RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Express Airlines has a transcontinental flight between Big City and Urbana - a distance of 1,500 km that it completes in three hours. Akatsuki is going from her home in Urbana to a convention in Big City that starts 5 hours after her plane leaves for Big City and ends 6 hours later. Akatsuki's plane suffers a mechanical failure and is forced to land at the Middlebrook airport, located 750 km away from both Big City and Urbana. What's the longest amount of time that Akatsuki can wait for repairs before she misses her convention?
A.10.5 hours
B.6 hours
C.5 hours
D.4.5 hours
Answer: A.10.5 hours
Explanation: Airplane's rate of speed: 1,500/3 = 500 km/h
Distance between Middlebrook and Big City: 750 km
Travel time between Middlebrook and Big City/Urbana: 750/500 = 1.5 hours
Time into flight: 1.5 hours.
Time until convention begins: 5 - 1.5 = 4.5 hours
Time until convention ends: 4.5 + 6 = 10.5 hours
IMO, the correct answer is "A."
Question: Compute the number of distinct line segments that can be drawn inside a square such that
the endpoints of the segment are on the square and the segment divides the square into two
congruent triangles.
A.5
B.4
C.3
D.2
Answer: D.2
Explanation: Cutting along opposite corners are the only valid ways, so there are 2 such pairs.
correct answer D
Question: If v is an integer, which of the following must be an even integer?
A.v^2-v-1
B.v^2-4v+6
C.v^2-5v+5
D.v^2+3v+8
Answer: D.v^2+3v+8
Explanation: Check the options by plugging in some values ( Preferably smaller integers like 1 and 2 )
A: v^2-v-1 = -1 { If v = 1 }
B: v^2-4v+6 = 3 { If v = 1 }
C: v^2-5v+5 = 1 { If v = 1 }
D: v^2+3v+8 = 12 { If v = 1 }v^2+3v+8 = 18 { If v = 2 }
E: v^2+2v+10 = 13 { If v = 1 }
Thus the only possible answer is (D)
Question: Varma can read a book in k minutes. What part of the book can he read in 12 minutes?(k>12)
A.(k - 8)/k
B.k/8
C.8 + k
D.12/k
Answer: D.12/k
Explanation: Option D
Explanation:
Part of the book he can read in 1 minute = 1/k
Part of the book he can read in 12 minutes =12/k.
Answer: D
Question: Remainder of (6^17+17^6)/7= ?
A.2
B.1
C.0
D.3
Answer: C.0
Explanation: 6^17/7 = (7-1)^17/7 => (-1)^17/7 = -1/7
17^6/7 = (2*7+3)^6/7 = 3^6/7 = 27^2/7 =(4*7-1)^2/7 =(-1)^2/7 = 1/7
so, (6^17+17^6)/7 = (-1+1)/7 => 0/7 rem = 0
ANSWER:C
Question: In a bag there are 3 Snicker's bars and 2 Milky Way bars. What is the probability of choosing at least one Snickers when choosing two consecutive candy bars randomly?
A.9/10
B.16/20
C.2/5
D.3/5
Answer: A.9/10
Explanation: P(at least one Snicker's Bar) = 1 - P(no Snicker's Bar, so 2 Milky Way Bars) = 1- 2/5*1/4 = 9/10.
Answer: A.
Question: The number of permutations of the letters of the word 'MESMERISE' is?
A.9!/(2!)2 3!
B.9!/(2!)2 8!
C.9!/(8!)2 3!
D.8!/(2!)2 3!
Answer: A.9!/(2!)2 3!
Explanation: n items of which p are alike of one kind, q alike of the other, r alike of another kind and the remaining are distinct can be arranged in a row in n!/p!q!r! ways.
The letter pattern 'MESMERISE' consists of 10 letters of which there are 2M's, 3E's, 2S's and 1I and 1R.
Number of arrangements = 9!/(2!)2 3!
Answer: A
Question: A password for a computer is six digits from 0 and 9. The six digit number is a prime number. What is the approximate probability that the last digit is a 3?
A.1/4
B.1/6
C.1/10
D.1/20
Answer: A.1/4
Explanation: If the last digit is 0, 2, 4, 6, or 8, the number is even and therefore not prime. If the last digit is 5, the number is divisible by 5 and therefore not prime. The only possibilities are 1, 3, 7, and 9. So the probability is approximately 1/4 (answer A). We say approximately because there is a certain degree of randomness in the distribution of prime numbers.
Question: The average price of 10 books is Rs. 12 while the average price of 8 of these books is Rs. 11.75. Of the remaining two books, if the price of one book is 60% more than the price of the other, what ia the pice of each of these two books ?
A.10,12
B.10,16
C.10,18
D.10,19
Answer: B.10,16
Explanation: Explanation:
Total pice of the two books = Rs. [(12 x 10) - (11.75 x 8)]
= Rs. (120 - 94) = Rs. 26.
let the price of one book be Rs. x
Then, the price of other book = Rs. (x + 60% of x) = Rs. = Rs.
So,
The prices of the two books are Rs. 10 and Rs. 16
Answer: B) 10,16
Question: A train covers a distance of 15 km in 10 min. If it takes 10 sec to pass a telegraph post, then the length of the train is?
A.240m
B.150 m
C.120 m
D.200 m
Answer: D.200 m
Explanation: Speed = (15/10 * 60) km/hr
= (90 * 5/18) m/sec
= 25 m/sec.
Length of the train
= 20 * 10
= 200m.
Answer: D
Question: If |4x+2| = 46, what is the sum of all the possible values of x?
A.2
B.-1
C.4
D.-5
Answer: B.-1
Explanation: There will be two cases
4x+2= 46 or 4x+2 = -46
=> x =11 or x= -12
sum of both the values will be -12 +11 = -1
Answer is B
Question: Total of ages of A,B and C at present is 90 years. If ratio of this ages is 2 : 3 : 4 what will be the age of C after 5 years?
A.45 years
B.42 years
C.40 years
D.37 years
Answer: A.45 years
Explanation: 2+3+4=9
4*(90/9)=40yrs
after 5yrs=45
ANSWER:A
Question: Profit of one hospital is 320 percent of the cost. If the cost increases by 25 % but the SP is same, approximately what % of the SP is the profit?
A.40%
B.45%
C.50%
D.70%
Answer: D.70%
Explanation: Let C.P.= Rs. 100. Then, Profit = Rs. 320, S.P. = Rs. 420.
New C.P. = 125% of Rs. 100 = Rs. 125
New S.P. = Rs. 420.
Profit = Rs. (420 - 125) = Rs. 295.
Required percentage = 295	x 100	%	=	1475	% = 70% (approximately).
420	21
D
Question: (1000)7÷(10)20=?
A.10
B.100
C.1000
D.10000
Answer: A.10
Explanation: Explanation:
=(103)7/(10)20
=(10)21/(10)20=10(1)=10
Option A
Question: The area of circle O is added to its diameter. If the circumference of circle O is then subtracted from this total, the result is 8. What is the radius of circle O?
A.–2/pi
B.2
C.3
D.4
Answer: D.4
Explanation: pi*r^2 + 2r -2*pi*r = 8
Simplifying the equation: pi*r(r-2)+2r=8
Without much algebraic: We can Test the answers quickly, then 4 is the only possible answer that will eliminate pi from equation.
Answer is D
Question: If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is ?
A.4/16
B.4/17
C.4/11
D.4/13
Answer: D.4/13
Explanation: P(SᴜK)
= P(S) + P(K) - P(S∩K), where S denotes spade and K denotes king.
P(SᴜK)
= 13/52 + 4/52 - 1/52
= 4/13
Answer:D
Question: There are 35 students in a hostel. If the no. of students increases by 5, the expenses of the mess increase by Rs.42/day while the average expenditure per head diminishes by Rs1. Find the original expenditure of the mess?
A.s. 64.80
B.s. 69.80
C.s. 72.80
D.s. 78.80
Answer: C.s. 72.80
Explanation: Suppose the average join the mess , total expenditure = 35x + 42
Now, the average expenditure = (35x + 42)/ (35 + 5) = x – 1
or, 35x + 42 = 40x – 40
or, x = 16.4
Thus the original expenditure of the mess = 35 x 16.4=574
Therefore x-1 = 15.4
hence 42 x 15.4 =646.80
646.80 - 574 = Rs. 72.80
C
Question: When the price of an article was reduced by 20% its sale increased by 80%. What was the net effect on the sale?
A.44% increase
B.44% decrease
C.60% increase
D.66% increase
Answer: A.44% increase
Explanation: if n items are sold for $p each, revenue is $np. If we reduce the price by 20%, the new price is 0.8p. If we increase the number sold by 80%, the new number sold is 1.8n. So the new revenue is (0.8p)(1.8n) = 1.44np, which is 1.44 times the old revenue, so is 44% greater.
ANSWER:A
Question: There are two circles of different radii. The are of a square is 784 sq cm and its side is twice the radius of the larger circle. The radius of the larger circle is seven - third that of the smaller circle. Find the circumference of the smaller circle.
A.9
B.10
C.12
D.18
Answer: C.12
Explanation: Let the radii of the larger and the smaller circles be l cm and s cm respectively. Let the side of the square be a cm.
a2 = 784 = (4)(196) = (22).(142)
a = (2)(14) = 28
a = 2l, l = a/2 = 14
l = (7/3)s
Therefore s = (3/7)(l) = 6 Circumference of the smaller circle = 2∏s = 12∏ cm.
Answer: Option C
Question: A whale goes on a feeding frenzy that lasts for 9 hours. For the first hour he catches and eats x kilos of plankton. In every hour after the first, it consumes 3 kilos of plankton more than it consumed in the previous hour. If by the end of the frenzy the whale will have consumed a whopping accumulated total 360 kilos of plankton, how many kilos did he consume on the sixth hour?
A.38
B.43
C.50
D.53
Answer: B.43
Explanation: If you list the amount eaten each hour, you'll get an equally spaced list, increasing by 3 each hour. In any equally spaced list, the median equals the mean. Here, the mean is 360/9 = 40, so the median is also 40, and that is the amount eaten in the 5th hour. We need to add 3 to find the total eaten in the next hour, so the answer is 43.
option B
Question: A, B and C have Rs.350 between them, A and C together have Rs.200 and B and C Rs.350. How much does C have?
A.A)200
B.B)190
C.C)180
D.D)170
Answer: A.A)200
Explanation: A+B+C = 350
A+C = 200
B+C = 350
--------------
A+B+2C = 550
A+B+C = 350
----------------
C = 200
Answer:A
Question: Xavier starts from P towards Q at a speed of 90 kmph and after every 12 mins increases his speed by 10 kmph. If the distance between P and Q is 51km, then how much time does he take to cover the distance?
A.30
B.32
C.30
D.36
Answer: D.36
Explanation: first 12min = 90 *12/60 =18km
2nd 12min = 100*12/60 =20km
3rd 12 min = 110*12/60 = 22 km
TOTAL time 12 *3 = 36 min
D
Question: The diameter of a garden roller is 1.4 m and it is 2 m long. How much area will it cover in 4 revolutions ? (use Ï€ = 22â„7)
A.35.2 m2
B.44 m2
C.48 m2
D.36 m2
Answer: A.35.2 m2
Explanation: Required area covered in 5 revolutions
= 4 Ã— 2Ï€rh = 4 Ã— 2 Ã— 22â„7 Ã— 0.7 Ã— 2 = 35.2 m2
Answer A
Question: From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first card is a spade and the second card is a jack is?
A.1/50
B.1/13
C.1/26
D.1/52
Answer: D.1/52
Explanation: Probability of a spade = 13/52 = 1/4
Probability of a jack = 4/52 = 1/13
Probability of both = P1*P2 = 1/(4*13) = 1/52
Answer is D.
Question: A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price?
A.17%
B.62%
C.12%
D.19%
Answer: C.12%
Explanation: Original price = 100
CP = 80
S = 80*(140/100) = 112
100 - 112 = 12%
Answer: C
Question: The compound interest on Rs.2800 for 1 1/2years at 10% per annum is
A.Rs.441.35
B.Rs.436.75
C.Rs.434
D.Rs.420
Answer: C.Rs.434
Explanation: Explanation:
Amount = Rs.[[2800×(1+10/100)](1+5/100)]
= Rs.[2800×11/100×21/20]= Rs.3234
C.I = Rs.(3234-2800)= Rs.434
Correct Option: C
Question: A coin is tossed live times. What is the probability that there is at the least one tail?
A.1/15
B.31/32
C.1/10
D.30/32
Answer: B.31/32
Explanation: Probability of getting least one tail at the coin tossed five times.
= There is not even a single tail.
= 1/32 ; P(T) = 1 - 1/32 = 31/32
ANSWER B
Question: The price of a car is marked at $11,000. If the car has successive discounts of 20%, 15% and 5%, then at what price does a customer buy the car?
A.$6702
B.$6924
C.$7106
D.$7348
Answer: C.$7106
Explanation: 0.95*0.85*0.8*11000 = $7106
The answer is C.
Question: Six students - 3 girls and 3 boys - are to sit side by side for a makeup exam. How many ways could they arrange themselves given that no two girls and no two boys can sit next to one another?
A.A)12
B.B)36
C.C)72
D.D)240
Answer: C.C)72
Explanation: in order not to have two girlss or two boys next to one another, we must make an alternate sitting arrangement. (B-G-B-G-B-G) or (G-B-G-B-G-B).
Total ways = 2C1*3!*3!
=2*6*6
=72
Ans - C
Question: The price of a coat in a certain store is $500. If the price of the coat is to be reduced by $300, by what percent is the price to be reduced?
A.10%
B.15%
C.20%
D.60%
Answer: D.60%
Explanation: price of a coat in a certain store = $500
the price of the coat is to be reduced by $300
% change = (Final Value - Initial Value)*100 / Initial Value
% Reduction= (Reduction in Price)*100 / Initial Value
i.e. % Reduction= (300)*100 / 500 = 60%
Answer: Option D
Question: What is the smallest positive integer that can be multiplied by 432 to make it a perfect square?
A.2
B.3
C.5
D.7
Answer: B.3
Explanation: 432=2^4*3^2*3
Therefore the smallest integer to multiplied to 1008 to make it a perfect square is 3.
Answer B.
Question: Obra drove 120π meters along a circular track. If the area enclosed by the circular track on which she drove is 57,600π square meters, what percentage of the circular track did Obra drive?
A.6.67%
B.12.5%
C.18.75%
D.25%
Answer: D.25%
Explanation: area enclosed by the circular track on which she drove is 57,600π square meters
So, π(r^2) = 57,600π ---> (r^2)=57,600 ---> r=240
Circumference of the circular track = 2πr = 480π
Therefore, part of circumference covered = 120π/480π =25%
Hence, answer is D.
Question: If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 6-letter code words to the number of 4-letter code words?
A.20
B.30
C.35
D.40
Answer: B.30
Explanation: Method #1: Using the permutation formula
# of 6 letter code words:
nPr = n! / (n – r)! = 10! / (10 – 6)! = 10*9*8*7*6*5
# of 4 letter code words:
nPr = 10! / (10 – 4)! = 10*9*8*7
# of 5 words / # of 4 words = (10*9*8*7*6*5)/(10*9*8*7) = 30
B
Question: A's speed is 15/13 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that B beats A by 25% of the length of the race?
A.35%
B.48%
C.52%
D.42%
Answer: A.35%
Explanation: First calculate the distance, B has covered with his speed in the time, in which A reached 80% of the race.
Then Add the remaining distance as head start for B to win the race.
Its best to apply Ratios concept here.
Since A's speed is 15/13 of B, therefore, B's speed is 13/15 of A
Distance covered by B = speed x time = (13/15) x (0.75) = 0.65%
(Which means B would have covered 0.65 of the race length during the time in which A has covered 0.75 of the race length.
Therefore to win, B needs a headstart of (1 - 0.65 = ) 0.35 of the race length.
So the answer is A
Question: There are X girls in a class, and their average height is P inches. In the same class, there are Y boys with an average height of Q inches. What is the average height of all the students in the class?
A.(X + Y)/(M + N)
B.(M + N)/(X + Y)
C.(XM + YN)/(M + N)
D.(XP + YQ)/(X + Y)
Answer: D.(XP + YQ)/(X + Y)
Explanation: Total height = XP+YQ
No of students = X+Y
Avg = (XP+YQ)/(X+Y)
Answer is D
Question: Three cannons are firing at a target. If their individual probabilities to hit the target are 0.2, 0.1, and 0.7 respectively, what is the probability that none of the cannons will hit the target after one round of fire?
prob. that all the cannons will hit the target = .06
prob. that none of the cannons will hit = 1 - .06 = .94
A.0.061
B.0.12
C.0.218
D.0.216
Answer: D.0.216
Explanation: The probability that eachdoesn'thit is: 0.8, 0.9, and 0.3. When we have multiple independent events, we multiply the probabilities:
.8*.9*.3 = 0.216.
Option: D
Question: A and B together have Sterling 1210. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does B have?
A.Sterling 460
B.Sterling 484
C.Sterling 550
D.Sterling 664
Answer: B.Sterling 484
Explanation: Explanation: 4/15A = 2/5B
A = (2/5 x 15/4)B
A = 3/2 B
A/B = 3/2
A : B = 3 : 2.
B's share = Sterling (1210 x 2/5) = Sterling 484.
Answer: Option B
Question: How many factors does 35^2 have?
A.2
B.8
C.24
D.25
Answer: C.24
Explanation: 36^2 = 6*6*6*6 = 2^4*3^4
Total factors = (4+1)*(4+1) = 6*4 = 24
Answer C.
Question: If the cost price of 24 chocolates is equal to the selling price of 16 chocolates, the gain percent is :
A.24%
B.8%
C.50%
D.40%
Answer: C.50%
Explanation: Explanation :
Solution: Let C.P. of each chocolate be Re. 1. then, C.P. of 16 chocolates = Rs. 16;
S.P. of 16 chocolates =Rs. 24.
.'. Gain% = 8*100/16 = 50%
Answer : C
Question: A volume of 11248 l water is in a container of sphere. How many hemisphere of volume 4l each will be required to transfer all the water into the small hemispheres?
A.2812
B.8231
C.2734
D.4222
Answer: A.2812
Explanation: a volume of 4l can be kept in 1 hemisphere
therefore, a volume of 11248l can be kept in (11248/4) hemispheres
ans.2812
ANSWER:A
Question: A train 200m long passes a standing man in 15 seconds. What is the speed of the train?
A.30km/hr
B.36km/hr
C.48km/hr
D.50km/hr
Answer: C.48km/hr
Explanation: Speed of the train = 200/15* 18/5 = 48km/hr
Answer is C
Question: The average number of shirts with Salman, Ambani and Dalmiya is 60, if all of them reached a shopping mall in Delhi and purchased 5 shirts each of them then average number of shirt each of them now has
A.65
B.63
C.62
D.64
Answer: A.65
Explanation: Required average
= Old average + New average
= 60 + 5 = 65
answer :A
Question: Two numbers A and B are such that the sum of 5% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B.
A.2 : 1
B.1 : 2
C.1 : 1
D.4 : 3
Answer: D.4 : 3
Explanation: Explanation :
5% of A + 4% of B = (2/3)(6% of A + 8% of B)
(5A/100) + (4B/100) = (2/3)((6A/100) + (8B/100))
⇒ 5A + 4B = (2/3)(6A + 8B)
⇒ 15A + 12B = 12A + 16B
⇒ 3A = 4B
⇒ A/B = 4/3
⇒ A:B = 4:3
Answer : Option D
Question: A tank contains 6,500 gallons of a solution that is 5 percent sodium chloride by volume. If 2,500 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride?
A. 5.12%
B. 6.12%
C. 7.12%
D. 8.12%
Answer: D. 8.12%
Explanation: We start with 6,500 gallons of a solution that is 5% sodium chloride by volume. This means that there are 0.05 x 6,500 = 325 gallons of sodium chloride.
When 2,500 gallons of water evaporate we are left with 4,000 gallons of solution. From here we can determine what percent of the 4,000 gallon solution is sodium chloride.
(sodium chloride/total solution) x 100 = ?
(325/4,000) x 100 = ?
0.0812 x 100 = ?
= 8.12%
Answer is D.
Question: The diagonals of a rhombus are 15 cm and 20 cm. Find its area?
A.399
B.266
C.150
D.277
Answer: C.150
Explanation: 1/2 * 15 * 20 = 150
Answer:C
Question: A, B and C can do a work in 90, 30 and 45 days respectively. If they work together, in how many days will they complete the work?
A.15
B.66
C.77
D.8
Answer: A.15
Explanation: One days's work of A, B and C = 1/90 + 1/30 + 1/45
= (1 + 3 + 2)/90 = 1/15
A, B and C together can do the work in 15 days.
Answer: A
Question: A car has a 20-gallon fuel to travel 500 miles.At this rate, how many gallons of fuel are needed for a 1000 mile car ?
A.10
B.30
C.20
D.40
Answer: D.40
Explanation: Number of gallons of fuel per mile = 500 /20 = 25 gallons per mile
Number of gallons of fuel for a 1000 mile car = 1000/25 = 40
ANSWER:D
Question: What is the area of square field whose side of length 15 m?
A.225
B.662
C.772
D.882
Answer: A.225
Explanation: 15 * 15
= 225 sq m
Answer:A
Question: A sum fetched a total simple interest of Rs. 4016.25 at the rate of 1% p.a. in 3 years. What is the sum?
A.122762
B.132877
C.122882
D.133875
Answer: D.133875
Explanation: Principal = (100 * 4016.25) / (1 * 3)
= Rs.133875.
Answer:D
Question: If a trader sold two cars each at Rs. 325475 and gains 12% on the first and loses 12% on the second, then his profit or loss percent on the whole is?
A.1.44%
B.1.74%
C.1.94%
D.2.44%
Answer: A.1.44%
Explanation: SP of each car is Rs. 325475, he gains 12% on first car and losses 12% on second car.
In this case, there will be loss and percentage of loss is given by = [(profit%)(loss%)]/100 = (12)(12)/100 %
= 1.44%
Answer:A
Question: Two cyclists are running on a circular track of 500m.They start from the same point A at the same time.If they meet for the first time at a point 100 m from A, which of the following could be the possible ratio of their speeds?
A.1:4
B.2:3
C.3:5
D.5:7
Answer: A.1:4
Explanation: well, the key aspect of this question is the distance mentioned, when they met for the first time, which is 100m away from the starting point. This distance between their first meeting can be less than 500 in only two circumstance.
1) if both are travelling in the same direction and one of them has been given a head start say by few meters.
2) or if both are travelling in the opposite direction.
now since they start their journey at the same time. hence option 1 is ruled out. hence they must be running in the opposite direction. hence answer should be 2:3.
Why?? here is a solution
As here time is constant, therefore, distance traveled will be directly proportional to the the respective velocities/speed of the two runners.(d1/d2=v1/v2)
now one of them has covered 100m, therefore other must have covered 400m, therefore ratio of their speeds/velocities will be 1:4
A
Question: If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number?
A.5:3
B.3:5
C.1:5
D.5:1
Answer: A.5:3
Explanation: Let 40% of A = 2/3 B
Then, 40A/100= 2B/3
= 2A/5 = 2B/3
= A/B = (2/3) x (5/2)= 5/3
Therefore, A : B = 5 : 3.
Answer is A.
Question: A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
A.152
B.150
C.289
D.369
Answer: B.150
Explanation: Length of the train be ‘X’
X + 150/15 = X + 250/20
4X + 600 = 3X + 750
X = 150m
Answer:B
Question: The sum of two numbers is 65 and their product is 1050. What will be the sum of their reciprocals?
A.(11/140)
B.(11/210)
C.(35/4)
D.(75/8)
Answer: B.(11/210)
Explanation: Solution
x+y=65 xy=1050 1/x+1/y=x+y/xy 65/1050 = (11/210).
Answer B
Question: In a covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay double his speed, then he would take 1 hour less than Sammer. Abhay's speed is?
A.5 km/hr
B.7 km/hr
C.9 km/hr
D.2 km/hr
Answer: A.5 km/hr
Explanation: Let Abhay's speed be x km//hr.
Then, 30/x - 30/2x = 3
x = 5 km/hr.
Answer:A
Question: Find the third proportional to 2 and 8?
A.10
B.32
C.36
D.19
Answer: B.32
Explanation: Formula = Third proportional = (b × b)/a
A = 2 and B = 8
(8 x 8 )/ 2 = 64/2 = 32
B
Question: Right triangle ABC is to be drawn in the xy-plane so that the right angle is at A and AB is parallel to the y-axis. If the x- and y-coordinates of A, B, and C are to be integers that are consistent with the inequalities -4 ≤ x ≤ 2 and 4 ≤ y ≤ 9 , then how many different triangles can be drawn that will meet these conditions?
A.54
B.432
C.864
D.2,916
Answer: C.864
Explanation: We have the rectangle with dimensions 9*4 (9 horizontal dots and 4 vertical). AB is parallel to y-axis and AC is parallel to x-axis.
Choose the (x,y) coordinates for vertex A: 9C1*4C1;
Choose the x coordinate for vertex C (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 B (as x coordinate is fixed by A): 3C1, (4-1=3 as 1 vertical dot is already occupied by A).
9C1*4C1*8C1*3C1=864.
Answer: C.
Question: Find the invalid no.from the following series 15 46 63 71 75 77 78
A.38
B.43
C.46
D.49
Answer: C.46
Explanation: In this question, if you start from the beginning, firstly the difference is 31, then the difference is 17, then the difference is 8. So there is no logic. If you start backwards,you can see that firstly, 1 is added, then 2 is added, then 4 is added, then 8,16 and 32 should have been added. So you have got the right clue. So 15 + 32 the first number should be 47 and afterwards, the series becomes + 16, + 8, + 4and so on.
C
Question: If a positive integer n, divided by 5 has a remainder 2, which of the following must be true
I. n is odd
II. n+1 cannot be a prime number
III. (n+2) divided by 7 has remainder 2
A.None
B.I only
C.I and II only
D.II and III only
Answer: A.None
Explanation: n can be written as :
n = 5k+2. Thus, taking k=0, we have n=2.
I.n=2,even.False
II.2+1=3, is a prime. False.
III.n+2 = 4,4 divided by 7 leaves a remainder of 4. False.
ANSWER:A