RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: lets say that the average (arithmetic mean) of seven numbers is 12.2
If the sum of four of these numbers is 42.8, what is the average of the other 3 numbers?
A.(a) 12.4
B.(b) 14.2
C.(c) 16.8
D.(d) 18.6
Answer: B.(b) 14.2
Explanation: We're told that the average of 7 numbers is 12.2
(Sum of numbers)/7 = 12.2
Sum of numbers = (12.2)(7) = 85.4
Next, we're told that the sum of 4 (of the 7) numbers is 42.8
From this information, we can calculate the sum of the OTHER 3 numbers:
85.4 - 42.8 = 42.6
The question asks for the AVERAGE of the OTHER 3 numbers....
42.6/3 = 14.2
B
Question: There are 680 students in a school. The ratio of boys and girls in this school is 3:5. Find the total of girls & boys are there in this school?
A.425
B.345
C.375
D.380
Answer: A.425
Explanation: In order to obtain a ratio of boys to girls equal to 3:5, the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys. The total number of boys and girls is 680. Hence
3x + 5x = 680
Solve for x
8x = 680
x = 85
Number of boys
3x = 3 × 85 = 255
Number of girls
5x = 5 × 85 = 425
A
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are picked at random, what is the probability that they are all blue?
A.fraction of 1/455
B.1/451
C.1/457
D.1/459
Answer: A.fraction of 1/455
Explanation: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
Probability that all the three marbles picked at random are blue = 3C3/15C3
= (1 * 3 * 2 * 1)/(15 * 14 * 13)
= 1/455
Answer: A
Question: If each side of a square is increased by 25%, find the percentage change in its area?
A.52.25%
B.42.55%
C.56.25%
D.36.55%
Answer: C.56.25%
Explanation: let each side of the square be a , then area = a x a
New side = 125a / 100 = 5a / 4
New area =(5a x 5a) / (4 x 4) = (25a²/16)
increased area== (25a²/16) - a²
Increase %= [(9a²/16 ) x (1/a² ) x 100]% = 56.25%
ANSWER : C
Question: A sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 45 paisa and Z gets 50 paisa. If the share of Y is RS. 27, what is the total amount?
A.115
B.116
C.117
D.118
Answer: C.117
Explanation: x:y:z = 100:45:50
20:9:10
9 --- 27
39 --- ? => 117
ANSWER:C
Question: Two trains of length 100 meters and 200 meters are 660 meters apart. They are moving towards each other on parallel tracks, at speeds of 90 km/h and 108 km/h. After how many seconds will the trains meet?
A.12
B.14
C.16
D.18
Answer: A.12
Explanation: The speeds are 90000/3600 = 25 m/s and 108000/3600 = 30 m/s
The relative speed is 55 m/s.
time = 660 / 55 = 12 seconds
The answer is A.
Question: In a mixture 60 litres, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2, then the quanity of water to be further added is:
A.20 litres
B.30 litres
C.40 litres
D.60 litres
Answer: D.60 litres
Explanation: Quantity of milk = (60 * 2/3)litres = 40 litres.
Quantity of water in it = (60- 40) litres = 20 litres.
New ratio = 1 : 2
Let quantity of water to be added further be x litres.
Then, milk : water = (40 / (20+x))
Now, (40 / (20+x)) = 1/2
20 + x = 80
x = 60.
Quantity of water to be added = 60 litres.
Answer = D
Question: How many integers between 324,805 and 458,705 have tens digit 2 and units digit 3?
A.1,352
B.1,359
C.1,329
D.1,349
Answer: D.1,349
Explanation: There is one number in hundred with 2 in the tens digit and 3 in the units digit: 23, 123, 223, 323, ...
The difference between 324,700 and 458,600 is 458,600-324,700=134,900 - one number per each hundred gives 133,900/100=1,349 numbers.
Answer: D.
Question: Two trains 121 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?
A.7.16
B.7.16
C.7.12
D.7.15
Answer: D.7.15
Explanation: T = (121 + 165)/ (80 + 65) * 18/5
T = 7.15
Answer: D
Question: The H.C.F. of two numbers is 15 and the other two factors of their L.C.M. are 11 and 15. The larger of the two numbers is:
A.225
B.300
C.299
D.322
Answer: A.225
Explanation: the numbers are (15 x 11) and (15 x 15).
Larger number = (15 x 15) = 225.
ANSWER :A
Question: Computer completes the first iteration in 10 seconds and then the following iterations are completed in 7 seconds as constants are already loaded. What is the maximum number of completed iterations under 5 minutes?
A.41
B.42
C.43
D.44
Answer: B.42
Explanation: b must be an integer as it is the number of completed iterations at a rate of 7sec/iteration
10 + 7b =5*60
7b = 290
b= 41
The total number of iterations --> 41+1 = 42 and
43rd iteration will be completed at 304seconds which is above 5 minutes
ANSWER: B
Question: Mr. Karan borrowed a certain amount at 6% per annum simple interest for 9 years. After 9 years, he returned Rs. 8110/-. Find out the amount that he borrowed.
A.Rs. 5266
B.Rs. 5269
C.Rs. 5228
D.Rs. 5218
Answer: A.Rs. 5266
Explanation: Explanation:
Let us assume Mr. Karan borrowed amount is Rs. A. (the principal)
By formula of simple interest, S.I. = PRT / 100
Where P = The principal, R = Rate of interest as a %, T = Time in years
S.I. = (P * 6 * 9)/100 = 54 P/100
Amount = Principal + S.I.
8110 = P + (54P/100)
8110 = (100P + 54P)/100
8110 = 154P/100
P = (8110 * 100)/154 = Rs. 5266.233
ANSWER: A
Question: A boat can travel 1.5 times the distance down the stream than up the stream in the same time. If the speed of the current is 2 KMPH, Find the speed of the boat in still water
A.5
B.10
C.15
D.20
Answer: B.10
Explanation: Simple question, messy language.
Lets say boat's speed is B and current's speed is C.
Upstream speed : B - C
Downstream speed : B + C
Distance will be the same both times. lets say D.
given : time it takes upstream = 1.5 times time it takes downstream
D/(B + C) = 1.5 * [D/(B - C)]
Solving B = 5 C
given : C is 2 KMPH
So B is 10 KMPH
B
Question: What profit percent is made by selling an article at a certain price, if by selling at 3/4rd of that price, there would be a loss of 20%?
A.20%
B.29%
C.7%
D.27%
Answer: C.7%
Explanation: SP2 = 3/4 SP1
CP = 100
SP2 = 80
3/4 SP1 = 80
SP1 = 107
100 --- 107 => 7%
Answer: C
Question: Mary passed a certain gas station on a highway while traveling west at a constant speed of 40 miles per hour. Then, 15 minutes later, Paul passed the same gas station while traveling west at a constant speed of 50 miles per hour. If both drivers maintained their speeds and both remained on the highway for at least 2 hours, how long after he passed the gas station did Paul catch up with Mary?
A.1/2
B.1
C.3/4
D.2
Answer: B.1
Explanation: d = rt
M: r = 40mph, t = t + 1/4hr
d = 40 (t + 1/4)
P: r = 50, t = t
d = 50t
since they went the same distance:
40t + 40/4 = 50t
10t = 10
t = 1 hr,
B
Question: 1.A committee that includes 6 members is about to be divided into 2 subcommittees with 3 members each. On what percent of the possible subcommittees that Michael is a member of is David also a member
A.A.10%
B.B.20%
C.C.25%
D.D.46%
Answer: D.D.46%
Explanation: A,B, C is too low so I eliminated those answers, E was too high of a number, so I chose D as my final answer.D
Question: What is the greatest integer that will always evenly divide the sum of seven consecutive integers?
A.2
B.3
C.4
D.7
Answer: D.7
Explanation: Let the three consecutive even integers be x , x + 7 , x+14 , x+21 , x+28 , x+35, x+42
Sum = x + x + 7 + x + 14 + x + 21 + x + 28 + x + 35 + x + 42
= 7x+147 = 7(x+21)
Therefore , 7 will always be a factor .
Answer D
Question: If the sides of a cube are in the ratio 7:3. What is the ratio of their diagonals?
A.9:4
B.8:4
C.7:4
D.7:3
Answer: D.7:3
Explanation: Explanation:
Diagonal of a Cube=a√3 where a is side
a1:a2 = 7:3
d1:d2 = 7:3 where√3 cancelled both side
ANSWER:D
Question: If the LCM and HCF of 12 and another number is 60 and 3 respectively. Find the other number ?
A.17
B.12
C.15
D.13
Answer: C.15
Explanation: HCF x LCM = Product of Numbers
3 x 60 = 12 x the other number
other number = (3 x 60) / 12
other number = 15
ANSWER : C
Question: A train running at the speed of 180 km/hr crosses a pole in 36 seconds. What is the length of the train?
A.450 m
B.500 m
C.550 m
D.600 m
Answer: D.600 m
Explanation: Speed=(180 * 5/18) m/sec
= (50/3) m/sec Length of the train
= (Speed x Time)
= (50/3 * 36) m = 600 m.
Answer:D
Question: Alok ordered 16 chapatis, 5 plates of rice, 7 plates of mixed vegetable and 6 ice-cream cups. The cost of each chapati is Rs.6, that of each plate of rice is Rs.45 and that of mixed vegetable is Rs.70. The amount that Alok paid the cashier was Rs.961. Find the cost of each ice-cream cup?
A.25
B.76
C.29
D.12
Answer: A.25
Explanation: Explanation:
Let the cost of each ice-cream cup be Rs.x
16(6) + 5(45) + 7(70) + 6(x) = 961
96 + 225 + 490 + 6x = 961
6x = 150 => x = 25.
Answer:A
Question: x, y and z are consecutive positive integers such that x < y < z; which of the following must be true?
1. yz is even
2. (z-x)(y-x+1) = 4
3. xy is odd
A.I only
B.I , II only
C.III only
D.I and II only
Answer: B.I , II only
Explanation: Since x, y and z are consecutive integers such that x < y < z, we can say x = y-1 and Z = y+1
Statement 1 yz =y*(y+1) ..if one is odd then other will be even and vice versa ..true
Statement 2 can be simplified if we write everything in terms of y as ((y+1)-(y-1))*(y-(y-1)+1) = 2*2 = 4 So, always true
Statement 3 talks about xy Since x and y are consecutive integers one of them is odd and other is even so product would always be even and hence not true.
So, I and II are always true and hence answer is
B
Question: A producer of tea blends two varieties of tea from two tea gardens one costing Rs 18 per kg and another Rs 20 per kg in the ratio 5 : 3. If he sells the blended variety at Rs 26 per kg, then his gain percent is
A.12%
B.39%
C.14%
D.15%
Answer: B.39%
Explanation: Explanation:
Suppose he bought 5 kg and 3 kg of tea.
Cost Price = Rs. (5 x 18 + 3 x 20) = Rs. 150.
Selling price = Rs. (8 x 26) = Rs. 208.
Profit = 208 - 150 = 58
So, Profit % = (58/150) * 100 = 39%
Option B
Question: The ratio of the volumes of two cubes is 125 : 512. What is the ratio of their total surface areas?
A.81 : 121
B.25 : 64
C.729 : 1331
D.27 : 121
Answer: B.25 : 64
Explanation: Ratio of the sides = Â³âˆš125 : Â³âˆš512 = 5 : 8
Ratio of surface areas = 5^2 : 8^2 = 25 : 64
ANSWER: B
Question: If â€˜MADURAIâ€™ is coded as â€˜DADCIAIâ€™, then â€˜DELHIâ€™ is coded as
A.DEHIE
B.DDEHI
C.EDDIH
D.DECHI
Answer: D.DECHI
Explanation: M=13,1+3=4=D
A=1=A
SIMILARLY,
M=13=1+3=4=D
D=4=D
E=5=E
L=12=1+2=C
H=8=H
I=9=I
SO ANS IS
DECHI
ANSWER:D
Question: Find the circumference and area of radius 7 cm.
A.124 cm²
B.144 cm²
C.154 cm²
D.184 cm²
Answer: C.154 cm²
Explanation: Area of circle = πr²
= 22/7 × 7 × 7 cm²
= 154 cm²
ANSWER:C
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 12 sec, then the speed of each train is?
A.22
B.88
C.36
D.77
Answer: C.36
Explanation: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (120 + 120)/12 => x = 10
Speed of each train = 10 m/sec.
= 10 * 18/5 =- 36 km/hr.
Answer:C
Question: If x^2+(1/x^2)=2, x^4+(1/x^4)=?
A.10
B.2
C.12
D.14
Answer: B.2
Explanation: -> x^4+(1/x^4)=(x^2)^2+(1/x^2)^2=(x^2+1/x^2)^2-2x^2(1/x^2)=2^2-2=2.
Thus, the answer is B.
Question: How many integers between 2000 and 3000 that have distinct digits and increase from left to right ?
A.10
B.20
C.60
D.120
Answer: B.20
Explanation: Since the numbers must be distinct and increasing from left to right,
The only arrangements we could come-up with are:
245_ --> 4
246_ --> 3
247_ --> 2
248_ --> 1
256_ --> 3
257_ --> 2
258_ --> 1
267_ --> 2
268_ --> 1
Number of integers =20
B
Question: How many positive integers less than 600 can be formed using the numbers 1, 2, 3, 5 and 6 for the digits?
A. 48
B. 130
C. 66
D. 68
Answer: B. 130
Explanation: Notice that we can find the number of 2 and 3 digit numbers by just assuming the first digit can also be zero:
0 1 1
1 2 2
2 3 3
3 5 5
5 6 6
Number of possibilities = 5*5*5 = 125.
Then, just add up the number of 1 digits numbers = 5, so total is 125+5 = 130.
Answer: B
Question: After an ice began to melt out from the freezer, in the first hour lost 3/4, in the second hour lost 3/4 of its remaining. If after two hours, the volume is 0.25 cubic inches, what is the original volume of the cubic ice, in cubic inches?
A.2.5
B.3.0
C.4.0
D.6.5
Answer: C.4.0
Explanation: Let initial volume of ice be = x
Ice Remaining after 1 hour = x - 0.75x = 0.25x
Ice Remaining after 2 hour = (1/4)x - (3/4 * 1/4 * x) = (1/16)x
(1/16)x = 0.25
x = 4
Alternate solution: Try to backsolve.
Initial volume = 4
After one hour --> (1/4)4 = 1
After two hours --> (1/4)1 = 0.25
Answer: C
Question: The speed of a boat in still water is 55kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
A.80,70 kmph
B.80,40 kmph
C.75,35 kmph
D.80,80 kmph
Answer: C.75,35 kmph
Explanation: Speed downstream = 55 + 20
= 75 kmph
Speed upstream = 55 - 20
= 35 kmph
Answer: C
Question: If y ≠ 3 and 2r/y is a prime integer greater than 2, which of the following must be true?
I. r = y
II. y = 1
III. r and y are prime integers.
A. None
B. I only
C. II only
D. III only
Answer: A. None
Explanation: Note that we are asked which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.
So we should try to make the listed statements not true for some r and y (which satisfy y≠3 and 2r/y=prime>2).
I. r = y --> not necessarily true: r=3 and y=2 (2r/y=3=prime>2);
II. y=1 --> not necessarily true: r=3 and y=2 (2r/y=3=prime>2);
III. r and y are prime integers --> not necessarily true: r=10 and y=4 (2r/y=5=prime>2).
Answer: A.
Question: ABCD is a square. E,F,G,H is the midpoint of the sides of square. J and K is the midpoint of the sides HG and FG . L is a point on sides EF such that LF= 1/3 EF. Find the ratio of area of triangle JKL to the area of square ABCD.
A.5: 46
B.5: 44
C.4: 48
D.5: 48
Answer: D.5: 48
Explanation: ratio = 5: 48
ANSWER:D
Question: sowdharya had 90 currency notes in all, some of which are of Rs 95 denomination and the remaining of Rs 45 denomination. The total amount of all these currency notes was Rs. 5000. How much amount (in Rs) did she have in the denomination of Rs 45?
A.75
B.72
C.71
D.76
Answer: C.71
Explanation: Let the number of 45-rupee notes = x
Then, the number of 95-rupee notes = (90 – x)
45x + 95(90 – x) = 5000 : x = 71
ANSWER:C
Question: Find the constant b so that the three points A(2 , 3), B(4 , 7) and C(8 , b) are collinear (i.e. on the same line).
A.5
B.10
C.15
D.20
Answer: C.15
Explanation: The slope of the line through A and B must be equal to the slope of the line through B and C.
(7 - 3)/(4- 2) = (b - 7)/(8 - 4)
solve the above for b to find b = 15.
correct answer C)15
Question: A feed store sells two varieties of birdseed: Brand A, which is 60% millet and 40% sunflower, and Brand B, which is 65% millet and 35% safflower. If a customer purchases a mix of the two types of birdseed that is 50% millet, what percent of the mix is Brand A?
A.40%
B.60%
C.50 %
D.45 %
Answer: B.60%
Explanation: Yes there is a simple method :
Consider the following method
Brand A : 60% millet and 40% sunflower
Brand B : 65% millet and 35% safflower
Mix : 50% millet
Here the weighted average is 50%,
Now Brand A has 60% millet, which is 10% more than the weighted average of mix = + 0.10 A --------------- I
Similarly, Brand B has 65 % millet, which is 15 % more than the weighted average of mix = + 0.15 B ------------ II
Now, both Brand A and Brand B are combined to give a 50% mix containing millet, so equate I and II
implies, 0.10 A = 0.15 B
Therefore A/B = 0.15/0.10 = 3/2
A : B : (A + B) = 3 : 2 : (3+2) = 3 : 2 : 5
We have to find, percent of the mix is Brand A i.e. A : (A + B) = 3 : 5 = (3 / 5) * 100 = 60 %
Here is a pictorial representation :
Brand A= 60%------------------------10% or 0.10 above average, A times-----------------Total above = + 0.10 A
----------------------------------------------------------------------------------------Average = 50% or 0.50
Brand B = 65 %--------------------------15% or 0.15 above average, B times-----------------Total above = + 0.15 B
Since the amount below the average has to equal the average above the average; therefore,
0.10 A = 0.15 B
A/B = 3/2
A:B: Total = 3:2:5
Therefore
A/Total = 3:5 = 60 %
Answer: B
Question: In an institute, 60% of the students are boys and the rest are girls. Further 15% of the boys and 7.5% of the girls are getting a fee waiver. If the number of those getting a fee waiver is 90, find the total number of students getting 50% concessions if it is given that 50% of those not getting a fee waiver are eligible to get half fee concession?
A.360
B.280
C.320
D.330
Answer: D.330
Explanation: Solution: Let us assume there are 100 students in the institute.
Then, number of boys = 60
And, number of girls = 40
Further, 15% of boys get fee waiver = 9 boys
7.5 % of girls get fee waiver = 3 girls
Total = 12 students who gets fee waiver
But, here given 90 students are getting fee waiver. So we compare
12 = 90
So, 1 = 90/12 = 7.5
Now number of students who are not getting fee waiver = 51 boys and 37 girls.
50% concession = 25.5 boys and 18.5 girls (i.e. total 44).
Hence, required students = 44*7.5 = 330.
Answer: Option D
Question: The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square.
A.200
B.345
C.255
D.Cannot be determined
Answer: D.Cannot be determined
Explanation: Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively.
4a = 2(l + b)
2a = l + b
l . b = 480
We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found .
Area of the square cannot be found.
Answer: Option D
Question: Find the value of 72519 x 9999 = m?
A.673223454
B.695546788
C.634899013
D.725117481
Answer: D.725117481
Explanation: 72519 x 9999 = 72519 x (10000 - 1)
= 72519 x 10000 - 72519 x 1
= 725190000 - 72519
= 725117481
D
Question: Find the area of trapezium whose parallel sides are 30 cm and 12 cm long, and the distance between them is 16 cm?
A.288 cm2
B.277 cm2
C.285 cm2
D.336 cm2
Answer: D.336 cm2
Explanation: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (30 + 12) * (16)
= 336 cm2
Answer: D
Question: A sum of money invested for a certain number of years at 8% p.a. simple interest grows to Rs.180. The same sum of money invested for the same number of years at 4% p.a. simple interest grows to Rs.120 only. For how many years was the sum invested?
A.25
B.37
C.36
D.29
Answer: A.25
Explanation: Explanation:
From the information provided we know that,
Principal + 8% p.a. interest on principal for n years = 180 …….. (1)
Principal + 4% p.a. interest on principal for n years = 120 ……… (2)
Subtracting equation (2) from equation (1), we get
4% p.a. interest on principal for n years = Rs.60.
Now, we can substitute this value in equation (2),
i.e Principal + 60 = 120
= Principal = Rs.60.
We know that SI = , where p is the principal, n the number of years and r the rate percent of interest.
In equation (2), p = Rs.60, r = 4% p.a. and the simple interest = Rs.60.
Therefore, 60 =(60*n*4)/100
=> n = 100/4 = 25 years.
Answer: A) 25years
Question: The first term of an arithmetic progression is 3 and the 10 th term is 21. Find 15 th and 22 nd terms.
A.21,35
B.31,45
C.30,46
D.29,40
Answer: B.31,45
Explanation: Exp. a = 3, T 10 = a +9d =21, 3 +9d = 21, d =18/9 = 2
T 15 = a + 14d =3 +14*2 = 31, T22 = a + 21d = 3+ 21*2 = 45
ANSWER:B
Question: Look at this series: 1.25, 7.5, ____, 270, 1620, ... What number should fill the blank?
A.50
B.65
C.45
D.55
Answer: C.45
Explanation: This is a simple multiplication series. Each number is 6 times greater than the previous number.
Answer: C
Question: Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together?
A.4
B.10
C.15
D.16
Answer: D.16
Explanation: L.C.M of 2,4,6,8,10,12 is 120. i.e after each 2 min they will toll together.So in 30 min they will toll 15 times.As they have initially tolled once,The answer will be 15+1=16.
ANSWER:D
Question: If the sales tax reduced from 3 1/2 % to 3 1/3%, then what difference does it make to a person who purchases an article with market price of Rs. 9000 ?
A.11
B.13
C.15
D.18
Answer: C.15
Explanation: Required difference = [3 ½ % of Rs.9000] – [3 1/3 % of Rs.9000]
= [(7/20-(10/3)]% of Rs.9000 =1/6 % of Rs.9000
= Rs. [(1/6)8(1/100)*9000] = Rs. 15.
Answer is C.
Question: Solve this logic number sequence puzzle by the correct digit
8080 = 6
1357 = 0
2022 = 1
1999 = 3
6666 = ?
A.four (4)
B.2
C.5
D.7
Answer: A.four (4)
Explanation: A
4
No Of circles in the number.
Question: A fish can go upstream at 35 kmph and downstream at 55 kmph, and then find the speed of the fish in still water?
A.45
B.55
C.35
D.65
Answer: A.45
Explanation: US = 35
DS = 55
M = (35 + 55)/2
= 45
Answer:A
Question: The average age of a committee of 10 members is 30 years. A member aged 60 years retired and his place was taken by another member aged 40 years . The average age of
present committee is;
A.39 years
B.28 years
C.36 years
D.35 years
Answer: B.28 years
Explanation: Total age of the committee = 30*10 = 300,
Total age when a member is retired
and a new one was joined = 300-60 +40, =280
Average age of present committee = 280/10 = 28.
ANSWER:B
Question: The function f is defined for all the positive integers s by the following rule: f(s) is the number of positive integers each of which is less than s and has no positive factor in common with s other than 1 . if p is a prime number then f(p)?
A.p-1
B.p-2
C.(p+1)/2
D.(p-1)/2
Answer: A.p-1
Explanation: The moment you put a prime number in the function f(s), notice that all the numbers lesser than s have no divisor clashing with divisor of s since s is prime!!.
For instance f(7)= {6, 5, 4, 3, 2, 1}
Thus for f(p) number of integers falling under this set will be p-1
Answer :- A
Question: The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 14000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is:
A.28
B.19
C.22
D.20
Answer: A.28
Explanation: Let the total number of workers be x. Then,
8000x = (14000 * 7) + 6000(x - 7)
= 2000x = 56000
= x = 28.
ANSWER:A
Question: Two teams Arrogant and Overconfident are participating in a cricket tournament. The odds that team Arrogant will be champion is 5 to 3, and the odds that team Overconfident will be the champion is 1 to 4. What are the odds that either Arrogant or team Overconfident will become the champion?
A.3 to 2
B.5 to 2
C.6 to 1
D.33 to 7
Answer: D.33 to 7
Explanation: Explanation :
Odds of winning Arrogant is 5/3, then their probability of winning is 5/ (5+3) i.e 5/8.
Similarly,
Odds of winning Overconfident is 1/4, then their probability of winning is 1/ (1+4) i.e 1/5.
Therefore, the probability of winning of Arrogant or Overconfident is :-
=>(5/8) + (1/5).
=>33/40.
Thus, the required odds will be 33/(40-33) i.e 33/7.
Answer : D
Question: The smallest number which when diminished by 3, is divisible by 12, 16, 18, 21 and 28 is
A.1008
B.1011
C.1022
D.1032
Answer: B.1011
Explanation: Required Number = (L.C.M of 12, 16, 18,21,28)+3
= 1008 + 3
= 1011
Answer: B
Question: Of the 150 people at a party, 70 were women, and 40 women tried the appetizer. If 50 people did not try the appetizer, what is the total number of men who tried the appetizer?
A.40
B.50
C.60
D.70
Answer: C.60
Explanation: Total people at party=150
Women=70
so Men 150-70=80
No. of pple who tried appetizer=150-50 (given info)=100
No of women who tried appetizer=40
So Remaining ppl(men) who tried the appetizer =100-40=60
Correct Option C