given ie sale price becomes 0.8x
it is given lise price is $80
=> 2x = 80
=> x = 40
and 0.8x = 32
so lowest sale price is 32, which is 40% of 80
hence, D is the answer
Question: 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
A.1/2
B.1
C.2/3
D.3/5
Answer: A.1/2
Explanation: Sol. Required probability = Pg.) x P(B) = (1— D x(1 —I) =: x 1=1/2
Ans.(A)
Question: A, B, C subscribe Rs. 50,000 for a business, A Subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 35,000, C receives :
A.8400
B.14703
C.37798
D.13777
Answer: A.8400
Explanation: Explanation:
Let C = x. Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.
So, x + x + 5000 + x + 9000 = 50000 <=> 3x = 36000 <=>
x = 12000.
A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.
C's share = Rs. (35000 * 12/50 ) = Rs. 8,400.
Answer: A)
Question: A computer program generates a single digit by a random process, according to which the probability of generating any digit is directly proportional to the reciprocal of one more than that digit. If all digits are possible to generate, then the probability R of generating an odd prime digit is between
A.0 and 1/6
B.1/6 and 1/3
C.1/3 and 1/2
D.1/2 and 2/3
Answer: B.1/6 and 1/3
Explanation: K (1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9+ 1/10) =1
Note that 1/10 is least value and is equal to 0.1 so we can write above series as
K (1+0.5+0.3+0.25+0.2+0.16+0.5+residual) = 1
K=1/3+
P (3 or 5 or 7) =K*13/24
Required probability R= 13/24 × 1/3+ = 4+/24 > 1/6
Answer should be B
P.s. 3+ denotes a value little greater than 3 .
Same for 4+.
Question: The speed of a boat in upstream is 70 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?
A.5 kmph
B.13 kmph
C.65 kmph
D.55 kmph
Answer: A.5 kmph
Explanation: Speed of the boat in still water
= (70+80)/2
= 75 kmph. Speed of the stream
= (80-70)/2
= 5 kmph.
Answer: A
Question: A painting is painted on a cardboard 19 cm and 14 cm wide, such that there is a margin of 1.5 cm along each of its sides. Find the total area of the margin.
A.80
B.85
C.88
D.90
Answer: D.90
Explanation: Length of the cardboard = 19 cm
Breadth of the cardboard = 14 cm
Area of the cardboard = 19 × 14 cm² = 266 cm²
Length of the painting excluding the margin = [19 - (1.5 + 1.5)] cm = 16 cm
Breadth of the painting excluding the margin = 14 - (1.5 + 1.5) = 11 cm
Area of the painting excluding the margin = (16 × 11) cm² = 176 cm²
Therefore, area of the margin = (266 - 176) cm² = 90 cm²
ANSWER : OPTION D
Question: When processing flower-nectar into honey bees' extract, a considerable amount of water gets reduced. How much flower-nectar must be processed to yield 1kg of honey, if nectar contains 50% water, and the honey obtained from this nectar contains 30% water?
A.1.2 kg
B.1.5 kg
C.1.4 kg
D.1.9 kg
Answer: C.1.4 kg
Explanation: Explanation :
Flower-nectar contains 50% of non-water part.
In honey this non-water part constitutes 70% (100-30).
Therefore 0.5 X Amount of flower-nectar = 0.70 X Amount of honey = 0.70 X 1 kg
Therefore amount of flower-nectar needed =
(0.70/0.51)kg=1.4 kgs
Answer : C
Question: A certain psychologist charges $40 more for the first hour of therapy than for each additional hour. If the total charge to a patient who receives 5 hours of therapy is $375, what is the total charge to a patient who receives only 2 hours of therapy ?
A. $120
B. $135
C. $150
D. $174
Answer: D. $174
Explanation: Let the charge for first hour = x+40
then charge for each additional hour = x
x+40 + 4x = 375
=> 5x = 335
=> x = 67
Total charge for patient for 3 hours of therapy = x+40 + x = 2x+40
= 174 $
Answer D
Question: 20% of employees are women with fair hair. 40% of fair-haired employees are women. What percent of employees have fair hair?
A.25
B.30
C.50
D.55
Answer: C.50
Explanation: 20% of employees are women with fair hair.
40% of fair-haired employees are women.
So,
20% * Employees = 40% * Fair Haired Employees (because both are equal to the number of fair haired women employees)
(1/2) * Employees = Fair Haired Employees
Answer (C)
Question: At 11:00 a.m., Tom begins traveling on a certain bike path from Riverdale at a constant rate of 10 mph. If, at 1:00 p.m., Jim begins traveling from Riverdale on the same path at a constant rate of 20 mph, at what time will he catch up to Peter?
A.3:00 p.m.
B.4:00 p.m.
C.5:00 p.m.
D.6:00 p.m.
Answer: A.3:00 p.m.
Explanation: By the time Jim starts, Tom has already covered = 2 hr * 10 mph = 20 miles
Relative speed = 20- 10 = 10mph
To catch up, Jim needs to cover 20 miles which can be covered in = 20/10= 2 hours
If Jim leaves at 1 pm, he will catch Tom at 3 pm
Answer: A
Question: Students are in cultural program as follows: music-10, Dance-15, and skits -6. No student is in all three cultural program , but 4 are in both music and Dance, 3 are in both music and skits, and 2 are in Dance and skits.
How many different students are in at least one of the three cultural program?
A.34
B.28
C.26
D.22
Answer: D.22
Explanation: Total students = M + D + S - (sum of 2-group overlaps) + (all three)
Total students = 10 + 15 + 6 - (3 + 4 + 2) + 0 = 22 students.
Answer is D
Question: You are distributing vegetable oil. there are 21 bottles in total out of which 7 are full, 7 half empty, 7 empty. the oil has to be distributed among three people. how will you distribute so that each person gets equal number of bottles and the same quantity of oil
A.1st person : 3 full, 1 half, 3 empty , 2nd person: 3 full, 1 half, 3 empty,, 3rd person : 1 full, 5 half, 1 empty
B.1st person : 1 full, 1 empty ,1half , 2nd person: 3 full, 1 half, 2 empty, 3rd person : 1 full, 2 half, 4 empty
C.1st person : 1 full, 2 half, 3 empty , 2nd person: 3 full, 1 empty , 3 empty, 3rd person : 3 full, 5 half, 2 empty
D.1st person : 1 full, 1 half, 2 empty , 2nd person: 2 full, 1 half, 1 empty, 3rd person : 1 full, 5 half, 2 empty
Answer: A.1st person : 3 full, 1 half, 3 empty , 2nd person: 3 full, 1 half, 3 empty,, 3rd person : 1 full, 5 half, 1 empty
Explanation: Correct Answer : A
Question: If 3x=8y=z, what is x+y, in terms of z?
A.z/2
B.2z
C.11z/24
D.3z/5
Answer: C.11z/24
Explanation: 3x=8y=z
x = z/3
and y = z/8
x+y = z/3 + z/8 = 11z/24
Answer is C
Question: A man walks from B to C, a distance of x miles, at 10 miles per hour and returns at 15 miles per hour. What is his average speed?
A.10 mph
B.12 mph
C.8.8 mph
D.8.4 mph
Answer: B.12 mph
Explanation: Total distance covered = 2x
Time taken12miles / hour = x/15 hrs
Time taken @ 8 miles / hour = x/10 hrs
Avg speed = 2x / (x/10 + x/15) = 12 mph
Ans is B
Question: When x is divided by y, the quotient is z with remainder t. Which of the following is equal to t?
A.yz – x
B.y/x−z
C.x – y – z
D.x – yz
Answer: D.x – yz
Explanation: (x/y)=z(+t)
(18/8)=2(+2)
x-yz
which is 18-(8*2)=2
Answer is D
Question: A list of numbers has six positive integers. Three of those integers are known: 4, 5 and 24 and three of those are unknown: x, y and z. The three unknowns are known to be distinct. It is also known that the mean of the list is 10 and the median lies between 7 and 8 (exclusive). Which of the following CANNOT be the value of any one of the unknowns?
A.13
B.12
C.11
D.10
Answer: C.11
Explanation: Mean = 10
Therefore sum of the 6 digits = 6*10 = 60 -------- (1)
The 3 digits are 4,5 & 24 -------------- (2)
Now, 7 < median < 8
-> 7 < (sum of 2 digits)/2 < 8
-> 14 < (sum of 2 digits) < 16
Therefore the sum of 2 digits = 15.
The 2 digits whose sum is 15 & whose median is b/w 7 & 8 can be :
1. 7, 8,
2. 6, 9,
3. 5, 10, or
But as soon as we take 4, 11 -> the series becomes 4,4,5,11,12,24 &
11 pairs up with 5 to give median as 8.
Hence the number can't be 11 !!
Answer : C
Question: Find the number of ways of arranging the boy and 12 guests at a circular table so that the boy always sits in a particular seat?
A.3!
B.8!
C.11!
D.12!
Answer: D.12!
Explanation: Ans.(D)
Sol. Total number of persons = 13 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 12 places => 12! Ways ... The number of required arrangements = 12! x 1= 12! = 12! ways
Question: A survey was conducted to find out how many people in a housing colony of 144 residents could swim, dance and drive a car. It was found that the number of people who could not swim was 85, the number of people who could not dance was 100 and that the number of people who could not drive a car was 91. If the number of people who could do at least two of these things, was found to be 37 and the number of people who could do all these things was found to be 6, how many people could not do any of these things?
A.28
B.31
C.33
D.35
Answer: B.31
Explanation: T=n(A)+n(B)+n(C)-n(Exactly two of the events)-2*n(All 3 Events)+n(None of the events)
T=144
n(A)=T-n(A')=144-85=59
n(B)=T-n(B')=144-100=44
n(C)=T-n(C')=144-91=53
n(Exactly two of the events)=n(At least 2 Events)-n(All 3 Events)=37-6=31
n(All 3 Events)=6
144=59+44+53-31-2*6+n(None of the events)
n(None of the events)=144-55-44-53+31+12=31
Ans:B
Question: Excluding stoppages, the speed of a train is 54 kmph and including stoppages it is 40 kmph. Of how many minutes does the train stop per hour?
A.A)13.55
B.B)14.55
C.C)15.55
D.D)16.55
Answer: C.C)15.55
Explanation: Explanation:
T = 14/54 * 60 = 15.55
Answer: Option C
Question: Rajan borrowed Rs.4000 at 5% p.a compound interest. After 2 years, he repaid Rs.2210 and after 2 more year, the balance with interest. What was the total amount that he paid as interest?
A.635.50
B.635.58
C.635.52
D.635.59
Answer: A.635.50
Explanation: 4000
200 ---- I
200
10 ---- II
---------------
4410
2210
--------
2000
110 ---- III
110
5.50 ---- IV
-----------
2425.50
2210
-----------
4635.50
4000
----------
635.50
Answer: A