RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A alone would take 8 days more to complete the job than if both A and B would together. If B worked alone, he took 4 1⁄2 days more to complete the job than A and B worked together. What time would they take if both A and B worked together?
A.7 days
B.5 days
C.4 days
D.6 days
Answer: D.6 days
Explanation: Let if both A and B work together, they take x days.
∴ (A + B)’s 1 days’s work = 1⁄x th work
A’s 1 day’s work = 1⁄(x + 8) th work.
B’s 1 day’s work = 1⁄(x + 9/2) th work.
Now, 1/x+8 + 2/2x+9==1/x
⇒ x(2x + 9 + 2x + 16) = (x + 8)(2x + 9)
⇒ 4x2 + 25x = 2x2 + 25x + 72
⇒ x2 = 36 ⇒ x = 6 days
Answer D
Question: In a T.V. factory, an average of 66 TVs are produced per day for the fist 25days of the months. A few workers fellill for the next five daysreducing the daily avg for the month to58 sets/day . The average production per day for day last 5days is ?
A.18
B.39
C.48
D.50
Answer: A.18
Explanation: Production during these 5 days = Total production in a month - production in first 25 days.
= 30 x 58 - 25 x 66
= 90
âˆ´ Average for last 5 days = 90 / 5
= 18
A
Question: Suppose f(x) is an odd function for which f(x + 2) = f(x) for all x, and
f(x) = x2 for x 2 (0, 1). Compute f(-3/2) + f(1).
A.-1
B.-1/2
C.-1/4
D.1/4
Answer: D.1/4
Explanation: Because f is periodic, we know that f(-3/2) = f(1/2) = (1/2)2 = 1=4. Because f
is odd, we know that f(1) = -f(/1), but because f is periodic, f(1) = f(-1). Therefore,
f(1) = 0 and the answer is 1=4.
correct answer D
Question: If you roll one fair six-sided die, what is the probability that the number is even or greater than 2?
A.1/2
B.2/3
C.4/5
D.5/6
Answer: D.5/6
Explanation: The numbers which satisfy the conditions are 2, 3, 4, 5, and 6.
The probability is 5/6
The answer is D.
Question: The speed of a railway engine is 96 Km per hour when no compartment is attached, and the reduction in speed is directly proportional to the square root of the number of compartments attached. If the speed of the train carried by this engine is 24 Km per hour when 9 compartments are attached, the maximum number of compartments that can be carried by the engine is:
A.19
B.18
C.16
D.17
Answer: C.16
Explanation: the reduction in speed is directly proportional to the square root of the number of compartments attached
Doesreductionmean amount subtracted? or percentage decrease? There are at least two interpretations, and the wording does not provide a clear interpretation between them.
Evidently what the question intends is the subtraction interpretation. What is subtracted from the speed is directly proportional to the square root of the number of compartments attached.
In other words, if S = speed, and N = number of compartments, then
S = 42 - k*sqrt(N)
wherekis a constant of the proportionality. In general, if A is directly proportional to B, we can write A = k*B and solve for k.
If N = 9, then S = 24
24 =96 - k*sqrt(9) = 96 - 3k
k = 24
Now, we need to know: what value of N makes S go to zero?
0 = 96 - 24*sqrt(N)
24*sqrt(N) = 96
sqrt(N) = 4
n = 4^2 = 16
Thus, 16 is the maximum number of cars the engine can pull and still move.
C
Question: Tough and Tricky questions: Work/Rate Problems.
If it takes 80 workers 3 hours to disassemble the exhibition rides at a small amusement park, how many hours would it take 30 workers to do this same job?
A.40/3
B.11
C.7
D.8
Answer: D.8
Explanation: 80 Workers = 3 hours then,
1 Worker = 3*80 Hours
30 Workers = (3*80) /(30) = 8 Answer.D
Question: There are r members in a certain department, including Michael. Two representatives are to be selected to attend a company conference. If there are 55 possible combinations in which Michael is not selected, what is the value of r?
A.11
B.12
C.15
D.18
Answer: B.12
Explanation: Combinations of two persons, in which Michael was not selected = 55
number of ways two persons can be selected from m people = m*(m-1)/2
Let m be the number of people excluding Michael, then m*(m-1) = 110 => m=11
Thus, r = m + 1(Michael) = 12
option B
Question: 8 persons can build a wall 140m long in 42 days. In how many days can 30 persons complete a similar wall 100 m long?
A.12
B.10
C.8
D.6
Answer: C.8
Explanation: Explanation:
Work done by 8 persons working 42 days = 140
Work done by 1 person working 42 days =140/8
Work done by 1 person working 1 day =140/8×42
Work done by 30 persons working 1 day
=30×140/8×42=100/8
Assume that 30 persons working xx days complete a similar wall 100 m
=> Work done by 30 persons working x days = 100
Hence x=100/(100/8)=8
Answer: Option C
Question: A person walks at a speed of 4 km/hr and runs at a speed of 8 km/hr. How many hours will the person require to cover a distance of 16 km, if the person completes half of the distance by walking and the other half by running?
A.2
B.2.5
C.3
D.3.5
Answer: C.3
Explanation: time = 8/4 + 8/8 = 3 hours
The answer is C.
Question: Salesperson A's compensation for any week is $360 plus 8 percent of the portion of A's total sales above $1,000 for that week. Salesperson B's compensation for any week is 8 percent of A's total sales for that week. For what amount of total weekly sales would both salepeople earn the same compensation?
A.$21,000
B.$18,000
C.$15,000
D.$ 7,750
Answer: D.$ 7,750
Explanation: sometime, setting up an equation is an easy way to go with:
350 + 0.04(x - 1000) = 0.08 x
x = 7,750
Ans : D
Question: A man can row upstream 10 kmph and downstream 20 kmph. Find the man rate in sƟll water and rate
of the stream.
A.0,5
B.5,5
C.15,5
D.10,5
Answer: C.15,5
Explanation: Explanation:
Please remember,
If a is rate downstream and b is rate upstream
Rate in still water = 1/2(a+b)
Rate of current = 1/2(a-b)
=> Rate in still water = 1/2(20+10) = 15 kmph
=> Rate of current = 1/2(20-10) = 5 kmph
Answer: C
Question: A certain quantity is measured on two different scales, the R scale and the S scale, that are related linearly. Measurements on the R scale of 6 and 24 correspond to the measurements on the S scale of 30 and 60 respectively. What measurement on the R scale corresponds to a measurement of 80 on the S scale?
A.26
B.28
C.32
D.36
Answer: D.36
Explanation: A change of +18 on the R scale is a change of +30 on the S scale.
R = (18/30)*S + K = 3S/5 + K
6 = 3(30)/5 + K
K = -12
R = 3S/5 - 12
R = 3(80)/5 - 12 = 48-12 = 36
The answer is D.
Question: A class is given an exam. 87% of students pass with a C or greater, the remaining students fail. Of the passing students, 48% received a C, and those who received an A was 25% of those who received a B. What percent of students received an A?
A.9.05%
B.16.10%
C.36.19%
D.12.00%
Answer: A.9.05%
Explanation: Percent of students who pass the exam: 87%
Percent of students who received a C: 87% x 48% = 41.76%
Percent of students who received an A or B = 87% - 41.76% = 45.24%
A students = 25% B students
.25 B + B = 45.24%
B = 36.19%
25% of 36.19% = 9.05% of students received an A
9.05+36.19+41.76+13=100% of students
Answer is A
Question: Mohan's salary was first increased by 20% and then decreased by 20%. If his present salary is Rs. 7200, then what was his original salary?
A.Rs.7506
B.Rs.7500
C.Rs.7572
D.Rs.7532
Answer: B.Rs.7500
Explanation: Let Mohan's salary be Rs.100.
When increased by 20%, Mohan's salary = Rs.120
Again when decreased by 20%, Mohan's salary = 120 - 24 = Rs. 96.
But present salary is Rs. 7200
for, 96 ---> 100 ; 7200 ---> ?
Required salary is 7200/96 * 100 = Rs.7500
Answer:B
Question: If a : b : : 3 : 5, b : c : : 4 : 3 and c : d : : 4 : 5, a : d = ?
A.4 :5
B.16 : 25
C.64 : 25
D.64 : 125
Answer: B.16 : 25
Explanation: Explanation:
a/b * b/c * c/d = 3/5 * 4/3 * 4/5 = 42/52 = 16/25
a : d = 16 : 25
ANSWER B
Question: Rahul went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
A.Rs 15
B.Rs 12.10
C.Rs 19.70
D.Rs 16.80
Answer: C.Rs 19.70
Explanation: Explanation :
Let the cost of the tax items = x
Given that tax rate = 6%
Cost of tax items, x*(6/100) = 30/100
x = 5 rs
Now non taxable item = total cost - cost for taxable item - tax
= 25 - 5 - 0.30
=19.70
Answer : C
Question: In a friendship gang Andrew has 8 gang, in how many ways can he invite one or more of the gang to his house?
A.200
B.255
C.260
D.265
Answer: B.255
Explanation: Andrew can select one or more than one of his 8 gang.
=> Required number of ways = 28 – 1= 255.
B
Question: A and B started business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 24,000. What will be B's share in the total profit of Rs. 20,000 earned at the end of 2 years from the starting of the business?
A.A)6792.45
B.B)7389
C.C)7379
D.D)7453
Answer: A.A)6792.45
Explanation: A:B:C = (20000 * 24) : (15000 * 24) : (24000 * 18) = 20:15:18
B's share = 20000 * 18/53 = Rs.6792.45
Answer: A
Question: City A to city B, Andrew drove for 1hr at 48 mph and for 3 hours at 60 mph. What was the average speed for the whole trip?
A.57
B.57.5
C.61
D.61.5
Answer: A.57
Explanation: The total distance is 1×48+3×60=228
And the total time is 4 hours. Hence,
Average Speed=(Total Distance/Total Time)
=228/4=57
A
Question: A large tanker can be filled by two pipes A and B in 10 and 5 hours respectively. How many hours will it take to fill the tanker from empty state if A and B fill it together?
A.3hr 20min
B.3hr 50min
C.4hr
D.4hr 10min
Answer: A.3hr 20min
Explanation: Part filled by A in 1hr = 1/10
Part filled by B in 1hr = 1/5
part filled by A+B = 1/10 + 1/5 = 3/10
Both the pipes can fill the tank in = 10/3 hours = 3 hr 20min
Answer is A
Question: In a row of 30 seats, six team of 4 persons each will be seated. The members of any one team always sit together in four consecutive seats in the same order. Different teams may be adjacent or separated by empty seats. In how many ways can the six teams be seated in the 30 seats?
A.(6!)(6!)
B.12!/6!
C.12C6
D.30C12
Answer: B.12!/6!
Explanation: There are total 30 seats, but 4 members of 6 different groups always sit together and in same sequence...
So the group can be taken as one seat, making the total as 12 seats..
12 seats include 6 empty chairs as total 6*4 chairs are filled in 30 seats and these 6 seats will be identical while the other 6 would be different as each consists of different group..
Ans 12!/6!
B
Question: As part of a promotion designed to attract visitors, an amusement park gives out 24,600 free tickets per year. Usually, the number of tickets given away each month is constant. Due to an employee error, only 8500 tickets were given out in the first four months of the year. How many tickets should the amusement park give out in the fifth month so that it will begin the sixth month back on its regular giveaway schedule?
A.2054
B.2501
C.2200
D.1750
Answer: D.1750
Explanation: 24600/12=2050
2050*5=10250
10250-8500=1750
Answer D
Question: X and Y invest Rs.21000 and Rs.17500 respectively in a business. At the end of the year, they make a profit of Rs.26400. What is the share of X in the profit?
A.14420
B.14400
C.14600
D.14800
Answer: B.14400
Explanation: Ratio of the investment
=21000:17500=210:175 =42:35=6:5
Share of X in the profit
=26400×6/11=2400×6=14400
Answer is B.
Question: In a box of 16 pens, a total of 3 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective?
A.1/6
B.2/9
C.6/20
D.13/20
Answer: D.13/20
Explanation: Method- 1
There are 9 fine pieces of pen and 3 defective in a lot of 16 pens
i.e. Probability of first pen NOT being defective = (13/16)
i.e. Probability of Second pen NOT being defective = (12/15) [15 pen remaining with 12 defective remaining considering that first was defective]
Probability of Both pen being NON-defective = (12/15)*(13/16) = 13/20
Answer: option D
Question: Find the average of first 4 multiples of 5?
A.10
B.15
C.12.5
D.13
Answer: C.12.5
Explanation: average = (5+10+15+20)/4 = 12.5
Answer is C
Question: The ratio of the length and the width of a rectangle is 4 : 3 and the area of the rectangle is 4332 sq cm. What is the ratio of the width and the area of the rectangle?
A.1:72
B.1:76
C.1:80
D.1:84
Answer: B.1:76
Explanation: Let the length and the width be 4x and 3x respectively.
Area = (4x)(3x) = 4332
12x^2 = 4332
x^2 = 361
x = 19
The ratio of the width and the area is 3x : 12x^2 = 1 : 4x = 1 : 76
The answer is B.
Question: What is the sum of all remainders obtained when the first 110 natural numbers are divided by 9?
A.397
B.401
C.403
D.405
Answer: C.403
Explanation: A positive integer can give only the following 9 remainders when divided by 9: 1, 2, 3, 4, 5, 6, 7, 8, and 0.
1 divided by 9 gives the remainder of 1;
2 divided by 9 gives the remainder of 2;
...
8 divided by 9 gives the remainder of 8;
9 divided by 9 gives the remainder of 0.
We'll have 11 such blocks, since 99/9=11. The last will be:
91 divided by 9 gives the remainder of 1;
92 divided by 9 gives the remainder of 2;
...
98 divided by 9 gives the remainder of 8;
99 divided by 9 gives the remainder of 0.
The last number, 100, gives the remainder of 1 when divided by 9, thus the sum of all remainders will be:
11(1+2+3+4+5+6+7+8+0)+1=403.
Answer: C.
Question: A is twice as good a workman as B and they took 7 days together to do the work B alone can do it in.
A.17 days
B.21 days
C.29 days
D.25 days
Answer: B.21 days
Explanation: WC = 2:1
2x + x = 1/7
x = 1/21 => 21 days
ANSWER:B
Question: At Jefferson Elementary School, the number of teachers and students (kindergarten through sixth grade) totals 510. The ratio of students to teachers is 16 to 1. Kindergarten students make up 1/10 of the student population and fifth and sixth graders account for 1/3 of the remainder. Students in first and second grades account for 1/4 of all the students. If there are an equal number of students in the third and fourth grades, then the number of students in third grade is how many greater or fewer than the number of students in kindergarten?
A.20 greater
B.17 fewer
C.28 fewer
D.36 fewer
Answer: A.20 greater
Explanation: Soln>> from the given ratio of 16:1 u can derive that ter are 480 students
KG= 1/10 * 480 =48
5th and 6th graders = 1/3 * 384= 128 (1/3 of remainder)
1st and 2nd grade = 1/4 * 480 =120 ( 1/4 of all students)
equal number of students in 3rd and 4th => 480 - 344= 136 and 136/2=68 each since equal number
(344 is the sum of remaining students)
thus 48-68 =20>>> therfore answer is 20 greater
A
Question: A train 455 m long, running with a speed of 63 km/hr will pass a tree in?
A.22 sec
B.16 sec
C.17 sec
D.39 sec
Answer: D.39 sec
Explanation: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 455 * 2/35 = 39 sec
Answer:D
Question: The ratio of the radius of two circles is 4: 3, and then the ratio of their areas is?
A.1: 8
B.1: 6
C.1: 9
D.16: 9
Answer: D.16: 9
Explanation: r1: r2 = 4: 3
Πr12: Πr22
r12: r22 = 16: 9
Answer:D
Question: {1,2,3,4,5,5,6,6}how many four digited numbers can be formed without repiting the numbers?
A.180
B.360
C.460
D.500
Answer: B.360
Explanation: n*(n-1)*(n-2)...
hence four digits with out repetition total 6 digits=n
6*5*4*3=360
ANSWER:B
Question: If k > 0, which of the following could be true?
I. k^3 > k^2
II. k^2 = k
III. k^2 > k^3
A.I only
B.III
C.IIIII
D.All of the above
Answer: D.All of the above
Explanation: 1. k^3 > k^2 Well this is true for all k > +1 (but not for values 0 < k < 1)
2. k^2 = k This is true for only one positive number, 1
3. k^2 > k^3 Again this is true only for values of k such that 0 < k < 1
So the answer is D, since there exists at least one value of k which satisfies the equation/ in equation(s)
Question: If m is an integer greater than 6, which of the following must be divisible by 3?
A.m (m+2) (m-1)
B.m (m+1) (m-4)
C.m (m+3) (m-5)
D.m (m+4) (m-2)
Answer: B.m (m+1) (m-4)
Explanation: anything in the form of (m-1) (m) (m+1) is divisible by 3. in other word, a product of any 3 consecutive intevers is divisible by 3.
m (m+1) (m-4) = m (m+1) ((m-1)-3) is equivalant to (m-1) (m) (m+1)
m (m+2) (m-1) is equivalant to (m+1) missing.
m (m+3) (m-5) is equivalant to (m-1) missing and m repeating.
m (m+4) (m-2) is equivalant to odd/even consqcutive integers
m (m+5) (m-6) is equivalant to (m+1) missing and m repeating.
Answer : B
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
B.7.5
C.2.25
D.2
Answer: D.2
Explanation: M = 6
S = x
DS = 6 + x
US = 6 - x
6 + x = (6 - x)2
6 + x = 12 -2x
3x = 6
x = 2
ANSWER:D
Question: Mr. Kutty has only hens and sheep. If the total number of their heads is 38 and the total number of legs is 100 then what is the ratio between the numbers of hens and sheep?
A.2 : 1
B.1 : 2
C.6 : 13
D.13 : 6
Answer: D.13 : 6
Explanation: Let the total number of hens and sheep be x and y respectively.
i.e., x + y = 38 and 2x + 4y = 100
∴ Ratio = 13 : 6
Answer D
Question: If |4x+6| = 50, what is the sum of all the possible values of x?
A.2
B.-2
C.4
D.-3
Answer: D.-3
Explanation: There will be two cases
4x+6= 50 or 4x+6 = -50
=> x =11 or x= -14
sum of both the values will be -14 +11 = -3
Answer is D
Question: A total of $20,000 was invested in two certificates of deposit at simple annual interest rates of 6 percent and 8 percent, respectively. If the total interest on the two certificates was $1,440 at the end of one year, what fractional part of the $20.000 was invested at the higher rate?
A.3/8
B.2/5
C.1/2
D.3/5
Answer: D.3/5
Explanation: Let "$x" be invested with the higher rate of 8%
Thus, "20000-x" must have been invested with lower rate of 6%
Simple Interest = Principal* Rate* Time
For the Amount invested at 8%
Principal = x
Rate = 0.08
Time = 1
Simple Interest = x* 0.08* 1= 0.08x
For the Amount invested at 6%
Principal = 20000-x
Rate = 0.06
Time = 1
Simple Interest = (20000-x)* 0.06* 1= 1200-0.06x
Total Interest = $1440
0.08x+1200-0.06x=1440
0.02x=240
x = 240/0.02=12000
Fraction of x per total amount = 12000/20000 = 12/20 = 3/5
Ans: "D"
Question: If ab = 3(a + 1) + b and a and b are integers, a could be any of the following values EXCEPT:
A.2
B.3
C.6
D.4
Answer: C.6
Explanation: ab = 3(a + 1) + b
ab - b = 3(a + 1)
b = 3(a + 1)/(a-1)
b won't be an integer only if a = 6 (from the options).
Answer: C
Question: If logX/(a2 + ab + b2) = log Y/(b2 + bc + c2) = logZ/(c2 + ca + a2), then Xa - b.Yb - c. Zc - a =?
A.0
B.-1
C.1
D.2
Answer: C.1
Explanation: Each ratio = k = log X = k(a2 + ab + b2)
=> (a - b)logX = k(a3 - b3)
Similarly, Yb - c = ek(b3 - c3), Zc - a= ek(c3 - a3)
Therefore, Xa - b.Yb - c.Zc - a = e0 = 1.
ANSWER:C
Question: If a, b, c are integers and ab>0, bc >0, ac<0, then which of the following is false?
I.	a=0, b>0, c>0
II.	a>0, b=0, c>0
III.	a>0, b>0, c=0
A.I only
B.II only
C.III only
D.I, II and III
Answer: D.I, II and III
Explanation: We could solve this easily.
I is false. If a=0 then ab=0, ac=0. But since ac<0, it is false.
II is false. If b=0 then ab=0, bc=0. But since bc>0, it is false.
III is false. If c=0 then ac=0, bc=0. But since ac<0, it is false.
So, the answer is D
Question: A man cycling along the road noticed that every 3 minutes a bus overtakes him and every 9 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses?
A.5 minutes
B.6 minutes
C.8 minutes
D.9/2 minutes
Answer: D.9/2 minutes
Explanation: Let's say the distance between the buses is d. We want to determine Interval=\frac{d}{b}, where b is the speed of bus.
Let the speed of cyclist be c.
Every 9 minutes a bus overtakes cyclist: \frac{d}{b-c}=9, d=9b-9c;
Every 3 minutes cyclist meets an oncoming bus: \frac{d}{b+c}=3, d=3b+3c;
d=9b-9c=3b+3c, --> b=2c, --> d=9b-9b/2=9b/2.
Interval=\frac{d}{b}=\frac{9/2b}{b}=9/2
Answer: D (9/2 minutes).
Question: A, B and C have Rs.400 between them, A and C together have Rs.200 and B and C Rs.350. How much does C have?
A.Rs.250
B.Rs.90
C.Rs.50
D.Rs.150
Answer: D.Rs.150
Explanation: A+B+C = 400
A+C = 200
B+C = 350
--------------
A+B+2C = 550
A+B+C = 400
----------------
C = 150
ANSWER:D
Question: How many quarters are equal to 5 dollars?
A.1
B.8
C.12
D.20
Answer: D.20
Explanation: 5*4 = 20 quarters
Answer : D
Question: Carmen made a sculpture from small pieces of wood. The sculpture is 2 feet 10 inches tall.Carmen places her sculpture on a base that is 6 inches tall. How tall are the sculpture andbase together?
A.3.1 feet
B.3.2 feet
C.3.3 feet
D.3.4 feet
Answer: C.3.3 feet
Explanation: we know 1 feet =12 inch then
2 feet =24 inch
24+10=34 then
34+6=40
40/12=3.3 feet
ANSWER:C
Question: The number 90 can be written as the sum of the squares of 4 different positive integers. What is the sum of these 4 integers?
A. 17
B. 16
C. 15
D. 14
Answer: B. 16
Explanation: 4^2 + 3^2 + 8^2 + 1^2 = 90 --> 1 + 3 + 8 + 4 = 16.
B
Question: In a simultaneous throw of two dice , what is the probability of getting to total of 10 or 11?
A.5/36
B.5/7
C.7/4
D.9/8
Answer: A.5/36
Explanation: n(S)36
n(E)=5
P(E)=5/36
Ans: A
Question: Two trains are traveling on parallel tracks in the same direction. The faster train travels at 130 miles per hour, while the slower train travels at 100 miles per hour. At 2 o’clock the faster train is 30 miles behind the slower one. How far apart are the two trains at 5 o'clock?
A.60 miles
B.80 miles
C.90 miles
D.120 miles
Answer: A.60 miles
Explanation: Answer = A. 60 miles
Relational speed = 130 - 100 = 30 miles per hour
In 3 hours, difference = 30 * 3 = 90 miles
Fast train trailing 30 miles, so effective difference = 90 - 30 = 60 miles
Question: How long does a train 100 m long travelling at 60 kmph takes to cross a bridge of 120 m in length?
A.15.8 sec
B.13.2 sec
C.12.4 sec
D.16.8 sec
Answer: B.13.2 sec
Explanation: B
13.2 sec
D = 100 + 120 = 220 m
S = 60 * 5/18 = 50/3
T = 220 * 3/50 = 13.2 sec
Answer is B
Question: A coin is weighted so that the probability of heads on any flip is 0.1, while the probability of tails is 0.9. If the coin is flipped 5 times independently, which of the following represents the probability that tails will appear no more than twice?
A.(0.1)^5 + 5(0.1)^4(0.9) + 10(0.1)^3(0.9)^2
B.(0.1)^5 + 4(0.1)^4(0.9) + 6(0.1)^3(0.9)^2
C.(0.6)^5 + 3(0.6)^4(0.4) + 2(0.6)^3(0.4)^2
D.(0.6)^5 + 2(0.6)^4(0.4) + (0.6)^3(0.4)^2
Answer: A.(0.1)^5 + 5(0.1)^4(0.9) + 10(0.1)^3(0.9)^2
Explanation: Probability of Head, P(H) = 0.1
Probability of Tail, P(T) = 0.9
Tail will appear NO more than twice
i.e. favourable cases
2 Tails and 3 Heads, Probability = 5C2*(0.1)^3*(0.9)^2
1 Tail and 4 Heads, Probability = 5C1*(0.1)^4*(0.9)^2
0 Tail and 5 Heads, Probability = (0.1)^5
Required Probability = Sum of all Favourable cases = (0.1)^5 + 5(0.1)^4(0.9) + 10(0.1)^3(0.9)^2
Answer: option A
Question: What is the positive difference between the sum of the squares of the first 8 positive integers and the sum of the prime numbers between the first square and fourth square?
A.161
B.162
C.163
D.164
Answer: C.163
Explanation: Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.
the sum of the squares of the first 4 positive integers = 1^2 + 2^2 + 3^2 +...+8^2= 204
the sum of the prime numbers between the first square(=1) and fourth square(=16) = 2+3+5+7+11+13=41.
So the difference between 41 and 204 is 163.
So the answer is (C).
Question: If (c - a)/(c - b) = 1, then (5b + 5a)/(c - a) =
A.10
B.1
C.1.5
D.2
Answer: A.10
Explanation: Let's say c=2, b=1, a=1 so that our 1st expression holds true. Now, ibsert those numbers in the second expression and we'll get10
Answer A (hopefully )))
Question: A man's speed with the current is 15 km/hr and the speed of the current is 2.8 km/hr. The man's speed against the current is?
A.9.4
B.20
C.50
D.30
Answer: A.9.4
Explanation: Man's speed with the current = 15 km/hr
=> speed of the man + speed of the current = 15 km/hr
speed of the current is 2.8 km/hr
Hence, speed of the man = 15 - 2.8 = 12.2 km/hr
man's speed against the current = speed of the man - speed of the current
= 12.2 - 2.8 = 9.4 km/hr
Answer is A.