divelab/Sys2Bench huggingface dataset:
Question: In how many ways can the letters of the word CREATION be arranged such that all the vowels always appear together?
Options:
A)5!*4!
B)8!
C)8!*4!
D)4!*4!
E)8!*5!
Rationale: The 8 letters can be grouped into 4 consonants and one set of 4 vowels.
The number of ways to arrange 5 units is 5!
Then, for each arrangement, the 4 vowels can be arranged in 4! ways.
The total number of arrangements is 5!*4!
The answer is A.
Answer: A
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 his son is:
Options:
A)14 years
B)18 years
C)20 years
D)22 years
E)16 years
Rationale: 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
Answer: D
Question: The average weight of 8 person's increases by 4 kg when a new person comes in place of one of them weighing 55 kg. What might be the weight of the new person?
Options:
A)80 kg
B)87 kg
C)90 kg
D)100 kg
E)110 kg
Rationale: Total weight increased = (8 x 4) kg = 32 kg.
Weight of new person = (55 + 32) kg = 87 kg.
B)
Answer: B
Question: A merchant gains or loses, in a bargain, a certain sum. In a second bargain, he gains 450 dollars, and, in a third, loses 30. In the end he finds he has gained 100 dollars, by the three together. How much did he gain or lose bv the first ?
Options:
A)320
B)-340
C)-320
D)348
E)None
Rationale: In this sum, as the profit and loss are opposite in their nature, they must be distinguished by contrary signs. If the profit is marked +, the loss must be -.
Let x = the sum required.
Then according to the statement x + 450 - 30 = 100
And x = -320.
Answer C
Answer: C
Question: When the perimeter of a regular polygon is divided by 5, the length of a side is 25. What is the name of the polygon? What is the perimeter?
Options:
A)125
B)126
C)127
D)128
E)129
Rationale: Regular polygon. A polygon with equal sides and equal sides.
Divided by 5 to get the length of a side. It is the pentagon since it has 5 sides.
So p = 5 × s
To get the perimeter, just multiply a side by 5.
Since 25 × 5 = 125, the perimeter is 125.
Answer A
Answer: A
Question: A total of 320 chocolates were distributed among 100 boys and girls such that each boy received 2 chocolates and each girl received 3 chocolates. Find the respective number of boys and girls?
Options:
A)10,10
B)30,40
C)70, 50
D)20,20
E)10,15
Rationale: Let the number of boys be x.
Number of girls is 100 - x.
Total number of chocolates received by boys and girls = 2x + 3(100 - x) = 320
=> 300 - x = 320 => x = 20.
So, the number of boys or girls is 20.
ANSWER:D
Answer: D
Question: According to a survey, at least 70% of people like apples, at least 75% like bananas and at least 85% like cherries. What is the minimum percentage of people who like all three?
Options:
A)15%
B)20%
C)25%
D)30%
E)35%
Rationale: It seems that something is wrong with your answer options.
1) minimum applesbananas:
[XXXXXXXXXXXXXX------] - apples
[-----XXXXXXXXXXXXXXX] - bananas
mimimum ab = 70 - (100-75) = 45%
2) minimum (applesbananas)cherries:
[XXXXXXXXX-----------] - applesbananas
[----XXXXXXXXXXXXXXXX] - cherries
mimimum ab = 45 - (100-85) =30%
D
Answer: D
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
Options:
A)25 km/hr
B)50 km/hr
C)12 km/hr
D)40 km/hr
E)43 km/hr
Rationale: Answer: Option B
Speed of the train relative to man = 125/10 = 25/2 m/sec.
= 25/2 * 18/5 = 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 5 = 45 => x = 50 km/hr.
Answer: B
Question: A brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 26 m * 2 m * 0.75 m?
Options:
A)26000
B)27782
C)27891
D)25000
E)18771
Rationale: 26 * 2 * 0.75 = 20/100 * 10/100 * 7.5/100 * x
26 = 1/1000 * x => x = 26000
Answer: A
Answer: A
Question: Rahul can do a work in 3 days while Rajesh can do the same work in 2days. Both of them finish the work together and get $355. What is the share of Rahul?
Options:
A)$50
B)$142
C)$60
D)$100
E)$90
Rationale: Rahul's wages: Rajesh's wages = 1/3 : 1/2 = 2:3
Rahul's share = 355*2/5 = $142
Answer is B
Answer: B
Question: During one month at a particular restaurant, 1/6 of the burgers sold were veggie burgers and 1/3 of the rest of the burgers sold were double-meat. If x of the burgers sold were double-meat, how many were veggie burgers?
Options:
A)x/8
B)x/2
C)2x/3
D)3x/5
E)4x/5
Rationale: Let y be the number of total burgers.
veggie = y/6 , non veggie = 5y/6
1/4 of the rest of the burgers sold were double-meat
=> 5y/6 * 1/3 = double meat = x
=> y/6 = 3x/5 = veggie
Hence D
Answer: D
Question: A pump can fill a tank with a water in 2 hours. Because of a leak, it took 6 hours to fill the tank. The leak can drain all the water of the full tank in how many hours?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: The rate of the pump + leak = 1/6
1/2 - leak's rate = 1/6
leak's rate = 1/2 - 1/6 = 1/3
The leak will empty the tank in 3 hours.
The answer is B.
Answer: B
Question: A toy store sells small, medium, large, and super-large toy trucks in each of the colors red, blue, black, green, orange, pink, and yellow. The store has an equal number of trucks of each possible color-size combination. If Paul wants a medium, red truck and his mother will randomly select one the trucks in the store, what is the probability that the truck she selects will have at least one of the two features Paul wants?
Options:
A)3/7
B)4/7
C)3/14
D)5/14
E)11/28
Rationale: Probability of NOT selecting medium out of 4 sizes = 3/4
Probability of NOT selecting red out of 7 colours = 6/7
Total probability of NOT selecting red and medium = (3/4)*(6/7) = 9/14
Required probability = 1 - 9/14 (this will select at least one of red and medium)
= 5/14
The answer is D.
Answer: D
Question: In how many ways can nine different rings be worn on four fingers of one hand?
Options:
A)10
B)129
C)135
D)126
E)182
Rationale: Required number of ways = ways of selecting 4 objects out of 9 given objects
= 9C4 = 9*8*7*6/24= 126
Answer D
Answer: D
Question: If 5x+2y=3x-4y,then what equation will arise?
Options:
A)x=-y
B)y=-x
C)A and B
D)x=y
E)None
Rationale: 5x+2y=3x-4y
5x-3x=4y-2y
2x=2y
x=y
Option:D
Answer: D
Question: United Telephone charges a base rate of $11.00 for service, plus an additional charge of $0.25 per minute. Atlantic Call charges a base rate of $12.00 for service, plus an additional charge of $0.20 per minute. For what number of minutes would the bills for each telephone company be the same?
Options:
A)2 minutes
B)10 minutes
C)20 minutes
D)40 minutes
E)60 minutes
Rationale: Lets take number of minutesx.
Given that, 11+0.25x=12+0.2x ->0.05x=2 -> x=20minutes
ANS C
Answer: C
Question: In a colony of 70 residents, the ratio of the number of men and women is 3 : 4. Among the women, the ratio of the educated to the uneducated is 1 : 4. If the ratio of the number of educated to uneducated persons is 8 : 27, then find the ratio of the number of educated to uneducated men in the colony?
Options:
A)A)1:6
B)B)1:2
C)C)1:8
D)D)1:9
E)E)1:3
Rationale: Number of men in the colony = 3/7 * 70 = 30.
Number of women in the colony = 47 * 70 = 40.
Number educated women in the colony = 1/5 * 30 = 6.
Number of uneducated women in the colony = 4/5 * 50 = 24.
Number of educated persons in the colony = 8 /35 * 70 = 16.
As 6 females are educated, remaining 10 educated persons must be men.
Number of uneducated men in the colony = 30 - 10 = 20.
Number of educated men and uneducated men are in the ratio 10 : 20 i.e., 1:2.
Answer:B
Answer: B
Question: Of the 400 members at a health club, 280 use the weight room and 300 use the pool. If at least 60 of the members do not use either, then the number of members using both the weight room and the pool must be between:
Options:
A)200 to 260
B)240 to 280
C)220 to 260
D)220 to 300
E)40 to 100
Rationale: W=280
P=300
ALL=400
N(NEITHER)=AT LEAST 60
BOTH=?
W+P-BOTH+N=ALL
280+300-BOTH+60=400
BOTH=240
now pay attention to the fact, that both at most can be 280, since W=280
B
Answer: B
Question: A patient was given a bottle of tablets by the doctor and he was asked to take five tablets in a gap of 8 minutes.
In how much time will he be able to take all the five tablets?
Options:
A)1 Hour.
B)2 Hour.
C)3 Hour.
D)None
E)32 min
Rationale: Suppose he takes the first tablet at 8:00 pm. Then the second will be consumed by him at 8:08, third at 8:16, fourth at 8:24 and fifth at 8:32.
Time = 32 min
Answer E
Answer: E
Question: A person can row at 9 kmph and still water. He takes 5 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?
Options:
A)60 km
B)87 km
C)89 km
D)67 km
E)24 km
Rationale: Let the distance between A and B be x km.
Total time = x/(9 + 1) + x/(9 - 1) = 5.5
=> x/10 + x/8 = 11/2 => (4x + 5x)/40 = 11/2 => x
= 24 km.
Answer:E
Answer: E
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 his son is:
Options:
A)14 years
B)18 years
C)20years
D)22 years
E)None of these
Rationale: 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
Answer: D
Question: Two train 200 m and 150 m long are running on parallel rails at the rate of 40 kmph and 45 kmph respectively. In how much time will they cross each other, if they are running in the same direction?
Options:
A)80 sec
B)252 sec
C)320 sec
D)330 sec
E)None
Rationale: Sol.
Relative speed = (45 - 40) kmph = 5 kmph = [5 * 5/18] m/sec = 25/18 m/sec.
Total distance covered = Sum of lengths of trains = 350 m.
∴ Time taken = [350 * 18/25] sec = 252 sec.
Answer B
Answer: B
Question: 85% of the population of a city is 85000. The total population of the city is?
Options:
A)95000
B)97500
C)100000
D)105000
E)102500
Rationale: X * (85/100) = 85000
X = 1000 * 100
X = 100000
Answer: C
Answer: C
Question: 2,200 has how many positive divisors?
Options:
A)12
B)16
C)20
D)24
E)32
Rationale: By factorization, we can write 2200 as 2200=2^3*5^2*11.
The number of factors is (3+1)(2+1)(1+1) = 24
The answer is D.
Answer: D
Question: At exactly what time past 6:00 will the minute and hour hands of an accurate working clock be precisely perpendicular to each other for the first time?
Options:
A)20 13/21 minutes past 7:00
B)20 13/17 minutes past 7:00
C)21 9/11 minutes past 6:00
D)21 9/11 minutes past 7:00
E)22 4/9 minutes past 7:00
Rationale: 5.5 is the angle between minute n hour, this is what I was taught...so shouldn't it be solve by dividing 90 with 5.5?
That would have been the case if your initial difference between the hour and the minute hand was = 0 degrees or in other words, both minute and hour hands were at the same location. But as per the question, you are asked for time AFTER 6:00. At 6:00, the angle between the hour and the minute hand is 210 degrees. you need to take this into account as well.
So in order for the difference to decrease to 90 degrees, the minute hand must eat away this difference of 210-90 = 120 degree at the rate of 5.5 degrees per minute ---> 120/5.5 = 21 9/11 minutes.
Thus, C is the correct answer.
Answer: C
Question: The two trains of lengths 400 m, 600 m respectively, running at same directions. The faster train can cross the slower train in 180 sec, the speed of the slower train is 48 km. then find the speed of the faster train?
Options:
A)87 Kmph
B)68 Kmph
C)67 Kmph
D)57 Kmph
E)41 Kmph
Rationale: Length of the two trains = 600m + 400m
Speed of the first train = X
Speed of the second train= 48 Kmph
1000/X - 48 = 180
1000/x - 48 * 5/18 = 180
50 = 9X - 120
X = 68 Kmph
Answer: B
Answer: B
Question: What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 5?
Options:
A)897
B)98,910
C)64,749
D)49,700
E)56,720
Rationale: Find the number , Upon Sum of 3 Digits of a number Gives a Reminder 2 when it is Divided by 5
Seeing the Options After Dividing and Finding the Reminder of 2
My Answer was B
Answer: B
Question: Sam invested $15000 @10% per annum for one year. If the interest is compounded half yearly, then the amount received by Sam at the end of the year will be?
Options:
A)$16537.50
B)$24512.56
C)$18475.89
D)$15478.56
E)$12456.35
Rationale: P = $15000
R = 10%
p.a. = 5%
T = 2 half years
Amount = 15000 * (1 + 5/100)^2 = 15000* 21/20 * 21/20 = $16537.50
Answer is A
Answer: A
Question: Two trains of equal lengths take 10 sec and 12 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
Options:
A)11 sec
B)12 sec
C)17 sec
D)21 sec
E)23 sec
Rationale: Speed of the first train = 120/10 = 12 m/sec.
Speed of the second train = 120/12 = 10 m/sec.
Relative speed = 12 + 10 = 22 m/sec.
Required time = (120 + 120)/22 = 11 sec.
Answer: A
Answer: A
Question: Find how many positive integers less than 10,000 are there suchthat the sum of the digits of the no. is divisible by 3?
Options:
A)1256
B)2354
C)2678
D)3334
E)3568
Rationale: If sum of the digits is divisible by 3, the number is divisible by 3.
Therefore, required number of non-negative integers is equal to count of numbers less than 10,000 which are divisible by 3.
Such numbers are (3, 6, 9, ... , 9999) (arithmetic progression with first term=3, last term=9999, common difference=3).
Count of such numbers =
9999
3
=
3333
99993=3333
But zero is also divisible by 3.
This makes our total count 3334
D
Answer: D
Question: On eight consecutive flips of a coin, what is the probability that all eight produce the same result?
Options:
A)1/16
B)1/128
C)1/8
D)1/4
E)1/2
Rationale: TTTTTTTT case --> P = (1/2)^8 = 1/256
HHHHHHHH case --> P = (1/2)^8 = 1/256
P(TTTTTTTT or HHHHHHHH) = 1/8 + 1/8 = 1/128
Answer: B
Answer: B
Question: Pradeep has to obtain 20% of the total marks to pass. He got 390 marks and failed by 25 marks. The maximum marks are
Options:
A)300
B)2075
C)800
D)1000
E)3900
Rationale: Explanation :
Let their maximum marks be x.
Then, 20% of x = 390 + 25
=>20/100x= 415
x = (41500/20)
x= 2075.
Answer : B
Answer: B
Question: Which of the following is a prime number ?
Options:
A)65
B)35
C)97
D)35
E)27
Rationale: C
97
Explanation: Clearly, 97 is a prime number.
Answer: C
Question: The population of a town increased from 1,33,400 to 1,93,500 in a decade. The average percent increase of population per year is:
Options:
A)4.5%
B)5.5%
C)6.5%
D)8.75%
E)None
Rationale: Explanation: Increase in 10 years = (193500 - 133400) = 60100.
Increase% = (60100/133400 x 100)% = 45%.
Required average = (45/10)% = 4.5%.
Answer: Option A
Answer: A
Question: Ratio between Rahul and Deepak is 4:3, After 22 Years Rahul age will be 26 years. What is Deepak present age
Options:
A)10
B)3
C)5
D)7
E)8
Rationale: Explanation:
Present age is 4x and 3x,
=> 4x + 22 = 26 => x = 1
So Deepak age is = 3(1) = 3
Answer: Option B
Answer: B
Question: A and B invests Rs.3000 and Rs.5000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit?
Options:
A)8:8
B)9:8
C)9:7
D)9:5
E)9:10
Rationale: (3*6 + 6*6): (5*12)
54:60 => 9:10
Answer: E
Answer: E
Question: 75 people are being divided into committees. However, the project calls for 9 teams of 9 people each. How many more people are needed to reach this quota?
Options:
A)6
B)8
C)19
D)10
E)2
Rationale: 9 x 9 = 81
81 - 75 = 6
The answer is A.
Answer: A
Question: Due to construction, the speed limit along an 7-mile section of highway is reduced from 55 miles per hour to 35 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options:
A) 2
B) 3
C) 4
D) 5
E) 6
Rationale: 7/35 - 7/55 = 7/5 * ( 11 - 7)/77
= 7/5 * 4/77 * 60 min
= 7 * 12 * 4/77
= 336/77 ~ 4.3
Answer - C
Answer: C
Question: The ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:10. If P invested the money for 2 months, find for how much time did Q invest the money?
Options:
A)8
B)10
C)18
D)4
E)12
Rationale: 7*5: 2*x = 7:10
x = 4
Answer:4
Answer is D
Answer: D
Question: Ram sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles?
Options:
A)Rs.2000
B)Rs.1980
C)Rs.1891
D)Rs.1750
E)Rs.1600
Rationale: Explanation:
(10*10)/100 = 1%loss
100 --- 99
? --- 1980 => Rs.2000
ANSWER IS A
Answer: A
Question: The value of 99^(93/99) x 99 is:
Options:
A)9989
B)9896
C)9894
D)9809
E)9810
Rationale: (100 â€“ 6/99) x 99 = 9900 â€“ 6
= 9894.
ANSWER:C
Answer: C
Question: A man can do a piece of work in 6 days, but with the help of his son, he can do it in 3 days. In what time can the son do it alone?
Options:
A)5
B)7
C)6
D)8
E)9
Rationale: Son's 1day's work = (1/3)-(1/6) = 1/6
The son alone can do the work in 6 days
Answer is C
Answer: C
Question: In how many ways can the letters of the word REPEATED be arranged?
Options:
A)1206
B)1348
C)6720
D)3000
E)3478
Rationale: REPEATED has 8 words, but E is repeated three times. Thus ways = 8! / 3! = 6720 ways
C
Answer: C
Question: One day a car rental agency rented 3/4 of its cars, including 5/6 of its cars with CD players. If 3/5 of its cars have CD players, what percent of the cars that were not rented had CD players?
Options:
A)13/20
B)11/15
C)7/10
D)4/7
E)2/5
Rationale: The cars with CD players which were not rented is (1/6)(3/5) = 1/10 of all the cars.
The cars which were not rented is 1/4 of all the cars.
The percent of non-rented cars which had CD players is (1/10) / (1/4) = 2/5
The answer is E.
Answer: E
Question: If the LCM of two integers I, J (where J> I and I>1) is I*J, then which of the following can not be true?
Options:
A)All Prime factors of I must be Prime factors of J.
B)Both I and J can be consecutive integers.
C)Both I and J can be Prime Numbers.
D)I and J do not share any Prime factors.
E)I and J do not have a common factor
Rationale: If LCM of two numbers I and J is the product IJ then both numbers are Co- prime.
(Co-prime numbers are any two numbers which have an HCF of 1 i.e. when two numbers have no common prime factor apart from the number 1).
Numbers that can be Co-Prime are :
1) Two consecutive natural numbers.
2) Two consecutive odd numbers.
3) Two prime numbers.
4) One prime number and the other a composite number such that the composite number is not a multiple of the prime number.
With above four statements it can be concluded that Options B,C,D and E are all true.
Only Option A cannot be true.
Hence answer is A
Answer: A
Question: Total of ages of A,B and C at present is 90 years. If ratio of this ages is 2 : 3 : 4 what will be the age of C after 6 years?
Options:
A)45 years
B)42 years
C)46 years
D)37 years
E)None of the above
Rationale: 2+3+4=9
4*(90/9)=40yrs
after 6yrs=46
ANSWER:C
Answer: C
Question: In a colony of 70 residents, the ratio of the number of men and women is 5 : 2. Among the women, the ratio of the educated to the uneducated is 1 : 4. If the ratio of the number of educated to uneducated persons is 8 : 27, then find the ratio of the number of educated to uneducated men in the colony?
Options:
A)A)1:4
B)B)1:1
C)C)1:8
D)D)1:9
E)E)1:3
Rationale: Number of men in the colony = 5/7 * 70 = 50.
Number of women in the colony = 2/7 * 70 = 40.
Number educated women in the colony = 1/5 * 30 = 6.
Number of uneducated women in the colony = 4/5 * 50 = 24.
Number of educated persons in the colony = 8 /35 * 70 = 16.
As 6 females are educated, remaining 10 educated persons must be men.
Number of uneducated men in the colony = 50 - 10 = 40.
Number of educated men and uneducated men are in the ratio 10 : 40 i.e., 1:4.
Answer:A
Answer: A
Question: Of the goose eggs laid at a certain pond, 2/3 hatched and 3/4 of the geese that hatched from those eggs survived the first month. Of the geese that survived the first month, 3/5 did not survive the first year. If 100 geese survived the first year and if no more than one goose hatched from each egg, how many goose eggs were laid at the pond?
Options:
A) 280
B) 400
C) 540
D) 500
E) 840
Rationale: Of the goose eggs laid at a certain pond, 2/3 hatched and 3/4 of the geese that hatched from those eggs survived the first month:
2/3*3/4 = 1/2 survived the first month.
Of the geese that survived the first month, 3/5 did not survive the first year:
(1-3/5)*1/2 = 1/5 survived the first year.
100 geese survived the first year:
1/5*(total) = 100 --> (total) = 500.
Answer: D.
Answer: D
Question: One night a certain hotel rented 4/5 of its rooms, including 2/3 of their air conditioned rooms. If 3/5 of its rooms were air conditioned, what percent of the rooms that were not rented were air conditioned?
Options:
A)60%
B)70%
C)80%
D)90%
E)100%
Rationale: The rooms which were not rented is 1/5
The AC rooms which were not rented is (1/3)*(3/5) = 1/5
The percentage of unrented rooms which were AC rooms is (1/5) / (1/5) = 1 = 100%
The answer is E.
Answer: E
Question: A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and
second half at the rate of 24 km/hr. Find the total journey in km
Options:
A)200 Km
B)222 Km
C)224 Km
D)248 Km
E)None of these
Rationale: Explanation:
Let time taken to travel the first half = x hr
Then time taken to travel the second half = (10 - x) hr
Distance covered in the the first half = 21x [because, distance = time*speed]
Distance covered in the the second half = 24(10 - x)
Distance covered in the the first half = Distance covered in the the second half
So,
21x = 24(10 - x)
=> 45x = 240
=> x = 16/3
Total Distance = 2*21(16/3) = 224 Km [multiplied by 2 as 21x was distance of half way]
Answer: C
Answer: C
Question: A semicircle has a radius of 9. What is the approximate perimeter of the semicircle?
Options:
A)16
B)25
C)33
D)46
E)58
Rationale: The perimeter of a circle is 2*pi*r.
The perimeter of a semicircle is 2*pi*r/2 + 2r = pi*r + 2r
The perimeter is pi*9 + 2*9 which is about 46.
The answer is D.
Answer: D
Question: The probability of two events A and B are 0.20 and 0.40 respectively. The probability that both A and B occur is 0.15. The probability that neither A nor B occur is _________
Options:
A)0.45
B)0.4
C)0.5
D)0.55
E)0.6
Rationale: we are apply that formula..............
P(AorB)=P(A)+P(B)-P(A AND B)
=.20+.40-.15
=.45
but the probability of neither A nor B=1-.45
=0.55
ANSWER:D
Answer: D
Question: A can work four times as fast as B. Together they can finish a job in 12 days. In how many days can A complete the job alone?
Options:
A)14
B)15
C)16
D)17
E)18
Rationale: B's rate is x and A's rate is 4x.
x + 4x = 1/12
x = 1/60
A's rate is 4x = 1/15
A can complete the job in 15 days.
The answer is B.
Answer: B
Question: 100 identical coins each with probability 'pp' showing up heads & tossed.
Options:
A)13/101
B)11/101
C)51/101
D)53/102
E)54/101
Rationale: Let aa be the number of coins showing heads
Then, P(A=50)=P(A=51)P(A=50)=P(A=51)
⇒100C50×P50×(1−P)50⇒100C51×P51×(1−P)49⇒100C50×P51×(1−P)50=100C51×P⇒51(1âˆ′P)=50P⇒P=51/101
C
Answer: C
Question: If a#b = ab – b + b^2, then 3#4 =
Options:
A)2
B)8
C)15
D)24
E)35
Rationale: Solution -
Simply substitute 3 and 4 in equation in the place of a and b respectively.
3#4 = 3*4 - 4 + 4^2 = 12 - 4 + 16 = 24. ANS D
Answer: D
Question: How many different four letter words can be formed (the words need not be meaningful using the letters of the word "MEDITERRANEAN" such that the first letter is E and the last letter is R?
Options:
A)59
B)77
C)36
D)99
E)17
Rationale: Explanation:
The first letter is E and the last one is R.
Therefore, one has to find two more letters from the remaining 11 letters.
Of the 11 letters, there are 2 Ns, 2Es and 2As and one each of the remaining 5 letters.
The second and third positions can either have two different letters or have both the letters to be the same.
Case 1: When the two letters are different. One has to choose two different letters from the 8 available different choices. This can be done in 8 * 7 = 56 ways.
Case 2: When the two letters are same. There are 3 options - the three can be either Ns or Es or As. Therefore, 3 ways.
Total number of possibilities = 56 + 3 = 59
Answer: A) 59
Answer: A