RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A rectangular lawn 70 m × 30 m has two roads each 5 metres wide, running in the middle of it, one parallel to the length and the other parallel to the breadth. Find the cost of gravelling the road at the rate of 4 per square metre.
A.2,000
B.1,800
C.1,900
D.1,700
Answer: C.1,900
Explanation: Total area of road
= Area of road which parallel to length + Area of road which parallel to breadth – overlapped road
= 70 × 5 + 30 × 5 – 5 × 5
= 350 + 150 – 25
= 500 – 25 = 475 m2
∴ Cost of gravelling the road
= 475 × 4 = 1900
Answer C
Question: A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 91000, then the share of B is?
A.A)44500
B.B)42000
C.C)44098
D.D)43007
Answer: B.B)42000
Explanation: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6
Total profit = Rs. 91000
Share of B = 6/13 (91000)
= Rs. 42000
Answer:B
Question: A spirit and water solution is sold in a market. The cost per liter of the solution is directly proportional to the part (fraction) of spirit (by volume) the solution has. A solution of 1 liter of spirit and 1 liter of water costs 30 cents. How many cents does a solution of 1 liter of spirit and 2 liters of water cost?
A.13
B.30
C.50
D.51
Answer: B.30
Explanation: Yes, ensure that you understand the relation thoroughly!
Cost per liter = K * Fraction of Spirit
30 cents is the cost of 2 liters of solution (1 part water, 1 part spirit). So cost per liter is 15 cents. Fraction of spirit is 1/2.
15 = K * (1/2)
K = 30
Cost per liter = 30 * (1/3) (1 part spirit, 2 parts water)
Cost for 3 liters = 30 * (1/3) * 3 = 50 cents
B. 30 cents
Question: A person covered one-fourth of the total distance at 26 kmph and remaining distance at 24 kmph. What is the average speed for the total distance?
A.64/8kmph
B.64/3kmph
C.64/9kmph
D.64/6kmph
Answer: B.64/3kmph
Explanation: Let the total distance be x km
total time taken = (x/4)/16 + (3x/4)/24
= x/64 + x/32 = 3x/64
Average speed = x/(3x/64) = 64/3kmph
= 21 (1/3)kmph.
Answer: B
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 60 m and they cross each other in 12 sec, then the speed of each train is?
A.30
B.35
C.18
D.12
Answer: C.18
Explanation: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (60 + 60)/12 => x = 5
Speed of each train = 10 m/sec.
= 5 * 18/5 = 18 km/hr.
Answer: Option C
Question: A crew can row a certain course up the stream in 84 minutes; they can row the same course down stream in 15 minutes less than they can row it in still water. How long would they take to row down with the stream
A.45 or 23 minutes
B.63 or 12 minutes
C.69 minutes
D.19 minutes
Answer: C.69 minutes
Explanation: A method has been discussed here to nullify the calculations though.
All I can input here is,
speed of a crew in still water = 1/2 ( speed upstream + speed downstream)
approximating this for time,
t = 1/2(84+ (t-15))
giving t = 69
C
Question: A set of 11 positive integers has an average of 30. Which of the following is the greatest possible value for the median of this set?
A.25
B.30
C.36
D.54
Answer: D.54
Explanation: for the median to be max , we should take all the values below meadian to be the lowest and the remaining values to be the same..
here 1 is the lowest value(positive int) so the lowest 5 int will equal 5..
remaining 6= 30*11-5=325..
therefore each valueof these 6 int =325/6=54
ans D
Question: The present ages of three persons in proportions 3 : 7 : 5. Eight years ago, the sum of their ages was 51. Find their present ages (in years).
A.8, 20, 28
B.16, 28, 36
C.15,35,25
D.18, 24, 32
Answer: C.15,35,25
Explanation: Explanation:
Let their present ages be 3x, 7x and 5x years respectively.
Then, (3x - 8) + (7x - 8) + (5x - 8) = 51
15x = 75
x = 5
Their present ages are 3x = 15 years, 7x = 35 years and 5x = 25 years respectively.
Answer: C
Question: The diagonal of a square is the height in an equilateral triangle. If the side of the square is x, what is the side of the equilateral triangle in terms of x?
A.√(2/3) × x
B.2/√3 × x
C.√3x
D.√(8/3) × x
Answer: D.√(8/3) × x
Explanation: The diagonal of the square
x* sqrt(2)
If that's the altitude of the equilateral triangle, the formula for which is side * sqrt(3)/2
Side is 2 sqrt(2)* x/ sqrt(3)
Answer: (Option D)
Question: What approximate value should come in place of the question mark (?) in the following equation’?
3 3⁄5 of 157.85 + 39% of 1847 = ? – 447.30
A.1200
B.1500
C.1600
D.1800
Answer: D.1800
Explanation: ? ≈ 18⁄5 × 160 + 40⁄1000 × 1850 + 450
≈ 576 + 740 + 450 ≈ 1760 ≈ 1800
Answer D
Question: Calculate the positive root of the polynomial (x - 1)(x - 2)(x - 3)(x - 4)- 63.
A.5+√37/2
B.4+√37/2
C.3+√37/2
D.2+√37/2
Answer: A.5+√37/2
Explanation: Note that
(x - 1)(x - 2)(x - 3)(x - 4) - 63 = [(x - 2)(x - 3)][(x -1)(x - 4)] - 63
= (x2-5x + 6)(x2 - 5x + 4) - 63
= [(x2 - 5x + 5 + 1)(x2 - 5x + 5 -1)] - 63
= [(x2 - 5x + 5)2 - 1] - 63
= (x2 -5x + 5)2 - 64
= (x2 - 5x + 5 + 8)(x2 -5x + 5 - 8)
= (x2 - 5x + 13)(x2- 5x - 3):
The polynomial x2 - 5x + 13 has no real roots, while the polynomial x2 -5x - 3 has roots
x=5+-√37/2.
since 5-√37/2<0,
the only positive root is 5+√37/2
correct answer A
Question: On a sum of money, the S.I. for 2 years is Rs. 660, while the C.I. is Rs. 696.30, the rate of interest being the same in both the cases. The rate of interest is?
A.22
B.99
C.27
D.11
Answer: D.11
Explanation: Difference in C.I. and S.I for 2 years = (696.30 - 660) = Rs. 36.30.
S.I for one year = Rs. 330.
S.I. on Rs. 330 for 1 year = Rs. 36.30
Rate = (100 * 36.30)/(330 * 1) = 11%.Answer: D
Question: In 1990 a total of 100 earthquakes occurred worldwide, some but not all of which occurred in Asia. If 20 of these earthquakes occurred in Asia, which of the following represents the ratio of the number of earthquakes that occurred in Asia to the number that did NOT occur in Asia?
A.1/7
B.1/6
C.1/2
D.1/4
Answer: D.1/4
Explanation: We're given a couple of facts to work with:
1) There were a total of 100 earthquakes
2) Of those earthquakes, 20 of them occurred in Asia
We're asked for the ratio of the number of earthquakes that occurred IN ASIA to the number of earthquakes that DID NOT occur in Asia.
Thus, there were 80 earthquakes that DID NOT occur in Asia....
The answer to the question is 20/80 ie. 1/4
Answer : D
Question: Danya prepared 4 different letters to 4 different addresses. For each letter, she prepared one envelope with its correct address. If the 4 letters are to be put into the four envelopes at random, what is the probability that only one letter will be put into the envelope with its correct address?
A.1/24
B.1/8
C.1/4
D.1/3
Answer: D.1/3
Explanation: Total Danya# of ways - 4! = 24.
Desired:
A-Mapped to the only correct address----------x 1 way only
B-Mapped to other two incorrect addresses - x 2 ways
C-Mapped to other two incorrect addresses - x 2 ways
D-Mapped to other two incorrect addresses - x 2 ways
Therefore, 1*2*2*2/24 = 1/3.?
Question: Excluding stoppages, the speed of a train is 67 kmph and including stoppages it is 51 kmph. Of how many minutes does the train stop per hour?
A.82
B.17
C.14
D.82
Answer: C.14
Explanation: Explanation:
T =16/67 * 60 = 14
Answer: Option C
Question: What was the day of the week on 28th May,2006 ?
A.Thursday
B.Friday
C.Saturday
D.Sunday
Answer: D.Sunday
Explanation: Solution
28 May,2006 =(2005 years + Period from 1.1.2006 to 28.5.2006)
Odd days in 1600 years = 0
Odd days in 400 years = 0
5 years =(4 ordinary years + 1 leap year)=(4 x 1 + 1 x 2) odd days
=6 odd days
Jan. Feb. March April May
(31 + 28 + 31 + 30 + 28) = 148 days =(21 weeks + 1 day)
= 1 odd day
Total number of odd days = (0 + 0 + 6 + 1)=7 = 0 odd day.
Given day is Sunday. Answer D
Question: Two goods trains each 250 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
A.24 sec
B.88 sec
C.48 sec
D.18 sec
Answer: A.24 sec
Explanation: Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 250 + 250 = 500 m.
Required time = 500 * 6/125 = 48 sec.
Answer:A
Question: If the perimeter of a rectangular park is 1000 m, its length when its breadth is 200 m is?
A.50
B.100
C.200
D.300
Answer: D.300
Explanation: 2(l + 200) = 1000 => l = 300 m Answer: D
Question: Two unbiased coins are tossed. What is probability of getting at most one tail ?
A.12
B.13
C.32
D.34
Answer: D.34
Explanation: Explanation:
Total 4 cases = [HH, TT, TH, HT]
Favourable cases = [HH, TH, HT]
Please note we need atmost one tail, not atleast one tail.
So probability = 3/4
Answer: D
Question: A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 according to the following constraints. The first digit cannot be 0 or 1, the second digit must be 0 or 1, and the second and third digits cannot both be 0 in the same code. How many different codes are possible?
A.144
B.152
C.160
D.168
Answer: B.152
Explanation: The first digit can be filled in 8 ways
For second digit , it can either be 0 or 1
Case 1 -
If second digit is 1 ,Third digit can take 10 values
number of codes = 8 * 1 * 10 = 80
Case 2 -
If second digit is 0,Third digit can take 9 values ( Third digit can't be zero)
number of codes = 8 * 1 * 9= 72
Total number of codes = 152
Answer B
Question: A sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 45 paisa and Z gets 30 paisa. If the share of Y is RS. 27, what is the total amount?
A.178
B.105
C.176
D.159
Answer: B.105
Explanation: x:y:z = 100:45:30
20:9:6
9 --- 27
35 --- ? => 105
Answer: B
Question: A monkey ascends a greased pole 10 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.10th minute
B.21st minute
C.17th minute
D.22nd minute
Answer: C.17th minute
Explanation: The money is climbing 1meter in 2min. This pattern will go on till he reaches 10meters. I mean this will continue for first 8*2=16mins. he would have reached 8meters. After that he will climb 2meters and he will reach the pole. So total time taken = 16 + 1 = 17mins.
So, asnwer will be C
Question: Which of the following equations has a solution in common with x^2 - 7x + 10 = 0 ?
A.x^2 - 3x - 10 = 0
B.4x^2 + 9x + 2 = 0
C.4x^2 + 6x + 2 = 0
D.x^2 + 10x + 25 = 0
Answer: A.x^2 - 3x - 10 = 0
Explanation: Given : x^2 - 7x + 10 = 0 => (x-2) (x-5) = 0 => 2 and 5 are the roots..
A. x^2 - 3x - 10 = 0 => (x+2) (x-5)
B. 4x^2 + 9x + 2 = 0 => (4x+1) (x+2)
C. 4x^2 + 6x + 2 = 0 => (2x+1) (2x+2)
D. x^2 + 10x + 25 = 0 => (x+5) (x+5)
None of the answer equations have exactly both the same roots as the question equation, but at least one of them does share one of the two roots.
So IMO "A" is correct answer... because it shares the one root (part of the solution), 5, from the (x-5) portion of its simplification.
Question: Find the difference between the local value and face value of 5 in the numeral 475240 is
A.4990
B.4890
C.4995
D.4885
Answer: C.4995
Explanation: Explanation:
(Local value of 5) - (Face value of 5)
= (5000 - 5) = 4995
Answer: Option C
Question: In a college, the ratio of the number of boys to girls is 8 : 5. If there are 100 girls, the total number of
students in the college is
A.420
B.520
C.620
D.260
Answer: D.260
Explanation: Explanation:
Let the boy are 8x and Girls are 5x
=> 5x = 100
=> x = 20
Total students = 8x+5x = 13x = 13(20) = 260
Answer: D
Question: There are 4 identical pens and 7 identical books. In how many ways can a person select at least one object from this set?
A.11
B.12
C.39
D.(2^4 - 1)(2^7 -1)
Answer: C.39
Explanation: 7 items can be chosen in 8 ways- 0,1,2..7 at a time
similarly 4 items can be chosen way will be 5- choosing 0, choosing 1.. choosing 4
total ways = 8*5=40..
But we are looking for AT LEAST 1, so subtract 1 way when both are 0..
ans 40-1=39.
ANSWER:C
Question: An article is bought for Rs.765 and sold for Rs.1000, find the gain percent?
A.30.6%
B.30.5%
C.30.7%
D.30.8%
Answer: C.30.7%
Explanation: 765 ---- 235
100 ---- ? => 30.7%
Answer:C
Question: If x/y = 2 and (a - x)/(3b - y) = 2, then the value of a/b is?
A. –3
B. -2
C. 6
D. 2
Answer: C. 6
Explanation: x = 2y
a - 2y = 2(3b - y)
a - 2y = 6b - 2y
a = 6b
a/b = 6
Answer: C
Question: At what rate percent on simple interest will Rs.750 amount to Rs.900 in 5 years?
A.5%
B.3 1/2%
C.4%
D.5 1/2 %
Answer: C.4%
Explanation: Explanation:
150 = (750*5*R)/100
R = 4%
ANSWER IS C
Question: A can give B 100 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?
A. 111.12 m
A.111.12 m
B.221.12 m
C.271.12 m
D.611.12 m
Answer: A.111.12 m
Explanation: Explanation:
A runs 1000 m while B runs 900 m and C runs 800 m.
The number of meters that C runs when B runs 1000 m,
= (1000 * 800)/900 = 8000/9 = 888.88 m.
B can give C = 1000 - 888.88 = 111.12 m.
Answer:A
Question: A money lender lends Rs.2000 for six months at 20% p.a. rate. It the interest is reckoned quarterly than find the amount given after time limit.
A.2205
B.3387
C.2882
D.2997
Answer: A.2205
Explanation: A = 2000(21/20)2 = 2205
Answer: A
Question: A number whose fifth part increased by 4 is equal to its fourth part diminished by 4 is ?
A.160
B.180
C.200
D.220
Answer: A.160
Explanation: Answer
Let the number be N.
Then, (N/5) + 4 = (N/4) - 4
â‡’ (N/4) - (N/5) = 8
â‡’ (5N - 4N)/20 = 8
âˆ´ N = 160
Option: A
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when a boy gets any no. of prizes?
A.53
B.58
C.64
D.69
Answer: C.64
Explanation: Ans.(C)
Sol. In this case, repetitions are allowed, so all the three prizes can be given in 4 ways, i.e. (4 x 4 x 4) ways = 43 ways = 64 ways Or nr ways = 43 ways = 64 ways
Question: A bullet train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the bullet train is 54 km/hr, what is the length of the platform?
A.240 m
B.220 m
C.260 m
D.224 m
Answer: A.240 m
Explanation: A
240 M
Speed = 54 x 5/18 = 15 m/s
Length of the bullet train = (15 x 20)m = 300 m.
Let the length of the platform be x metres.
Then, (x + 300)/36 = 15
--> x + 300 = 540
x = 240m.
Question: The timing of a college is from 12 p.m to 5.00 p.m. Five lectures are held in the given duration and a break of 5 minutes after each lecture is given to the students. Find the duration of each lecture.
A.56 minutes
B.45 minutes
C.30 minutes
D.48 minutes
Answer: A.56 minutes
Explanation: Explanation:
Total time a student spends in college = 5 hours 00 minutes = 300 minutes
As there are 5 lectures, the number of breaks between lectures is 4. Total time of the break = 20 minutes
Hence, the duration of each lecture is = (300 â€“ 20)/5
= 56 minutes
ANSWER A
Question: If n is a positive integer and the product of all the integers from 1 to n, inclusive, is a multiple of 8, what is the least possible value of n?
A.7
B.4
C.5
D.3
Answer: B.4
Explanation: We need 3 factors of 2, so n must be at least 4. Therefore, the answer is B.
Question: A third of Paul's marks in Mathematics exceeds a half of his marks in English by 30. If he got 240 marks in the two subjects together, how many marks did he get in English?
A.50
B.40
C.45
D.60
Answer: D.60
Explanation: Let Paul's marks in Mathematics and English be x and y respectively.
Then, x/3 - y/2 = 30, the LCM of 3,2 is 6 by cross multiplying we get 2x - 3y = 180 -- (I)and we know (x + y = 240) * 2 ==>
2x +2y = 480 --(II)
subtract (I) from (II) we get 5y = 300 ==> y = 60.
so Paul's marks in English is 60.
The correct answer is option D) 60.
Question: If A : B : C = 3 : 4 : 7, then what is the ratio of (A / B) : (B / C) : (C / A)?
A.63 : 48 : 196
B.66 : 49 : 190
C.56 : 40 : 186
D.46 : 38 : 160
Answer: A.63 : 48 : 196
Explanation: EXPLANATION:
Hint: If a = kb for some constant k, then we can say that a is directly proportional to b.
A : B : C = 3 : 4 : 7
Assume, A = 3 k, B = 4 k, C = 7 k
Therefore,
A/B	=	(3k)/(4K)	,	B/C	=	(4k)/(7K)	,	C/A	=	(7k)/(3K)
A/B	=	(3)/(4)	,	B/C	=	(4)/(7)	,	C/A	=	(7)/(3)
L.C.M of 3, 4, 7 is 84
(3 x 84) / 4 = 63
(4 x 84) / 7 = 48
(7 x 84) / 3 = 196
Ratio of (A/B) : (B/C) : (C/A) = 63:48:196
ANSWER IS A
Question: In how many ways 4 boys and 1 girls can be seated in a row so that they are alternate.
A.144
B.288
C.24
D.256
Answer: C.24
Explanation: Solution: Let the Arrangement be,
B B B B G
4 boys can be seated in 4! Ways.
Girl can be seated in 1! Ways.
Required number of ways,
= 4!*1! = 24.
Answer: Option C
Question: How long will it take for a sum of money to grow from Rs.5000 to Rs.20,000, if it is invested at 10% p.a simple interest?
A.30 years
B.64 years
C.72 years
D.56 years
Answer: A.30 years
Explanation: In this case, Rs. 5000 has become Rs.20,000.
Therefore, the interest earned = 20,000 – 5000 =15000
Interest for Rs 5000 @ 10% for 1 year = 500
500 - 1
15000 - ? => 30 years
Answer : A
Question: Find the area of the quadrilateral of one of its diagonals is 20 cm and its off sets 9 cm and 6 cm?
A.128 cm2
B.150 cm2
C.172 cm2
D.177 cm2
Answer: B.150 cm2
Explanation: 1/2 * 20(9 + 6)
= 150 cm2
Answer:B
Question: By selling an article for $100 a man gains $20 then his gain%?
A.25%
B.30%
C.50%
D.20%
Answer: A.25%
Explanation: S.P. = $100
Gain = $20
C.P. = 100-20 = 80
Gain% = 20/80 * 100 = 25%
Answer is A
Question: 1, 2, 9, 24, 120, 36,?
A.4040
B.5040
C.3040
D.2040
Answer: B.5040
Explanation: 1!=1
2!=2
3^2=9
4!=24
5!=120
6^2=36
and according to the sequence now
7!=5040
ANSWER:B
Question: A cab driver 5 days income was $200, $150, $750, $400 , $500. Then his average income is?
A.$420
B.$410
C.$400
D.$390
Answer: C.$400
Explanation: avg = sum of observations/number of observations
avg income=(200+150+750+400+500)/5 = 400
Answer is C
Question: At a school, three-fifths of the male students and two-thirds of the female students speak a foreign language. If the number of males is equal to the number of females, what fraction of the students speak a foreign language?
A.17/30
B.19/30
C.11/15
D.7/15
Answer: B.19/30
Explanation: Let x be the number of students in the school.
The number of males who speak a foreign language is (3/5)(1/2)x = (3/10)x
The number of females who speak a foreign language is (2/3)(1/2)x = (1/3)x
The total number of students who speak a foreign language is (3/10)x + (1/3)x = (19/30)x
The answer is B.
Question: In a urban village of india named "owlna" , 90% people have refrigerator , 86% people have television , 80% people got computers and 80% got Air-conditionor. how many people(minimum) got all these luxury.
A.23%
B.36%
C.30%
D.34%
Answer: B.36%
Explanation: B
10%
100 - [ (100-90)+(100-86)+(100-80) +(100-80)]
=100-(10+14+20+20)
=100-64
Question: If a man lost 1% by selling oranges at the rate of 16 a rupee at how many a rupee must he sell them to gain 44%?
A.12
B.14
C.7
D.11
Answer: D.11
Explanation: 99% ---- 16
144% ---- ?
99/144* 16 = 11
Answer: D
Question: If a farmer wants to plough a farm field on time, he must plough 340 hectares a day. For technical reasons he ploughed only 85 hectares a day, hence he had to plough 2 more days than he planned and he still has 40 hectares left. What is the area of the farm field and how many days the farmer planned to work initially?
A.280
B.490
C.720
D.435
Answer: A.280
Explanation: Let x be the number of days in the initial plan. Therefore, the whole field is 340â‹…x hectares. The farmer had to work for x+2 days, and he ploughed 85(x+2) hectares, leaving 40 hectares unploughed. Then we have the equation:
340x=85(x+2)+40
255x=210
x=0.823
So the farmer planned to have the work done in 6 days, and the area of the farm field is 340(0.823)=280 hectares
correct answer A
Question: What percent is 120 of 90?
A.133 1/3 %
B.132 1/3%
C.132 2/3%
D.132 2/5%
Answer: A.133 1/3 %
Explanation: 120/90 = 4/3
4/3 × 100 = 400/3 = 133 1/3 %
A)
Question: A boy sells a horse for Rs.800 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse?
A.860
B.880
C.900
D.920
Answer: A.860
Explanation: CP = SP + 1CP = SP - g
800 + x = 980 - 2x
3x = 180 => x = 60
CP = 800 + 60 = 860
A
Question: How many bricks each measuring 25cm x 11.25cm x 6cm, will be needed to build a wall 8m x 6m x 22.5m
A.5600
B.600
C.6400
D.7200
Answer: C.6400
Explanation: Explanation:
no. of bricks= volume of the wall/volume of 1 brick = (800 x 600 x 22.5) / (25 x 11.25 x 6) = 6400
Answer: C
Question: 79 laboratories raise the bacterium, the laboratory have 48 culture dishes on average, which has about 25,070 bacteria each. How many bacteria are there approximately?
A.10^7
B.10^8
C.10^9
D.10^10
Answer: B.10^8
Explanation: 79 laboratories raise the bacterium, the laboratory have 48 culture dishes on average, which has about 25,070 bacteria each. How many bacteria are there approximately?
A. 10^7
B. 10^8
C. 10^9
D. 10^10
E. 10^11
-> Due to approximately, 79=80, 48=50, 25,070=25,000 are derived, which makes (79)(48)(25,075)=(80)(50)(25,000)=10^8. The answer is B.
Question: A and B can do a piece of work in 10 days, while B and C can do the same work in 15 days and C and A in 25 days. they started working together, after 4 days A left. After another 4 days B left. In how many days C can finish the remaining work?
A.16
B.32
C.64
D.96
Answer: D.96
Explanation: Let the rates of A, B and C be a, b, and c respectively.
A and B can do a piece of work in 10 days: a + b = 1/10;
B and C can do the same work in 15 days: b + c = 1/15;
C and A can do the same work in 25 days: c + a = 1/25.
Sum the above 3 equations: 2(a + b + c) = 31/150 --> a + b + c = 31/300
Subtract a + b = 1/10 from above to get c = 1/300.
For 4 days all 3 worked and completed 4*(a + b + a) = 124/300 of the work.
For the next 4 days B and C worked and they completed 4(b + c) = 4/15 = 80/300 of the work.
So, by the time C is left alone 1 - (124/300 + 80/300) = 96/300 of the work is left to be completed by C alone.
Time = Job/Rate = (96/300)/(1/300) = 96 days.
Answer: D
Question: What is the smallest integer k for which 64^k > 4^16?
A.4
B.5
C.6
D.7
Answer: C.6
Explanation: 64^k > 4^16
4^(3k) > 4^16
3k > 16
k = 6
The answer is C.
Question: Find the average of all prime numbers between 30 and 50?
A.24.7
B.39.8
C.12.3
D.41.3
Answer: B.39.8
Explanation: There are five prime numbers between 30 and 50.
They are 31,37,41,43 and 47.
Therefore the required average=(31+37+41+43+47)/5 = 199/5 = 39.8.
Ans: B
Question: The average of first six prime numbers greater than 3 is?
A.16
B.10
C.12
D.19
Answer: C.12
Explanation: 5 + 7 +11 + 13 + 17 + 19 = 72/6 = 12
Answer: C
Question: The average expenditure of a man for the first five months is Rs.60 and for the next seven months it is Rs.130. If he saves Rs.290 in that year, his monthly average income is :
A.Rs.125
B.Rs.150
C.Rs.165
D.Rs.170
Answer: A.Rs.125
Explanation: Explanation:
Total income = Rs.(60Ã—5+130Ã—7+290)=Rs.1500
Average monthly income
= Rs. (1500/12)=Rs.125
Correct Option: A
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 50 sq. feet, how many feet of fencing will be required?
A.34
B.40
C.25
D.88
Answer: C.25
Explanation: We have: l = 20 ft and lb = 50 sq. ft.
So, b = 2.5 ft.
Length of fencing = (l + 2b) = (20 + 5) ft = 25 ft.
ANSWER:C
Question: A bag contains 3 red, 4 black and 2 white balls. What is the probability of drawing a red and a white ball in two successive draws, each ball being put back after it is drawn?
A.2/27
B.1/9
C.1/3
D.4/27
Answer: D.4/27
Explanation: P=2∗3/9∗2/9=4/27
We are multiplying by 2 as there are two possible wining scenarios RW and WR.
Answer: D.
Question: A car rental company charges for mileage as follows: 9 dollars per mile for the first n miles and 10 dollars per mile for each mile over n miles. How much will the mileage charge be, in dollars, for a journey of d miles, where d > n ?
A.d-n
B.6d-n
C.10d-n
D.8d-n
Answer: C.10d-n
Explanation: Total Distance in miles = d
Millage Charge = 9n + (d-n) 10
9n --> For the first n Miles
(d-n)10--> Total no of miles after traveling the first n miles is d-n and the rate after n miles is 10 .
If we solve the equation , We will get 10d-n
Answer : C