RikoteMaster/aqua-rat-mcqa huggingface dataset:
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 150 m from A, which of the following could be the possible ratio of their speeds?
A.1:3
B.2:3
C.3:5
D.3:7
Answer: D.3:7
Explanation: well, the key aspect of this question is the distance mentioned, when they met for the first time, which is 150m 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 150m, therefore other must have covered 350m, therefore ratio of their speeds/velocities will be 3:7
D
Question: Walking with 4/5 of my usual speed, I arrive at the bus stop 10 minutes later than normal. How many minutes does it take to walk to the bus stop at my usual speed?
A.32
B.36
C.40
D.44
Answer: C.40
Explanation: Let t = usual time = distance / usual speed
t + 10 = distance / (4* usual speed/5) = (5 * distance) / (4 * usual speed) = 5t/4
t = 40
The answer is C.
Question: AMOUNT OF BACTERIA PRESENT
Time Amount
1:00 P.M. 8.0 grams
4:00 P.M. x grams
7:00 P.M. 12.4 grams
Data for a certain biology experiment are given in the table above. If the amount of bacteria present increased by the same fraction during each of the two 3-hour periods shown, how many grams of bacteria were present at 4:00 P.M.?
A.12.0
B.12.1
C.12.2
D.10.0
Answer: D.10.0
Explanation: The question says that bacteria increased by same fraction, not by same amount in 2 intervals of 3 hours.
Let X represent the amount of bacteria present at 4:00 PM. Since the fractional increase must remain constant from 1 to 4pm as it is from 4pm to 7pm:
Fractional increase from 1 PM to 4 PM = X / 8.0
Fractional increase from 4 PM to 7 PM = 12.4 / X
X \ 8 = 12.4 \ X
X^2 = 12.4 * 8
X = 10
answer : D
Question: A man can swim in still water at 6 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
A.3.9
B.4.2
C.5.3
D.2
Answer: D.2
Explanation: M = 5
S = x
DS = 6 + x
US = 6 - x
6 + x = (6 - x)2
6 + x = 12 -2x
3x = 6
x = 2
Answer:D
Question: Let G represent a set of four distinct prime numbers. If the sum of the numbers in G is even and x is a member of G, then what is the least possible value that x can be?
A.1
B.2
C.3
D.5
Answer: C.3
Explanation: We are told that G is a set of four distinct prime numbers, and the sum of the numbers in G is even. Since the question involves odds, evens and the smallest possible prime, you should immediately think of 2, the smallest prime number and the only even prime number.
If 2 were a member of the set, then we would have one even number and three odd numbers. Since such sum would always be odd, 2 cannot be a member of the set. Thus, all the members of G must be odd to yield an even sum.
Since all the members of the set must be odd prime numbers, the answer is the smallest odd prime number, which is 3.
The correct answer is choice (C).
Note:1 is not a prime number.
Question: How many numbers between 11 and 90 are divisible by 7?
A.10
B.7
C.11
D.19
Answer: C.11
Explanation: The required numbers are 14,21,28,...........,84.
This is an A.P with a=14,d=7.
Let it contain n terms
then T =84=a+(n-1)d
=14+(n-1)7
=7+7n
7n=77 =>n=11.
ANSWER C
Question: The sum of all two digit numbers divisible by 7 is
A.910
B.510
C.728
D.628
Answer: C.728
Explanation: Required numbers are 14,21,28 . . . . . 98
This is an A.P. in which a=14,d=7 and l=98.
Let the number of terms in it be n.Then t=98
So a+(n-1)d=98.
14+(n-1)*7=98,
14+7n-7=98
7+7n=98
7n=98-7
n = 91/7
then n=13.
Required sum
=n/2(a+l)
=13/2(14+98)
=728
Answer is C.
Question: If a2 + b2 + c2 = 390 and ab + bc + ca = 5, then a + b + c is
A.19
B.20
C.25
D.30
Answer: B.20
Explanation: by formula ,
(a + b + c)^2= a^2 + b^2 + c^2 + 2(ab + bc + ca),
since, a^2 + b^2 + c^2 = 390 and ab + bc + ca = 5,
(a + b + c)^2 = 390 + 2(5)
= 400
= 20^2
therefore: a + b + c = 20
ANSWER:B
Question: A & B started a partnership business. A's investment was thrice the investment of B and the period of his investment was two times the period of investments of B. If B received Rs 5000 as profit , what is their total profit?
A.28000
B.30000
C.32000
D.35000
Answer: D.35000
Explanation: Explanation :
Suppose B's investment = x. Then A's investment= 3x
Suppose Bs period of investment = y, then A's period of investment = 2y
A : B = 3x * 2y : xy
= 6 : 1
Total profit * 1/7 = 5000
=> Total profit = 5000*7 = 35000. Answer : Option D
Question: If the circus were to sell all of its 220 tickets for this month's performance at its usual price, the revenue from sales would be 10% greater than that collected last month. If the circus raised the ticket price by 6% and sold only 200 tickets as a result, what percent less would last month's revenue be compared to this month's revenue?
A.2
B.5
C.300/53
D.110/53
Answer: C.300/53
Explanation: Let price be 10/ticket
then 220 tickets for this month's performance at its usual price=2200
which is 10%greater than last month(let X)---->x(1+10/100)=2200----->x=2000
now new revenue this month=200*10.6=2120
as per question asked 2000=2120(1-A/100)----->A=300/53%
Ans C
Question: The radius of a cylinder is 2 r units and height is 3 r units. Find the curved surface?
A.862
B.298
C.440
D.278
Answer: C.440
Explanation: r = 7
h = 3
2πr(h + r) = 2 * 22/7 * 7(10)
= 440
Answer: C
Question: A man buys a cycle for Rs.1400 and sells it at loss of 15%. What is the selling price of the cycle?
A.1192
B.1191
C.1118
D.1190
Answer: D.1190
Explanation: Explanation:
S.P = 85% of Rs.1400 ⇒ Rs.(8510085100 ×1400) = Rs.1190.
Answer: D
Question: We can rent a boat for x cents per minute for the first 60 minutes and then y cents for each additional minute. How much will it cost to rent a boat for z minutes, where z>60?
A.x + 60y
B.60x+(z-60)y
C.x + zy
D.60y+(z-60)x
Answer: B.60x+(z-60)y
Explanation: The first 60 minutes cost 60x.
The next (z-60) minutes cost (z-60)y.
The total cost is 60x+(z-60)y.
The answer is B.
Question: The average of 11 numbers is 10.9. If the average of first six is 10.5 and that of the last six is 11.4 the sixth number is?
A.9.5
B.10
C.10.5
D.11.5
Answer: D.11.5
Explanation: Explanation:
1 to 11 = 11 * 10.9 = 119.9
1 to 6 = 6 * 10.5 = 63
6 to 11 = 6 * 11.4 = 68.4
63 + 68.4 = 131.4 – 119.9 = 11.5
6th number = 11.5
Option D
Question: A certain stock exchange designates each stock with a two-letter or three-letter code, where each letter is selected from the 26 letters of the alphabet. If the letters may be repeated and if the same letters used in a different order constitute a different code, how many different stocks is it possible to uniquely designate with these codes without using the letter A?
A.16,250
B.16,500
C.16,750
D.17,000
Answer: A.16,250
Explanation: The number of two-letter codes is 25*25=625.
The number of three-letter codes is 25*25*25=15,625.
The total number of codes is 625+15,625=16,250.
The answer is A.
Question: The ages of two person differ by 20 years. If 8 years ago, the elder one be 5 times as old as the younger one, their present ages(in years) are respectively
A.33, 13
B.25, 5
C.29, 9
D.50, 30
Answer: A.33, 13
Explanation: Let their ages be x and (x + 20) years.
Then, 5(x - 8) = (x + 20 - 8)
=> 4x = 52
=>x =13
Their present ages are 33 years and 13 year.
ANSWER:A
Question: If 6 (A's capital) = 8 (B's capital) = 10 (C's capital). Then the ratio of their capitals is?
A.20:15:15
B.20:15:18
C.20:15:12
D.20:15:14
Answer: C.20:15:12
Explanation: 6A = 8B = 10C
A:B:C = 1/6:1/8:1/10
= 20:15:12
Answer: C
Question: Maxwell leaves his home and walks toward Brad's house at the same time that Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 72 kilometers, Maxwell's walking speed is 6 km/h, and Brad's running speed is 12 km/h. What is the distance traveled by Maxwell when they meet in the middle?
A.14
B.24
C.16
D.18
Answer: B.24
Explanation: Consider Max starts from Point A and Brad Starts from Point B and move towards each other.
Assume they shall meet at point O after Time 'T'. The question asks us to find OA.
From the question stem we can make out :- Distance OA = 50km - Distance OB
=> 6xT = 72 - 12xT (i.e distance =Speed x Time)
=> 18T = 72
Hence T = 4
OA = 6 x 4 = 24 Km
Answer : B
Question: How many prime numbers between 1 and 100 are factors of 67830?
A.4
B.5
C.6
D.3
Answer: C.6
Explanation: factor of 67830 = 2*3*5*7*17*19--- 6 prime numbers
C
Question: What is the sum of 20 consecutive integers from -9 inclusive, in a increasing order?
A.-9
B.9
C.-10
D.10
Answer: D.10
Explanation: From -9 to -1 --> 9 nos.
zero --> 1 number
from +1 to +9 --> 9 nos.
When we add up nos. from -9 to +9 sum will be zero. Total 19 nos will be added.
20th number will be 10.
Sum of these 20 nos. = 10.
D is the answer.
Question: The area of a triangle is with base 4m and height 5m?
A.15
B.19
C.56
D.10
Answer: D.10
Explanation: Explanation:
Area=1/2*b*h
1/2 * 4 * 5 = 10 m^2
Answer : D
Question: Car A runs at the speed of 65km/hr & reaches its destination in 8hr. Car B runs at the speed of 70 km/h & reaches its destination in 4h. What is the respective ratio of distances covered by Car A & Car B?
A.3 : 7
B.4 : 9
C.13 : 7
D.5 : 7
Answer: C.13 : 7
Explanation: Sol. Distance travelled by Car A = 65 × 8 = 520 km
Distance travelled by Car B = 70 × 4 = 280 km
Ratio = 520/280 = 13 : 7
C
Question: There are 8 periods in each working day of a school. In how many ways can one organize 7 subjects such that each subject is allowed at least one period?
A.112456
B.145678
C.141120
D.11456
Answer: C.141120
Explanation: 7 subjects can be arranged in 8 periods in 8P7 ways.
Remaining 1 period can be arranged in 7P1 ways.
Two subjects are alike in each of the arrangement. So we need to divide by 2! to avoid overcounting.
Total number of arrangements = (8P7 x 7P1)/2! = 141120
ANSWER:C
Question: Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.1600?
A.3000
B.4200
C.2025
D.1205
Answer: C.2025
Explanation: 1800* 9/8 * 9/8
= 2025
Answer: C
Question: (1000)7÷(10)17=?
A.10
B.100
C.1000
D.10000
Answer: D.10000
Explanation: Explanation:
=(103)7/(10)17
=(10)21/(10)17=10(4)=10000
Option D
Question: If u and v are both negative and uv < v^2, which of the following must be true?
A.u < v < u^2 < v^2
B.u < v < v^2 < u^2
C.v < u < u^2 < v^2
D.u^2 < v^2 < v < u
Answer: C.v < u < u^2 < v^2
Explanation: Because uv < v^2 and both are negative, I thought u < v. So I crossed off answers c), d), and e).
And because u< v , u^2 < v^2.
ans C
Question: The greatest ratio out of 2:3, 5:8, 3:1, 8:9 and 8:5 is?
A.2:3
B.3:1
C.5:8
D.8:5
Answer: B.3:1
Explanation: 2/3=0.666
5/8=0.625
3/1=3
8/9=0.888
8/5=1.6
ANSWER:B
Question: How many two-digit numbers yield a remainder of 1 when divided by both 4 and 17?
A.0
B.1
C.2
D.3
Answer: B.1
Explanation: Easier to start with numbers that are of the form 17p+1 ---> 18,35,52,69,86.
Out of these, there is only one (69) is also of the form 4q+1. Thus 1 is the answer. B is the correct answer.
Question: A man sells two articles for Rs.3600 each and he gains 35% on the first and loses 35% on the next. Find his total gain or loss?
A.9% loss
B.400
C.12.25%loss
D.324
Answer: C.12.25%loss
Explanation: (35*35)/100 = 12.25%loss
ANSWER:C
Question: Albert invested an amount of Rs. 8000 in a fixed deposit scheme for 2 years at compound interest rate 5 p.c.p.a. How much amount will Albert get on maturity of the fixed deposit?
A.Rs. 8600
B.Rs. 8620
C.Rs. 8820
D.Rs. 8000
Answer: C.Rs. 8820
Explanation: Explanation:
Amount
= Rs.[8000x(1+5/100)2]
=Rs.(8000x21/20x21/20)
=Rs.8820.
ANSWER IS C
Question: There are two box,one containing 39 red balls and the other containing 26 green balls. You are allowed to move the balls between the boxes so that when you choose a box at random and a ball at random from the chosen box, the probability of getting a red ball is maximized. This maximum probability is
A..60
B..50
C..70
D..80
Answer: D..80
Explanation: Here we are allowed to transfer the balls between the two boxes, so we keep only one red ball in first box and move all the remaining balls to the second box, so that we get maximum probability of drawing red ball from first box
So first box--- only one red ball
second box--- 38 red and 26 green
Probability of choosing any box is 1/ 2.
probability of choosing the red ball from first box is 1
probability of choosing the red ball from second box is 38/64
So probability of taking one red ball = [(1/2)×(1)]+[(1/2)*(38/64)]≃0.8
ANSWER:D
Question: If a car went the first third of the distance at 80 kmh, the second third at 30 kmh, and the last third at 48 kmh, what was the average speed of the car for the entire trip?
A.36 kmh
B.40 kmh
C.42 kmh
D.45 kmh
Answer: D.45 kmh
Explanation: Assume D/3 = 240 (this number is convenient because it is divisible by 80, 30 and 48)
So:
240 = 80*T1 = 3 hrs
240 = 30*T2 = 8 hrs
240 = 48*T3 = 5 hrs
T = T1 + T2 + T3 = 16 hrs
D = RT
(240*3) = R*16
R = 45
ANSWER: D
Question: Calculate the speed of a stream if a boat going upstream at
4km/hr and downstream at 8km/hr
A.1 kmph
B.2 kmph
C.3 kmph
D.6 kmph
Answer: B.2 kmph
Explanation: Sol.
Speed of stream = 1/2(8 -4) kmph = 2 kmph.
Answer B
Question: A batch of cookies was divided among three tins: 2/3 of all the cookies were placed in either the blue tin or the green tin, and the rest were placed in the red tin. If 1/4 of all the cookies were placed in the blue tin, what fraction R of the cookies that were placed in the other tins were placed in the green tin?
A.15/2
B.9/4
C.5/9
D.7/5
Answer: C.5/9
Explanation: Blue tin or red tin: 2/3 (N)
Red tin: (1/3)N
Blue tin: (1/4)N
What the last statment meant, is it wants this fraction: (# of cookies in green tin)/(# of cookies in red and green tin)
# of cookies in green tin = 2N/3 - N/4 = 8N- 3N/12 = 5N/12
# of cookies in red and green tin = N/3 + 5N/12 = 9N/12
Fraction R= 5N/12 * 12/9N = 5/9 (C)
Question: Which of the following is closest to the difference between sum Q of all proper fractions (fractions less than 1) in the form 1/x , where x is a positive digit, and the product of all proper fractions in the form y/(y+1), where y is a positive digit?
A.2.82
B.2.72
C.1.82
D.1.72
Answer: D.1.72
Explanation: Sum Q of all proper fractions (fractions less than 1) in the form 1/x, where x is a positive digit:
1/1 + 1/2 + 1/3 +.....+ 1/9
This is a harmonic progression. Harmonic progression is inverse of arithmetic progression.
Approximate sum of a harmonic progression with even number of terms = number of terms * (average of middle 2 terms)
Approximate sum of a harmonic progression with odd number of terms = number of terms * (middle term)
The actual sum will be slightly more than the approximation.
Here we have 9 terms (odd).
Sum = 9 * 1/5
= 9/5
Product of all proper fractions in the form y/(y+1), where y is a positive digit:
1/2 * 2/3 * 3/4 *.....*9/10
We will be left with 1/10.
Required = 9/5 - 1/10
= 1.8 - 0.1
= 1.7
Closest is 1.72
Answer (D).
Question: A can run a kilometer race in 4 1/2 min while B can run same race in 5 min. How many meters start can A give B in a kilometer race, so that the race mat end in a dead heat?
A.400 m
B.500 m
C.250 m
D.100 m
Answer: D.100 m
Explanation: Explanation:
A can give B (5 min - 4 1/2 min) = 30 sec start.
The distance covered by B in 5 min = 1000 m.
Distance covered in 30 sec = (1000 * 30)/300 = 100 m.
A can give B 100m start.
ANSWER D
Question: If x > 3000, then the value of (3x)/(2 x^1.21 - 1111^1.3) is closest to?
A.1/6
B.1/3
C.10/21
D.4/10
Answer: D.4/10
Explanation: assume x = 3002
(3x)/(2 x^1.21 - 1111^1.3) = 9006 / (2 * (3002)^1.21 - 1111^1.3)
=9006 / 23154
= = 4 /10
D
Question: Q. How many 9-digit even numbers less than 3,000,000 can be formed using the following digits: 1, 2, 2, 3, 5, 5, 6, 6, 7?
A.180
B.140
C.210
D.270
Answer: B.140
Explanation: the number is less than 3000000 so we will have the digit on the left most side to be either 1 or 2
i.e your number can be 1 _ _ _ _ _ _ or 2 _ _ _ _ _ _
case 1 > 1 _ _ _ _ _ _ here the units digit can be either 2 or 6
when the units digit is 2 i.e 1 _ _ _ _ _ 2
number of ways this can be done would be 5! / 2! (as 5 is repeated twice) = 60
when the units digit is 6 i.e. 1 _ _ _ _ _ 6, number of ways would be 5!/(2! * 2!) {both 2 and 5 repeat twice} = 30
case 2 > 2 _ _ _ _ _ _ (here units digit may be 2 or 6)
number of ways this can be done would be 5! / (2!) for 2 =60
and 5! / 2! for 6 ... = 60
adding all of these ... gives the answer 140 ...
the explanation looks difficult but this technique helps if you are familiar with the concept of permutations when the numbers/alphabets repeat
B
Question: Find the 100th place digit of a number forming from digits 1 to 9 without repeatation and number passes the divisibility test of 11 means difference of sum of alternative digits is 0 or divisible by 11.
A.1
B.2
C.3
D.4
Answer: D.4
Explanation: Largest no is 987652413
So digit will be 4
ANSWER:D
Question: n is a whole number which when divided by 4 gives 3 as remainder. What will be the remainder when 2*n is divided by 4 ?
A.8
B.2
C.6
D.7
Answer: B.2
Explanation: Explanation:
Let n=4*q + 3. Then, 2*n = 8*q + 6 = 4(2*q + 1) + 2.
Thus when 2*n is divided by 4, the reminder is 2.
Answer: B) 2
Question: A candidate got 30% of the votes polled and he lost to his rival by 4000 votes. How many votes were cast?
A.7500
B.2028
C.2775
D.10000
Answer: D.10000
Explanation: 30%-----------L
70%-----------W
------------------
40%----------4000
100%---------? => 10000
Answer:D
Question: The average of first 10 odd numbers is?
A.12
B.10
C.87
D.23
Answer: B.10
Explanation: Sum of 10 odd no.
= 100
Average = 100/10
= 10
Answer:B
Question: A cricketer scored 138 runs which included 12 boundaries and 2 sixes. What percent of his total score did he make by running between the wickets.
A.46.2%
B.54.54 %
C.63%
D.56.52%
Answer: D.56.52%
Explanation: Explanation :
Number of runs made by running = 138 - (12 x 4 + 2 x 6)
= 138 - (60)
= 78
Now, we need to calculate 72 is what percent of 138.
=> 78/138 * 100 = 56.52 %
Answer : D
Question: If 36 men can do a piece of work in 25 hours, in how many hours will 15 men do it ?
A.10 hours
B.40 hours
C.20 hours
D.60 hours
Answer: D.60 hours
Explanation: Let the required number of hours be x. Then,
Less men, More hours	(Indirect Proportion)
15 : 36 : : 25 : x = (15 x x) = (36 x 25) = (36 x 25)/15 = 60
Hence, 15 men can do it in 60 hours.
Answer is D.
Question: Calculate the value of q from the below equation: q^3âˆ’25q+5=173
A.7
B.4
C.6
D.9
Answer: A.7
Explanation: Use elimination method to find the correct option. you find that of all the options 7 is the correct value for q
Answer: A
Question: The area of a rectangular field is equal to 200 square meters. Its perimeter is equal to 60 meters. Find the width of this rectangle.
A.5
B.10
C.15
D.20
Answer: B.10
Explanation: L * W = 200 : area , L is the length and W is the width.
2 L + 2 W = 60 : perimeter
L = 30 - w : solve for L
(30 - W) * W = 200 : substitute in the area equation
W = 10 and L = 20 :
correct answer B
Question: 417 x 417 + 383 x 383=?
A.320578
B.80578
C.80698
D.81268
Answer: A.320578
Explanation: =(417)^2 + (383)^2
=(400+17)^2 + (400-17)^2
=2[(400)^2+(17)^2]
=2[160000+289]
=2 x 160289 = 320578
Answer is A
Question: Operation # is defined as: a # b = 4a^2 + 4b^2 + 8ab for all non-negative integers. What is the value of (a + b) + 5, when a # b = 100?
A.5
B.8
C.10
D.13
Answer: C.10
Explanation: OFFICIAL SOLUTION:
(B) We know that a # b = 100 and a # b = 4a² + 4b² + 8ab. So
4a² + 4b² + 8ab = 100
We can see that 4a² + 4b² + 8ab is a well-known formula for (2a + 2b)². Therefore
(2a + 2b)² = 100.
(2a + 2b) is non-negative number, since both a and b are non-negative numbers. So we can conclude that 2(a + b) = 10. (a + b) + 5 = 10/2 + 5 = 10.
The correct answer is C.
Question: If the median of a list of numbers is m, the first quartile of the list is the median of the numbers in the list that are less than m. What is the first quartile of the list of numbers 42, 24, 30, 28, 26, 19, 33 and 35 ?
A.33
B.28
C.27
D.25
Answer: D.25
Explanation: It is given that a quartile is the middle number of all numbers less than median..
so lets arrange the number in ascending order- 42, 24, 30, 28, 26, 19, 33 and 35
19, 24, 26, 28, 30 , 33, 35, 42...
numbers less than median are 19, 24, 26, 28..
the median of these numbers = center of 24 and 26 = 25
D
Question: A vessel of capacity 90 litres is fully filled with pure oil. Nine litres of oil is removed from the vessel and replaced with water. Nine litres of the solution thus formed is removed and replaced with water. Find the quantity of pure oil in the final oil solution?
A.83.9 litres
B.54.9 litres
C.37.9 litres
D.72.9 litres
Answer: D.72.9 litres
Explanation: D
72.9 litres
Let the initial quantity of oil in vessel be T litres.
Let us say y litres of the mixture is taken out and replaced by water for n times, alternatively.
Quantity of oil finally in the vessel is then given by [(T - y)/T]n * T
For the given problem, T = 90, y = 9 and n = 2.
Hence, quantity of oil finally in the vessel
= [(90 - 9)/90]2 (90) = 72.9 litres.
Question: A set of football matches is to be organized in a "round-robin" fashion, i.e., every
participating team plays a match against every other team once and only once. If 21
matches are totally played, how many teams participated?
A.4
B.5
C.6
D.7
Answer: D.7
Explanation: 2 ways to solve this problem..
summation(x)=n(n-1)/2
n(n-1)/2=21;
n^2-n-42=0
factors : 7,-6
Ans : 7
ANSWER:D
Question: If each letter in the English alphabet is assigned an even number such as A = 2, B = 4 and so on, then what will be the total value of the letters in the word LEAD?
A.42
B.40
C.46
D.44
Answer: D.44
Explanation: GIven the Condition:
L=24,E=10, A=2 and D=8
Hence the addition is 44
ANSWER:D
Question: What is the unit digit in the product (3^65 x 6^59 x 7^71)?
A.4
B.8
C.6
D.2
Answer: A.4
Explanation: Unit digit in 3^4 = 1 Unit digit in (3^4)16 = 1
Unit digit in 3^65 = Unit digit in [ (3^4)16 x 3 ] = (1 x 3) = 3
Unit digit in 6^59 = 6
Unit digit in 7^4 ==> Unit digit in (7^4)17 is 1.
Unit digit in 7^71 = Unit digit in [(7^4)17 x 7^3] = (1 x 3) = 3.
Required digit = Unit digit in (3 x 6 x 3) = 4.
Answer A)4.
Question: A man can row
9 1/3
kmph in still water and finds that it takes him thrice as much time to row up than as to row, down the same distance in the river. The speed of the current is.
A.3 2/3kmph
B.4 2/3kmph
C.5 2/3kmph
D.6 2/3kmph
Answer: B.4 2/3kmph
Explanation: Explanation:
Friends first we should analyse quickly that what we need to calculate and what values we require to get it.
So here we need to get speed of current, for that we will need speed downstream and speed upstream, because we know
Speed of current = 1/2(a-b) [important]
Let the speed upstream = x kmph
Then speed downstream is = 3x kmph [as per question]
speed in still water = 1/2(a+b)
=>1/2(3x+x)
=>2x as per question we know,
2x=9 1/3
=>2x=28/3
=>x=14/3
So,
Speed upstream = 14/3 km/hr, Speed downstream 14 km/hr.
Speed of the current
=1/2[14−14/3]
=14/3=4 2/3kmph
Option B
Question: A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered.If the area of the field is 800 sq.ft, how many feet of fencing will be required ?
A.100feet
B.120feet
C.150feet
D.180feet
Answer: A.100feet
Explanation: Explanation:
We are given with length and area, so we can find the breadth.
as Length * Breadth = Area
=> 20 * Breadth = 800
=> Breadth = 40 feet
Area to be fenced = 2B + L = 2*40 + 20
= 100 feet
Answer: Option A