RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Evaluate combination
98C96=98!/(96)!(2)!
A.1617
B.4753
C.1417
D.4353
Answer: B.4753
Explanation: Explanation:
nCr=n!/(r)!(n−r)!
98C96=98!/(96)!(2)!
=98∗97*96!/(96)!(2)!
=98*97/2∗1
=4753
Option B
Question: The average weight of a group of boys is 30 kg. After a boy of weight 35 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?
A.4
B.5
C.8
D.7
Answer: A.4
Explanation: Let the number off boys in the group originally be x.
Total weight of the boys = 30x
After the boy weighing 35 kg joins the group, total weight of boys = 30x + 35
So 30x + 35 + 31(x + 1) = > x = 4.
ANSWER A
Question: The length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec is?
A.377
B.367
C.237
D.245
Answer: D.245
Explanation: Speed = 45 * 5/18 = 25/2 m/sec.
Time = 30 sec
Let the length of bridge be x meters.
Then, (130 + x)/30 = 25/2
x = 245 m.
Answer: D
Question: If a 3-number code is formed of the integers from 1 to 16 inclusively, and each of the numbers in the code is different, how many possible codes are there?
A.3140
B.3250
C.3360
D.3470
Answer: C.3360
Explanation: 16*15*14=3360
The answer is C.
Question: Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?
A.4
B.6
C.8
D.5
Answer: B.6
Explanation: Let rate = R% and time = R years.
Then, (1200 * R * R) / 100 = 432
12R2 = 432
R2 = 36 => R = 6.
Answer: B
Question: How many integers are there between 55 and 95, inclusive?
A.41
B.55
C.56
D.57
Answer: A.41
Explanation: I guess the easiest way to answer this is -
Say you have two positive integers, x and y where y > x
Then the number of integers between x and y is given by - (y - x) + 1
In this case, it's (95 - 55) + 1 = 41. Option A
Question: In how many different ways can the letters of the word 'JUDGE' be arranged such that the vowels always come together?
A.None of these
B.48
C.32
D.64
Answer: B.48
Explanation: Explanation :
The word 'JUDGE' has 5 letters. It has 2 vowels (UE) in it and these 2 vowels should
always come together. Hence these 2 vowels can be grouped and considered as a single
letter. That is, JDG(UE).
Hence we can assume total letters as 4 and all these letters are different.
Number of ways to arrange these letters = 4!= 4 x 3 x 2 x 1 = 24
In the 2 vowels (UE), all the vowels are different.
Number of ways to arrange these vowels among themselves = 2! = 2 x 1 = 2
Total number of ways = 24 x 2 = 48. Answer : Option B
Question: Four different children have jelly beans: Aaron has 3, Bianca has 7, Callie has 8, and Dante has 11. How many jelly beans must Dante give to Aaron to ensure that no child has more than 1 fewer jelly beans than any other child?
A. 2
B. 3
C. 4
D. 5
Answer: C. 4
Explanation: Since Bianca and Callie are both within 1 jelly bean of each other and Aaron has 5, Dante must provide 3 of his 11 jelly beans so each child has no more than 1 fewer jelly bean than any other child.
Dante + Aaron = 11+3 =14/2 = 7
11-7 = 4 so Dante must provide 3 jelly beans to Aaron.
Answer (C)
Question: At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party?
A.12
B.15
C.17
D.19
Answer: A.12
Explanation: In general, with n+1 people, the number of handshakes is the sum of the first n consecutive numbers: 1+2+3+ ... + n.
Since this sum is n(n+1)/2, we need to solve the equation n(n+1)/2 = 66.
This is the quadratic equation n2+ n -132 = 0. Solving for n, we obtain 11 as the answer and deduce that there were 12 people at the party.
Since 66 is a relatively small number, you can also solve this problem with a hand calculator. Add 1 + 2 = + 3 = +... etc. until the total is 66. The last number that you entered (11) is n.
Question: A shopkeeper sells his goods at cost price but uses a faulty meter that weighs 900 grams. Find the profit percent.
A.100/17%
B.100/23%
C.100/9%
D.100/13%
Answer: C.100/9%
Explanation: Explanation:
(100 + g) / (100 + x) = True measure / Faulty measure
x = 0
true measure = 1000
faulty measure = 900
100 + g / 100 + 0 = 1000 / 900
100+g = 10/9*100
g = 100/9 %
ANSWER: C
Question: The price of a T.V. set worth Rs. 40000 is to be paid in 20 installments of Rs. 2500 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be?
A.29997
B.28088
C.27098
D.37500
Answer: D.37500
Explanation: Money paid in cash = Rs. 2500
Balance payment = (40000- 2500) = Rs. 37500.
Answer:D
Question: Find out the C.I on Rs.5000 at 4% p.a. compound half-yearly for 1 1/2 years.
A.Rs.420.20
B.Rs.319.06
C.Rs.306.04
D.Rs.294.75
Answer: C.Rs.306.04
Explanation: A = 5000(51/50)3
= 5306.04
5000
-----------
306.04
ANSWER:C
Question: From an island, it is possible to reach the mainland by either Ferry P or Ferry Q. Ferry P travels for 3 hours at 8 kilometers per hour, while Ferry Q takes a route that is three times longer. If Ferry P is slower than Ferry Q by 1 kilometer per hour, how many hours longer is the journey of Ferry Q compared with the journey of Ferry P?
A.5
B.7
C.8
D.10
Answer: A.5
Explanation: The distance traveled by Ferry P is 24 km.
Then the distance traveled by Ferry Q is 72 km. Ferry Q travels at a speed of 9 kph. The time of the journey for Ferry Q is 72/9 = 8 hours, which is 5 hours more than Ferry P. The answer is A.
Question: Two pipes A and B can separately fill a tank in 2 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank?
A.8
B.10
C.12
D.14
Answer: B.10
Explanation: 4/12 + x/15 = 1
x = 10 min
ANSWER B
Question: The average number of shirts with Salman, Ambani and Dalmiya is 60, if all of them reached a shopping mall in Delhi and purchased 6 shirts each of them then average number of shirt each of them now has
A.66
B.63
C.62
D.can't be determined
Answer: A.66
Explanation: Answer
Required average
= Old average + New average
= 60 + 6 = 66
Correct Option: A
Question: If James has to pay 12 % interest per year on an amount of $60,000 for 12 year then what is total interest paid?
A.33000
B.35410
C.36074
D.35973
Answer: B.35410
Explanation: For simple interest, I = P * N * R / 100
let Principle P = x
I = x * 12 * 12 / 100
I = 1.44 * x
Amount = P + I
60000 = 1.44 x + x
x = 24590.16 = P
I = 1.44 * 24590.16
I = 35409.83
B
Question: By approximately what percent is x greater than 5/11 if (4/11)(x) = 1?
A.730%
B.560%
C.410%
D.505%
Answer: D.505%
Explanation: what percent is x greater than 5/11 if (4/11)(x) = 1?
=> x = 11/4
% change =[(11/4 -5/11) /(5/11) ] * 100
= 505%
Ans ,D
Question: A farmer used 1,034 acres of land for beans, wheat, and corn in the ratio of 5 : 2 : 4, respectively. How many E acres were used for corn?
A. 188
B. 258
C. 376
D. 470
Answer: C. 376
Explanation: consider 5x acres of land used for bean
consider 2x acres of land used for wheat
consider 4x acres of land used for corn
Total given is 1034 acres
11x =1034
x = 94
land used for corn E= 4 * 94 = 376
correct option - C
Question: The cash difference between the selling prices of an book at a profit of 4% and 6% is $3. The ratio of the two selling prices is:
A.55:23
B.52:33
C.52:53
D.45:53
Answer: C.52:53
Explanation: C
52:53
Let C.P. of the book be $x.
Then, required ratio = 104% of x / 106% of x
= 104/106 = 52/53 = 52:53
Question: if z=100^2-x^2,then for how many value of x, z is divisible by 6.
A.33
B.66
C.44
D.55
Answer: B.66
Explanation: x can be negative also.
33*2=66
ANSWER:B
Question: In how many ways can the letters of the word ACUMEN be rearranged such that the vowels alwaysappear together?
A.124 ways
B.144 ways
C.134 ways
D.154 ways
Answer: B.144 ways
Explanation: ACUMEN
AUE will come together as a group which can be arranged in 3!=6 ways.
AUE, C,M,N can be arranged in 4!=24 ways.
total possible arrangements = 24*6=144 ways
ANSWER:B
Question: How many cuboids of length 5 m, width 3 m and height 2 m can be farmed from a cuboid of 18 m length, 15 m width and 2 m height.
A.106
B.109
C.108
D.101
Answer: C.108
Explanation: (18 × 15 × 12)/(5 × 3 × 2) = 108
Answer is C.
Question: A work which could be finished in 9 days was finished 3 days earlier after 10 more men joined. The number of men employed was?
A.22
B.20
C.99
D.277
Answer: B.20
Explanation: x ------- 9
(x + 10) ---- 6
x * 9 = (x + 10)6
x = 20
Answer: B
Question: The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).
A.8, 20, 28
B.16, 28, 36
C.20, 35, 45
D.20, 35, 48
Answer: B.16, 28, 36
Explanation: Let the present ages are 4x, 7x, 9x.
=> (4x-8) + (7x-8) + (9x-8) = 56
=> 20x = 80
=> x = 4
So their present ages are: 16,28,36
ANSWER:B
Question: The average (arithmetic mean) of six numbers is 5. If 3 is subtracted from each of four of the numbers, what is the new average?
A.1.5
B.2
C.3
D.4
Answer: C.3
Explanation: Sum of 6 numbers = 6*5 =30
If 3 is subtracted from each of four of the numbers , we subtract 3*4=12 from the total sum
Sum of 6 number after subtracting 3 from each of four of the numbers = 30 - 12 = 18
New average = 18/6 = 3
Answer C
Question: 9.6 , 9.6 , 10.0 , 10.0 , 10.0 , 10.1 , 10.2 , 10.5
The mean and the standard deviation of the 8 numbers shown above is 10 and 0.278 respectively. What percent of the 8 numbers are within 1 standard deviation of the mean?
A.62.5%
B.85%
C.80.67%
D.75.50%
Answer: A.62.5%
Explanation: Within 1 standard deviation of the mean- means in the range {mean-1*sd; mean+1*sd} = {10-1*0.278; 10+0.278} = {9.722; 10.278}.
From the 8 listed numbers, 5 are within this range so 5/8=62.5%.
Answer: A.
Question: Two different types of tea are mixed, at 6 Kg of type 1 and 4 Kg of type 2. One Kg of type 1 is Rs. 6 and that of type 2 is Rs. 7. The seller get 10% profit, by this action. Find at what price, he had sold the mixture/Kg?
A.Rs 5.04
B.Rs 7.04
C.Rs 6.04
D.Rs 8.04
Answer: B.Rs 7.04
Explanation: CP of 6 kg tea of type 1= 6*6=36 Rs.
CP of 4 kg tea of type 2= 4*7=Rs 28
CP of 10 kg mixed tea = Rs Rs 64
SP of mixture for 10% profit = 64*1.1= Rs 70.4
SP of 1kg mixed tea = Rs 7.04
ANSWER:B
Question: The distance between 2 cities A and B is 1000km. A train starts from A at 12 p.m. and travels towards B at 100 km/hr. Another starts from B at 1 p.m. and travels towards A at 150 km/hr. At what time do they meet?
A.11am.
B.12p.m.
C.5pm.
D.2p.m.
Answer: C.5pm.
Explanation: Suppose they meet x hrs after 12 p.m.
Distance moved by first in x hrs + Distance moved by second in (x-1)hrs = 1000
100x + 150 (x-1) = 1000
x = 4.60 = 5 hrs
They meet at 10+5 = 5 p.m.
Answer is C
Question: If a – b = 3 and a2 + b2 = 29, find the value of ab.
A.10
B.12
C.15
D.18
Answer: A.10
Explanation: EXPLANATION
2ab = (a2 + b2) – (a – b)2
= 29 – 9 = 20
ab = 10.
Answer A
Question: A trader purchased two colour televisions for a total of Rs. 35000. He sold one colour television at 30% profit and the other 40% profit. Find the difference in the cost prices of the two televisions if he made an overall profit of 30%?
A.Rs. 28985
B.Rs. 40985
C.Rs. 20985
D.Rs. 21000
Answer: C.Rs. 20985
Explanation: Let the cost prices of the colour television sold at 30% profit and 40% profit be Rs. x and Rs. (35000 - x) respectively.
Total selling price of televisions = x + 30/100 x + (35000 - x) + 40/100 (35000 - x)
=> 130/100 x + 140/100 (35000 - x) = 35000 + 30/100 (35000)
x = 27985
35000 - x = 6985
Difference in the cost prices of televisions = Rs. 20985
ANSWER:C
Question: If f(x) = Log(x), then f -1(x) =
A.10 x
B.-10 -x
C.1 / 10 x
D.x 10
Answer: A.10 x
Explanation: Solution
y = Log(x) if and only if
x = 10y
Interchange x and y
y = 10x
Hence
f -1(x) = 10x
Answer A
Question: An aeroplane covers a particular distance at a speed of 240 kmph in 5 hours. To cover the same distance in 1 hour, it must travel at a speed of
A.300 kmph
B.720 kmph
C.700 kmph
D.450 kmph
Answer: B.720 kmph
Explanation: distance=(240*5) = 1200 km
speed=dist/time
req speed = 1200/(5/3)=>720km/hr
ANSWER B
Question: Machine A takes 100 hours to complete a certain job and starts that job at 6AM. After ten hour of working alone, machine A is joined by machine B and together they complete the job at 6PM. How long would it have taken machine B to complete the job if it had worked alone for the entire job?
A.24.65
B.22.27
C.2.273
D.11.62
Answer: C.2.273
Explanation: Let us assume total job = 100 units
A finishes 100 units in 100 hrs(given)
Hence A (working rate)= 1 units /hr
Now Given that A works for 10 hr( so 10 units done) then A and B finish total work in 12 hours. Hence A and B finish 90 units in 2 hours. Of these 1x2=2 units were done by A. Hence B did 88units in 2 hours.
Hence B(working rate)= 44 units /hr
Hence B takes 100/44 = 2.273 hours to complete the job.
Answer C.
Question: A pipe can empty 3/4th of a cistern in 12mins. In 8 mins, what part of the cistern will be empty?
A.1/2
B.3/7
C.4/9
D.3/8
Answer: A.1/2
Explanation: 3/4 ---- 12
? ----- 8 ==> 1/2
A
Question: The population of a town is 176400. If it increase at the rate of 5% per annum. What was its population 4 years ago?
A.152460
B.214560
C.145125
D.210000
Answer: C.145125
Explanation: population 2 years ago = 176400/(1 + 5/100)^4
Answer is C
Question: Frank is 13 years younger then John. In 5 years John will be twice as old as Frank. How old will Frank be in four years?
A.8
B.10
C.12
D.14
Answer: C.12
Explanation: Frank is 15 years younger then John --> F+13=J;
In 5 years John will be twice as old as Frank (in 5 year John will be J+5 years old and Frank will be F+5 years old) --> J+5=2*(F+5) --> (F+13)+5=2*(F+5) --> F=8;
In 4 years Frank will be 8+4=12 years old.
Answer: C.
Question: In a certain game there are 7 steps, referred to as step 1, step 2, and so on with the final step being step 7. The steps are played one after the other. In each step a score of 1, 2,3 or 4 is obtained. Mary played the game, getting at least one score of each of 1, 2, 3 and 4 and never getting the same score in consecutive steps. What is the greatest possible score that Mary could have gotten?
A.20
B.19
C.17
D.18
Answer: D.18
Explanation: There are two conditions:
1. Mary got at least one score of each of 1, 2, 3 and 4.
2. She never got the same score in consecutive steps.
Taking that into account, the greatest possible score that Angel could have gotten is 4 + 1 + 4 + 2+4+3 = 18
Answer: D.
Question: A 200 meter long train running at the speed of 120 kmph crosses another train running in the opposite direction at the speed of 80 kmph in 9 seconds.What is the lenght of other train.
A.210m
B.300m
C.230m
D.240m
Answer: B.300m
Explanation: Relative speeds=(120+80)km/hr
=200km/hr=(200*5/18)m/s=(500/9)m/s
let length of train be xm
x+200/9=500/9
x=300
Ans is 300m
ANSWER:B
Question: A train running at the speed of 54 km/hr crosses a pole in 9 seconds. Find the length of the train?
A.135
B.272
C.278
D.277
Answer: A.135
Explanation: Speed = 54*(5/18) m/sec = 15 m/sec
Length of Train (Distance) = Speed * Time
(15) * 9
= 135 meter
Answer: A
Question: From given equation find the value of x: 2x² + 9x − 5
A.−5
B.-4
C.-3
D.3
Answer: A.−5
Explanation: That quadratic is factored as follows:
2x² + 9x − 5 = (2x − 1)(x + 5).
Lesson 17.
Now, it is easy to see that the second factor will be 0 when x = −5.
As for the value of x that will make
2x − 1 = 0,
we must solve that little equation. (Lesson 9.)
We have:
2x = 1
x = 1
2
The solutions are:
x = 1/2 or −5
A
Question: A and B working separately can complete a piece of work in 9 and 12 days respectively. If they work alternatively starting from A in how many days will the work be completed?
A.10.21 days
B.10.23 days
C.18.25 days
D.10.25 days
Answer: D.10.25 days
Explanation: Explanation:
A takes 9 days to complete a piece of work. B takes 12 days to complete a piece of work.
=> In one day A came complete 1/9th of the task(x/9)
=> In one day B can complete 1/12th of the job.(x/12)
First day x/9th work will be done next day x/12th and so on:
Together A and B can do x/9 + x/12 work.
=>(x/9) + (x/12) = 7/36th work done
In 10 days 35/36th of the work will be done.
On 11th day it will be A’s chance. It takes A 1 day to complete 1/9th work.
So, 1/36th work will be done in 1/4 days.
=>10.25 days
ANSWER: D
Question: Find the value of (875 233/899) × 899
A.788658
B.786858
C.788865
D.786588
Answer: B.786858
Explanation: =(875 233/899) × 899
=(786625 + 233)/899 × 899
=786858/899 × 899
=786858
Answer is B.
Question: If c = (1/4)a and b = 7c, then which of the following represents the average (arithmetic mean) of a, b, and c, in terms of c ?
A.2b
B.3b
C.4b
D.5b
Answer: C.4b
Explanation: a = (4)c and b =7c.
The mean = (a + b + c)/3 = (4c + 7c + b)/3 = 4b.
Answer is C
Question: A train of length 230 metres takes 58 seconds to cross a tunnel of length 60 metres. What is the speed of the train in km/hr?
A.58 km/hr.
B.60 km/hr.
C.30 km/hr.
D.18 km/hr.
Answer: D.18 km/hr.
Explanation: Sol.
Speed = [230 + 60 / 58] m/sec = [290 /58 * 18/5] km/hr = 18 km/hr.
Answer D
Question: The speed of a boat in upstream is 30 kmph and the speed of the boat downstream is 70 kmph. Find the speed of the boat in still water and the speed of the stream?
A.22 kmph
B.20 kmph
C.21 kmph
D.26 kmph
Answer: B.20 kmph
Explanation: Speed of the boat in still water = (30+70)/2 = 50 kmph. Speed of the stream
= (70-30)/2
= 20 kmph.
Answer:B
Question: The average of the marks of 12 students in a class is 36. If the marks of each student are doubled, find the new average?
A.72
B.82
C.97
D.268
Answer: A.72
Explanation: Sum of the marks for the 12 students = 12 * 36 = 432. The marks of each student are doubled, the sum also will be doubled.
The new sum = 432 * 2 = 864. So, the new average
= 864/12
= 72.
Answer:A
Question: A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B's share?
A.500
B.1500
C.2000
D.1220
Answer: C.2000
Explanation: Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively.
Then, 4x - 3x = 1000
x = 1000.
B's share = Rs. 2x = Rs. (2 x 1000) = Rs. 2000.
so the answer is option C) 2000
Question: 5, 11, 23, 41, 64, _
A.95
B.96
C.97
D.98
Answer: A.95
Explanation: 5+6=11
11+6*2;11+12=23
23+6*3;23+18=41
41+6*4;41+24=65 65+6*5;65+30=95
ANSWER:A
Question: In a family 19 people eat only vegetarian, 9 people eat only non veg., 12 people eat both veg and non veg.. How many people eat veg in the family?
A.20
B.31
C.9
D.31
Answer: B.31
Explanation: Total people eat veg = only veg + both veg and non veg
Total= 19+12= 31
Answer = B
Question: The traffic lights at 3 different roads change after every 36 sec, 72 sec, 108 sec respectively. If they all change simultaneously at 9:15 AM then at what time will they again change simultaneously.
A.9:18:36
B.9:42:15
C.10:15:24
D.9:54:12
Answer: A.9:18:36
Explanation: LCM of 36,72,108 = 216 = 3mnts 36sec
The lines will change every 3m 36sec
The light will change again after 9:15 AM is = 9:15+0:03:36 = 9:18:36
Answer is A
Question: 20 14 8
10 5 10
5 ? 3
A.2
B.3
C.4
D.5
Answer: C.4
Explanation: difference bet 20&14=6 and 14&8=6
10&5=5 and 5&10=5
similarly
5&4=1 and 4&3=1
ans is 4
ANSWER:C
Question: find value for x from given equation ? x + 1 = -3
A.1
B.x=-4
C.-3
D.-5
Answer: B.x=-4
Explanation: 1. Subtract 1 from both sides:
x + 1 - 1 = -3 - 1
2. Simplify both sides:
x = -4
B
Question: Solve This
6 + 7 = 12
8 + 9 = 16
5 + 6 = 10
7 + 8 = 14
Then, 9 + 3 = ??
A.11
B.12
C.13
D.14
Answer: A.11
Explanation: 11
ANSWER:A
Question: A boat can move upstream at 20 kmph and downstream at 34 kmph, then the speed of the current is?
A.7
B.6
C.8
D.4
Answer: A.7
Explanation: US = 20
DS = 34
M = (34 - 20)/2 = 7 Answer:A
Question: 13, 35, 57, 79, 911, ?
A.1145
B.1113
C.1117
D.1110
Answer: B.1113
Explanation: The terms are formed by joining together consecutive odd numbers in order. i.e. 1 and 3, 3 and 5, 5 and 7, 7 and 9, 9 and 11,....
Answer : B.
Question: 9 - 3 ÷ 1/3 + 6 = ?
A.1
B.3
C.6
D.9
Answer: C.6
Explanation: 9 - 3 1/3 + 6
=9-3÷1/3+6
=9-(3X3) +6
=9-9+6
=6
CORRECT ANSWER : C
Question: A man is walking at a speed of 10 km per hour. After every kilometre, he takes rest for 6 minutes. How much time will be take to cover a distance of 6 kilometres?
A.48 min.
B.50 min.
C.66 min.
D.55 min.
Answer: C.66 min.
Explanation: Rest time = Number of rest Ã— Time for each rest
= 5 Ã— 6 = 30 minutes
Total time to cover 6 km
= (6â„10 Ã— 60)minutes + 30 minutes = 66 minutes
Answer C
Question: 3 friends A, B, C went for week end party to McDonald’s restaurant and there they measure there weights in some order In 7 rounds. A, B, C, AB, BC, AC, ABC. Final round measure is 175kg then find the average weight of all the 7 rounds?
A.100 kgs
B.88.5 kgs
C.86.5 kgs
D.67.5 kgs
Answer: A.100 kgs
Explanation: Average weight = [(a + b + c + (a+b) + (b+c) + (c+a)+(a+b+c)] / 7 = 4 (a+b+c) /7 = 4 x 175/7 = 100 kgs
Answer:A
Question: A CAN FINISH A WORK IN 6 DAYS AND B CAN DO THE SAME WORK IN15 DAYS. B WORKED FOR 10 DAYS AND LEFT THE JOB. IN HOW MANY DAYS, A ALONE CAN FINISH THE REMAINING WORK?
A.2
B.5 1/2
C.6
D.8
Answer: A.2
Explanation: B'S 10 DAY'S WORK=(1/15*10)=2/3 REMAINING WORK = (1-2/3)=1/3
NOW, 1/18 WORK IS DONE BY A IN 1 DAY
1/3 WORK IS DONE BY A IN (6*1/3)=2 DAYS.
CORRECT OPTION:A
Question: A certain collage has total of 400 seniors each majoring in exactly one of six subjects. A minimum of 30 seniors major in each six subjects. If three quarter of the seniors major in one of four subjects, what is the greatest possible number of seniors majoring in one of the other two subjects?
A.90
B.60
C.70
D.20
Answer: A.90
Explanation: Answer is A.
Six majors are as follows: a + b + c + d + e + f
Each has at least 20 seniors: 30 + 30 + 30 + 30 + 30 + 30
4 of the majors have 300 seniors: a + b + c +d = 300
There are a total of 400 seniors.
So e + f = 120. One of the subjects has to be 20 for the other to be maximized. If e = 30, then f = 90.
A
Question: Circles X and Y are concentric. If the radius of circle X is four times that of circle Y, what is the probability that a point selected inside circle X at random will be outside circle Y?
A.13
B.Pi/3
C.Pi/2
D.15/16
Answer: D.15/16
Explanation: Small circle radius = a, so area = PI a ^ 2
Large circle radius = 4a, so area = 9. PI a ^ 2
Area of shaded region = 16PI a^2 - PI a^2 = 15 PI a^2
So, probability = ( 15 PI a^2 ) / (16 PI a^2 )
= 15/16= Answer = D
Question: A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
A.178 m
B.168 m
C.120 m
D.168 m
Answer: C.120 m
Explanation: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec
= 20 m/sec.
Length of the train = 20 * 6
= 120 m.
Answer: C
Question: The ratio between the speeds of two Bullet trains is 7: 8. If the second Bullet train runs 440 kms in 5 hours, then the speed of the first train is:
A.89.25 km/hr.
B.77 km/hr.
C.90.25 km/hr.
D.94.25 km/hr.
Answer: B.77 km/hr.
Explanation: Let the speed of two bullet trains be 7x and 8x km/hr.
Then, 8x = (440/5) = 88
x = (88/8) = 11
Hence, speed of first bullet train = (7 x 11) km/hr = 77 km/hr.
B
Question: The probability of pulling a black ball out of a glass jar is 1/X. The probability of pulling a black ball out of a glass jar and breaking the jar is 1/Y. What is the probability of breaking the jar?
A.1/(XY).
B.X/Y.
C.Y/X.
D.1/(X+Y)
Answer: B.X/Y.
Explanation: pulling a black ball out of a glass jar and breaking the jar both are independent events.
For 2 independent events, we know, P(a) * P(b) = P(a∩b)
If Prob of pulling a black ball out of a glass jar = P(a) and Prob of breaking the jar = P(b)
1/x * P(b) = 1/y ---> P(b) = x/y
Hence, answer B.
Question: What will be the difference between simple and compound interest at 8% per annum on a sum of Rs. 1000 after 4 years?
A.64.19
B.64.12
C.40.5
D.64.1
Answer: C.40.5
Explanation: S.I. = (1000 * 8 * 4)/100 = Rs. 320
C.I. = [1000 * (1 + 8/100)4 - 1000] = Rs. 360.5
Difference = (360.5 - 320) = Rs. 40.5
Answer: C
Question: If the wheel is 14 cm then the number of revolutions to cover a distance of 1056 cm is?
A.18
B.27
C.26
D.12
Answer: D.12
Explanation: 2 * 22/7 * 14 * x = 1056
=> x = 12
Answer: D