RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: In a garden, there are 10 rows and 17 columns of mango trees. The distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden. The length of the garden is
A.20 m
B.22 m
C.34 m
D.26 m
Answer: C.34 m
Explanation: Explanation:
Each row contains 17 plants.
There are 15 gapes between the two corner trees (16 x 2) metres and 1 metre on each side is left.
Therefore Length = (32 + 2) m = 34 m.
Answer: C
Question: A car traveling with 5/75/7 of its actual speed covers 4242 km in 11 hr 4040 min 4848 sec. What is the actual speed of the car?
A.30 km/hr
B.35 km/hr
C.25 km/hr
D.40 km/hr
Answer: B.35 km/hr
Explanation: Explanation:
time =1=1 hr 4040 min 4848 sec
=1=1 hr +4060+4060 hr +483600+483600 hr
=1+23+175=12675hr=1+23+175=12675hr
distance =42=42 km
speed=distancetime=42(12675)speed=distancetime=42(12675) =42Ã—75126=25 km/hr=42Ã—75126=25 km/hr
â‡’57â‡’57 of the actual speed =25=25
â‡’â‡’ Actual speed =25Ã—75=35 km/hr
Answer is B
Question: The average of 45 results is 10. The average of first 22 of them is 16 and that of last 22 is 20. Find the 23 result?
A.600
B.480
C.538
D.650
Answer: C.538
Explanation: 23th result = sum of 45results - sum of 44 results
10*45-16*22+20*22 = 450-352+440 = 538
Answer is C
Question: In a class, the average age of 30 boys is 13 years and the average of 20 girls is 12 years. what is the average age of the whole class?
A.12.5 Yrs
B.14.2 Yrs
C.12.3 Yrs
D.12.6 Yrs
Answer: D.12.6 Yrs
Explanation: Total age of 50 students
(30X 13+20 X 12) = 630
Average = 630/50 = 12.6 Years
ANSWER IS D
Question: A car started running at a speed of 30 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 11 hours of the journey.
A.342 km
B.352 km
C.642 km
D.440 km
Answer: D.440 km
Explanation: The total distance covered by the car in the first 11 hours = 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 +48 + 50 = sum of 11 terms in AP whose first term is 30 and last term is 50 = 11/2 [30 + 50] = 440 km.
ANSWER:D
Question: The cash difference between the selling prices of an article at a profit of 4% and 8% is Rs 3. The ratio of two selling prices is
A.51:52
B.52:54
C.53:54
D.54:55
Answer: B.52:54
Explanation: Explanation:
Let the Cost price of article is Rs. x
Required ratio = (104% of x) / (108% of x)
=104/108
=52/54 = 52:54.
Answer: B
Question: A walks around a circular field at the rate of one round per hour while B runs around it at the rate of eleven rounds per hour. They start in the same direction from the same point at 7.30 a.m. They shall first cross each other after___ minutes?
A.6 min
B.12 min
C.10 min
D.15 min
Answer: A.6 min
Explanation: Since A and B move in the same direction along the circle, so they will first meet each other when there is a difference of one round between the two.
Relative speed of A and B = 11 - 1 = 10 rounds per hour.
Time taken to complete one round at this speed = 1/10 hr = 6 min.
A
Question: A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68 percent of the distribution lies within one standard deviation d of the mean, what percent F of the distribution is less than m +d ?
A.16%
B.32%
C.48%
D.84%
Answer: D.84%
Explanation: D
The prompt says that 68% of the population lies between m-d and m+d.
Thus, 32% of the population is less than m-d or greater than m+d.
Since the population is symmetric, half of this 32% is less than m-d and half is greater than m+d.
Thus, F=(68+16)% or (100-16)% of the population is less than m+d.D
Question: Which of the following inequalities is equivalent to −6 < x < 8?
A.|x - 1| < 7
B.|x + 2| < 6
C.|x + 3| < 5
D.|x - 2| < 6
Answer: A.|x - 1| < 7
Explanation: We know that |x| < a means -a < x < a, where Sum of lower limit of x (i.e -a) and the upper limit of x (i.e a), is 0
Given is, -6 < x < 8, let's say by adding y to this inequality we will get into the above format
-6+y < x+y < 8+y
Now, to move this into the mod format, we need to have (-6+y) + (8+y) = 0 => y = -1
Thus, -7 < x-1 < 7 => |x-1| < 7.
Hence, answer is A
Question: I bought two books; for Rs.480. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?
A.298
B.280
C.279
D.267
Answer: B.280
Explanation: x*(85/100) = (480 - x)119/100
x = 280
Answer:B
Question: Of the 150 employees at company X, 60 are full-time, and 100 have worked at company X for at least a year. There are 20 employees at company X who aren’t full-time and haven’t worked at company X for at least a year. How many full-time employees of company X have worked at the company for at least a year?
A.20
B.30
C.50
D.80
Answer: D.80
Explanation: Full time employee who have NOT worked for at least one year = a
Full time employee who have worked for at least one year = b
NON Full time employee who have worked for at least one year = c
NON Full time employee who have NOT worked for at least one year = d
a+b+c+d = 150
a+b = 80
i.e. c+d = 70
b+c = 100
i.e. a+d = 50
d = 20
i.e. c = 70-20 = 50
i.e. b = 100-50 = 50
i.e. a = 80-50 = 30
b = 80
Answer: Option D
Question: Mr Katial buys a house for Rs 1,00,000 and rents it. He puts 12.5% of each month’s rent aside for upkeep and repairs, pays Rs 325 per year as taxes and realizes 5.5% annually on his investment . Find the monthly rent?
A.Rs 634.76
B.Rs 554.76
C.Rs 654.76
D.Rs 664.76
Answer: B.Rs 554.76
Explanation: Let the monthly rent be Rs X.
We have,
5.5% of 100000 = 12 (X - 12.5% of X) - 325
5500/12 = X - (X/8) - 325/12
5500/12 + 325/12 = 7/8 x X
X = 5825/12 x 8/7
Rs 554.76 per month
ANSWER:B
Question: On dividing a number by 357, we get 41 as remainder.On dividing the same number by 17, what will be the remainder ?
A.4
B.5
C.8
D.7
Answer: D.7
Explanation: Let x be the number and y be the quotient.Then,
x=357*y+41
=(17*21*y)+(17*2)+7
=17*(21y+2)+7.
Required number =7.
Answer is D
Question: If (1.001)^1259=3.52 and (1.001)^2062=7.85 then (1.001)^3321=?
A.27.632
B.29.632
C.17.632
D.39.632
Answer: A.27.632
Explanation: Values Given :
(1.001)^1259 = 3.52
(1.001)^2060 = 7.85
Therefore,
--> (1.001)^1259+2062 = (1.001)^1259 * (1.001)^2062
Substitute the values which is given. Then,
--> (1.001)^3321 = 3.52 * 7.85
--> (1.001)^3321 = 27.632
ANSWER:A
Question: s(n) is a n-digit number formed by attaching the first n perfect squares, in order, into one integer. For example, s(1) = 1, s(2) = 14, s(3) = 149, s(4) = 14916, s(5) = 1491625, etc. How many digits Y are in s(99)?
A.Y=350
B.Y=353
C.Y=354
D.Y=356
Answer: B.Y=353
Explanation: Focus on the points where the number of digits in squares change:
1, 2, 3 - Single digit squares. First 2 digit number is 10.
4 , 5,...9 - Two digit squares. To get 9, the last number with two digit square, think that first 3 digit number is 100 which is 10^2. so 9^2 must be the last 2 digit square.
10, 11, 12, ... 31 - Three digit squares. To get 31, think of 1000 - the first 4 digit number. It is not a perfect square but 900 is 30^2. 32^2 = 2^10 = 1024, the first 4 digit square.
32 - 99 - Four digit squares. To get 99, think of 10,000 - the first 5 digit number which is 100^2.
So number of digits in s(99) = 3*1 + 6*2 + 22*3 + 68*4 = 3 + 12 + 66 + 272 = 353.B
Question: The digit at the ten’s place of a 2 digit no. is twice the digit at the unit’s place. If the sum of this no. and the no. formed by reversing the digits is 66. Find the no.
A.26
B.28
C.32
D.42
Answer: D.42
Explanation: Let the unit place digit = x
Ten’s place digit = 2x
Number formed = 10(2x ) + x = 20 x + x = 21x
Reversing the digit :
Unit digit = 2x
Ten’s digit = x
New number formed = 10 (x) + 2x = 10x + 2x = 12x
As the sum of the number is 66.
21x + 12 x = 66
33x = 66
X = 2
So unit digit = 2
Number = 21x = 21(2)
=42
D
Question: Find the base K of the number system, if (524)8 = (664)K ?
A.4
B.5
C.6
D.7
Answer: D.7
Explanation: 5*8^2 + 2*8^1 + 4*8^0 = 6*K^2 + 6*K^1 + 4*K^0
320 + 16 + 4 = 6(K^2) + 6K + 4
340 = 6(K^2) + 6K + 4
6(K^2) + 6K + 4 - 340 = 0
6(K^2) + 6K - 336 = 0
dividing by 6;
(K^2) + K - 56 = 0
solving this quadratic equation we get, K=7 and K=-8
thus K=7
ANSWER:D
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.1/3
B.2/5
C.1/6
D.1/7
Answer: B.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.
B
Question: Ray writes a two digit number. He sees that the number exceeds 4 times the sum of its digits by 3. If the number is increased by 18, the result is the same as the number formed by reversing the digits. Find the sum of the digits of the number.
A.8
B.9
C.10
D.12
Answer: A.8
Explanation: Explanation:
Let the two digit number be xy.
4(x + y) +3 = 10x + y - - - (1)
10x + y + 18 = 10 y + x - - - (2)
Solving 1st equation,
4x + 4y + 3 = 10x + y
3y + 3 = 6x
6x – 3y = 3
Therefore, 2x – y = 1 - - - (3)
Solving 2nd equation,
xy + 18 = yx
⇒⇒ (10x + b) + 18 = 10y + x
⇒⇒ 18 = 9y – 9x
⇒⇒ 2 = y – x
we get y - x = 2 - - - (4)
adding 3 and 4, we get x = 3
By substituting in (4), we get y = 5
So the given number is 35. Sum of the digits = 8.
Correct option: A
Question: In a shop, 40% socks are white and rest are black. 60% socks are made of cotton and rest are made of wool. 25% white socks are made of cotton and 20 of the black socks are made of wool. How many black socks B are made of cotton?
A.100
B.80
C.60
D.50
Answer: A.100
Explanation: I'll prefer to solve this with plug n play method.
As we know, White Cotton socks are only 25% and Total Cotton socks is 60% - Hence Black Cotton socks B has to be [highlight]HIGH[/highlight]number. Thats why we've to pick high number... say 100 or 80.
100 fits perfectly after relevant calculations. Hence answer A.
Question: Indu gave Bindu Rs.3125 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
A.s.10
B.s.2
C.s.5
D.s.3
Answer: C.s.5
Explanation: 3125 = D(100/4)2
D = 5
ANSWER:C
Question: A and B can do a piece of work in 8 days. B and C can do it in 12 days and A and C in 16 days. Working together they will complete the work in how many days?
A.7.78 days
B.7.88 days
C.7.38 days
D.7.38 days
Answer: D.7.38 days
Explanation: A + B = 1/8
B + C = 1/12
C + A = 1/16
-------------------------------
2(A + B +C) = 1/8 + 1/12 + 1/16 = 13/48
A + B +C = 13/96
96/13 = 7.38 days
Answer: D
Question: Which of the following CANNOT be a product of two distinct positive integers p and q?
A.p
B.q
C.3q + 2p
D.q - p
Answer: D.q - p
Explanation: In these questions it is best to take an example as if something is true for all positive integers than it as to be true for the smallest and the easiest integers to work with
take p = 1 and q = 2 and work with the options
pq = 2
A) p take p =2, q = 1
B) q take p = 1 q = 2
C) 3q + 2p Seems tricky, lets see other options and then come back to it.
D) q - p take q = 1 and p = 2 --> q - p = -1 .. How the hell can product of two positive integers be negative ?? or less than each of them?
E)qp Always true
You don't even have to worry what C is !
ans D
Question: John can complete a given task in 10 days. Jane will take only 20 days to complete the same task. John and Jane set out to complete the task by beginning to work together. However, Jane was indisposed 4 days before the work got over. In how many days did the work get over from the time John and Jane started to work on it together?
A.8
B.9
C.8.5
D.9.5
Answer: C.8.5
Explanation: In such questions, you need to start from the end. Last 4 days John works alone and completes 4 * (1/10) = 2/5 of the work.
So 3/5 of the work should have been completed by the two of them together before Jane left.
Their combined rate of work is 1/20 + 1/12 = 8/60
Time taken to complete 4/5 of the work = (3/5)/(8/60) = 9/2 days.
So total number of days taken to complete the work =9/2 + 4 = 8.5 days.
C
Question: The greatest number by which the product of two consecutive multiples of 3 is always divisible is
A.54
B.76
C.18
D.162
Answer: C.18
Explanation: Solution
Required number	= Product of first three multiplies of 3
= (3 Ã— 6)= 18.
Answer C
Question: Seven female friendsseven male friends will be pictured in a advertising photo. If the photographer wants to line them up in one row, with menwomen alternating. How many possible arrangements may she chose?
A.50803200
B.1680
C.1152
D.576
Answer: A.50803200
Explanation: now any of the alternate 8 places can be filled by 7 male or female in 7!
similarily,
other 7 alternate places can be filled in 7!
hence required probability= 2*7!*7!=5,08,03,200
hence A
Question: A man can row downstream at 18 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?
A.14,7
B.64,4
C.18,4
D.14, 4
Answer: D.14, 4
Explanation: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 18 --- (1)
and x - y = 10 --- (2)
From (1) & (2) 2x = 28 => x
= 14, y = 4.
Answer:D
Question: A batsman makes a score of 85 runs in the 17th inning and thus increases his averages by 3.Find his average after 17th inning?
A.19
B.29
C.37
D.49
Answer: C.37
Explanation: let the average after 17th inning =x
Then average after 16th inning=(x-3)
Therefore 16(x-3)+85=17x
Therefore x=37
ANSWER:C
Question: When x is multiplied by 3, the result is 20 more than the result of subtracting x from 20. What is the value of x?
A.10
B.-2
C.11
D.13
Answer: A.10
Explanation: The equation that can be formed is:
3x-20=20-x
or, 4x=40
or, x=10.
Answer : A
Question: $366 is divided amongst A,B and C so that A may get 1/2 as much as B and C together, B may get 2/3 as much as A and C together, then the share of A is
A.$122
B.$150
C.$176
D.$200
Answer: A.$122
Explanation: A:(B+C) = 1:2
A's share = 366*1/3 = $122
Answer is A
Question: Lamp A flashes every 6 seconds, Lamp B flashes every 8 seconds, Lamp C flashes every 10 seconds. At a certain instant of time all three lamps flash simultaneously. During the period of 3 minutes after that how many times will exactly two lamps flash? (Please include any flash of exactly two lights which occurs at the 3 minute mark.)
A.14
B.15
C.16
D.17
Answer: A.14
Explanation: 3 minutes is 180 seconds.
Lamp A and Lamp B will flash together every 24 seconds.
180/24=7 plus remainder.
In the time period, Lamp A and Lamp B will flash together 7 times.
Lamp A and Lamp C will flash together every 30 seconds.
180/30=6.
In the time period, Lamp A and Lamp C will flash together 6 times.
Lamp B and Lamp C will flash together every 40 seconds.
180/40=4 plus remainder.
In the time period, Lamp B and Lamp C will flash together 4 times.
All three lights will flash together every 2*2*2*3*5=120 seconds.
180/120=1 plus remainder.
We have counted these triple flashes three times, so we need to subtract three times the number of times that all three lights flash together.
The number of times that exactly two lights flash together is 7+6+4-3=14 times.
The answer is A.
Question: A set consist of 2p-1 element. What is the number of subsets of this set which contain at most p-1 elements?
A.2^(2p-2)
B.2^(2p) - 2
C.2^(2p) -1
D.2^(2p)
Answer: A.2^(2p-2)
Explanation: I used p=3, so then we have
5!/2!3! + 5!/4!1! + 5!/0!5!
10 + 5 + 1 = 16
So our target is 16
Now replace in answer choices
A gives us 2^4 = 16
Hence A is the correct option
Read carefully it says at most so keep in mind that picking a small number such as 3 will help you save time since you have to list fewer outcomes
Avoid 2 since you will get 1 arrangement (p-1) and may be risky since 1 is a number with certain unique properties
Question: Distance between A and B is 36 miles. Two men started walking from A and B at the same time towards each other. The person who started from A traveled uniformly with average speed 2 mph. While the other man traveled with varying speeds as follows: In first hour his speed was 1 mph, in the second hour it was 1.25 mph, in the third hour it was 1.5 mph, and so on. When will they meet each other?
A. 12 miles away from A
B. 12 miles away from B
C. after 6 hours from start
D. after 9 hours from start
Answer: D. after 9 hours from start
Explanation: Since the question is asking when A and B will meet each other, the answer will be one involving time elapsed.
In such questions, look for the symmetrical situation to find a rough estimate or range. For example, in many work-rate questions, it helps if you figure out the situation in which the rate of both people is the same.
Here the average speed of A (assuming guy who starts from A is A) is 2 mph and distance is 36 miles. So this means that A would take a total of 36/2 = 18 hours to cover the distance from A to B. So, if B's speed were also 2, both A and B would travel for 9 hours to meet in the middle.
B has uniform speed per hour so its average will be the simple average of all speeds: 1, 1.25, 1.5, 1.75, 2, 2.25, 2.5...
and 2 is actually right in the middle of the 9 speeds, implying both A and B have the same average speed.
Since 2 is actually right in the middle of the 9 speeds, this implies both A and B will have the same average speed.
So the correct answer is (D): A and B will meet after 9 hours (midway between A and B.)
Had it been determined that B's average speed was more than 2 then that would indicate A and B would meet closer to point A and will take less than 9 hours and so on...
The correct answer is (D).
Question: At a game of billiards, A can give B 15 points in 60 and A can give C to 20 points in 60. How many points can B give C in a game of 90?
A.11 points
B.12 points
C.15 points
D.10 points
Answer: D.10 points
Explanation: "A can give 15 points to B in 60".
=> In a game of 60, A starts with 0 points where B starts with 15 points
"A can give 20 points to C in 60".
=> In a game of 60, A starts with 0 points where C starts with 20 points
ie, in a game of 60-15-45, B can give C 20-15=5 points
=> ie, in a game of 90, B can give C 5×2=10 points
Answer is D
Question: If 4x = 8^y, which of the following expresses x in terms of y?
A.2^(y-2)
B.2^(y-1)
C.2^(3y-2)
D.2^(2y-3)
Answer: C.2^(3y-2)
Explanation: By exponential simplification. 4 = 2^2 and 8=2^3 therefore (2^2)x=(2^3)^y gives x=(2^3y)/(2^2) further simplified to x=(2^3y)(2^-2) which gives x=2^(3y-2) (because exponential is additive in multiplication. i.e. a^b*a^c=a^(b+c). Answer: C
Question: Dan’s car gets 32 miles per gallon. If gas costs $4/gallon, then how many miles can Dan’s car go on $58 of gas?
A.242
B.353
C.464
D.575
Answer: C.464
Explanation: 58/4 = 14.5 gallons
14.5*32 = 464 miles
The answer is C.
Question: The number of arrangements that can be made with the letters of the word MOTHER so that the vowels occupy the even places?
A.48
B.25
C.21
D.3
Answer: A.48
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 2 even places in 2! i.e., 2 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 * 2 = 48.
Answer:A
Question: Each of the products produced yesterday was checked by worker x or worker y. 0.5% of the products checked by worker x are defective and 0.8% of the products checked by worker y are defective. If the total defective rate of all the products checked by worker x and worker y is 0.6%, what fraction of the products was checked by worker y?
A.1/5
B.1/4
C.1/3
D.2/5
Answer: C.1/3
Explanation: x: 0.5% is 0.1%-points from 0.6%.
y: 0.8% is 0.2%-points from 0.6%.
Therefore the ratio of products checked by y:x is 1:2.
Thus, worker y checked 1/3 of the products.
The answer is C.
Question: There are 5 identical pens and 7 identical books. In how many different ways can a person select at least one object from this set?
A.11
B.12
C.39
D.47
Answer: D.47
Explanation: We can select from 0 to 5 pens and from 0 to 7 books.
Thus the total possible ways to select objects is 6*8 = 48
We must subtract 1 for the case with 0 pens and 0 books.
The answer is D.
Question: If m^(-1) = -1/5 then m^(-2) is equal to
A.-9
B.-3
C.-1/9
D.1/25
Answer: D.1/25
Explanation: You made a mistake here.
You're right till
m^-2 = 1/m^2 and m^-1 = 1/m^1 = 1/m
given m^-1 = -(1/5) so, 1/m = -(1/5) solving this, m = -5
Now, m^-2 = 1/m^2 = 1/(-5)^2 = 1/25 ANS D
Question: The average of first 15 natural numbers is?
A.5.2
B.5.5
C.8
D.9
Answer: C.8
Explanation: Sum of 15 natural no. = 240/2 = 120
Average =120/15 = 8
Answer:C
Question: A train overtakes two persons walking along a railway track. The first person walks at 4.5 km/hr and the other walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?
A.81 km/hr
B.88 km/hr
C.62 km/hr
D.46 km/hr
Answer: A.81 km/hr
Explanation: Let x is the length of the train in meter and y is its speed in kmph
x/8.4 = (y - 4.5)(10/36) ---(1)
x/8.5 = (y - 5.4)(10/36) ---(2)
Dividing 1 by 2
8.5/8.4 = (y - 4.5)/ (y - 5.4)
=> 8.4y - 8.4 × 4.5 = 8.5y - 8.5 × 5.4
0.1y = 8.5 × 5.4 - 8.4 × 4.5
=> .1y = 45.9 - 37.8 = 8.1
=> y = 81 km/hr
ANSWER:A
Question: A special lottery is to be held to select a student who will live in the only deluxe room in a hostel. There are 100 Year-III, 150 Year-II and 200 Year-I students who applied.
Each Year-III's name is placed in the lottery 3 times; each Year-II's name, 2 times and Year-I's name, 1 time. What is the probability that a Year-III's name will be chosen?
A.1/8
B.2/9
C.2/7
D.3/8
Answer: D.3/8
Explanation: Explanation :
Total names in the lottery,
=3×100+2×150+200
=800.
Number of Year-III's names,
=3×100
=300.
The required probability,
=300/800.
=3/8.
Answer : D
Question: A basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is?
A.25/42
B.25/45
C.25/29
D.25/87
Answer: A.25/42
Explanation: Total fruits = 9
Since there must be at least two apples,
(⁵C₂ * ⁴C₁)/⁹C₃ + ⁵C₃/⁹C₃
= 25/42.
Answer: A
Question: If x is an integer, which of the following must be an even integer?
A.x^2-x-1
B.x^2-4x+6
C.x^2-5x+5
D.x^2+3x+8
Answer: D.x^2+3x+8
Explanation: Check the options by plugging in some values ( Preferably smaller integers like 1 and 2 )
A: x^2-x-1 = -1 { If x = 1 }
B: x^2-4x+6 = 3 { If x = 1 }
C: x^2-5x+5 = 1 { If x = 1 }
D: x^2+3x+8 = 12 { If x = 1 } & x^2+3x+8 = 18 { If x = 2 }
E: x^2+2x+10 = 13 { If x = 1 }
Thus the only possible answer is (D)
Question: If Rs. 595 be divided among A, B, C in such a way that A gets 2/3 of what B gets and B gets 1/4 of what C gets, then their shares are respectively?
A.s.420
B.s.360
C.s.389
D.s.368
Answer: A.s.420
Explanation: (A = 2/3 B and B = 1/4 C) = A/B = 2/3 and B/C = 1/4
A:B = 2:3 and B:C = 1:4 = 3:12
A:B:C = 2:3:12
A;s share = 595 * 2/17 = Rs. 70
B's share = 595 * 3/17 = Rs. 105
C's share = 595 * 12/17 =Rs.420.
Answer:A
Question: Robert is traveling on his cycle and has calculated to reach point A at 2 p.m. if he travels at 10 km/hr; he will reach there at 12 noon if he travels at 15 km/hr. At what speed must he travel to reach A at 1 p.m.?
A.17 kmph
B.13 kmph
C.12 kmph
D.18 kmph
Answer: C.12 kmph
Explanation: Let the distance traveled be x km.
Then, x/10 - x/15 = 2
3x - 2x = 60 => x = 60 km.
Time taken to travel 60 km at 10 km/hr = 60/10 = 6 hrs.
So, Robert started 6 hours before 2. p.m. i.e., at 8 a.m.
Required speed = 60/5 = 12 kmph.
Answer: C