RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: In the coordinate plane, points (x, 3) and (5, y) are on line k. If line k passes through the origin and has slope 3/5, then x + y =
A.9
B.8
C.7
D.5
Answer: B.8
Explanation: Line k passes through the origin and has slope 3/5 means that its equation is y=3/5*x.
Thus: (x, 3)=(3, 5) and (5, y) = (3, 5) --> x+y=3+5=8.
Answer: B
Question: The value of x + x(xx) when x = 4
A.A) 60
B.B) 66
C.C)68
D.D) 56
Answer: C.C)68
Explanation: x + x(xx)
Put the value of x = 4 in the above expression we get,
4 + 4(44)
= 4 + 4(4 Ã— 4)
= 4 + 4(16)
= 4 + 64
= 68 The answer is (C)
Question: If the average (arithmetic mean) of a list of numbers is 12 and the standard deviation of that list of numbers is 1.3, then which of the following numbers is more than two standard deviations from the mean?
I. 14.7
II. 15.3
III. 9.5
A.I only
B.I and II only
C.II only
D.III only
Answer: B.I and II only
Explanation: Mean = 12
SD = 1.3
2 SD above mean = 12+2*1.3 = 14.6
2 SD below mean = 12-2*1.3 = 9.4
only 9.5 lies in the range of 2SD from mean
Answer: Option B
Question: The sum of the present age of Henry and Jill is 41. What is their present ages if 7 years ago Henry was twice the age of Jill?
A.and 25
B.and 24
C.and 22
D.and 29
Answer: A.and 25
Explanation: Let the age of Jill 7 years ago be x, age of Henry be 2x
x+7 + 2x+7 = 41
x = 9
Present ages will be 16 and 25
Answer : A
Question: Which of the following options is the possible total number of people in a hall given that the number of people is a multiple of both 4 and 20.?
A.28
B.60
C.32
D.36
Answer: B.60
Explanation: the number of people are a multiple of both 7 and 13, so it must be divisible by 7 and 13.
using the elimination method look for a number that is both divisible by 7 and 13,
of all the options only 60 is divisible by 4 and 20.
[ 60/4=15 and 60/20=3]
answer :B
Question: The length of the bridge, which a train 145 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
A.200 m
B.230 m
C.245 m
D.250 m
Answer: B.230 m
Explanation: Let the length of the bridge:L
The equation now is L+145/12.5m/s(45km/hr or12.5m/s)=30
Solving, L =230m
ANSWER:B
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.3/22
B.4/21
C.2/21
D.1/14
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: There are five same model cars parked in the same direction in parking. If 3 cars are red, 1 is black and 1 is green, in how many ways they can be arranged in the parking?
A.10 ways.
B.20 ways.
C.30 ways.
D.40 ways.
Answer: B.20 ways.
Explanation: 5!/(3!*1!*1!) = (5*4*3*2*1)/(3*2*1) = 120/6 = 20 ways.
ANSWER:B
Question: A constructor estimates that 10 people can paint Mr khans house in 4 days. If he uses 5 people instead of 10,how long will they take to complete the job?
A.10
B.4
C.5
D.8
Answer: D.8
Explanation: Explanation:
Use formula For a work Members Ã— days = constant
10 Ã— 4 = 5Ã— a
a = 8
so answer is 8 days
Answer: D
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train?
A.150
B.277
C.299
D.662
Answer: A.150
Explanation: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 9 = 150 meter
Answer: A
Question: 1/2+[(2/3*3/8)+4]-3/16=
A.29/16
B.61/16
C.15/16
D.9/13
Answer: B.61/16
Explanation: 1/2+[(2/3*3/8)+4]-3/16=
1/2+[(1/4)+4]-3/16=
1/2+[17/4]-3/16=
8/16 + 68/16 - 3/16 = 61/16
B
Question: Excluding stoppages, the average speed of a bus is 60 km/hr and including stoppages, the average speed of the bus is 40 km/hr. For how many minutes does the bus stop per hour?
A.18 min
B.17 min
C.19 min
D.20 min
Answer: D.20 min
Explanation: In 1hr, the bus covers 60 km without stoppages and 40 km with stoppages.
Stoppage time = time take to travel (60 - 40) km i.e 20 km at 60 km/hr.
stoppage time = 20/60 hrs =20 min.
Answer: D
Question: A toothed wheel of diameter 50 cm is attached to a smaller wheel of diameter 30 cm. How many revolutions will the smaller wheel make when the larger one makes 15 revolutions?
A.18
B.20
C.22
D.25
Answer: D.25
Explanation: Solution
Distance covered by smaller wheel in 1 revolution = (2Π x 15) cm
= (30 Π) cm.
Distance covered by larger wheel in 1 revolution = (2Π x 25) cm
= (50 Π) cm.
Let k x 30 Π = 15 x 50 Π.
Then, k = [15 x 50 Π / 30 Π] = 25.
∴ Required number of revolutions = 25.
Answer D
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 46, the dividend is:
A.5336
B.5340
C.5342
D.5344
Answer: A.5336
Explanation: Divisor = (5 * 46) = 230
= 10 * Quotient = Divisor
=> Quotient = 230/10 = 23
Dividend = (Divisor * Quotient) + Remainder
Dividend = (230 * 23) + 46 = 5336.
A
Question: The cost of the paint is Rs. 36.50 per kg. If 1 kg of paint covers 16 square feet, how much will it cost to paint outside of a cube having 8 feet each side.
A.Rs. 850
B.Rs. 860
C.Rs. 876
D.Rs. 886
Answer: C.Rs. 876
Explanation: Explanation:
We will first calculate the Surface area of cube, then we will calculate the quantity of paint required to get answer.
Here we go,
Surface area =6a2=6∗8(2)=384sq feet
Quantity required =38416=24kg
Cost of painting =36.50∗24=Rs.876
Option C
Question: The exam scores of all 500 students were recorded and it was determined that these scores were normally distributed. If Jane's score is 0.8 standard deviation above the mean, then how many, to the nearest unit, students scored above Jane?
A.394
B.250
C.400
D.106
Answer: D.106
Explanation: Solution
Let m be the mean and s be the standard deviation and find the z score.
z = (x - m) /s = (0.8 s + m - m) / s = 0.8
The percentage of student who scored above Jane is (from table of normal distribution).
1 - 0.7881 = 0.2119 = 21.19%
The number of student who scored above Jane is (from table of normal distribution).
21.19% 0f 500 = 106
Answer D
Question: A jeep takes 7 hours to cover a distance of 420 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
A.48 Kmph
B.52 Kmph
C.40 Kmph
D.63 Kmph
Answer: C.40 Kmph
Explanation: Time = 7
Distance = 420
3/2 of 7 hours = 7 * 3/2 = 10.5 Hours
Required speed = 420/10.5 = 40 Kmph
C)
Question: What will be the fraction of 12.5%
A.1/4
B.1/5
C.1/10
D.1/8
Answer: D.1/8
Explanation: Explanation:
It will 12.5*1/100 = 1/8
Answer: Option D
Question: What comes next?
2, 7, 22, 67, 202, ?
A.765
B.345
C.798
D.607
Answer: D.607
Explanation: D
607
x 3 + 1 at each stage.
Question: What is the median of a set of consecutive integers if the sum of nth number from the beginning and nth number from the end is 120?
A.60
B.25
C.50
D.75
Answer: A.60
Explanation: Surprisingly no one answered this easy one.
property of a set of consecutive integerz.
mean=median=(first element+last element)/2 = (second element+last but one element)/2 =(third element+ third last element)/2 Etc. Etc.
So mean=median=120/2=60
Answer is A
Question: If a farmer sells 5 of his goats, his stock of feed will last for 4 more days than planned, but if he buys 10 more goats, he will run out of feed 3 days earlier than planned. If no goats are sold or bought, the farmer will be exactly on schedule. How many goats does the farmer have?
A.12
B.20
C.48
D.55
Answer: B.20
Explanation: Say farmer has n goat and he is good for d days.:-
We have 3 equations given in question:-
(n-5) * d+4 =(n+10) *(d-3) = n * d
Solving these: (You can solve 1st and 3rd and 2nd and 3rd together)
We get:
10d-3n=30
4n-5d =20
=> n=20
Ans B it is!
Question: If the simple interest on a sum of money for 2 years at 5% per annum is Rs.50, what will be the compound interest on same values
A.Rs.51.75
B.Rs 51.50
C.Rs 51.25
D.Rs 51
Answer: C.Rs 51.25
Explanation: Explanation:
S.I.=P∗R∗T/100P
=50∗100/5∗2=500
Amount=500(1+5100)2
500(21/20∗21/20)=551.25
C.I.=551.25−500=51.25
Option C
Question: If log 27 = 1.431, then the value of log 9 is:
A.0.954
B.0.93
C.0.933
D.0.96
Answer: A.0.954
Explanation: If log 27 = 1.431, then the value of log 9 is:
A.	0.934
B.	0.945
C.	0.954
D.	0.958
Answer: Option C
Explanation:
log 27 = 1.431
log (33 ) = 1.431
3 log 3 = 1.431
log 3 = 0.477
log 9 = log(32 ) = 2 log 3 = (2 x 0.477) = 0.954.
ANSWER A
Question: Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P, Q and R respectively. What is the proportion of solution R in the liquid in the tank after 3 minutes?
A.6/15
B.6/11
C.6/14
D.6/12
Answer: B.6/11
Explanation: Part filled by (A + B + C) in 3 minutes = 3(1/30 + 1/20 + 1/10) = 11/20
Part filled by C in 3 minutes = 3/10
Required ratio = 3/10 * 20/11 = 6/11
Answer: B
Question: Kevin, David, and Catherine each try independently to solve a problem. If their individual probabilities for success are 1/2, 2/9 and 3/4, respectively, what is the probability all three will solve the problem?
A.1/12
B.1/8
C.1/3
D.1/4
Answer: A.1/12
Explanation: P(Kevin will solve)= 1/2
P(David will solve)= 2/9
P(Catherine will solve) = 3/4
P= (1/2)*(2/9)*(3/4) = 6/72 = 1/12
Answer:A
Question: A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used?
A.6 months
B.8 months
C.10 months
D.7 months
Answer: D.7 months
Explanation: 7 * 8 : 9 * x = 8:9 => x= 7
ANSWER:D
Question: Which of the following is equal to 10^-(-2)^3?
A.1/(10^8)
B.1/(10^9)
C.1/(10^5)
D.1/(10^4)
Answer: A.1/(10^8)
Explanation: 10^-(-2)^3 => 10^-(-2^3) => 10^-(8) = 1/(10^8)
Answer : A
Question: Find the odd man out. 1, 5, 11, 17, 23, 29
A.29
B.17
C.11
D.1
Answer: D.1
Explanation: Explanation :
All given numbers except 1 are prime numbers.
One is not a prime number because it does not have two factors. It is divisible by only 1.. Answer : Option D
Question: Pane and Thomas are among the 8 people from which a committee of 4 people is to be selected. How many different possible committees of 4 people can be selected from these 8 people if at least one of either Pane or Thomas is to be selected?
A.28
B.46
C.55
D.63
Answer: C.55
Explanation: Ans:C
Solution:
P+T+6 = total 8 ,
we need to select at least one of the P and T or both= total 4 out of 8 - 4 out of 6
8C4 - 6C4
=55
Question: If each digit in the set A = {1, 2, 3, 4, 5, 6, 7, 8} is used exactly once, in how many ways can the digits be arranged?
A.36,100
B.38,210
C.40,320
D.42,430
Answer: C.40,320
Explanation: 8! = 40,320
The answer is C.
Question: The average age of a group of persons going for picnic is 16 years. Twenty new persons with an average age of 15 years join the group on the spot due to which their average age becomes 15.5 years. The number of persons initially going for picnic is?
A.10
B.20
C.37
D.26
Answer: B.20
Explanation: Let the initial number of persons be x. Then,
16x + 20 * 15 = 15.5 (x + 20) <=> 0.5x
= 10 <=> x = 20.
Answer: B
Question: The letters of the word 'SARITI' are written in all possible orders and these words are written in alphabetical order. Then what is the rank of the word 'SURITI'
A.- 235
B.- 245
C.- 307
D.- 315
Answer: A.- 235
Explanation: Total Number of Words = 6!/2! = 360 [(number of characters)/(repeating group )!]
After S, we have T and A.
Number of words starting with T = 5!/2! = 60
Number of words starting with U = 5!/2! = 60
So any word starting with S will have rank < 360 - 60(for Us) - 60(for Ts) = 240
Only option A < 240, so Answer is A.
Question: If each digit in the set A = {1, 2, 3, 4, 5, 6, 7} is used exactly once, in how many ways can the digits be arranged?
A.4830
B.5040
C.5250
D.5460
Answer: B.5040
Explanation: 7! = 5040
The answer is B.
Question: Which of the following is equal to the average (arithmetic mean) of (x+3)^2 and (x-3)^2?
A.x^2
B.x^2+2
C.x^2 +4
D.x^2+9
Answer: D.x^2+9
Explanation: Avg = [(x+3)^2 + (x-3)^2] / 2
Expanding and simplifying, (x^2 + 6x + 9 + x^2 - 6x + 9 ) / 2 = x^2 + 9
Answer D.
Question: The probability of a team winning a match given Matt is playing the match is 0.60. The probability of the team winning a match given Matt is not playing the match is 0.5. The probability of Matt playing any match is 0.8.
If it is known that the team has won the last match, what is the probability that Matt played the match?
A.0.8321
B.0.7
C.0.8571
D.0.8275
Answer: D.0.8275
Explanation: Out of 100 matches:
Matt is plays in 80 and not plays in 20.
Out of 80 matches Matt plays in, team wins 0.60*80 = 48.
Out of 20 matches Matt does not play in, team wins 0.5*20 = 10.
So, out of 100 matches 48 + 10 = 58 are won.
It is known that the team has won the last match. Out of 58 matches won, Matt is in 48: 48/58 = 0.8275...
Answer: D.
Question: 2,7,17,3,11,19,5,13,__
A.20
B.21
C.22
D.23
Answer: D.23
Explanation: 2=1st prime no.
3=2nd p.n.
5=3rd p.n.
7=4th p.n.
11=5th p.n.
13=6th p.n.
17=7th p.n.
19=8th p.n., and
23=9th p.n.
2,7,17=1st p.n., (1+3)th p.n., (1+3+3)th p.n.
3,11,19=2nd p.n., (2+3)th p.n., (2+3+3)th p.n.
5,13,23=3rd p.n., (3+3)th p.n., (3+3+3)th p.n.
ANSWER:D
Question: A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 2:4 and B:C = 2:5. If the total runs scored by all of them are 100, the runs scored by B are?
A.20.23
B.20.13
C.30.93
D.25
Answer: D.25
Explanation: A:B = 2:4
B:C = 2:5
A:B:C = 4:8:20
8/32 *100 = 25
ANSWER:D
Question: If a book is sold at 7% profit instead of 7% loss, it would have brought Rs 14 more. Find out the cost price of the book
A.75
B.100
C.60
D.70
Answer: B.100
Explanation: Let C.P. of the book be Rs. ’X’
Given, 1.07 X - 0.93X = 14
=> 0.14 X = 14 = 14/0.14 = Rs 100
ANSWER:B
Question: A sum of Rs. 125000 amounts to Rs. 15500 in 4 years at the rate of simple interest. What is the rate of interest?
A.3%
B.4%
C.5%
D.6%
Answer: D.6%
Explanation: S.I. = (15500 - 12500) = Rs. 3000\
Rate = (100 * 3000) / (12500 * 4) = 6%
ANSWER:D
Question: 96% of the population of a village is 23040. The total population of the village is?
A.22777
B.24000
C.27876
D.26676
Answer: B.24000
Explanation: X * (96/100) = 23040
X = 240 * 100
X = 24000
Answer:B
Question: The average of first 10 prime numbers is?
A.12.6
B.12.5
C.12.9
D.12.2
Answer: C.12.9
Explanation: Sum of 10 prime no. = 129
Average = 129/10 = 12.9.Answer: C
Question: Rahul can do a work in 3 days while Rajesh can do the same work in 2days. Both of them finish the work together and get $150. What is the share of Rahul?
A.$50
B.$40
C.$60
D.$100
Answer: C.$60
Explanation: Rahul's wages: Rajesh's wages = 1/3 : 1/2 = 2:3
Rahul's share = 150*2/5 = $60
Answer is C
Question: A can do a piece of work in 4 days. B can do it in 5 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it?
A.10
B.20
C.5
D.4
Answer: B.20
Explanation: C = 1/2 - 1/4 - 1/5 = 1/20 => 20 days
ANSWER B
Question: If Y < X and XM < YM, what must be true?
A.M < X
B.M < Y.
C.X < 0.
D.M < 0
Answer: D.M < 0
Explanation: X>Y, bus as soon as M is multiplied to both sides inequality sign changes.
This is only possible when -ve is multiplied on both sides. That means M is -ve
D is the answer
Question: 1.20 can be expressed in terms of percentage as
A.120%
B.0.120%
C.1.20%
D.0.209%
Answer: A.120%
Explanation: Explanation:
While calculation in terms of percentage we need to multiply by 100, so
1.20 * 100 = 120
Answer: Option A
Question: At what rate percent on simple interest will a sum of money double itself in 70 years?
A.1 3/7%
B.3 1/9%
C.3 9/3%
D.3 2/3%
Answer: A.1 3/7%
Explanation: P = (P*70*R)/100
R = 1 3/7%
Answer: A
Question: When is |x-5| = 5-x?
A.x=5
B.x=0
C.x<=5
D.x>5
Answer: C.x<=5
Explanation: When is |x-5| = 5-x?
Choice A: X=5, it is true but X cannot be always 5
Choice B: X=0, it is also true, but X cannot be always 0
Choice C: X>5, it is false, for e.g. X=6, then one side of equation is 2 and the other side is -2
Choice D: X<=5, this choice encapsulate Choice A, Choice B and for all other conditions and is true for above said equation. Hence the answer choice is C.
Question: A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 380 m long platform?
A.50
B.27
C.29
D.47
Answer: A.50
Explanation: Let the length of the train be x m.
When a train crosses an electric pole, the distance covered is its own length.
So, x = 12 * 36 * 5 /18 m = 120 m.
Time taken to cross the platform = (120 +380)/ 36 * 5/18
= 50 min.
Answer:A
Question: The radius of a circle is increased by 1%. Find how much % does its area increases?
A.2.71%
B.2.21%
C.8.01%
D.2.01%
Answer: D.2.01%
Explanation: r = 100 r = 101
r2 = 10000 r2 = 10201
10000 ---- 201
100 ---- ? => 2.01%
Answer:D
Question: Marry has 3 trousers in cupboard. One of them is grey the 2nd blue and the 3rd brown. In his wardrobe he also has 4 shirts. One of them is grey and the other 3are white. He opens his cupboardin the dark and pick out one shirt trouser pair without examination the color. What is the likelihood that neither the shirt nor the trouser is grey?
A.1/2
B.2/3
C.3/5
D.5/7
Answer: A.1/2
Explanation: Probability that trouser is not grey = 2/3
Probability that shirt is not grey = 3/4
∴ Required probability = 2/3 x 3/4 = 1/2
A
Question: Last Sunday a certain store sold copies of Newspaper A for $1.00 each and copies of Newspaper B for $1.25 each, and the store sold no other newspapers that day. If r percent of the store’s revenues from newspaper sales was from Newspaper A and if p percent of the newspapers that the store sold were copies of newspaper A, which of the following expresses r in terms of p?
A.100p/(125 – p)
B.150p/(250 – p)
C.300p/(375 – p)
D.400p/(500 – p)
Answer: D.400p/(500 – p)
Explanation: News A) A= $1
(News B) B = $1.25 or $5/4
Total newspaper sold= x
No. of A Newspaper sold = p/100 *x is r% of total revenue
Total revenue: p/100*x*$1 + (100-p)/100*x*$5/4
Equation: px/100=r/100(px/100+(500/4-5p/4)x/100)
px/100=r/100(4px+500x-5px/400)
removing common terms as 100 and x out and keeping only r on RHS
p=r(500-p)/400 or r=400p/(500-p)..Answer..D
Question: A batsman scored 150 runs which included 5 boundaries and 10 sixes. What percent of his total score did he make by running between the wickets?
A.45%
B.46.67%
C.600/11
D.55%
Answer: B.46.67%
Explanation: Explanation :
Number of runs made by running,
=>150−(5×4+10×6).
=>150−80
=>70
Hence, the required percentage is:-
=>70/150 *100
=>46.67%
Answer : B
Question: 10 people can write 55 book in 12 days working 8 hour a day.then in how many day 198 can be written by 48 people?
A.9
B.13
C.21
D.24
Answer: A.9
Explanation: work per day epr hour per person= 55/(12*8*10) // eq-1
people=48; let suppose day=p; per day work for 8 hours
acc. to condition
work per day epr hour per person= 198/(p*8*48) // eq-2
eq-1==eq-2;
p= 9
ANSWER:A
Question: The number N is 5,2H4, where H represents the ten's digit. If N is divisible by 9, what is the value of H?
A.1
B.3
C.5
D.7
Answer: D.7
Explanation: If the number is divisible by 9, it must also be divisible by 3. Only 7 yields such a number.
Answer: D
Question: A man 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.2882
B.279
C.287
D.860
Answer: D.860
Explanation: CP = SP + 1CP = SP - g
800 + x = 980 - 2x
3x = 180 => x = 60
CP = 800 + 60 = 860
Answer: D
Question: If
BAT = 58
HAT = 52
CAT = 57
then
whats RAT = ?
A.42
B.45
C.34
D.76
Answer: A.42
Explanation: A
42
Question: The Number of students learning Three subjects are as follows
Maths = 40
English = 50
Science = 35
If the Number of students learning exactly two subjects is maximum and no student learns all the three subjects, then what is the minimum number of students learning exactly one subject?
A.0
B.1
C.25
D.35
Answer: B.1
Explanation: Let's assume the following :
a = Only Math
b = both Math and English
c = Only english
d = English and Science
e = Only Science
f = Math and Science
g = All three ( = 0 )
Now, to make the Only subjects (a+c+e) minimum, we need to maximize the both subject (b+d+f)
Since, we have minimum no. of students in science, we can consider Only Science(e) = 0 and Both(English and Science & Math and Science) = d+f = 35
also, we have a+b+f = 40 --(1)
and , b+c+d = 50 --(2)
Adding (1) and (2),
a+2b+c+f+d = 90;
or a+2b+c = 55
Now, we have to maximize b and minimize a and c,
if a+c = 0 ==> 2b =55 -- Not possible.
If a+c =1 ==> 2b = 54 => b=27, Possible.
So, we can say a+c+e = 1(Minimum value),
Hence B.
Question: If a is an integer greater than 6 but less than 17 and b is an integer greater than 3 but less than 29, what is the range of a/b?
A.15/4
B.13/2
C.9/7
D.1/5
Answer: A.15/4
Explanation: The way to approach this problem is 6<a<17 and 3<b<29
Minimum possible value of a is 7 and maximum is 16
Minimum possible value of b is 4 and maximum is 28
Range = max a/min b - min a/max b
(Highest - lowest)
16/4 - 7/28 = 15/4
Hence A
Question: The positive value of x that satisfies the equation (1 + 2x)^5 = (1 + 3x)^3 is between
Bunuel, can you please explain this one?
A.0 and 0.5
B.0.5 and 1
C.1 and 1.5
D.1.5 and 2
Answer: D.1.5 and 2
Explanation: Trial and error would probably be the easiest way to solve this problem. When x is large enough positive number, then because of the exponents (5>4), LHS will be more than RHS (as you increase the positive value of x the distance between the values of LHS and RHS will increase).
Try x=1 --> LHS=3^5=81*3=243 and RHS=4^4=64*4=256, so (1 + 2x)^5 < (1 + 3x)^4. As you can see LHS is still slightly less than than RHS. So, the value of x for which (1 + 2x)^5 = (1 + 3x)^4 is slightly more than 1.
Answer: D.
Question: Diana is painting statues. She has 1/2 of a gallon of paint remaining. Each statue requires 1/4 gallon of paint. How many statues can she paint?
A.2
B.20
C.28
D.14
Answer: A.2
Explanation: number of statues=all the paint÷amount used per statue
=1/2 ÷ 1/4
=1/2*4/1
=2
Answer is A
Question: 80% of 5/8 =
A.0.2
B.0.5
C.0.6
D.0.75
Answer: B.0.5
Explanation: Should be simple.
0.8*5/8 = 4/8 = 1/2 = 0.5
Correct Option : B
Question: A boy owes his Dad $50 which he can clear by washing the dishes. His father clears $2 every time he washes the dishes. If his son misses a day, the clearing balance value reduces by 50%. If his son washes the dishes for two weeks starting from Monday to Sunday, but forgets to wash on Monday of the second week. How much money does the boy still have to pay after two weeks?
A.20
B.28
C.14
D.30
Answer: D.30
Explanation: Week one is $2*7 days=$14
Clearing balance reduces to 0.50*$2= $1.
Week two is $1*6 days= $6
Total balance left to pay after two weeks is $50-($14+$6)= $30.
Answer is D
Question: total 22 matches are conducted in Knockout match type. How many players will be participated in that tournament?
A.24
B.26
C.21
D.20
Answer: C.21
Explanation: 21 players
ANSWER:C
Question: In how many ways can the letters of word ABDUCTION be arranged such that NO two vowels appear together?
A.9!
B.5!*4!
C.4!*5!
D.5!*4!*2!
Answer: C.4!*5!
Explanation: No 2 vowels together = the only arrangement possible will be C V C V C V C V C (with V=vowel, C=consonant). This is true as we have 4 vowels and 5 consonants and any other combination will force us to pair 2 vowels together.
Thus, the number of arrangements possible : 5 *4 *4 *3 *3 *2 *2*1 = 4!*5! ----> C is the correct answer.
Question: There are 36 people in a party. If everyone is to shake hands with one another, how many hand shakes are possible?
A.435
B.367
C.630
D.597
Answer: C.630
Explanation: Explanation:
Total number of persons = n = 36
Shake hands involve only 2 persons = r = 2
Number of shake hands = nCr = 36C2
36C2 = (36 * 35) /(2 * 1) = 630
ANSWER:C