RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow?
A.2/29
B.2/26
C.2/21
D.2/22
Answer: C.2/21
Explanation: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = ³C₂/¹⁵C₂ = (3 * 2)/(15 * 14) = 1/35
Probability that both are yellow = ²C₂/¹⁵C₂ = (2 * 1)/(15 * 14) = 1/105
Probability that one blue and other is yellow = (³C₁ * ²C₁)/¹⁵C₂ = (2 * 3 * 2)/(15 * 14) = 2/35
Required probability = 1/35 + 1/105 + 2/35
= 3/35 + 1/105 = 1/35(3 + 1/3)
= 10/(3 * 35) = 2/21
Answer:C
Question: A train running at 54 kmph takes 20 seconds to pass a platform. Next it takes.12 sec to pass a man walking at 6 kmph in the same direction in which the train is going. Find the length of the train and the length of the platform
A.120m
B.125m
C.132m
D.140m
Answer: D.140m
Explanation: Explanation:
Let the length of train be x metres and length of platform be y metres.
Speed of the train relative to man = (54 - 6) kmph = 48 kmph
= 48×(5/18) m/sec = 40/3 m/sec.
In passing a man, the train covers its own length with relative speed.
Length of train = (Relative speed × Time) = ( 40/3)×12 m = 160 m.
Also, speed of the train = 54 ×(5/18)m / sec = 15 m / sec.
(x+y)/15 = 20 <=> x + y = 300 <=> Y = (300 - 160) m = 140 m.
Answer: Option D
Question: The radius of a circular wheel is 1.75 m, how many revolutions will it make in traveling 1 km?
A.1000
B.2777
C.2976
D.2988
Answer: A.1000
Explanation: 2 * 22/7 * 1.75 * x = 11000
x = 1000
Answer: A
Question: On the xy-plane, each point on circle C has coordinates such
that x 0 and y 0. If the center of circle C is the point (3; 12),
what is the maximum possible area of C?
A. 6
B. 9
C. 24
D. 32
Answer: D. 32
Explanation: I think that theintentof this question is that the circle will have NO CO-ORDINATES that fit the following 2 forms: (0, Y) or (X, 0). In real basic terms, this circle will NEITHER touch (nor cross) the X-axis NOR will it touch (nor cross) the Y-axis.
With a center at (3,8), the longest possible radius would ALMOST touch the X-axis, so the radius would be a little less than 3.
If the radius WAS 3 exactly, then the area would be 9pi, which is approximately 28.26
Since the circle CAN'T touch the X-axis, the area has to be LESS than approximately 28.26
As it's written, none of the answers is clearly the correct one.
D
Question: The distance between two stars is 6.52 × 10^5 light years. What is the distance between the two stars in parsecs? (1 parsec = 3.26 light years)
A.2 × 10^5
B.4 × 10^6
C.5 × 10^7
D.7 × 10^7
Answer: A.2 × 10^5
Explanation: 6.52 × 10^5 ly / (3.26 ly/parsec) = 2 x 10^5 persec
The answer is A.
Question: The distance between two planets is 3.02 × 10^6 light years. What is the distance between the two planets, in parsecs? (1 parsec = 3.26 light years)
A. 9.3 × 10^5
B. 9.9 × 10^6
C. 9.3 × 10^7
D. 9.9 × 10^7
Answer: A. 9.3 × 10^5
Explanation: 3.02*10^6 light years = 3.02*10^6/3.26 parsecs.
3.02/3.26 is a little bit less than 1, something like 0.9, thus 3.02*10^6/3.26 = ~0.93*10^6 = 9.3*10^5.
Answer: A.
Question: A boy rides his bicycle 10 km at an average speed of 12 km/hr and again travels 12 km at an average speed of 10 km/hr. His average speed for the entire trip is approximately?
A.12.9
B.10.8
C.26.2
D.17.8
Answer: B.10.8
Explanation: Total distance traveled = 10 + 12 = 22 km /hr.
Total time taken = 10/12 + 12/10 = 61/30 hrs.
Average speed = 22 * 30/61 = 10.8 km/hr.
Answer: B
Question: In 1995, there are 28 days in February and there are 365 days in the year. In 1996, there are 29 days in February and there are 366 days in the year. If the date March 15, 1995 is a Monday, then which one of the following would the date March 15, 1996 be?
A.Monday
B.Tuesday
C.Friday
D.Wednesday
Answer: D.Wednesday
Explanation: From the information given,March 15, 1996 is 366 days after March 15, 1995.
366 days = 52 weeks and 2 more days. Therefore if March 15, 1995 is a Monday, then March 15, 1996 is Monday + 2 days = Wednesday
Answer: D
Question: 15c6+15c7+16c8=== 17cx
find x?
A.6
B.7
C.8
D.9
Answer: D.9
Explanation: 15c6=5005
15c7=6435
16c8=12870
15c6+15c7+16c8=17c9
ANSWER:D
Question: Find the value of X, Y by solving the below equations
X + Y = 16
X - Y = 14
A.16, 0
B.14, 2
C.15, 1
D.13, 3
Answer: C.15, 1
Explanation: X + Y = 16 ---(I)
X - Y = 14 -----(II) by adding (I) and (II)
------------
2X = 30 ==> X = 30/2 = 15
By Replacing the value of X in (I) we get 15 + Y = 16 ==>
Y = 16 - 15 = 1.
So, X = 15, Y = 1
Answer C) 15, 1
Question: A man's speed with the current is 16 km / hr and the speed of the current is 2 km / hr. The man's speed against the current is
A.8.5 km / hr
B.9 km / hr
C.12 km / hr
D.12.5 km / hr
Answer: C.12 km / hr
Explanation: Sol.
Man's rate in still in water = (16 - 2) km / hr = 14 km / hr.
Man's rate against the current = (14 - 2) km / hr = 12 km / hr.
Answer C
Question: If $ 5,000 is invested in an account that earns 4% interest compounded semi-annually, then the interest earned after one year would be how much greater than if the $ 5,000 had been invested at 8% simple yearly interest?
A.$ 4
B.$ 8
C.$ 12
D.$ 16
Answer: A.$ 4
Explanation: Solution
Amount (CI) = P+(1+r/n)^nt = 5000+(1+0.04/2)^2= 5404
Amount (SI) = P+PTR/100 = 5000+(5000*1*4/100)=5400
Difference = 5404-5400=4 $
A
Question: The price of a T.V. set worth Rs. 12000 is to be paid in 20 installments of Rs. 1200 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be?
A.29997
B.10800
C.27098
D.19000
Answer: B.10800
Explanation: Money paid in cash = Rs. 1200
Balance payment = (12000 - 1200) = Rs. 10800 .Answer:B
Question: If a boat goes 7 km upstream in 42 minutes and the speed of the stream is 3 kmph,then the speed of the boat in still water is :
A.4.2 km/hr
B.9 km/hr
C.13 km/hr
D.21 km/hr
Answer: C.13 km/hr
Explanation: Solution
Rate upstream =(7/42x60)kmph = 10 kmph.
Speed of stream = 3 kmph.
Let speed in still water be x km/hr.Then, speed upstream =( x-3 ) km/hr.
∴ x - 3 = 10 or x = 13 km/hr. Answer C
Question: The cost per unit of electricity during a 4 year period is as follows:
Year 1, $2 per unit;
Year 2, $3 per unit;
Year 3, $4 per unit;
Year 4, $5 per unit.
If a factory spent equal dollars on electricity each year, what was the average cost of a unit of electricity during the 4 year period?
A.$3.82
B.$3.62
C.$5.12
D.$3.12
Answer: D.$3.12
Explanation: Let money spent each year = $60
Units bought first year = 30
Units bought second year = 20
Units bought third year = 15
Units bought fourth year = 12
Total number of units = 77
Total money spent = 60*4 = 240
Average = 240/77 = 3.12
Answer : D
Question: If x and y are odd integers, which of the following must always be a non-integer
A.xy/4
B.xy
C.x/y
D.y/x
Answer: A.xy/4
Explanation: as X and Y are odd, multiplication of x and y would result in odd integer
(Odd Integer)/4 will always be non integer
A
Question: A person walking at the rate of 5 km/hr crosses a bridge in 15 minutes. Find the length of the bridge
A.1200
B.1250
C.1224
D.1300
Answer: B.1250
Explanation: speed = (5x5/18)m/sec
= 25/18 m/sec.
Dist 15 min(covered) =(25/18 x 15 x 60) ==> 1250 m
ANSWER B
Question: A car travels at a speed of 12 miles per hour. How far will it travel in 5 hours?
A.50 miles
B.60 miles
C.72 miles
D.22 miles
Answer: B.60 miles
Explanation: During each hour, the car travels 65 miles. For 5 hours it will travel
12 + 12 + 12 + 12 + 12 = 5 *12 = 60 miles correct answer B
Question: If in a cricket one day match, there were no wide balls, no wides, no extras and no overthrows.
What is the maximum number of runs that a batsman can score in 35 overs in an ideal case scenario?
A.1158
B.1651
C.1653
D.1654
Answer: A.1158
Explanation: Solution:
1158
Explanation:
For an ideal case, the batsman will hit a six on each ball. But if he hits six on the last ball of the over, the strike will change in the next over. Thus, the best he can do in the last ball is run 3 runs so that he retains the strike even in the next over. Thus the total runs that he can score in each over:
6 * 5 + 3 = 33
But this will have to go like it only till the 34th over. In the 35th over, he can hit a six in the last ball as well as that will be the last ball of his destination.
Thus runs for the 35th over will be 6 * 6 = 36.
Hence the maximum runs = 33 * 34 + 36 = 1158
Answer A
Question: A box contains 4 yellow balls and 6 black balls. One by one, every ball is selected at random without replacement. What is the probability that the fourth ball selected is black?
A.2/3
B.1/2
C.5/8
D.3/5
Answer: D.3/5
Explanation: Each ball has an equal chance (1/10) of being selected fourth.
The probability that a black ball is selected fourth is 6/10 = 3/5.
The answer is D.
Question: The variables m and n are positive integers. When m is divided by 18, there is a remainder of 12, and when n is divided by 24, there is a remainder of 14. Which of the following are possible values of m + n?
I. 50
II. 70
III. 92
A.I only
B.III only
C.I and II
D.I​ and III
Answer: D.I​ and III
Explanation: m = 18k + 12 --> Values are 12, 30, 48, 66, 84
n = 24k + 14 --> Values are 14, 38, 62, 86
I. 50 --> 12 + 38 --> Possible
II. 70 --> Not possible
III. 92 --> 30 + 622 --> Possible
Answer: D
Question: Lally's internet provider offers unlimited traffic which costs $0.5 per day charged off at 12 a.m. The service is discontinued when client's debt exceeds $5. If today in the morning Lally makes a payment of $7, for how many days, including today, will she be connected to the internet without any additional payments, given her initial balance was $0?
A. 15
B. 24
C. 25
D. 26
Answer: C. 25
Explanation: day 0- payment of $7 is made in the morning (after 12 am midnight)
day 1 onwards(after 12 am midnight) internet service will begin and will run for 7*2=14 days i.e. at the end of day 15 balance will be zero.
now Lally can still use the internet till her debt reaches $5 which means total of 5*2=10 days.
now the question states for how many days, including today, will she be connected to the internet without any additional payments i.e. we will have to include day0 also in our final answer. therefore total no. of days =1+14+10=25=C
Question: A fair 2 sided coin is flipped 7 times. What is the probability that tails will be the result at least twice, but not more than 7 times?
A.119/128
B.120/113
C.114/210
D.121/141
Answer: A.119/128
Explanation: at least twice, but not more than 7 timesmeans exactly 2 times, 3 times, 4 times, 5 times, 6 times, 7 times
The probability of getting exactly k results out of n flips is nCk/2^n
7C2/2^7+7C3/2^7+7C4/2^7+7C5/2^7+7C6/2^7=119/128
Option: A
Question: A family has two children. find the probability that both the children are girls given that at least
one of them is a girl?
A.2/5
B.1/3
C.2/7
D.3/5
Answer: B.1/3
Explanation: Let b stand for boy and g for girl. The sample space of the experiment is
S = {(g, g), (g, b), (b, g), (b, b)}
Let E and F denote the following events :
E : ‘both the children are girls’
F : ‘at least one of the child is a girl’
Then E = {(g,g)} and F = {(g,g), (g,b), (b,g)}
Now E n F = {(g,g)}
Thus P(F) = 3/4
and P (E n F )= 1/4
Therefore P(E|F) = P(E ∩ F)/P(F) = (1/4)/(3/4) = 1/3
B
Question: The cricket team of 11members is 26yrs old & the wicket keeper is 3yrs older. If the ages ofthese 2are excluded, the average age of the remainingplayers is 1 year less than the average age of the whole team. What is the average age of the team ?
A.18
B.21
C.23
D.25
Answer: C.23
Explanation: Let the average age of the whole team be x years.
11x - (26 + 29) = 9 (x - 1)
=> 11x - 9x = 46
=> 2x = 46
=> x = 23.
So, average age of the team is 23 years.
C
Question: 2 men catch 2 fish in 2 minutes. At this rate, how many men could catch 500 fish in 500 minutes?
A.2
B.4
C.6
D.500
Answer: A.2
Explanation: 2 men.....there are no other!!!!
Question: Right triangleXYZ is the base of the prism in the figure above. If XY=XZâˆš4 and the height of the prism is 5, what is the volume of the prism?
A.15/2
B.6
C.4
D.2/5
Answer: A.15/2
Explanation: Volume of prism = Area of base * height = 1/2* (square root of 3) * (square root of 3)*5 =15/2
Answer: A
Question: A tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume. If 4,000 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride?
A.6.85%
B.7.25%
C.7.76%
D.8.33%
Answer: D.8.33%
Explanation: The amount of sodium chloride is 0.05*10,000 = 500 gallons
500/6000 = 1/12 which is about 8.33%
The answer is D.
Question: If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 2 years the amount to be paid is?
A.1227
B.2088
C.26788
D.8112
Answer: D.8112
Explanation: A = 7500(26/25)2 = 8112
Answer: D
Question: The value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 24,000 is made?
A.1,20,005
B.1,20,000
C.1,20,001
D.1,20,002
Answer: B.1,20,000
Explanation: The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000
SP such that a profit of Rs. 24,000 is made = 96,000 + 24,000 = Rs. 1,20,000
Answer: B
Question: In a certain game, you perform three tasks. You flip a quarter, and success would be tails. You roll a single die, and success would be a six. You pick a card from a full playing-card deck, and success would be picking a spades card. If any of these task are successful, then you win the game. What is the probability of winning?
A.1/48
B.11/16
C.11/12
D.5/16
Answer: B.11/16
Explanation: First lets get the overview
Event 1(A) = Flipping the quarter( Probability of both winning/loosing = 1/2)
Event 2(B) = Rolling a dice( Probability of winning = 1/6 ;Probability of loosing= 1 - 1\6 =5\6)
Event 3(C) = Drawing a card( SPADES) Probability of winning = 13/52=3/4 ;Probability of loosing= 1 - 3/4 =1/4)
So now as above we have three events A,BC.
1st method(This is lengthy method)
Possible cases in which it's a win( the highlighted green event is a win and red is loose.
1.ABC= 1/2*5/6*3/4
OR
2.ABC= 1/2*1/6*3/4
OR
3.ABC= 1/2*5/6*1/4
OR
4.ABC= 1/2*1/6*3/4
OR
5.ABC= 1/2*5/6*1/4
OR
6.ABC= 1/2*5/6*1/4
OR
7.ABC= 1/2*1/6*1/4
As we now OR means add
Adding up all of them we'll get the probability of winning ie 11/16
Answer : B
Question: If a code word is defined to be a sequence of different letters chosen from the 8 letters A, B, C, D, E, F, G, AND H, what is the ratio of the number of 5-letter code words to the number of 4-letter code words?
A.4
B.8
C.5
D.10
Answer: A.4
Explanation: Method #1: Using the permutation formula
# of 5 letter code words:
nPr = n! / (n – r)! = 8! / (8 – 5)! = 8*7*6*5*4
# of 4 letter code words:
nPr = 8! / (8 – 4)! = 8*7*6*5
# of 5 words / # of 4 words = (8*7*6*5*4)/(8*7*6*5) = 4 = 4
A
Question: A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days,then B alone could do it in :
A.15 days
B.20 days
C.25 days
D.30 days
Answer: C.25 days
Explanation: Solution
(A +B)’s 1 day’s work =1/50; C's 1 day's work = 1/50
(A+B+C)’s 1 day’s work = (1/10+1/50)=6/50=3/25…..(i)
Also,A’s 1 day’s work =(B +C)’s 1 day’s work ……(ii)
From (i) and (ii),we get : 2 × (A’s 1 day’s work) =3/25
⇒ A’s 1 day’s work = 3/50
∴ B’s 1 day’s work = (1/10-3/50)=2/50=1/50
So, B alone could do the work in 25 days.
Answer C
Question: How many days are there in x weeks x days
A.14x
B.8x
C.7x2
D.7
Answer: B.8x
Explanation: Explanation :
x weeks x days = (7 × x) + x = 7x + x = 8x days .Answer : Option B
Question: Find the L.C.M of 20,50,100
A.400
B.200
C.600
D.800
Answer: A.400
Explanation: 20=2^2*5 50=2*5^2 100=2^4*5^2
L.C.M=2^4*5^2=400
Answer=(A)
Question: In how many T ways can the letters of the word JUPITER be arranged in a row so that the vowels appear in alphabetic order?
A. 736
B. 768
C. 792
D. 840
Answer: D. 840
Explanation: three letters can be arranged in 3! ways.
only one combination EIU is required.
7 letters can be arranged in 7! ways.
thus T=7!/ 3! * 1 = 840.
D
Question: There are 8436 steel balls, each with a radius of 1 cm, stacked in a pile, with 1 ball on top, 3 balls in the second layer, 6 in the third layer, 10 in the fourth and so on. the number of horizontal layer on the pile is
A.34
B.38
C.36
D.32
Answer: C.36
Explanation: Explanation :
Assume the number of layers in horizontal pile is n.
So, Σn(n+1)/2 = 8436.
=> (1/2) [ Σn2 + Σn ] = 8436.
=> n(n+1)(n+2)/12 +n(n+1)/4 = 8436.
=> n(n +1) [(2n + 4) / 12 ] = 8436.
=> n(n +1)(n+2) / 6 = 8436.
=> n(n +1)(n+2) = 36 x 37 x 38.
So, n=36.
Answer : C
Question: A shopkeeper loses 15%,if an article is sold for Rs. 119. What should be the selling price of the article to gain 20%?
A.s.177
B.s.168
C.s.144
D.s.129
Answer: B.s.168
Explanation: Given that SP = Rs. 119 and loss = 15%
CP = [100(SP)]/(100 - l%) = (100 * 119)/85 = Rs. 140.
To get 20% profit, New SP = [(100 + p%)CP]/100
= (140 * 120)/100
= Rs.168
Answer:B
Question: The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 48 kmph, find the speed of the stream?
A.16 kmph
B.19 kmph
C.14 kmph
D.11 kmph
Answer: A.16 kmph
Explanation: The ratio of the times taken is 2:1.
The ratio of the speed of the boat in still water to the speed of the stream
= (2+1)/(2-1) = 3/1
= 3:1
Speed of the stream
= 48/3 = 16 kmph.
Answer: A
Question: 0.1+0.1^2+ 0.1^3=
A. 0.1
B. 0.111
C. 0.1221
D. 0.2341
Answer: B. 0.111
Explanation: You have a mistake in your question. Choice B should be (.111) and not (.11).
The equation in the solution can be simplified to (.1 + .01 + .001).
Adding those together you get:
.100
.010
.001
------
.111 - Which is answer choice (B)
Question: A Bus running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the Bus?
A.160 metres
B.150 metres
C.130 metres
D.120 metres
Answer: B.150 metres
Explanation: B
150 metres
Speed= 60 x 5/18 m/sec = 50/3 m/sec.
Length of the Bus = (Speed x Time).
Length of the Bus = 50/3 x 9 m = 150 m.
Question: A train 200 m long crosses a platform 150 m long in 20 sec; find the speed of the train?
A.73
B.63
C.65
D.70
Answer: B.63
Explanation: D = 200 + 150 = 350
T = 20
S = 350/20 * 18/5 = 63 kmph.
Answer: B
Question: Income and expenditure of a person are in the ratio 3 : 2. If the income of the person is Rs. 21000, then find his savings?
A.6000
B.7000
C.8000
D.9000
Answer: B.7000
Explanation: Let the income and the expenditure of the person be Rs. 3x and Rs. 2x respectively.
Income, 3x = 21000
=> x = 7000
Savings = Income - expenditure
= 3x - 2x = x
So, savings =Rs.7000.
Answer: B
Question: If q and r are both odd numbers M, which of the following must also be odd?
A.q – r
B.(q + r)^2
C.q(q + r)
D.(qr)^2
Answer: D.(qr)^2
Explanation: We're told that q and r are both ODD numbers M. We're asked which of the following must also be odd.
IF...
q = 1
r = 3
Answer A) q – r = 1-3 = -2 NOT odd
Answer B) (q + r)^2 = (1+3)^2 = 16 NOT odd
Answer C) q(q + r) = (1)(4) = 4 NOT odd
Answer D) (qr)^2 = (3)^2 = 9 This IS ODD
Answer E) q/r = 1/3 NOT odd
Final Answer:
D
Question: If W is a positive integer, which of the following must be odd?
A.x+1
B.W^2W
C.W^2+W+1
D.x^2−1
Answer: C.W^2+W+1
Explanation: A. W+1 = can be odd or even. Since O + O =E or E + O = O
B. W^2 + W = W(W+1). Since from the above derivation we already know the term W+1 can be Odd or Even, directly substitute here. W(ODD) = Even (When W is Even) or W(EVEN) = EVEN [When W is ODD]
C. Here's the answer. Since we know the term W^2 + W can always take a EVEN number, EVEN + 1 = ODD
Hence C.
Question: A can finish a work in 6 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work?
A.6
B.5
C.5.5
D.2
Answer: D.2
Explanation: B's 10 day's work = ( 1 x 10 ) = 2 .
15 3
Remaining work = ( 1 - 2 ) = 1 .
3 3
Now, 1 work is done by A in 1 day.
6
Therefore 1 work is done by A in ( 6 x 1 ) = 2 days.
D
Question: A certain bacteria colony doubles in size every day for 10 days, a which point it reaches the limit of its habitat and can no longer grow. If two bacteria colonies start growing simultaneously, how many days will it take them to reach the habitat’s limit?
A.6.33
B.9
C.10
D.15
Answer: B.9
Explanation: Case 1: Consider the bacteria num to be B. As it doubles every day, number of bacteria at the end of each day would be
Day 1 – B
Day 2 – 2B
Day 3 – 4B
Day 4 – 8B
.
.
.
Day 10 – 2^19 B
It can be implied that the capacity of the habitat is 2^19 B.
Case 2: There are 2 bacteria which keep doubling every day. So, the count would be
Day 1 – 2B
Day 2 – 4B
Day 3 – 8B
.
.
.
Day 18 – 2^18 B
Day 19 – 2^19 B --> this is the point where the habitat is filled to its capacity.
Hence, 9 is the answer
B
Question: How many terms are in the G.P. 3, 6, 12, 24, ......., 3072 ?
A.8
B.9
C.11
D.5
Answer: C.11
Explanation: Explanation:
Here a = 3 and r = 6/3 = 2. Let the number of terms be n.
Then, t = 3072 => a * r^(n-1) = 3072
=> 3 * 2^(n-1) = 3072 => 2^(n-1) = 1024 = 2^(10)
=> n-1 = 10 => n = 11
Answer: C
Question: Convert 50miles into yards?
A.25630 yards
B.35200 yards
C.88000 yards
D.42560 yards
Answer: C.88000 yards
Explanation: 1 mile = 1760 yards
50 miles = 50*1760 = 88000 yards
Answer is C
Question: The length of a rectangular landscape is 4times its breadth. There is a playground in it whose area is 1200 square mtr & which is 1/3rd of the total landscape. What is the length of the landscape?
A.100
B.140
C.120
D.160
Answer: C.120
Explanation: Sol. x * 4x = 3 * 1200
x = 30
Length = 4 * 30 = 120
C
Question: Eshan and Mary each wrote two or three poem every day over a period of time eshan wrote 43 poems while Mary wrote 61. The number of days in this period is.....
A.19
B.21
C.20
D.18
Answer: B.21
Explanation: suppose, Eshan writes 2poems in first 18days 18*2=36.
2poems in next 2 days 2*2=4, 36+4=40
and 3poems in next 1day 1*3=3, 40+3=43
So, Ultimately he takes (18+2+1) = 21days to write 43 poems.
now suppose, Marry writes 3poems in 1st 18days 18*3=54
2poems in next 2days 2*2=4, 54+4=58
3poems in next 1 day 1*3=3, 58+3=61
So ultimately marry takes (18+2+1)= 21days to write 61poems.
ANSWER:B
Question: What is the product of all positive factors of 25?
A.39
B.324
C.125
D.150
Answer: C.125
Explanation: Positive factors of 25 are 1, 5, 25.
Product of positive factors: 25*5=125
Answer: C
Question: A truck rental agency has the following terms. If a truck is rented for 8 hours or less the charge is RS.100 per hour or RS.8 per km whichever is more. On the other hand , if the truck is rented for more than 8 hours,the charge is RS.80 per hour or RS.6 per km whichever is more. A company rented a truck from the agency, and used it for 120 km and paid RS.800. For how many hours did the company rent the truck?
A.6
B.8
C.10
D.12
Answer: C.10
Explanation: We can check each answer by substitution as it is fairly simple.
a) Cost = Max(960,600) = 960. Wrong
b) Cost = Max(960,800) = 960. Wrong
c) Cost = Max(720,800) = 800. Correct answer.
d) Cost = Max(720,960) = 960. Wrong
Answer is hence C.
Question: 4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat-weavers in 8 days?
A.4
B.16
C.8
D.1
Answer: B.16
Explanation: Explanation:
Let the required number of mats be x
More mat-weavers, more mats (direct proportion)
More days, more mats (direct proportion)
Hence we can write as
(mat-weavers) 4:8
(days) 4:8}::4:x
⇒4×4×x=8×8×4
⇒x=2×2×4=16
Answer: Option B
Question: If f(x) + f(1 - x) + f(1 + x) + f(2 + x) = 2x for all real value of x. If f(0) = 1, then find the value of f(4)
A.1
B.2
C.8
D.7
Answer: B.2
Explanation: For x = 0, f(0) + f(1) + f(2) = 0 ............. (i)
For x = 1, f(1) + f(0) + f(3) = 2 ............. (ii)
subtracting (i) from (ii), we get f(3) - f(1) = 2 .......... (a)
For x = 2, f(2) + f(-1) + f(3) + f(4) = 4 ........ (iii)
For x = -1, f(-1) + f(2) + f(0) + f(1) = -2 ......... (iv)
subtracting from (iii) from (iv), we get
⇒f(0)−f(4)−2=−6⇒f(0)−f(4)−2=−6 [ from (a) we know that f(3) - f(1) = 2]
Answer:B