RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A desalination process is able to remove 2/3 of salt in each cycle. If we have 1 liter of sea water that has 5% salt (i.e. 5 g in a liter), how much salt would have been removed from the liter of water after 3 cycles of the desalination process?
A.4.15
B.4.21
C.4.52
D.4.81
Answer: D.4.81
Explanation: X is the initial quantity of salt in the water.
After a cycle of desalination the quantity of salt left would be X1=X-2/3X i.e. X1=1/3X
Same thing for X2, X3 respectively representing the quantity of salt left after 2, 3 cycles of desalination.
So we have:
X1=1/3 X
X2=1/3 X1
X3=1/3 X2
By multiplying both ends of the equations we get:
X1*X2*X3 = (1/3)^3 X*X1*X2
Simplification leaves us with:
X3 = (1/3)^3 X
X3 is the quantity of salt left after three cycles. So the cumulative quantity of salt (Q3) which has been removed after 3 cycles is: Q3= X-X3=X-(1/3)^3 X i.e. Q3 = X (1-(1/3)^3)
In this case, given X was: X=5 g
So we have Q3=5 * (1-1/27) = 5 * 26/27 = 4.814 g rounded Q3=4.81
Answer: D
Question: The expression pq+p is odd when the p and q are integers. Which of the following expressions must be even?
A.p
B.q
C.p + q
D.pq - p
Answer: B.q
Explanation: pq+p is odd
p and q are integers
If p were even pq+p would be even despite any value of q.
q can't be odd, so q must be even.
Ans : B
Question: What will be the ratio of simple interest earned by certain amount at the same rate of interest for 12 years and that for 28 years?
A.5 : 7
B.4 : 7
C.3 : 7
D.Data inadequate
Answer: C.3 : 7
Explanation: Let the principal be P and rate of interest be R%.
∴ Required Ratio = [(P×R×12/100) /(P×R×28/100)]=12PR/28PR=12/28=3:7
Answer C
Question: Two trains are moving in opposite directions with speed of 110 km/hr and 90 km/hr respectively. Their lengths are 1.10 km and 0.9 km respectively. the slower train cross the faster train in --- seconds
A.26
B.48
C.47
D.36
Answer: D.36
Explanation: Explanation:
Relative speed = 110+90 = 200 km/hr (Since both trains are moving in opposite directions)
Total distance = 1.1+.9 = 2km
Time = 2/200 hr = 1/100 hr = 3600/100 = 36 seconds
Answer: Option D
Question: There are 15 points in a given plane, no three of which are on the same line. If one of the points is represented as 'P, then how many triangles can be determined with the 15 points that contain the point P?
A.91
B.105
C.182
D.210
Answer: C.182
Explanation: Fist point is P which is fixed so can be selected in 1 way
Second point can be selected in 14 ways
Third point can be selected in 13 ways
so total ways = 1x14x13 = 182
but answer is 91 which is 182/2=C
Question: A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 42 years now, the son's age 5 years back was?
A.12yr
B.15yr
C.14yr
D.16yr
Answer: D.16yr
Explanation: Let the son's present age be x years
Then, 42-x = x
x = 21
Son's age 5 years back = 21-5 = 16years
Answer is D
Question: How many odd prime numbers are there less than 50?
A.15
B.1
C.2
D.14
Answer: D.14
Explanation: Odd prime number less than 50 :3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
There is 14 the odd prime number
Answer is D
Question: The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 5 years hence?
A.100
B.80
C.70
D.20
Answer: C.70
Explanation: A + B = 60, A = 2B
2B + B = 60 => B = 20 then A = 40.
5 years, their ages will be 45 and 25.
Sum of their ages = 45 + 25 = 70.
answer is C.
Question: A person crosses a 600m long street in 4 minnutes. What is his speed in km per hour?
A.5.8km/hr
B.7.2km/hr
C.9km/hr
D.2.5km/hr
Answer: C.9km/hr
Explanation: Speed = 600/4*60 = 2.5m/sec
=2.5*18/5
=9km/hr
Answer is C
Question: A man rows his boat 90 km downstream and 5` km upstream, taking 3 hours each time. Find the speed of the stream?
A.7 kmph
B.5 kmph
C.2 kmph
D.8 kmph
Answer: A.7 kmph
Explanation: Speed downstream = d/t = 90/(3) = 30 kmph
Speed upstream = d/t = 51/(3) = 17 kmph
The speed of the stream = (30 - 17)/2 = 7 kmph
Answer:A
Question: Two persons start running simultaneously around a circular track of length 200 m from the same point at speeds of 15 km/hr and 25 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?
A.11
B.10
C.18
D.27
Answer: C.18
Explanation: Time taken to meet for the first time anywhere on the track
= length of the track / relative speed
= 200 / (15 + 25)5/18 = 200* 18 / 40 * 5 = 18 seconds.
Answer: C
Question: If you drew a dot on the edge of a wheel and traced the path of the dot as the wheel rolled one complete revolution along a line, then the path formed would be called a cycloid, combining both forward and circular motion. What is the length of the path formed by one complete revolution? Assume the wheel has a radius of r.
A.5r
B.7r
C.4r
D.8r
Answer: D.8r
Explanation: Imagine the circle resting on coordinate (0,0) and moving east.
Also magine the point on the circle to start at (0,0).
Let t be the angle between the point on the circle and the center of the circle.
The position of the point on the circle, relative to t, is:
x = rt - r×sin(t)
y = r - r×cos(t)
Taking the derivatives:
dx/dt = r - r×cos(t)
dy/dt = r×sin(t)
The change in arc length can be defined as ( (dx/dt)2 + (dy/dt)2 ) 1/2.
So the total arc length is the integral from 0 to 2pi of ( (dx/dt)2 + (dy/dt)2 ) 1/2.
After a few steps this integral becomes:
r×21/2 × (1-cos(t))1/2.
Using the hint:
r×21/2 × 21/2 × integral of sin(t/2) dt from 0 to 2×pi
= 2×r × (-2×cos(t/w) from 2×pi to 0)
= 8r
Hint: (1-cos(t))0.5 = 20.5×sin(t/2)
Question: Diane find 6 and a half cans of paint are just enough to paint one third of her room. How many more cans of paint will she need to finish her room and paint a second room of the same size?
A.5
B.7 and a half
C.10
D.32 and a half
Answer: D.32 and a half
Explanation: She will need 13 cans to paint the rest of this room and 19 1/2 for the next room for a total of 32 1/2 cans.
D
Question: A bullock cart has to cover a distance of 80km in 10hrs. If it covers half of the journey in 3/5th time. what should be its speed to cover the remaining distance in the time left.
A.8 km/h
B.10 km/h
C.12 km/h
D.14 km/h
Answer: B.10 km/h
Explanation: Time left = 10 - 3/5*10
= 4 hr 10 km/h
speed =40 km /4 hr
=10 kmph
Answer : B.
Question: 8, 12, 18, 27, 40.5, (...)
A.60.75
B.62
C.58
D.60.5
Answer: A.60.75
Explanation: Explanation :
8
(8×3)÷ 2 = 12
(12×3)÷ 2 = 18
(18×3)÷ 2 = 27
(27×3)÷ 2 = 40.5
(40.5×3)÷ 2 = 60.75
Answer : Option A
Question: Ada and Paul received their scores on three tests. On the first test, Ada's score was 10 points higher than Paul's score. On the second test, Ada's score was 4 points higher than Paul's score. If Paul's average (arithmetic mean) score on the three tests was 5 points higher than Ada's average score on the three tests, then Paul's score on the third test was how many points higher than Ada's score?
A.9
B.14
C.17
D.29
Answer: D.29
Explanation: My take is Option D (23)
I followed a simple approach (explained below):
Test 1: Ada's score = Paul's score + 10
Test 2: Ada's score = Paul's score + 4
Avg. of Paul's score = 5 points higher than Avg. of Ada's score
This implies that : Sum of Paul's score [3 Tests] = 15 points higher than Sum of Ada's score [3 Tests] (9 points higher since 3 points were given in terms of average of 3 scores)
So, Paul needs to score 29 points higher than Ada in Test 3, since Paul needs to compensate for the lower score in test 1 and Test 2 ( 29 = 10 + 4 + 15)
D
Question: If n is a positive integer and the product of all integers from 1 to n, inclusive, is a multiple of 420, what is the least possible value of n?
A.5
B.7
C.9
D.11
Answer: B.7
Explanation: 420 = 2*2*3*5*7, so n must be at least 7.
The answer is B.
Question: The 7th grade French and Spanish classes each have 23 students in them, and there are seven students in the 7th grade taking both languages. If everyone in the 7th grade is in at least one of the two language classes, how many students are taking just one of the two classes?
A.26
B.28
C.30
D.32
Answer: D.32
Explanation: French class + Spanish class = 46 students.
Seven students are in both classes so they were counted twice.
The number of students taking just one class is 46 - 2(7) = 32.
The answer is D.
Question: A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio Q of revenue from car sales in 1996 to revenue from truck sales in 1996?
A. 1:2
B. 4:5
C. 1:1
D. 3:2
Answer: A. 1:2
Explanation: A.. I have probably solved this question 3-4 times by now.. Remember the answer.. 1:2
Question: If p and q are prime numbers, how many divisors does the product p^3 * q^7 have?
A.25
B.30
C.32
D.35
Answer: C.32
Explanation: when a number N=a^x*b^y, where a and b are prime numbers, and x, y are positive integers, the number of divisors of N=(x+1)(y+1)
Therefore, the answer is C. 4*8=32
Question: The second day of a month is Friday, What will be the last day of the next month which has 31 days?
A.Friday
B.Saturday
C.Wednesday
D.Data inadequate
Answer: D.Data inadequate
Explanation: Explanation:
We cannot find out the answer because the number of days of the current month is not given.
Answer: Option D
Question: John and Peter are among the nine players a basketball coach can choose from to field a five-player team. If all five players are chosen at random, what is the probability of choosing a team that includes John and Peter?
A.1/9
B.1/6
C.2/9
D.5/18
Answer: D.5/18
Explanation: Total possible ways of selecting a 5-member team:
a combination problem, not permutation since order does not matter:
9x8x7x6x5/(5x4x3x2x1) = 126.
The ways of selecting a 5-member team including John and Peter:
It is again a combination, not permutation. Since John and Peter are already included, you don't bother about them any more. The possible ways will be the combination of the rest of the 3 players from the rest of 7 player:
7x6x5/(3x2x1) = 35.
so the probability = 35/126 = 5/18.
Answer is D: 5/18.
Question: A car started running at a speed of 34 km/hr and the speed of the car was increased by 2 km/hr at the end of every hour. Find the total distance covered by the car in the first 10 hours of the journey.
A.43 km
B.76 km
C.25 km
D.15 km
Answer: A.43 km
Explanation: A
43 km
The total distance covered by the car in the first 10 hours = 34 + 36 + 38 + 40 + 42 + 44 + 46 + 48 + 50 + 52= sum of 10 terms in AP whose first term is 34 and last term is 52 = 10/2 [34 + 52] = 430 km.
Question: Two trains A and B starting from two points and travelling in opposite directions, reach their destinations 9 hours and 4 hours respectively after meeting each other. If the train A travels at 70kmph, find the rate at which the train B runs.
A.40
B.60
C.120
D.105
Answer: D.105
Explanation: If two objects A and B start simultaneously from opposite points and, after meeting, reach their destinations in ‘a’ and ‘b’ hours respectively (i.e. A takes ‘a hrs’ to travel from the meeting point to his destination and B takes ‘b hrs’ to travel from the meeting point to his destination), then the ratio of their speeds is given by:
Sa/Sb = √(b/a)
i.e. Ratio of speeds is given by the square root of the inverse ratio of time taken.
Sa/Sb = √(4/9) = 2/3
This gives us that the ratio of the speed of A : speed of B as 2:3.
Since speed of A is 70 kmph, speed of B must be 70*(3/2) = 105 kmph
Answer D
Question: A monkey ascends a greased pole 6 meters high. He ascends 2 meters in the first minute and then slips down 1 meter in the alternate minute. If this pattern continues until he climbs the pole , in how many minutes would he reach at the top of the pole ?
A.9th minute
B.21st minute
C.11th minute
D.22nd minute
Answer: A.9th minute
Explanation: The money is climbing 1meter in 2min. This pattern will go on till he reaches 4 meters. I mean this will continue for first 4*2=8 mins. he would have reached 4meters. After that he will climb 2meters and he will reach the pole. So total time taken = 8 + 1 = 9mins.
So, asnwer will be A
Question: A basket contains 5 apples, of which 1 is spoiled and the rest are good. If Henry is to select 2 apples from the basket simultaneously and at random, what is the probability T that the 2 apples selected will include the spoiled one?
A.a. 1/5
B.b. 3/10
C.c. 2/5
D.d. 1/2
Answer: C.c. 2/5
Explanation: there can be two ways in which one can select a spoiled apple and a good apple.
1. you pick the spoiled one first and the good one later..
Prob of picking bad one = 1/5 (one bad apple)
Prob of picking a good one from the remaining 4 good apples (4/4 =1)
therefore the total prob for case 1 = i/5 * 1 = 1/5
Total prob T= porb1 + prob2 = 1/5+1/5 = 2/5.C
Question: A Prototype fuel-efficient car (P-Car) is estimated to get 87% more miles per gallon of gasoline
than does a traditional fuel-efficient car (T-Car). However, the P-Car requires a special type
of gasoline that costs 27% more per gallon than does the gasoline used by a T-Car. If the two
cars are driven the same distance, what percent less than the money spent on gasoline for the
T-Car is the money spent on gasoline for the P-Car?
A.16 2/3%
B.32 %
C.50%
D.60%
Answer: B.32 %
Explanation: Assumption
Miles/Gallon
T = 100
P = 187 ( 87% more)
$/gallon
T = 100
P = 127 (27% more)
Miles
100 for both
Cost = (Miles X $/ Gallon)/ M/gallon
T = 100
P = 67.9
Hence 100 - 67.9 = 32%
Ans B
Question: Raja's Bank's saving amount is decreased 40% due to loan payment and current balance is Rs.30000. Find the actual balance before deduction?
A.8000
B.8500
C.50000
D.9500
Answer: C.50000
Explanation: 40% decreased
60% Balance = 30000
100% = 30000/60*100 = 50000
Answer : C
Question: If each side of a square is increased by 325% in length, find the percentage change in its area?
A.54%
B.957%
C.956.25%
D.958.25%
Answer: C.956.25%
Explanation: let each side of the square be a , then area = a x a
New side = 325a / 100 = 13a / 4
New area =(13a x 13a) / (4 x 4) = (25a²/16)
increased area== (169a²/16) - a²
Increase %= [(153a²/16 ) x (1/a² ) x 100]% = 956.25%
answer :C
Question: The present population of a town is 220. Population increase rate is 10% p.a. Find the population of town after 1 years?
A.100
B.120
C.200
D.242
Answer: D.242
Explanation: P = 220
R = 10%
Required population of town = P*(1 + R/100)^T
= 220*(1 + 10/100)
= 220*(11/10)
= 242
Answer is D
Question: The average age of a group of 10 friends is 15 yr. If one friend leaves the group, the average becomes 16 yr. Find the age of the friend who left the group.
A.5 yr
B.4 yr
C.6 yr
D.None of these
Answer: C.6 yr
Explanation: Answer
Age of friend left = Previous average of the age - Number of persons present x Increase in average age
= 15 - ( 10-1 ) x ( 16-15 )
= 15- 9 x 1
= 15 - 9 = 6yr
Correct Option: C
Question: The prices of tea and coffee per kg were the same in june. In july the price of coffee shot up by 10% and that of tea dropped by 20%. if in july , a mixture containing equal quantities of tea and coffee costs 50/kg. how much did a kg of coffee cost in june ?
A.50
B.45
C.52.63
D.40
Answer: C.52.63
Explanation: Let the price of tea and coffee be x per kg in June.
Price of tea in July = 1.1x
Price of coffee in July = 0.8x .
In July the price of 1/2 kg (500gm) of tea and 1/2 kg (500gm) of coffee (equal quantities) = 50
1.1x(1/2) + 0.8x(1/2) = 50
=> x =52.63
C
Question: How many four-digit numbers that do not contain the digits 2, 3, or 6 are there?
A.2058
B.3584
C.4096
D.5040
Answer: A.2058
Explanation: The 1st digit can be filled up by the numbers: {1,4,5,7,8,9} = 6 ways
The 2nd digit can be filled up by the numbers: {0,1,4,5,7,8,9} = 7 ways
The 3rd digit can be filled up by the numbers: {0,1,4,5,7,8,9} = 7 ways
The 4th digit can be filled up by the numbers: {0,1,4,5,7,8,9} = 7 ways
The total number of such four-digit numbers is 6*7*7*7 = 2058
The answer is A.
Question: All of the citizens of a country have a seven-character or eight-character national identification code that is created using the 26 letters of the alphabet and the 10 digits from 0 to 9. What is the maximum number of citizens who can be designated with these codes?
A.36^15
B.35(36^7)
C.35(36^8)
D.37(36^7)
Answer: D.37(36^7)
Explanation: The number of possible 7-digit codes is 36^7.
The number of possible 8-digit codes is 36^8.
The total sum is 36^7 + 36^8 = 36^7(1+36) = 37(36^7)
The answer is D.
Question: A girl swims downstream 112 km and upstream 32 km taking 8 hours each time, what is the speed of the girl in still water?
A.8
B.9
C.10
D.11
Answer: B.9
Explanation: 112 --- 8 DS = 14
? ---- 1
32 ---- 8 US = 4
? ---- 1 M = ?
M = (14 + 4)/2 = 9
Answer:B
Question: A train 125 m long crosses a platform 125 m long in 14 sec; find the speed of the train?
A.87 kmph
B.64 kmph
C.54 kmph
D.16 kmph
Answer: B.64 kmph
Explanation: D = 125 + 125 = 250
T = 14
S = 250/14 * 18/5 = 64 kmph
Answer:B
Question: The largest four-digit number which when divided by 4, 7 or 13 leaves a remainder of 3 in each case,is :
A.8739
B.9831
C.9834
D.9893
Answer: B.9831
Explanation: Solution
Greatest number of 4 digits is 9999. L.C.M. of 4, 7, and 13 = 364.
on dividing 9999 by 364, remainder obtained is 171.
So, greatest number of 4 digits divisible by 4,7, and 13 = (9999 - 171) = 9828.
Hence, required number = (9828 + 3) = 9831.Answer B
Question: At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.50000?
A.6620
B.3277
C.16550
D.2998
Answer: C.16550
Explanation: A = 50000(11/10)3
= 66550
= 50000
----------
16550
Answer:C
Question: A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is:
A.6
B.9
C.8
D.2
Answer: B.9
Explanation: Explanation:
Let the required number of revolutions made by larger wheel be x.
Then, More cogs, Less revolutions (Indirect Proportion)
{\color{Black} \therefore } 14 : 6 :: 21 : x {\color{Black} \Rightarrow } 14 x x = 6 x 21
x={\color{Black} \frac{6\times 21}{14} } {\color{Black} \Rightarrow } x=9
Answer: B) 9
Question: If the average (arithmetic mean) of a and b is 120, and the average of b and c is 150, what is the value of a − c?
A.−60
B.−100
C.100
D.135
Answer: A.−60
Explanation: a+b = 240
b+c = 300
a-c = -60.
IMO option A.
Question: Which one of the following is not a prime number?
A.31
B.61
C.71
D.91
Answer: D.91
Explanation: 91 is divisible by 7. So, it is not a prime number.
Answer: Option D
Question: A person can swim in still water at 10 km/h. If the speed of water 8 km/h, how many hours will the man take to swim back against the current for 16km?
A.3
B.7
C.5
D.8
Answer: D.8
Explanation: M = 10
S = 8
US = 10 - 8 = 2
D = 16
T = 16/2 = 8
Answer: D
Question: A polling company reports that there is a 40% chance that a certain candidate will win the next election. If the candidate wins, there is a 60% chance that she will sign Bill X and no other bills. If she decides not to sign Bill X, she will sign either Bill Y or Bill Z, chosen randomly. What is the chance that the candidate will sign Bill Z?
A.10
B.8
C.6
D.4
Answer: B.8
Explanation: Fairly straight forward...
40% - Candidate Elected
100%-60% = 40% - Candidate does not sigh Bill X
50% - Candidate randomly chooses between two bills.
These are multiplicative:
40% x 40% x 50%
0.4 x 0.4 x 0.5 = 0.08 = 8%
Answer (B)
Question: electric running buzzer rang after every 60 sec.and second buzzer rang after every 62 sec.both rung together at 10'o clock.after that at what time both rang together?
A.morning 10:30
B.morning 10:31
C.morning 10:59
D.morning 11:00
Answer: B.morning 10:31
Explanation: difference of time between together ringing of buzzer=l.c.m of 60 sec. and 62 sec.
(2*30*31) sec.={2*30*31}/60=31 minute
hence,next time they rang together at morning 10:31
answer B
Question: If both 7^2 and 3^3 are factors of the number a*4^3*6^2*13^11, then what is the smallest possible value of a?
A.99
B.147
C.363
D.1200
Answer: B.147
Explanation: The number a must include at least 3*7^2 = 147
The answer is B.
Question: Life expectancy is defined by the formula 2SB/G, where S = shoe size, B = average monthly electric bill in dollars, and G = GMAT score. If Melvin's GMAT score is twice his monthly electric bill, and his life expectancy is 100, what is his shoe size?
A.100
B.55
C.85
D.40
Answer: A.100
Explanation: Solution -
Given that, G = 2B and Life expectancy(L) = 100
L=2SB/G -> 100 = 2SB/2B --> S=100.
ANS A
Question: Of the 300 math majors at a certain university, 30 percent will be assigned to advanced calculus on Monday and Wednesday and the remaining 70 percent will be assigned to advanced calculus on Tuesday and Thursday. However, 40 percent of the math majors prefer Tuesday and Thursday and 60 percent prefer Monday and Wednesday. What is the lowest possible number of math majors who will NOT be assigned to the days they prefer?
A. 15
B. 20
C. 30
D. 45
Answer: C. 30
Explanation: 30% of students are assigned to Monday and Wednesday = 0.3*200 = 60
70% of students are assigned to Tuesday and Thursday = 0.7*200 = 140
60% of students prefer Monday and Wednesday = 0.6*200 = 120
40% of students prefer Tuesday and Thursday = 0.4*200 = 80
Since we need theleastnumber of students who will not be assigned to their preferred days, we shall fit in themaximumpossible students as per their preference:
All of the 40% of students who prefer Tuesday and Thursday can be accommodated to their preferred days, whereas only 60 out of 120 students who prefer Monday and Wednesday can be accommodated to their preferred days.
The remaining 30 students who prefer Monday and Wednesday will be allocated to Tuesday and Thursday by default, which is not their choice.
Answer is C.
Question: Given that 1 + 3x > 4 and 2x - 3 < 5, all values of x must be between which of the following pairs of integers?
A.3 and 8
B.1 and 4
C.3 and 12
D.4/3 and 5/2
Answer: B.1 and 4
Explanation: Given, 1 + 3x > 4 and 2x - 3 < 5
i.e. 3x > 3 and 2x < 8
i.e. x > 1 and x < 4
Answer: Option B
Question: Find the odd man out
1, 2, 6, 24, 120, 620
A.2
B.620
C.120
D.24
Answer: B.620
Explanation: 1.1 =1
1*2 =2
2*3 =6
6*4 =24
24*5=120
120*6=720
ANSWER:B
Question: 5216 x 51 = ?
A.266016
B.212016
C.266436
D.216314
Answer: A.266016
Explanation: Explanation :
Normal way of multiplication may take time. Here are one alternative.
5216 x 51 = (5216 x 50) + 5216 = (5216 x 100/2) + 5216
= 521600/2 + 5216 = 260800 + 5216 = 266016. Answer : Option A
Question: A cycle is bought for Rs.900 and sold for Rs.1120, find the gain percent?
A.11
B.24
C.99
D.77
Answer: B.24
Explanation: 900 ---- 220
100 ---- ? => 24%
Answer: B
Question: A & B are two towns. A person covers the distance from A to B on cycle at 17kmph and returns to A by a boat running at a uniform speed of 8kmph. His average speed for the whole journey is
A.09.88kmph
B.12.88kmph
C.10.88kmph
D.16.45kmph
Answer: C.10.88kmph
Explanation: C
10.88kmph
When same distance is covered with different speeds, then the average speed = 2xy / x+y = 10.88kmph
Question: The sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter?
A.23.9 cm
B.62.9 cm
C.91.5 cm
D.26.8 cm
Answer: C.91.5 cm
Explanation: Perimeter of the sector = length of the arc + 2(radius)
= (135/360 * 2 * 22/7 * 21) + 2(21)
= 49.5 + 42
= 91.5 cm
Answer:C
Question: A right triangle ABC has to be constructed in the xy-plane so that the right angle is at A and AB is parallel to x axis. The coordinates of A, B and C are to satisfy the inequalities -3 ≤ x ≤ 5 and 2 ≤ y ≤11 and x and y are integers. The number of different triangles that can be constructed with these properties are?
A.100
B.6480
C.2320
D.1500
Answer: B.6480
Explanation: We have the rectangle with dimensions 9*10 (9 horizontal dots and 10 vertical). AB is parallel to x-axis and AC is parallel to y-axis.
Choose the (x,y) coordinates for vertex A: 9C1*10C1=90;
Choose the x coordinate for vertex B (as y coordinate is fixed by A): 8C1, (9-1=8 as 1 horizontal dot is already occupied by A);
Choose the y coordinate for vertex C (as x coordinate is fixed by A): 9C1, (10-1=9 as 1 vertical dot is already occupied by A).
9C1*10C1*8C1*9C1=6480.
Answer: B.