RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Given that 2x + 17 > 5 and 5x - 13 < 7, all values of x must be between which of the following pairs of integers?
A.-4 and -1
B.-1 and 4
C.-4 and 1
D.-6 and 4
Answer: D.-6 and 4
Explanation: 2x + 17 > 5
i.e 2x >5-17
i.e. 2x > -12
i.e. x > -6
Also, 5x - 13 < 7
i.e. 5x <7+13
i.e 5x < 20
i.e x < 4
i.e. -6 < x < 4
Answer: Option D
Question: For the positive numbers, n, n + 2, n + 4, n + 6, and n + 8, the mean is how much greater than the median?
A.n+l
B.1
C.0
D.n+2
Answer: C.0
Explanation: Let’s first calculate the mean (arithmetic average).
mean = sum/quantity
mean = (n + n + 2 + n + 4 + n + 6 + n + 8)/5
mean = (5n + 20)/5
mean = n + 4
Next, we determine the median. The median is the middle value when the terms are ordered from least to greatest. The terms ordered from least to greatest are as follows:
n, n + 2, n + 4, n + 6, n + 8
The median is n + 4.
Finally we are asked how much greater the mean is than the median. To determine the difference we can subtract the smaller value (the median) from the larger value (the mean) and we get:
n + 4 – (n + 4) = n + 4 – n – 4 = 0
The answer is C
Question: if 7v passes to that wire and a current of 260mA then find the resistance
A.26.9
B.27.9
C.28.9
D.29.9
Answer: A.26.9
Explanation: V=IR
=> R=V/I = 7 V / 260 mA = 7 V / 260*10^(-3) A = 26.92 ohm
ANSWER:A
Question: An urn contains 5 red, 6 blue and 8 green balls. 4 balls are randomly selected from the urn, find the probability that the drawn ball are 1 blue and 2 red and 1 green balls ?
A.20/323
B.40/323
C.60/273
D.50/373
Answer: B.40/323
Explanation: Sample space = no. of ways 4 balls were drawn from urn = 19C4 = 3876
No. ways 1 blue and 2 red and 1 green balls were drawn from bag = 6C1 * 5C2 * 8C1 = 480
Probability = 480 / 3876 = 40/323
Ans - B
Question: In a garden, trees are planted in rows. In each row there are as many trees as the number of rows in the garden. If the total number of trees in that garden is n, then :
A.n is a perfect square
B.n is an odd number
C.n is an even number
D.n is a perfect cube.
Answer: A.n is a perfect square
Explanation: If there are, for example, 4 rows of trees, each row would have 4 trees. The total would be 4*4=16, which is a perfect square.
Answer: A
Question: A glucose molecule contains 6 carbon, 12 hydrogen and 6 oxygen atoms. During photosynthesis, green plants create glucose daily. If, over a period of 15 days, an eucalyptus plant (a green plant) creates 15,000 molecules of glucose then approximately how many more atoms of hydrogen than carbon are created on average per day?
A.60,000
B.6,000
C.2,500
D.250
Answer: B.6,000
Explanation: Solution:
We know that 15,000 glucose molecules are created over a period of 15 days. Therefore 15,000/15 = 1,000 glucose molecules are created on average per day.
Each glucose molecule contains 6 carbon atoms and 12 hydrogen atoms. So 1,000 glucose molecules contain 6 × 1,000 = 6,000 carbon atoms and 12 × 1,000 = 12,000 hydrogen atoms. The difference is 12,000 – 6,000 = 6,000.
The correct answer is B.
Question: Sum of the squares of three numbers is 138 and the sum of their products taken two at a time is 131. Find the sum?
A.20
B.24
C.27
D.28
Answer: A.20
Explanation: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 138 + 2* 131
a + b + c = √400 = 20
A
Question: Out of 470 students of a school, 325 play football, 175 play cricket and 50 neither play football nor cricket. How many students play both football and cricket ?
A.80
B.150
C.100
D.180
Answer: A.80
Explanation: n(A)=325,n(B)=175,n(AuB)=470-50=420.
Required number = n(AnB)=n (A)+n (B)-n(AuB)=325+175-420=80.
Answer is A
Question: For 6-digit integer 46x,y12, when x and y are drawn at random from {3,5,8}, what is the probability T that the integer drawn is divisible by 8?
* A solution will be posted in two days.
A.1/6
B.1/3
C.1/2
D.2/3
Answer: D.2/3
Explanation: In general, the remainder divided by integer n is the same as the remainder that up to tens of n is divided by 8.
Thus, in order for 46,x,y12 to be divided by 8, y12 should be divided by 8.
Amongst 3,5,8, 3 and 5 can be divided by 8.
Therefore,T two out of three can be divided and the answer is D.
Question: 8 people decided to split the restaurant bill evenly. If the bill was $314.12 dollars, how much money did they 1 cent is the smallest unit?
A.$314.16
B.$314.17
C.$314.18
D.$314.19
Answer: A.$314.16
Explanation: If the last three digits of a whole number are divisible by 8, then the entire number is divisible by 8
the last 3 digit 412 not divisible by a
Hence, we need to add 4 to this number for it to be divisible by 8
Correct Option: A
Question: The sum Q of the arithmetic sequence a, a+d, a+2d,..., a+(n-1)d is give by Qn = (n/2)*(2a + n-1)d. What is the sum of the integers 1 to 100 inclusive, with the even integers between 25 and 63 omitted.
A.4345
B.4302
C.4258
D.4214
Answer: D.4214
Explanation: a method to do it under one minutes is to take advantage of the choices given...
lets work on the last digit as we have different units digit in each choice...
total sum of 1 to 100 inclusive will have 0 as the last digit..
this is so because the resultant will be 10*(sum of all single digits)... and since we are multiplying by 10,units digit will be 0...
now for single digit in sum Q of even number from 25 to 63..
25 to 65 will have 4 times sum of single digit even int, 4*(2+4+6+8+0)=4*20..
here too the units digit is 0, but 64 has to be excluded from the total..
two ways from here on..
1) we are subtracting 0 from 0
so units digit should be 0, but we have to add 64..
so last/units digit =4..
2)we subtract 64 from sum of even int..
so units digit=80-4=76..
or units digit =6...
so our answer should have units digit as 10-6=4..
only D has 4 as units digit..
ans D
Question: A company hired a printer to produce a total of x + 1 envelopes. The job consisted of two types of envelopes, 4¢ envelopes and 7¢ envelopes. If the company requested 3 more 4¢ envelopes than 7¢ envelopes, which of the following expressions denotes the cost, in cents, of the total x + 1 envelopes ?
A.(9x-12)/2
B.4x+13
C.3x+34
D.6x-4
Answer: D.6x-4
Explanation: We can take
X+1 = 11
X= 10
So 4c envelopes will be 7
and 7c envelopes will be 4
So total cost will be 56
Then that is our target
Plug x =10 in answer choices
Only D works
Correct Answer :D
Question: If six persons sit in a row, then the probability that three particular persons are always together is -
A.1/9
B.1/7
C.1/5
D.1/1
Answer: C.1/5
Explanation: Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6!
= 1/5
Answer: C
Question: A man is 24 years older than his son.In two years,his age will be twice the age of his son.The present age of the son is:
A.14 years
B.18 years
C.20 years
D.22 years
Answer: D.22 years
Explanation: Solution
Let the son's present age be x years.Then,man's present age =(x + 24)years.
∴ (x + 24)+ 2 =2(x + 2) ⇔ x + 26 =2x + 4 ⇔ x =22. Answer D
Question: Sakshi can do a piece of work in 5 days.Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work :
A.4
B.16
C.18
D.25
Answer: A.4
Explanation: Solution
Ratio of times taken by Sakshi and Tanya = 125 : 100 = 5 : 4 .
Suppose Tanya taken x days to do the work.
5 : 4 : : 5 : x ⇒ x = (5x4/5) ⇒ x = 4 days.
Hence,Tanya takes 16 days is complete the work.
Answer A
Question: A die is thrown twice and the sum of the numbers appearing is observed to be 6.
find the conditional probability that the number 4 has appeared at least once?
A.2/5
B.4/5
C.5/7
D.7/11
Answer: A.2/5
Explanation: Let E be the event that ‘number 4 appears at least once’ and F be
the event
that ‘the sum of the numbers appearing is 6’.
Then, E = {(4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (1,4), (2,4), (3,4),
(5,4), (6,4)}
and F = {(1,5), (2,4), (3,3), (4,2), (5,1)}
We have P(E) = 11/36
and P (F) = 5/36
Also EnF = {(2,4), (4,2)}
Therefore P(EnF) = 2/36
the required probability
P(E|F) = P(EnF)/P(F) = (2/36)/(5/36) = 2/5
A)
Question: Find the rate at Simple interest, at which a sum becomes four Ɵmes of itself in 15 years.
A.10%
B.20%
C.30%
D.40%
Answer: B.20%
Explanation: Explanation:
Let sum be x and rate be r%
then, (x*r*15)/100 = 3x [important to note here is that simple interest will be 3x not 4x, beause 3x+x =
4x]
=> r = 20%
Answer: B
Question: The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?
A.22
B.88
C.27
D.89
Answer: C.27
Explanation: The total of seven numbers = 7X18 = 126
The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99
So, the middle number is (126 - 99 ) = 27
Answer: C
Question: Find the least number of complete years in which a sum of money put out at 25% compound interest will be more than double of itself?
A.6 years
B.9 years
C.5 years
D.4 years
Answer: D.4 years
Explanation: 4 years
Answer: D
Question: Four rooms of the same type were advertised to be let in a locality. four men made separate applications for a house. What is the probability that each of them applied for the same house.
A.1/16
B.1/256
C.1/64
D.4/64
Answer: C.1/64
Explanation: Each men can choose any of the three houses, hence the total number of ways they can apply is 4^4 = 256.
Each of them to apply for the same house means each of them applying for house A, B or C,D.
P = 4/256 = 1/64.
Answer: C.
Question: Jim and John are workers in a department that has a total of 8 employees. Their boss decides that two workers from the department will be picked at random to participate in a company interview. What is the probability that both Jim and John are chosen?
A.1/25
B.1/14
C.1/28
D.1/7
Answer: C.1/28
Explanation: Probability = 2c2/8c2
= 1/28
Answer C
Question: If x>y>0, which of the following must be true:
I. |x|>y
II. x^4 > y^4
III. x^2>y^2
A.I only
B.II only
C.III only
D.II and III
Answer: D.II and III
Explanation: Assuming x and y to be integers
X=3,Y=2
X^2=3^2=9
Y^2=2^2=4
So I is true
Now lets look at option III because if option 3 is true E is the answer or else A
As per question X>Y>0 Hence |X| >Y
So OA=D
Question: There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is
A.20
B.80
C.100
D.200
Answer: C.100
Explanation: Let the number of students in rooms A and B be x and y respectively.
Then, x - 10 = y + 10 x - y = 20 .... (i)
and x + 20 = 2(y - 20) x - 2y = -60 .... (ii)
Solving (i) and (ii) we get: x = 100 , y = 80.
The required answer A = 100.
Correct answer is 100
Question: A can do a piece of work in 24 days and B can do it in 15 days and C can do it 20 days. They started the work together and A leaves after 2 days and B leaves after 4 days from the beginning. How long will work lost?
A.10
B.12
C.13
D.11
Answer: C.13
Explanation: 2/24 + 4/15 + x/20 = 1
x = 13 Answer: C
Question: What is the dividend. divisor 17, the quotient is 9 and the remainder is 5?
A.148
B.154
C.156
D.158
Answer: D.158
Explanation: D = d * Q + R
D = 17 * 9 + 5
D = 153 + 5
D = 158
Question: In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples?
A.5/21
B.5/28
C.5/20
D.5/22
Answer: A.5/21
Explanation: Number of ways of (selecting at least two couples among five people selected)
As remaining person can be any one among three couples left.
Required probability
= (10 * 6)/252 = 5/21
Answer: A
Question: A fair is coin is tossed repeatedly. If head appears on first four tosses then what is the probability of appearance of tail in the fifth toss?
A.2/3
B.1/2
C.1/8
D.1/0
Answer: B.1/2
Explanation: As the given coin is a fair coin, the probability of getting tail on the fifth toss is independent of the out comes in the previous 4 tosses. So probability = 1/2
Answer:B
Question: a is an integer greater than 39 but less than 51, b is an integer greater than 49 but less than 61, what is the range of a/b?
A.1/4
B.1/3
C.3/4
D.1
Answer: B.1/3
Explanation: min value of a/b will be when b is highest and a is lowest ---> a=40 and b=60
So, a/b =2/3
max value of a/b will be when b is lowest and a is highest ---> a=50 and b=50
So, a/b = 1
Range is 1-(2/3) = 1/3.
Answer should be B.
Question: Over a three-week period, the price of an ounce of gold increased by 25% in the first week, decreased by 20% in the following week, and increased by 5% in the third week. If the price of gold was G dollars per ounce at the beginning of the three weeks, what was the price, in terms of G, at the end of the three weeks?
A.0.95G
B.1G
C.1.05G
D.1.1G
Answer: C.1.05G
Explanation: Initial price =G
By end of first week increased by 25% => Price =1.25G
By end of second week decreased by 20% => Price= 1.25*0.8G
By end of third week increased by 5% => Price=1.25*0.8*1.05G
=> Price= 1.05G
ANSWER:C
Question: A sum of money deposited at C.I. amounts to Rs.2442 in 2 years and to Rs.2926 in 3 years. Find the rate percent?
A.11
B.20
C.28
D.24
Answer: B.20
Explanation: Explanation:
2420 --- 484
100 --- ? => 20%
Answer: Option B
Question: Three persons invested Rs.9000 in a joint business. The second person invested Rs.1000 more than the first and the third Rs.1000 more than second. After two years, they gained Rs.5400. How much third person will get?
A.2400
B.2408
C.24028
D.24128
Answer: A.2400
Explanation: First persons investment = x
Second persons investment = x + 1000
Third persons investments = x + 2000
x + x + 1000 + x + 2000 = 9000
3x = 6000
x = 2000
Ratio = 2000 : 3000 : 4000
2:3:4
4/9 * 54000 = 2400
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; 4),
what is the maximum possible area of C?
A. 6
B. 9
C. 24
D. 32
Answer: B. 9
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.
B
Question: Roger can read a book in k minutes. What part of the book can he read in 7 minutes? (k>8)
A.8+k
B.k/8
C.7/k
D.(k+ 8)/k
Answer: C.7/k
Explanation: Let's sayk = 24
That is, it takes 24 minutes to read the entire book.
So, in 8 minutes, Roger can read1/3of the book
So, we're looking for the answer choice that yields an OUTPUT of1/3whenk = 24
A) 8+24=32ELIMINATE
B) 8/24=1/3KEEP
C)24/8 =3ELIMINATE
D) (24+ 8)/24=32/24 = 4/3ELIMINATE
E) (24-8) /24=16/24 = 2/3ELIMINATE
Answer: C
Question: If n = 2×3×5×7×11×13×16, then which of the following statements must be true?
I. n^2 is divisible by 600
II. n + 19 is divisible by 19
III. (n + 4)/2 is even
A.I only
B.II only
C.III only
D.I and III
Answer: D.I and III
Explanation: Statement I: 600 = (2^3)*(3)*(5^2) this is true.
Statement 2 this is NOT true.
Statement 3: (n+4)/2 = n/2 + 2, So this is true.
Hence option (D).
Question: Let f(x) = 3x2+2x+6. Two distinct lines l1 and l2 exist that are tangent to f(x) and intersect
at the origin. Given that l1 is tangent to f(x) at (x1; f(x1)) and that l2 is tangent to f(x) at
(x2; f(x2)), compute x1x2.
A.-1
B.-2
C.-3
D.-4
Answer: B.-2
Explanation: At any point (x0, y0) in f(x), the slope of the tangent line is
m = 6x0 + 2
Hence, the equation of the tangent line is given by
(y - y0) = m(x- x0)
y - (3x2
0 + 2x0 + 6) = (6x0 + 2)(x - x0)
y = (6x0 + 2)x - 6x2
0- 2x0 + 3x2
0 + 2x0 + 6
y = (6x0 + 2)x- 3x2
0 + 6
For the tangent line to cross the origin, we must have 3x2
0 - 6 = 0. This equation has two
solutions, the product of which is given by 􀀀6
3 = -2 .
correct answer B
Question: The salary of a typist was at first raised by 10% and then the same was reduced by 5%. If he presently draws Rs.1045.What was his original salary?
A.2888
B.1266
C.1000
D.2779
Answer: C.1000
Explanation: X * (110/100) * (95/100) = 1045
X * (11/10) * (1/100) = 11
X = 1000
Answer: C
Question: B alone can do piece of work in 10 days. A alone can do it in 15 days. If the total wages for the work is Rs 5000, how much should B be paid if they work together for the entire duration of the work?
A.267
B.7
C.76
D.8
Answer: A.267
Explanation: Answer:A
Question: If x and y are both odd prime numbers and x < y, how many distinct positive integer T factors does 2xy have?
A.3
B.4
C.6
D.8
Answer: D.8
Explanation: Since 2xy prime T factors are x^1*y^1*2^1, its total number or factors must be (1+1)(1+1)(1+1)=2^3=8. Thus, I think D would be the correct answer.
Question: If each of 4 subsidiaries of Corporation R has been granted a line of credit of $464,800 and each of the other 3 subsidiaries of Corporation R has been granted a line of credit of $112,000, what is the average (arithmetic mean) line of credit granted to a subsidiary of Corporation R?
A. $1,568,000
B. $448,000
C. $406,000
D. $313,600
Answer: D. $313,600
Explanation: My take is D.
(464800*4 + 112000*3)/7 = 313600
Question: A bag contains 40 black balls and 40 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
A.2/5
B.5/7
C.1/2
D.1/4
Answer: C.1/2
Explanation: Total number of balls = 40+40 = 80
no. of white balls = 40
probability of drawing a white ball = 40/80 = 1/2
Answer is C
Question: At 9:00 a.m., Tom begins traveling on a certain bike path from Riverdale at a constant rate of 10 mph. If, at 2:00 p.m., Jim begins traveling from Riverdale on the same path at a constant rate of 20 mph, at what time will he catch up to Peter?
A.4:00 p.m.
B.5:00 p.m.
C.6:00 p.m.
D.7:00 p.m.
Answer: D.7:00 p.m.
Explanation: My ans: D
By the time Jim starts, Tom has already covered = 5 hr * 10 mph = 50 miles
Relative speed = 20- 10 = 10mph
To catch up, Jim needs to cover 50 miles which can be covered in = 50/10= 5 hours
If Jim leaves at 2 pm, he will catch Tom at 7 pm.
Answer: D
Question: If a jury of 12 people is to be selected randomly from a pool of 15 potential jurors, and the jury pool consists of 2/3 men and 1/3 women, what is the probability that the jury will comprise at least 2/3 men?
A.24/91
B.45/91
C.2/3
D.67/91
Answer: D.67/91
Explanation: We have a pool of 10 men and 5 women
We need a jury of 12 people
What is the probability that the jury will comprise at least 2/3 men?
2/3 of a jury of 12 = 8 men. There will always be at least 8 men on the jury unless all 5 women are selected, in that case there will be 7 men and 5 women.
15C12 = 455 ways to select a jury of 12 from a pool of 15
5C5 = 1 way to select all 5 women
10C7 = 120 ways to select 7 men from a pool of 10
1*120 = 120 ways to select a jury with fewer than 8 men
(455-120)/455 = 335/455 = 67/91
Answer D
Question: A company produces 60000 bottles of water everyday. If a case can hold 5 bottles of water .How many cases are required by the company to hold its one day production
A.12000
B.4500
C.5000
D.8000
Answer: A.12000
Explanation: Number of bottles that can be held in a case = 5
Number of cases required to hold 60000 bottles = 60000/5=12000 cases.
So the answer is A =12000
Question: What is the average (arithmetic mean) of all the multiples of ten from 10 to 160 inclusive?
A.90
B.95
C.70
D.105
Answer: C.70
Explanation: 10 and 190 inclusive would mean there are 15 terms.
No need to add up all the terms and further divide by 15 since the terms are evenly spaced in ascending order from 10, 20, 30........160
The middle term is the average which is the tenth term = 70
C is the answer.
Question: Vijay's salary is Rs. 21,600 per month. In the first month of the year, he spends 30% of his income on clothing, 20% of the remaining on entertainment and some percentage of the remaining on food. He saves of the amount he spends. Find the percentage of spending on food as a percentage of saving.
A.180%
B.124%
C.160%
D.154%
Answer: B.124%
Explanation: Let monthly income be = x on clothing =.3x on entertainment = .2(.7x) =.14x on food = (.16x)k saving =( .3x .14x .16xk)*13 solving we get k =.31.16 putting the value and we get ...... on the food =.31x ,and saving =.25x %on food / %on saving = .06x/.25x =24%
correct answer - B
Question: The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period(in years) is?
A.2 years
B.6 years
C.7 years
D.9 years
Answer: A.2 years
Explanation: Amount = (30000 + 4347) = Rs. 34347
Let the time be n years. Then,
30000(1 + 7/100)n = 34347
= (107/100)n = 34347/30000 = (107/100)2
n = 2 years.
Answer: A:
Question: 5% people of a village in Sri Lanka died by bombardment, 15% of the remainder left the village on account of fear. If now the population is reduced to 3553, how much was it in the beginning?
A.3238
B.2667
C.4400
D.2977
Answer: C.4400
Explanation: X * (95/100) * (85/100) = 3553
X = 4400
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. 52000, then the share of B is?
A.24029
B.24000
C.24028
D.24014
Answer: B.24000
Explanation: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6
Total profit = Rs. 52000
Share of B = 6/13 (52000) = Rs. 24000
Answer:B
Question: A cistern has a leak which empty it in 8 hrs, A tap is turned on which admits 6 liters a minute into the cistern, and it is now emptied in 12 hours, How many liters does the cistern hold ?
A.8640
B.8740
C.8840
D.8540
Answer: A.8640
Explanation: Inflow of water in 12hrs with rate 6 lit/min= 6*60*12= 4320
But, the same volume is emptied in 12 hrs, so the total capacity = total inflow + total outflow= 4320+4320= 8640
ANSWER:A
Question: Kanul spent $5000 in buying raw materials, $200 in buying machinery and 30% of the total amount he had as cash with him. What was the total amount?
A.$7456.00
B.$7500.55
C.$7428.57
D.$7852.56
Answer: C.$7428.57
Explanation: Let the total amount be x
then, (100-20)% of x = 5000+200
70% of x = 5200
70x/100 = 5200
x = $52000/7
x = $7428.57
Answer is C
Question: There are n cities. What is the number of airlines that connected 2 different cities (airline from city A to city B is different with airline from city B to city A)?
A.n(n-1)
B.n(n+1)
C.n(n-1)/2
D.n(n+1)/2
Answer: A.n(n-1)
Explanation: the Q basically asks to choose two cities out of n and since the DIRECTION is important, we are looking at Permutations or combinations with Order..
nP2=nC2∗2!=n(n−1)2∗2=n(n−1)
ANSWER:A
Question: A certain manufacturer of cake, muffin, and bread mixes has 100 buyers, of whom 50 purchases cake mix, 40 purchase muffin mix, and 16 purchase both cake mix and muffin mix. If a buyer is to be selected at random from the 100 buyers, what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix?
A.1/10
B.13/50
C.1/2
D.7/10
Answer: B.13/50
Explanation: C+M+B-CM-MB-CB-2CMB = 100
C - cake buyers, M - muffin and B - Bread buyers. CM,MB,CB and CMB are intersecting regions.
the question asks for people who have bought only bread mixes = B-CB-MB-2CMB has to be found out.
50 + 40 + B-CB-MB-16-2CMB = 100
B-CB-MB-2CMB =26
hence the probability = 26/100 = 13/50.
B
Question: A jeep takes 8 hours to cover a distance of 280 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
A.28 Kmph
B.52 Kmph
C.20 Kmph
D.23 Kmph
Answer: D.23 Kmph
Explanation: Time = 8
Distance = 280
3/2 of 8 hours = 8 * 3/2 = 12 Hours
Required speed = 280/12= 23 Kmph
D)
Question: If k is an integer and 0.00010101 x 10^k is greater than 10, what is the least possible value of k?
A.3
B.4
C.5
D.6
Answer: C.5
Explanation: 0.00010101 * 10^k > 10
We need to move the decimal point to the right 5 places to get 10.101
This is equivalent to multiplying by 10^5.
The answer is C.