RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Divide 2379 into 3 parts so that their amounts after 2, 3 and 4 years respectively may be equal, the rate of interest being 5% per annum at simple interest. The first part is:
A.759
B.792
C.818
D.828
Answer: D.828
Explanation: Let the parts be x, y and [2379 – (x + y)].
x + (x × 2 × 5⁄100) = y + (y × 3 × 5⁄100)
= z + (z × 4 × 5⁄100)
⇒ 11x⁄10 = 23y⁄20 = 6z⁄5 = k ⇒ x = 10k⁄11, y = 20k⁄23, z = 5k⁄6
But x + y + z = 2379.
⇒ 10k⁄11 + 20k⁄23 + 5k⁄6 = 2379
⇒ 1380 k + 1320 k + 1256 k = 2379 × 11 × 23 × 6
⇒ k = 2379×11×23×6/3965=3×11×23×6/5
∴ x = (10/11×3×11×23×6/5)=828
Hence, the first part is 828.
Answer D
Question: Sum of two numbers is 15. Two times of the first exceeds by 5 from the three times of the other. Then the numbers will be?
A.5
B.9
C.11
D.13
Answer: A.5
Explanation: Explanation:
x + y = 15
2x – 3y = 5
x = 10 y = 5
A)
Question: What is the greatest of 3 consecutive integers whose sum is 39?
A.14
B.15
C.16
D.17
Answer: A.14
Explanation: 39 / 3 = 13
The three numbers are 12, 13, and 14.
The answer is A.
Question: Ann and Bob drive separately to a meeting. Ann's average driving speed is greater than Bob's avergae driving speed by one-third of Bob's average driving speed, and Ann drives twice as many miles as Bob. What is the ratio E of the number of hours Ann spends driving to the meeting to the number of hours Bob spends driving to the meeting?
A.8:3
B.3:2
C.4:3
D.2:3
Answer: B.3:2
Explanation: Say the rate of Bob is 3mph and he covers 6 miles then he needs 6/3=2 hours to do that.
Now, in this case the rate of Ann would be 3+3*1/3=4mph and the distance she covers would be 6*2=12 miles, so she needs 12/4=3 hours for that.
The ratio E of Ann's time to Bob's time is 3:2.
Answer: B.
Question: What is the area of a square field whose diagonal of length 22 m?
A.288
B.289
C.242
D.112
Answer: C.242
Explanation: d2/2 = (22 * 22)/2
= 242
Answer: C
Question: How many 5 letter words ( with or without meaning) can be formed using all the following 5 letters P,Q,R,S,and W so that letter P is to the left of letter R?
A.70
B.50
C.60
D.90
Answer: C.60
Explanation: Two positions can be selected out of 5 positions in 5C2 ways = 10 ways.
And the remaining 3 letters can be placed in 3 posions in 3! Ways = 6 ways.
So the final Answer = number of ways letters P and R can be arranged x number
of ways the other 3 letters can be arranged
Final Answer = 10 x 6 = 60 ways
C
Question: In a group of ducks and cows, the total number of legs are 28 more than twice the no. of heads. Find the total no.of buffaloes.
A.11
B.12
C.14
D.16
Answer: C.14
Explanation: Let the number of buffaloes be x and the number of ducks be y
=> 4x + 2y = 2 (x + y) + 28
=> 2x = 28 => x = 14
C
Question: Susan weighs m pounds more than Anna does, and together they weigh a total of n pounds. Which of the following represents Anna’s weight in pounds?
A.(n - m)/2
B.(n + m)/2
C.n/2 - m
D.2n − m
Answer: A.(n - m)/2
Explanation: Let Anna's weight = a
Susan's weight = a + m
Together their weight is 2a + m = n
2a = n-m
Hence a = #(n-m)/2#
ANSWER:A
Question: The sum of three integers is 33. The largest integer is 3 times the middle integer, and the smallest integer is 23 less than the largest integer. What is the product of the three integers?
A.192
B.203
C.214
D.225
Answer: A.192
Explanation: Let x be the middle integer. Then the largest is 3x and the smallest is 3x - 23.
3x - 23 + x + 3x = 33
x = 8
The three integers are 1, 8, and 24.
The product is 1*8*24 = 192
The answer is A.
Question: If a:b=1:2 and b:c=3:4 find a:b:c?
A.3:5:8
B.3:6:8
C.3:7:8
D.3:6:4
Answer: B.3:6:8
Explanation: a:b = 1:2, b:c = 3:4
1:2
3:4
(a = 1 × 3 = 3, b = 2 × 3 = 6 and c = 2 × 4 = 8)
(a = a × b, b = b × b and c = b × c)
a:b:c = 3:6:8
B
Question: By selling a watch for Rs.640/-, a man loses 20% what is that watch cost price?
A.Rs. 600/-
B.Rs. 700/-
C.Rs. 800/-
D.Rs. 850/-
Answer: C.Rs. 800/-
Explanation: 80 % ------> 640 (80 * 8 = 640)
100 % ------>800 (100 * 8 = 800)
Cost price = Rs. 800/-
C)
Question: A football coach must choose 3 freshers from a team of 12players. How many different ways can the coach choose the freshers?
A.220
B.650
C.729
D.800
Answer: A.220
Explanation: Choose 3 starters from a team of 12 players. Order is not important.
\inline {\color{Black} 12C_{3}}= 220
A
Question: In the first round of the elections, the only two candidates got exactly the same number of votes. During the second round, 24,000 votes switched from the first candidate to the second one. The total number of votes remained the same in both rounds, and no other votes switched sides. If, in the second round, the winning candidate got four times as many votes as the other candidate, how many people have voted in each round?
A.15,000
B.25,000
C.80,000
D.50,000
Answer: C.80,000
Explanation: Let A be the first candidate and B be the second one.
Given x+24000 = 4(x-24000) => x = 40000
2x = 80000
IMO option C.
Question: Find the probability that a number selected from numbers 1, 2, 3,..., 40 is a prime number, when each of the given numbers is equally likely to be selected?
A.10/40
B.12/40
C.8/40
D.3/40
Answer: B.12/40
Explanation: Let X be the event of selecting a prime number.
X = {2, 3, 5, 7, 11, 13, 17, 19,23,29,31,37}
n(X) = 12,
n(S) = 40
Hence, the required probability is 12/40.
ANSWER:B
Question: If logX = (logY)/2 = (logZ)/5, then X4.Y3.Z-2 =?
A.2
B.10
C.1
D.0
Answer: C.1
Explanation: (log X)/1 = (logY)/2 = (logZ)/5 = K
=> logX = K, log Y = 2k, log Z = 5K
Thus, log(X4.Y3.Z-2) = 4logX +3logY - 2logZ = 0.
=> X4.Y3.Z-2 = 1.
ANSWER:C
Question: In how many ways can the letters of word TREATMENT be arranged such that all the vowels as well as all the Consonants always appear together?
A.9!
B.3!*6!*2!
C.5!*5!
D.5!*4!*2!
Answer: B.3!*6!*2!
Explanation: Since all the vowels and consonants have to be together there can only be there are 3! way to order the vowels and 6! to order the consonants. But they must be together either vowels come first or consonants so you multiply by 2.
So 3!6!2! (B)
Question: The number of arrangements that can be made with the letters of the word MEADOWS so that the vowels occupy the even places?
A.156
B.144
C.165
D.182
Answer: B.144
Explanation: The word MEADOWS has 7 letters of which 3 are vowels.
-V-V-V-
As the vowels have to occupy even places, they can be arranged in the 3 even places in 3! i.e., 6 ways. While the consonants can be arranged among themselves in the remaining 4 places in 4! i.e., 24 ways.
Hence the total ways are 24 * 6 = 144.
Answer: B
Question: In a class of 40 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 10 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed?
A.3
B.5
C.8
D.13
Answer: A.3
Explanation: Total # of students = 40
Avg # of books per student = 2
Total # of books = 40*2 = 80
# of student borrowed at least 3 books = 40-2-12-10 = 16
# of books borrowed by above 16 students = 80-(12*1)-(10*2) = 48
Considering that 15 out of above 16 students borrowed only 3 books, # of books borrowed = 15*3 = 45
So maximum # of books borrowed by any single student = 48-45 = 3
option A
Question: The some of present ages of father and son is 60.If 6 years ago fathers age was five times the sons age,then what will be sons age after six years??
A.15
B.18
C.20
D.22
Answer: C.20
Explanation: Let f nd s be the present ages of father nd son
f + s = 60
f = 60 - s
(f-6) = 5(s-6)
f-6 = 5s - 30
f = 5s - 24
Equate "f"
60 - s = 5s - 24
6s = 84
s = 14
f = 60 - 14
f = 46
Present age of son is 14
Age of son after 6 years = 14+6 = 20
ANSWER:C
Question: A number when divided by a divisor leaves a remainder of 30. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?
A.12
B.13
C.35
D.43
Answer: D.43
Explanation: Let the number is N, the divisor = D,
I will make the two equations-
N = xD+30
2N = yD+11
where x and y are integers
Solving them: D(y-2x) = 43
as D is also integer and 43 is a prime number, the D should be 43 to satisfy the above equation.
Hence answer is 'D'
Question: Two employees X and Y are paid a total of Rs. 600 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
A.s.200.72
B.s.250.72
C.s.272.72
D.s.300.72
Answer: C.s.272.72
Explanation: Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 600
But x = 120% of y = 120y/100 = 12y/10
∴12y/10 + y = 600
⇒ y[12/10 + 1] = 600
⇒ 22y/10 = 600
⇒ 22y = 6000
⇒ y = 6000/22 = Rs.272.72
C
Question: A train covers a distance of 18 km in 3 min. If it takes 4 sec to pass a telegraph post, then the length of the train is?
A.370
B.380
C.390
D.400
Answer: D.400
Explanation: Speed = (18/3 * 60) km/hr = (360 * 5/18) m/sec = 100 m/sec.
Length of the train = 100 * 4 = 400 m.
Answer: Option D
Question: The average runs scored by a batsman in 15 matches is 30. In the next 20 matches the batsman scored an average of 15 runs. Find his average in all the 30 matches?
A.31.56
B.25.65
C.21.43
D.28.36
Answer: C.21.43
Explanation: Total score of the batsman in 15 matches = 450.Total score of the batsman in the next 20 matches = 300.Total score of the batsman in the 35 matches = 750.Average score of the batsman = 750/35 = 21.43.Answer: C
Question: 16 boys or 24 girls can construct the wall in 6 days. the number of days that 8 boys and 6 girls Will take to construct?
A.7 days
B.14 days
C.6 days
D.8 days
Answer: D.8 days
Explanation: Explanation:
16 boys =24 girls, 1 boy = 24/16 girls
1 boy = 6/4 girls
8 boys +6 girls = 8 Ã— 6/4 + 12 = 12 + 6 = 18 girls
8 days to complete the work
Answer: Option D
Question: In how many ways can a leap year have 53 Sundays?
A.365C7
B.7
C.4
D.5
Answer: D.5
Explanation: Explanation :
In a leap year there are 366 days i.e. 52 weeks + 2 extra days.
So, to have 53 Sundays one of these two days must be a Sunday.
This can occur in only 2 ways.
i.e. (Saturday and Sunday) or (Sunday and Monday).
Thus, the required number of ways is 2.
Answer : D
Question: If the tens digit of positive integers h, y are 6, how many values of the tens digit of 2(h+y) can be there?
A.2
B.3
C.4
D.5
Answer: C.4
Explanation: If the tens digit of positive integers h, y are 6, how many values of the tens digit of 2(h+y) can be there?
A. 2
B. 3
C. 4
D. 5
E. 6
-> If h=y=60, 2(h+y)=240 is derived. If h=y=69, 2(h+y)=276 is derived, which makes 4,5,6,7 possible for the tens digit. Therefore, the answer is C.
Question: By investing Rs. 1620 in 8% stock, Michael earns Rs. 135. The stock is then quoted at:
A.96
B.70
C.75
D.80
Answer: A.96
Explanation: To earn Rs. 135, investment = Rs. 1620.
To earn rs 8 investment = (1620/135*8) = 96
Market value of rs 100 stock = rs 96
ANSWER A
Question: Machine A can make 350 widgets in 1 hour, and machine B can make 250 widgets in 1 hour. If both machines work together, how much time will it take them to make a total of 1500 widgets?
A.2 hour and 20 minutes
B.2 hour and 24 minutes
C.2 hour and 30 minutes
D.2 hour and 36 minutes
Answer: C.2 hour and 30 minutes
Explanation: (350+250)t=1500
600t=1500
t=5/2
t=2 hour and 30 minutes
Answer: C
Question: Pipe A can fill a tank in 4 hours, pipe B in 8 hours and pipe C in 8 hours. If all the pipes are open, in how many hours will the tank be filled?
A.2
B.3
C.4
D.5
Answer: A.2
Explanation: Answer:	Part filled by A + B + C in 1 hour = 1/4 + 1/8 + 1/8= 1/2
All the three pipes together will fill the tank in 2 hours.
Answer: A
Question: A part of certain sum of money is invested at 9% per annum and the rest at 12% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is?
A.7:3
B.4:9
C.4:3
D.2:3
Answer: C.4:3
Explanation: 12:9
= 4:3
Answer:C
Question: A man pointing to a photo says "The lady in the photograph is my nephew’s maternal grandmother". How is the lady in the photograph related to the man’s sister who has no other sister ?
A.Cousin
B.Sister-in-law
C.Mother
D.Mother-in-law
Answer: C.Mother
Explanation: Since the man is referring to his nephew, the nephew’s parent has to be a sibling to the man. Now the last part says that the man’s sister has no other sister and hence the brother-sister relationship is established between the man and his nephew’s mother. Now the lady in the picture is the grandmother of the nephew and hence she is the mother of the man’s sister.
ANSWER:C
Question: Which of the following is a multiple of 4!+6?
A.2!+3
B.4!+12
C.5!+6
D.5!+30
Answer: D.5!+30
Explanation: considering prime factors:
4! + 6 = 4 * 3 * 2 + 6 = 6(4 + 1) = 6 * 5 = 2 * 3 * 5
So the correct answer is the one which is a multiple of 2, of 3 and of 5.
ANSWER:D
Question: Aden and Brad can do a piece of work in 18 days. Brad can Cody can do it in 24 days and Cody and Aden can do it in 36 days. If Aden, Brad, Cody work together, in how many days will they finish the work?
A.10 days
B.12 days
C.14 days
D.16 days
Answer: D.16 days
Explanation: (Aden + Brad)’s 1 day’s work = 1/18
(Brad + Cody)’s 1 day’s work = 1/24
(Cody + Aden)’s 1 day’s work = 1/36
Therefore, 2 (Aden + Brad + Cody)’s 1 day’s work = 1/18 + 1/24 + 1/36
= (4 + 3 + 2)/72
= 9/72
= 1/8
(Aden + Brad + Cody)’s 1 day’s work = 1/2 × 8 = 1/16
Therefore, Aden, Brad, Cody together will complete this work in 16 days. ANSWER : D
Question: A man swims downstream 30 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water?
A.9
B.8
C.6
D.4
Answer: B.8
Explanation: 30 --- 3 DS = 10
? ---- 1
18 ---- 3 US = 6
? ---- 1 M = ?
M = (10 + 6)/2 = 8
Answer:B
Question: The average age of 37 students in a group is 14 years. When teacher's age is included to it, the average increases by one. What is the teacher's age in years ?
A.35 years
B.45 years
C.51 years
D.52 years
Answer: D.52 years
Explanation: Explanation:
Age of the teacher = (38 * 15 - 37 * 14) years = 52 years. Answer: D
Question: The length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec is?
A.257 m
B.632 m
C.245 m
D.737 m
Answer: C.245 m
Explanation: Speed = 45 * 5/18 = 25/2 m/sec.
Time = 30 sec
Let the length of bridge be x meters.
Then, (130 + x)/30 = 25/2
x = 245 m.
Answer:C
Question: A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 5000. He sold both the items together for Rs. 25000. What percentage of profit did he make?
A.1.00%
B.15.21%
C.41.10%
D.19.04%
Answer: D.19.04%
Explanation: The total CP = Rs. 16000 + Rs. 5000
= Rs. 21000 and SP = Rs. 25000
Profit(%) = (25000 - 21000)/21000* 100
= 19.04%
Answer: D
Question: If 'a' and 'b' are non-zero numbers such that their sum is five times the product, what is the value of 1/a + 1/b?
A.4
B.5
C.6
D.10
Answer: B.5
Explanation: a+b = 5ab
1/a + 1/b = (b + a)/(ab) = 5.
The answer is B.
Question: The G.C.D of 1.08, 0.36 and 0.9 is
A.0.13
B.0.17
C.0.18
D.0.12
Answer: C.0.18
Explanation: Given numbers are 1.08, 0.36 and 0.90.
H.C.F of 108, 36 and 90 is 18.
H.C.F of a given numbers = 0.18
Answer:C
Question: A shipment of 250 smartphones contains 76 that are defective. If a customer buys two smartphones at random from the shipment, what is the approximate probability that both phones are defective?
A.1/250
B.1/84
C.1/11
D.1/9
Answer: C.1/11
Explanation: Probability of chosing one defective phone from a lot of 250 which ontains 76 defective phones is = (76/250)
Probability of chosing one defective phone from a lot of 249(we already picked one) which ontains 75(we already picked one) defective phones is = (75/249)
Combined probability of series of events = product of the probabilities = (76/250)*(75/249)
76/250 is close to (7/23) and (75/249)= (25/83)
so answer is (7/23)*(25/83) = (1/11)
So, answer will be C
Question: The sum of four consecutive even numbers is 140. What would be the smallest number?
A.32
B.88
C.70
D.123
Answer: A.32
Explanation: Let the four consecutive even numbers be 2(x - 2), 2(x - 1), 2x, 2(x + 1)
Their sum = 8x - 4 =140 => x = 18
Smallest number is: 2(x - 2) = 32
Answer: A
Question: Carol budgeted 18 dollars for gifts for each of the 15 people on her Christmas list. After a disagreement with some of her neighbors, she reduces her Christmas list to 10 people. How much can she spend on each?
A.20
B.27
C.18
D.23
Answer: B.27
Explanation: A1*P1=A2*P2
18*15=A2*10 => A2=27
Answer:B
Question: In how many ways 2 boys and 2 girls can be seated in a row so that boys and girls are alternate?
A.7
B.8
C.9
D.10
Answer: B.8
Explanation: number of ways = 2*2!*2! = 8
Answer is B
Question: A goods train runs at the speed of 72 km/hr and crosses a 260 m long platform in 26 sec. What is the length of the goods train?
A.278
B.166
C.151
D.260
Answer: D.260
Explanation: Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 260)/26 = 20
x = 260 m.
Answer:D
Question: The length of a room is 5.5 m and width is 3.75 m. Find the cost of paying the floor by slabs at the rate of Rs. 1200 per sq.metre.
A.Rs. 15,000
B.Rs. 24,750
C.Rs. 15,600
D.Rs. 16,500
Answer: B.Rs. 24,750
Explanation: Solution
Area of the floor	= (5.5 x 3.75)m²
= 20.635m ²
Cost of paying	= Rs. (1200 x 20.625)
= Rs.24,750.
Answer B
Question: When two different numbers are divided by a certain divisor the remainders are 147 and 192. When the sum of the two numbers is divided by the same divisor the remainder is 38: Find the divisor.
A.300
B.301
C.302
D.303
Answer: B.301
Explanation: Let divisior be x.so 1st no.=a+147
2nd no=b+192.
After adding:(a+147+b+192)/x=>a+b+339/x
Remainder of above expression is 38(given).so rem[a+b+(301+38)]/x=>38 therefore x would be 301.
ANSWER:B
Question: An gun can take a maximum of four shots at an enemy plane moving away from it. The probability of hitting the plane at the 1st, 2nd, third and 4th shots are 1.4, 1.3, 1.2 & 1.1 respectively.
What is the probability that the plane is hit when all the four shots are fired?
A.0.6976
B.0.783
C.0.986
D.1.243
Answer: A.0.6976
Explanation: Required probability:
=(0.4×0.7×0.8×0.9)+(0.6×0.3×0.8×0.9)+(0.6×0.7×0.2×0.9)+(0.6×0.7×0.8×0.1)+(0.4×0.3×0.8×0.9)+(0.4×0.7×0.2×0.9)+(0.4×0.7×0.8×0.1)+(0.6×0.3×0.2×0.9)+(0.6×0.3×0.8×0.1)+(0.6×0.7×0.2×0.1)+(0.4×0.3×0.2×0.9)+(0.6×0.3×0.2×0.1)+(0.4×0.3×0.8×0.1)+(0.4×0.7×0.2×0.1)+(0.4×0.3×0.2×0.1)=(0.4×0.7×0.8×0.9)+(0.6×0.3×0.8×0.9)+(0.6×0.7×0.2×0.9)+(0.6×0.7×0.8×0.1)+(0.4×0.3×0.8×0.9)+(0.4×0.7×0.2×0.9)+(0.4×0.7×0.8×0.1)+(0.6×0.3×0.2×0.9)+(0.6×0.3×0.8×0.1)+(0.6×0.7×0.2×0.1)+(0.4×0.3×0.2×0.9)+(0.6×0.3×0.2×0.1)+(0.4×0.3×0.8×0.1)+(0.4×0.7×0.2×0.1)+(0.4×0.3×0.2×0.1)
=0.2016+0.1296+0.756+0.336+0.864+0.504+0.224+0.324+0.144+0.0084+0.0216+0.0036+0.0096+0.0056+0.002=0.2016+0.1296+0.756+0.336+0.864+0.504+0.224+0.324+0.144+0.0084+0.0216+0.0036+0.0096+0.0056+0.002
=0.6976=0.6976
Edit: Thank you Vaibhav for providing an alternative method.
Alternate Method:
probability that the plane is hit when all the four shots are fired,
P=1−probability of not hitting the targetP=1−probability of not hitting the target
=1−(0.6×0.7×0.8×0.9)=1−(0.6×0.7×0.8×0.9)
=1−0.3024=1−0.3024
=0.6976
A
Question: A carpenter worked alone for 1 day on a job that would take him 4 more days to finish. He and another carpenter completed the job in 2 more days. How many days would it have taken the second carpenter to do the complete job working alone?
A.5
B.7
C.9
D.14
Answer: A.5
Explanation: A carpenter worked only 1 day on something that takes him 4 MORE days.
Means;
Carpenter finishes his work in 5 days.
Let his buddy finish the same task in x days.
Respective rates per day:
1/5 AND 1/x
To complete 1 work:
First guy worked for 3 days @ rate=1/5 per day.
Second one worked for 2 days @ rate=1/x per day
Expression:
Days*Rate=Work
3*1/5+2*1/x=1
3x+10=5x
2x=10
x=5 days.
Ans:A
Question: Two trains 121 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?
A.7.16
B.7.19
C.7.13
D.7.15
Answer: D.7.15
Explanation: T = (121 + 165)/ (80 + 65) * 18/5
T = 7.15
Answer:D
Question: Among 400 students, 56% study sociology, 44% study mathematics and 40% study biology. If 42% of students study both mathematics and sociology, what is the largest possible number of students who study biology but do not study either mathematics or sociology?
A.30
B.90
C.120
D.168
Answer: D.168
Explanation: I would just like to add a bit of explanation after the step where you calculate that the number of students studying both M and S = 168
Using your analysis:
We see that the total number of students who study either Maths or Sociology = 176 + 224 - 168 = 232
So, in the image we know that the number of students in the zone with the black boundary = 232
Let's assume the number of students who studyonlybiology to beb(this is the number that we have to maximize)
And, let's assume the number of students who study none of the three subjects, that is the number of students in the white space =w
Since the total number of students = 400, we can write:
232 +b+w= 400
Or,b+w= 400 - 232 = 168
That is,b= 168 -w
So, the maximum value ofbwill happen forw= 0
This is how we get, the maximum value ofb= 168
D
Question: If points A and B are (6-1) units apart, which of the following can have only one possible value?
I. The area of a square region with side AB
II. The circumference of a circle passing through points A and B
III. The area of a rectangular region with diagonal AB
A.I only
B.II only
C.III only
D.I and II only
Answer: A.I only
Explanation: I. The area of a square region with side AB --> side=AB=(6-1) or 5 --> the area of a square is 5^2=25, so only one possible value;
II. The circumference of a circle passing through points A and B --> circle is not defined by only two points, hence the circumference of a circle passing through points A and B can take infinitely many values. For example consider when AB=diameter and when points A and B are not the endpoints of the diameter;
III. The area of a rectangular region with diagonal AB --> consider the case when AB is the diagonal of a square (the area is 25/2) and the case when AB is the diagonal of a rectangle with the sides equal to 3 and 4 (the area 12).
Answer: A.
Question: Three seventh of a number is 12 more than 40% of that number. What will be the 50% of that number?
A.A)148
B.B)210
C.C)105
D.D)248
Answer: C.C)105
Explanation: 3/7 x – 40/100 x = 12
x = 35 * 12
35 * 12 * 50/100 = 210/2 = 105
ANSWER:C
Question: Tough and Tricky questions: Absolute Values.
If |a| = 1/4 and |b| = 1/2, which of the following CANNOT be the result of a + b?
A.-1
B.-1/4
C.3/4
D.-3/4
Answer: A.-1
Explanation: |a| = 1/4
Absolute value of 'a' can have two values = 1/4 and -(1/4)
|b| = 1/2
Absolute value of 'b' can have two values = 1/2 and -(1/2)
Now different combinations of a + b are as follows:
a + b = (1/4) + (1/2) = 3/4
- a - b = -(1/4) - (1/2) = -3/4
a - b = (1/4) - (1/2) = -(1/4)
-a + b = -(1/4) + (1/2) = 1/4
Cross verifying with the given options, left over option is A.
Question: A train passes a platform in 34 seconds. The same train passes a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, The length of the platform is
A.280 meter
B.240 meter
C.210 meter
D.200 meter
Answer: C.210 meter
Explanation: Explanation:
Speed of the train = 54 km/hr = (54×10)/34 m/s = 15 m/s
Length of the train = speed × time taken to cross the man = 15×20 = 300 m
Let the length of the platform = L
Time taken to cross the platform = (300+L)/15
=> (300+L)/15 = 34
=> 300+L = 15×34 = 510
=> L = 510-300 = 210 meter
Answer: Option C
Question: Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 6970, then what will be the share of Sameer in the profit?
A.Rs.2389
B.Rs.2380
C.Rs.2317
D.Rs.2329
Answer: B.Rs.2380
Explanation: Kamal : Sameer = (9000 * 12) : (8000 * 7)
= 108:56 = 27:14
Sameer's share = 6970 * 14/41 = Rs.2380.
Answer: B