divelab/Sys2Bench huggingface dataset:
Question: What Is The Next Number
12 13 15 17 111 113 117 119 ?
Options:
A)123
B)220
C)129
D)428
E)224
Rationale: 123.
These are the first 10 prime numbers (2, 3, 5...) prefixed with a 1
Answer : A
Answer: A
Question: If x and y are integers and xy = 330, x or y must be divisible by which of the following?
Options:
A)4
B)5
C)6
D)20
E)30
Rationale: xy = 330 = 2 * 3 * 5 * 11
One of x or y must be divisible by 5.
The answer is B.
Answer: B
Question: 60% of the employees of a company are men. 60% of the men in the company speak French and 50% of the employees of the company speak French. What is % of the women in the company who do not speak French?
Options:
A)4%
B)10%
C)96%
D)90%
E)65%
Rationale: No of employees=100(say)
Men=60
Women=40
Men speaking french=0.6*60=36
Employees speaking french=0.5*100=50
Therefore women speaking French=50-36=14
And women not speaking French=40-14=26
% of women not speaking French=26/40*100=65%
Answer E
Answer: E
Question: How much is 80% of 40 is greater than 4/5 of 25?
Options:
A)15
B)7
C)18
D)12
E)23
Rationale: (80/100) * 40 – (4/5) * 25
32 - 20
= 12
Answer: D
Answer: D
Question: Steve gets on the elevator at the 11th floor of a building and rides up at a rate of 57 floors per minute. At the same time Joyce gets on an elevator on the 51st floor of the same building and rides down at a rate of 63 floors per minute. If they continue traveling at these rates, at which floor will their paths cross?
Options:
A)19
B)28
C)30
D)32
E)44
Rationale: Using Speed Formula: Speed = Distance / Time
Distance to be covered = 51-11 = 40
Speed of approach = 57 + 63 floors/min
Time = 40/120 = 1/3
So Steve will cover 57x 1/3 floors in that time = 19
So he will be in 19 + 11 floor = 30th Floor
ANSWER:C
Answer: C
Question: A thief goes away with a SANTRO car at a speed of 25 kmph. The theft has been discovered after half an hour and the owner sets off in a bike at 60 kmph when will the owner over take the thief from the start?
Options:
A)5/7 hours
B)2/7 hours
C)2/3 hours
D)1/3 hours
E)2/5 hours
Rationale: -----------25--------------------|
60 25
D = 25
RS = 60 â€“ 25 = 35
T = 25/35 = 5/7 hours
ANSWER:A
Answer: A
Question: A club with a total membership of 30 has formed 3 committees, M, S and R, which have 7, 12 and 5 members respectively. If no members of committee M is on either of the other 2 committees, what is the greatest possible number of members in the club who are on none of the committees?
Options:
A)5
B)7
C)8
D)10
E)11
Rationale: As no member of committee M is on either of the other 2 committees then 30-M=30-7=23 people are on committee S, committee R or on none of the committee. We want to maximize the last group: members in the club who are on none of the committees
General rule for such kind of problems:
to maximize one quantity, minimize the others;
to minimize one quantity, maximize the others.
So we should minimize total # of people who are on committee S and committee R. Now if ALL 5 people who are the members of committee R are also the members of committee S (if R is subset of S) then total # members of committee S and committee R would be minimized and equal to 12. Which means that 23-12=11 is the greatest possible number of members in the club who are on none of the committees.
Answer: E.
Answer: E
Question: An empty fuel tank with a capacity of 200 gallons was filled partially with fuel A and then to capacity with fuel B. Fuel A contains 12% ethanol by volume and fuel B contains 16% ethanol by volume. If the full fuel tank contains 28 gallons of ethanol, how many gallons of fuel A were added?
Options:
A)160
B)150
C)100
D)80
E)50
Rationale: Say there are A gallons of fuel A in the tank, then there would be 200-A gallons of fuel B.
The amount of ethanol in A gallons of fuel A is 0.12A;
The amount of ethanol in 200-A gallons of fuel B is 0.16(200-A);
Since the total amount of ethanol is 28 gallons then 0.12A+0.16(200-A)=28 --> A=100.
Answer: C.
Answer: C
Question: 45 x ? = 25% of 900
Options:
A)16.2
B)4
C)5
D)500
E)None
Rationale: Answer
Let 45 x A = (25 x 900)/100
∴ A = (25 x 9)/45 = 5
Correct Option: C
Answer: C
Question: There is a sequence A(n) such that A(n+1)=2A(n)-1 and A(1)=3, where n is a positive integer. What is the value of A(66)-A(65)?
Options:
A)2^22+1
B)2^65
C)2^23+1
D)2^24
E)2^23+1
Rationale: A1= 3
A2= 2*3-1= 5
A3= 2*5-1= 9
A4= 2*9-1= 17
We can notice that there is a squence
A2-A1= 2^1
A3-A2= 2^2
A4-A3= 2^3
Hence A66-A65= 2^65
B is the answer
Answer: B
Question: At the wholesale store you can buy an 8-pack of hot dogs for $1.55, a 20-pack for $3.05, and a 250-pack for $22.95. What is the greatest number of hot dogs you can buy at this store with $205?
Options:
A)1,108
B)2,100
C)2,140
D)2,124
E)2,256
Rationale: I think it should be C.
I can buy 8 250-pack for Rs 22.95*8 = $183.60
Now, I can buy 7 20-pack for 3.05*7 = $21.35
Now, I am left with only $1.15. I cannot but anything with this.
Hence Total Hotdogs = 250*8 + 20*7= 2140
Answer: C
Question: How many integers k greater than 100 and less than 900 are there such that if the hundreds and the unit digits of k are reversed, the resulting integer is k + 99?
Options:
A)50
B)60
C)70
D)80
E)90
Rationale: Not sure if this is the shortest.. But this is how I did this
There are 7 sets of integers with hundreds and units digits exchanged that satisfies k + 99.
1. 102 | 201 (satisfies k+99, where k = 102)
2. 203 | 302 (satisfies k+99, where k = 203)
3. ...
4. ...
5. ...
6. ...
7. 708 | 807
Each set has 10 such numbers.
1. 102 | 201 (still k+99 holds good)
2. 112 | 211
3. 122 | 221
4. 132 | 231
5. ...
6. ...
7. ...
8. ...
9. 182 | 281
10. 192 | 291
Therefore, 7 sets with 10 such number in each set will give 7 x 10 = 70 integers.
C
Answer: C
Question: A five-person team is to be formed from a pool of 6 East All Stars and 6 West All Stars. What is the probability that the team will contain at least 2 East All Stars?
Options:
A)fraction of 29/33
B)81/169
C)57/120
D)47/144
E)119/720
Rationale: The question with at- least can be easily tackled by
At least = Total cases - unwanted cases
So atleast 2 player = total cases - cases with no east all stars person - case with only one east all person
Total number of cases = 12C5 = 798
Cases with no east all person = 6C5(All person from west all stars) = 6
Cases with exactly one east all person = 6C4*6C1 (4from west all stars and 1 from east all stars)= 90
So total no. of cases with with at least two members = 798-6-90 = 702
Probability = 702/798 = 29/33
answer:A
Answer: A
Question: A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train?
Options:
A)79.2 km/hr
B)23.9 km/hr
C)22.9 km/hr
D)22.7 km/hr
E)23.8 km/hr
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 8 => x = 8y
(x + 264)/20 = y
y = 22
Speed = 22 m/sec = 22 * 18/5
= 79.2 km/hr.
Answer:D
Answer: D
Question: A recycling facility is staffed by 15 floor workers and one manager. All of the floor workers are paid equal wages, but the manager is paid n times as much as a floor worker. If the manager’s wages account for 1/14 of all wages paid at the facility, what is the value of n?
Options:
A)8
B)9
C)10
D)15/13
E)11
Rationale: Say each floor worker is paid $x, then the manager is paid $xn.
Total salary would be 15x+xn and we are told that it equals to 14xn:
15x+xn=14xn --> reduce by x: 15+n=14n -->13n=15
n = 15/13
Answer: D
Answer: D
Question: A can do a piece of work in 20 days; B can do the same in 30 days. A started alone but left the work after 10 days, then B worked at it for 10 days. C finished the remaining work in 10 days. C alone can do the whole work in?
Options:
A)70 days
B)65 days
C)40 days
D)50 days
E)60 days
Rationale: 10/20 + 10/30 + 10/x = 1
x = 60 days
ANSWER:E
Answer: E
Question: In a group of ducks and cows, the total number of legs are 24 more than twice the number of heads. Find the total number of cows.
Options:
A)A)14
B)B)12
C)C)16
D)D)8
E)E)6
Rationale: Explanation :
Let the number of ducks be d
and number of cows be c
Then, total number of legs = 2d + 4c = 2(d + 2c)
total number of heads = c + d
Given that total number of legs are 24 more than twice the number of heads
=> 2(d + 2c) = 24 + 2(c + d)
=> d + 2c = 12 + c + d
=> 2c = 12 + c
=> c = 12
Answer : B
Answer: B
Question: Solution Y is 30 percent liquid X and 70 percent water. If 2 kilograms of water evaporate from 10 kilograms of solution Y and 2 kilograms of solution Y are added to the remaining 6 kilograms of liquid, what percent of this new solution is liquid X?
Options:
A)34
B)35
C)36
D)37 1/25
E)40
Rationale: In 8 kilograms of solution Y there are 0.3*10=3 kilograms of solution X;
After 2 kilograms of water are replaced by 2 kilograms of solution Y, to the existing 2.4 kilograms of solution X, 0.3*2=0.6 kilograms of solution X are added, so in the new solution of 8 kilograms there are 3+0.6=3.6 kilograms of solution X, which is 3.6/10*100=36% of this new solution.
Answer: C.
Answer: C
Question: For an employee to qualify for early retirement at a certain company, the sum of the employee’s age and years of service must be at least 50, If Sue was K years old when she was hired by the company, what is the minimum age at which she could possibly qualify for early retirement.
Options:
A)K+35
B)2K+35
C)(70+K)/2
D)(50+K)/2
E)2(70-K)
Rationale: Say Sue was hired when she was already 50 years old (k=50), then she could retire right away, at the age of 50. Now, plug k=50 in the answer choices and see which yields 50. Only C fits.
Answer: D.
Answer: D
Question: A man purchases an electric heater whose printed price is Rs.160. If he received two successive discounts of 20% and 10%; he paid :
Options:
A)Rs.112
B)Rs.129.60
C)Rs.119.60
D)Rs.115.20
E)None
Rationale: Explanation:
Price after Ist discount = 100% of Rs.160 = Rs. 128
Price after 2nd discount = 90% of Rs.128 = Rs.115.20
Correct Option : D
Answer: D
Question: What are the last two digits of 24*62*33*48*39*16?
Options:
A)40
B)08
C)64
D)34
E)12
Rationale: 24*62*33*48*39*16?=
We have to focus on the last two digits only, so 24*62=88*33=04*48=92
39*92=88 therefore 88*16=08
Hence Answer is B
Answer: B
Question: The ratio of ages of Aman, Bren, and Charlie are in the ratio 5:8:7 respectively. If 8 years ago, the sum of their ages was 76, what will be the age of Bren 12 years from now?
Options:
A)17
B)25
C)27
D)52
E)60
Rationale: Let the present ages of Aman, Bren, and Charlie be 5x, 8x and 7x respectively.
5x-8 + 8x-8 + 7x-8 = 76
x = 5
Present age of Bren = 8*5 = 40
Bren's age 12 years hence = 40+12 = 52
Answer = E
Answer: E
Question: A father told his son "I was as old as you are at present, at the time of your birth". If the father is 38 years old now, then what was the son's age five years ago in years?
Options:
A)14
B)19
C)38
D)33
E)35
Rationale: et son's present age is =x
then 38-x=x
x=19
son's age 5 years back is 19-5=14 years.
ANSWER:A
Answer: A
Question: A man is walking at the rate of 10 km/hr crosses a bridge in 15 minutes. The length of the bridge is
Options:
A)1000 meters
B)1050 meters
C)1200 meters
D)1250 meters
E)2500 meters
Rationale: Explanation:
We need to get the answer in meters. So we will first of change distance from km/hour to meter/sec by multiplying it with 5/18 and also change 15 minutes to seconds by multiplying it with 60.
Speed=10âˆ—5/18=25/9m/sec
Time=15âˆ—60seconds=900seconds
Distance=Timeâˆ—Speed/Distance=25/9âˆ—900=2500meter
Option E
Answer: E
Question: Three factories of Conglomerate Corporation are capable of manufacturing hubcaps. Two of the factories can each produce 1000 hubcaps in 15 days. The third factory can produce hubcaps 30% faster. Approximately how many days would it take to produce a 10,000 hubcaps with all three factories working simultaneously?
Options:
A)38
B)42
C)46
D)50
E)54
Rationale: since third factory is 30% faster , thus it will create 1300 hubcaps in 15 days
in 15 days total number of hubcaps made by all three will be :
1000+1000+1300=3300
in 30 days:
3300+3300=6600
in 45 days:
6600+3300=9900
now only 100 more hubcaps are required , which will take 1 day
thus in all 46 days.
Ans:C
Answer: C
Question: There are 32 balls which are red, blue or green. If 15 balls are green and the sum of red balls and green balls is less than 23, at most how many red balls are there?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: r+g+b=32
g=15
r + g < 23
=> r + 15 < 23
=> r < 8
=> at most 7 red balls
ANSWER:D
Answer: D
Question: A train 275 m long, running with a speed of 90 km / hr will pass a tree in
Options:
A)11 sec
B)15 sec
C)16 sec
D)20 sec
E)None
Rationale: Sol.
Speed = (90 x 5/18) m/sec.
= 25 m / sec.
Time taken = (275 x 1/25) sec = 11 sec
Answer A
Answer: A
Question: The smallest 3 digit positive integer obtained by adding two positive two digit numbers, one of which has the units and tens places interchanged as the other is _____
Options:
A)100
B)101
C)105
D)110 is answer
E)121
Rationale: Ans: D
Solution: as those numbers has digit interchanged and added to get the three digit number means the sum is: = 11(a+b)
so the final number must be multiple of 11. we are looking for smallest three digit number multiple of 11= 110 Ans D
Answer: D
Question: If one of the followings is the product of the two 3-digit integers 8K6 and 6L9 (K and L denote the tens digit of the respective integers), then that product must be
Options:
A) 478,823
B) 511,913
C) 531,875
D) 538,424
E) 569,112
Rationale: To know the unit digit you can multiply both digit number: 6 x 9 = 54
This eliminates A,C, B, and E, because the number must end with a 4
So the answer is D
Answer: D
Question: A property decreases in value every year at the rate of 6 1/4% of its value at the beginning of the year its value at the end of 3 years was Rs.21093. Find its value at the beginning of the first year?
Options:
A)25600.24
B)25600.28
C)25600.26
D)25600.22
E)25600.21
Rationale: 6 1/4% = 1/16
x *15/16 * 15/16 * 15/16 = 21093
x = 25600.24
Answer:A
Answer: A
Question: A coin is tossed four times. What is the probability that there is at the least one tail?
Options:
A)15/16
B)31/37
C)31/18
D)31/10
E)31/19
Rationale: Let P(T) be the probability of getting least one tail when the coin is tossed four times.
= There is not even a single tail.
i.e. all the outcomes are heads.
= 1/16 ; P(T) = 1 - 1/16 = 15/16
Answer: A
Answer: A
Question: If a randomly selected positive single digit multiple of 3 is multiplied by a randomly selected prime number less than 20, what is the probability Q that this product will be a multiple of 45?
Options:
A)1/32
B)1/28
C)1/24
D)1/16
E)1/14
Rationale: There are 3 single digit multiple of 3, that is, 3,6,9.
There are 8 prime nos less than 20 - 2,3,5,7,11,13,17,19
Total outcome - 8*3 = 24
Favourable outcome = 1 (9*5)
Hence required probability Q= 1/24. Answer C.
Answer: C
Question: A train moving at 2/3 rd of its normal speed reaches its destination 20 minutes late. Find the normal time taken?
Options:
A)1 hour
B)1/3 hour
C)2/3 hour
D)3/4 hour
E)1/4 hour
Rationale: Let the original speed and time is S and T
then distance =S*T
Now the speed changes to 2/3S and T is T+20
As the distance is same
S*T=2/3S*(T+20)
solving this we get t=40 minutes
=40/60=2/3 hour
ANSWER:C
Answer: C
Question: Convert the 17/36 m/s into kilometers per hour?
Options:
A)1.7
B)1.5
C)1.3
D)1.1
E)1.2
Rationale: 17/36 m/s = 17/36 * 18/5 = 17/10
= 1.7 kmph.
Answer: A
Answer: A
Question: A bar over a sequence of digits in a decimal indicates that the sequence repeats indefinitely. What is the value of (10^4 -10^2)(0.0017)?
Options:
A)14.83
B)17.83
C)18.83
D)16.83
E)26.83
Rationale: You get 10^2 (100-1) (.0017)
we know 17/10000 = .0017
10^2 (99) * (17/10000)
10^2 = 100 and 100^2 = 10000
Cancel out the 100 with the 10^2
Left with 99(17/100).
0.99*17 = 16.83
Answer : D
Answer: D
Question: If x + y = 6 and x – y = 3, then x^2 - y^2 =
Options:
A)-4
B)4
C)10
D)19
E)40
Rationale: The fastest approach has already been shown. Here's one more option.
Given:
x + y = 6
x – y = 3
Add the two equations to get: 2x = 9, which means x = 4.5
If x = 4.5, we can plug that value into either equation, to conclude that y = 1.5
If x = 4.5 and y = 1.5, then x² - y² = 4.5² - 1.5² = 19
Answer: D
Answer: D
Question: P beats Q by 125 meter in a kilometer race. Find Q's speed if P's speed is 8 meter/sec.
Options:
A)12.25 meter/sec
B)7 meter/sec
C)14 meter/sec
D)18 meter/sec
E)28 meter/sec
Rationale: P's speed = 8 m/s
P's distance = 1000 m (as it is a km race)
t = 1000/8 = 125 sec
Q's distance = 1000-125= 875m
Q's time to complete this distance is also 62.5 sec.
Q's speed = dist/time = 875/125 = 7 m/s
Hence B is the answer.
Answer: B
Question: How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length?
Options:
A)12.7 sec
B)12.1 sec
C)18.1 sec
D)17.1 sec
E)12.7 sec
Rationale: Speed = 72 * 5/18
= 20 m/sec
Total distance covered
= 110 + 132 = 242 m.
Required time = 242/20 '
= 12.1 sec.
Answer:B
Answer: B
Question: A train 600m long is running at 54km/hr. How much time will it take to cross a pole?
Options:
A)30 secs.
B)42 secs.
C)35 secs.
D)45 secs.
E)40 secs.
Rationale: Distance covered =600m =3/5km speed =54km/hr. Time =3/5*54 =1/90hrs. =1/90*3600 =40 secs. Answer : E
Answer: E
Question: The S.I. on a certain sum of money for 6 years at 16% per annum is half the C.I. on Rs. 8000 for 2 years at 20% per annum. The sum placed on S.I. is?
Options:
A)3000.33
B)2802.33
C)1833.33
D)2990.33
E)2982.33
Rationale: C.I. = [8000 * (1 + 20/100)2 - 8000]= (8000 * 6/5 * 6/5 - 8000) = Rs. 3520.Sum = (3520 * 100)/(6 * 16)= Rs.1833.33Answer:C
Answer: C
Question: In how many ways can a cricket eleven be chosen out of a batch of 15 players.
Options:
A)1784
B)4561
C)1450
D)1365
E)1250
Rationale: Required number of ways
= 15C 11 = 15C (15-11)
= 15 C 4
15C4 = 15 * 14 * 13 * 12 / 4 * 3 * 2 *1
= 1365
Ans: D
Answer: D
Question: Ramesh purchased a refrigerator for Rs. 16500 after getting a discount of 20% on the labelled price. He spent Rs. 125 on transport and Rs. 250 on installation. At what price should it be sold so that the profit earned would be 10% if no discount was offered?
Options:
A)34778
B)26888
C)22899
D)23100
E)32778
Rationale: Price at which the TV set is bought = Rs. 16,500
Discount offered = 20%
Marked Price = 16500 * 100/80 = Rs. 20625
The total amount spent on transport and installation = 125 + 250 = Rs. 375\Total price of TV set = 20625 + 375 = Rs. 21000
The price at which the TV should be sold to get a profit of 10% if no discount was offered = 21000 * 110/100
= Rs. 23100
Answer: D
Answer: D
Question: There are 7 players in a bowling team with an average weight of 94 Kg. If two new players join the team, one weighs 110 Kg and the second weighs 60 Kg, what will be the new average weight?
Options:
A)75 Kg.
B)80 Kg.
C)86 Kg.
D)90 Kg.
E)92 Kg.
Rationale: The New average will be= (94*7+110+60)/9= 92 kgs
E is the answer
Answer: E
Question: In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 75 questions and secures 125 marks, the number of questions he attempts correctly, is :
Options:
A)38
B)40
C)26
D)25
E)11
Rationale: Explanation:
Let the number of correct answers be x.
Then numbers of incorrect answers will be 75 – x
We get 4x – (75 – x)×1= 125
On solving the equation we get x= 40
Answer: B
Answer: B
Question: 3889 + 12.952 – ? = 3854.002
Options:
A)47.095
B)47.752
C)47.932
D)47.95
E)None of these
Rationale: Solution
Let 3889 + 12.952 - x = 3854.002.
Then, x = (3889 + 12.952) - 3854.002 = 3901.952 - 3854.002 = 47.95. Answer D
Answer: D
Question: A satellite is composed of 24 modular units, each of which is equipped with a set of sensors, some of which have been upgraded. Each unit contains the same number of non-upgraded sensors. If the number of non-upgraded sensors on one unit is 1/4 the total number of upgraded sensors on the entire satellite, what fraction of the sensors on the satellite have been upgraded?
Options:
A)5/6
B)1/5
C)1/6
D)1/7
E)1/24
Rationale: Let x be the number of upgraded sensors on the satellite.
The number of non-upgraded sensors per unit is x/4.
The number of non-upgraded sensors on the whole satellite is 24(x/4) = 6x.
The fraction of sensors which have been upgraded is x / (x+6x) = x/7x = 1/7
The answer is D.
Answer: D
Question: In a two-digit number, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 280, then the number is:
Options:
A)16
B)24
C)27
D)35
E)46
Rationale: Let the ten's digit be x. Then, unit's digit = x + 2. Number = 10x + (x + 2) = 11x + 2
Sum of digits = x + (x + 2) = 2x + 2
(11x + 2)(2x + 2) =280
22(x)(x) + 26x - 276 = 0
11(x)(x) + 13x -138 = 0
(x - 3)(11x + 46) = 0
x = 3
Hence, required number = 11x + 2 = 35.
ANSWER:D
Answer: D
Question: A cargo ships engines failed 100 miles away from the port. Due to the changing wind direction, it is moving 12 miles towards the port and 6 miles away from the port. If the wind pattern remains same, how many miles it will travel before reaching the port?
Options:
A)A - 179
B)B - 240
C)C - 280
D)D - 100
E)E - 155
Rationale: Ships overall distance covered per cycle is +6 miles
take 100 - 6
take 94/6 to lowest divisible number - 90/6
This means that it will take 15 "overall" actions to reach the 90th mile. -15*18 miles added later
Set cycle start at 90. travel 10 miles and reach the anchor point - add 10 to total
15*18 + 10 = 280 miles in total
Answer: C
Answer: C
Question: If m=4p where p is a prime number greater than 2, how many different positive even divisors does m have, including m?
Options:
A)two
B)three
C)four
D)six
E)eight
Rationale: m=2, 2, p (p is in the prime factorization since were told it is a prime number in the question)
2
4 (because of 2*2)
2p (because of 2 * p)
4p (because of 2 * 2 * p)=C
Answer: C
Question: Ramu bought an old car for Rs. 45000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent?
Options:
A)A)12.5%
B)B)16%
C)C)18%
D)D)22%
E)of these
Rationale: Total CP = Rs. 45000 + Rs. 13000 = Rs. 58000 and SP = Rs. 64900
Profit(%) = (64900 - 58000)/55000 * 100 = 18%
ANSWER:A
Answer: A
Question: Two pipes A and B can fill a cistern in 12 and 15 minutes respectively. Both are opened together but after 6 minutes A is turned off. After how much more time will the cistern be filled?
Options:
A)8 1/7
B)8 1/1
C)8 1/4
D)1 1/2
E)8 3/7
Rationale: 6/12 + (6 + x)/15 = 1
x = 1 1/2
Answer: D
Answer: D
Question: What is the place value of 4 in the numeral 2436?
Options:
A)400
B)500
C)700
D)800
E)840
Rationale: Option 'A'
4 * 100 = 400
Answer: A
Question: The sum of how many terms of the series 6 + 12 + 18 + 24 + ... is 1800 ?
Options:
A)20
B)24
C)28
D)32
E)24
Rationale: This is an A.P. in which a = 6, d = 6 and Sn = 1800
Then, n [2a + (n - 1)d] = 1800
2
n [2 x 6 + (n - 1) x 6] = 1800
2
3n (n + 1) = 1800
n(n + 1) = 600
n2 + n - 600 = 0
n2 + 25n - 24n - 600 = 0
n(n + 25) - 24(n + 25) = 0
(n + 25)(n - 24) = 0
n = 24
Number of terms = 24.
B)
Answer: B
Question: what is the 49 th word if the letters of the word ABUSER is arranged in alphabetical order
Options:
A)ARBESV
B)ARBESW
C)ARBESU
D)ARBESS
E)ARBESE
Rationale: Firstly arrange it in alphabatical order i.e
ABERSU
Take first two letter as a constant i.e ABersu
(remaining ersu can be arranged in 4! ways)
the next letter according to dictionary is AEbrsu take first two letter as a constant i.e AEbrsu(remaining brsu can be arranged in 4! ways)
when AB constant no of words will formed = 24
when AE constant no of words will formed = 24
so far we had completed 48 words the
49 word is ARBESU
ANSWER:C
Answer: C
Question: Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is:
Options:
A)228gallons
B)267gallons
C)120gallons
D)767gallons
E)167gallons
Rationale: Explanation:
Work done by the waste pipe in 1 minute ={\color{Black} \frac{1}{15}-\left ( \frac{1}{20}+\frac{1}{24} \right )=\left ( \frac{1}{15}-\frac{11}{120} \right )=-\frac{1}{40}} [-ve sign means emptying]
Volume of {\color{Black} \frac{1}{40}} part = 3 gallons
Volume of whole = (3 x 40) gallons = 120 gallons.
Answer: C
Answer: C