divelab/Sys2Bench huggingface dataset:
Question: There are 60 doors marked with numbers 1 to 60. There are 60 individuals marked 1 to 60.
An operation on a door is defined as changing the status of the door from open to closed or vice versa. All the doors are closed to start with. One at a time, one randomly chosen individual goes and operates the doors. The individual however operates only those doors which are a multiple of the number he/she is carrying. For example, the individual marked with number 5 operates the doors marked with 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, and 60. If every individual in the group gets one turn, then how many doors are open at the end?
Options:
A)0
B)2
C)5
D)7
E)9
Rationale: If a door is closed at the start, it requires an odd number of people to operate to be open at the end. Only the perfect squares have an odd number of factors.
The doors which are open at the end are: 1, 4, 9, 16, 25, 36, 49 for a total of 7 doors.
The answer is D.
Answer: D
Question: A ferry can transport 100 tons of vehicles. Automobiles range in weight from 1,800 to 3,200 pounds. What is the greatest number of automobiles that can be loaded onto the ferry?
Options:
A)115
B)120
C)110
D)100
E)90
Rationale: to get maximum vehicles we must take into consideration the minimum weight i.e 1800 pounds here
since , 1 ton = 2000 pounds
78 tons will be 200,000 pounds
from the answer choices:
let max number of vehicles be 110
total weight will be = 110*1800 = 198000 pounds , which is lesser than the maximum weight allowed .
Ans: C
Answer: C
Question: The sum of the present age of Henry and Jill is 40. What is their present ages if 11 years ago Henry was twice the age of Jill?
Options:
A)and 27
B)and 24
C)and 23
D)and 29
E)of these
Rationale: Let the age of Jill 11 years ago be x, age of Henry be 2x
x+11 + 2x+11 = 40
x = 6
Present ages will be 17 and 23
Answer : C
Answer: C
Question: A train covers a distance of 12 km in 10 minutes. If it takes 6 seconds to pass a telegraph post, then the length of the train is :
Options:
A)120 m
B)140 m
C)240 m
D)300 m
E)None
Rationale: Sol.
Speed = [12/10 * 60] km/hr = [72 * 5/18] m/sec = 20 m/sec.
Length of the train = (speed * Time) = (20 * 6) m = 120 m.
Answer A
Answer: A
Question: The radius of a cone is 14 m, slant height is 20 m. Find the curved surface area?
Options:
A)770
B)550
C)110
D)880
E)330
Rationale: Cone curved surface area = πrl
22/7 × 14 × 120 = 44 × 20 = 880 m(power2)
Answer is D.
Answer: D
Question: If a and b are multiples of 5 then which are all the multiples of 5
1) a/b
2) a*b
3) a+b
4) a-b
5) a^b
Options:
A)1,2,5
B)all of these
C)1,3
D)2,3,4,5
E)1,2,3,5
Rationale: a*b a^b a+b a-b are multiples of 5 except a/b
ANSWER:D
Answer: D
Question: The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is:
Options:
A)200
B)210
C)245
D)230
E)265
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X) = 750 ==> X = 245 m.
Answer: Option C
Answer: C
Question: If k is the sum of the digits of integer m, and m=13n, where n is an integer, which of the following must be true?
Options:
A)k is a multiple of 6
B)The sum of the digits of k is divisible by 3
C)m is a multiple of 10k
D)k is divisible by 2
E)value of k contains prime number also
Rationale: m= 13n i.e n =1,2,3 ,4 etc or -1,-2.-3 ,-4 then m =13,26,39,52 or -13 ,-26 ,-39 ,-52 then k 4,8,12,7, or -(1+3) , -(2+6) , -(3+9) ,-(5+2) .
ans E
Answer: E
Question: If x,y ,and z are positive real numbers such that x+y-z =50 , y-z+x =60 , and z-x+y = 80, then find the z value?
Options:
A)10
B)20
C)5
D)15
E)25
Rationale: x+y-z =50, ------1)
y-z+x =60 , ------2)
z-x+y = 80------3)
from (1)&(2)
2z=10
z=5
correct option is C
Answer: C
Question: At what approximate time between 4 and 5 am will the hands of a clock be at right angle?
Options:
A)4 : 40 am
B)4 : 38 am
C)4 : 35 am
D)4 : 39 am
E)None of these
Rationale: Here H × 30 = 4 × 30 = 120°.
(Since initially the hour hand is at 4. ∴ H = 4).
Required angle A = 90° and since, H × 30 > A° so, there will be two timings.
Required time T = 2⁄11(H × 30 ± A) minutes past H.
∴ One timing = 2⁄11(4 × 30 + 90) minutes past 4
= 382⁄11 minutes past 4.
Or 4 : 38 approx.
Answer B
Answer: B
Question: A can do a piece of work in 90 days & Y can do it in 80 days. They began working together but A leaves after some days and then B completed the remaining work in 46 days. The number of days after which A left the work was?
Options:
A)10 days
B)11 days
C)16 days
D)17 days
E)18 days
Rationale: A and B did the work for some days.
After that , B completed the remaining work in 46 days .
In 46 days, word done by B =
1
80
x 46 =
23
45
Remaining work = 1 – 23/45
= 17/45
Remaining work is done by both A and B together =
17/45x 90 x 80/90 + 80
= 16 days
C
Answer: C
Question: The speed of a car is 90 km in the first hour and 30 km in the second hour. What is the average speed of the car?
Options:
A)50 kmph
B)60 kmph
C)75 kmph
D)85 kmph
E)90 kmph
Rationale: Explanation:
S = (90 + 30)/2 = 60 kmph
B)
Answer: B
Question: Two persons start at the same point, walk in opposite directions with 7 km/hr and 4.5 km/hr respectively.
What is the distance separated after 2 and half hrs?
Options:
A)26.250 km
B)27.250 km
C)28.750 km
D)29.250 km
E)25.250 km
Rationale: As the two persons are moving in the opposite direction, so they will be separateed in 1 hour = 7 + 4.5 = 11.5 km.
They will be separated in 2.5 hours = 11.5 * 2.5 = 28.750 km
ANSWER:C
Answer: C
Question: John can complete a given task in 20 days. Jane will take only 12 days to complete the same task. John and Jane set out to complete the task by beginning to work together. However, Jane was indisposed 4 days before the work got over. In how many days did the work get over from the time John and Jane started to work on it together?
Options:
A)6
B)10
C)8
D)7.5
E)3.5
Rationale: John 6*20=120
Jane 10*12=120
In 4 days working alone John did: 4 Days * Rate = 4*6=24, so working together they did 120-24=96 --> Rate(A+B)*t=96 -> 16*t=96, t=6. hence the answer is B (John worked 4 days + 6 days they worked together = 10 days)
Answer: B
Question: 1, 5, 13, 25, 41, ?
Options:
A)61
B)56
C)74
D)57
E)32
Rationale: The pattern is + 4, + 8, + 12, + 16, +20
Answer : A.
Answer: A
Question: B and C start a business with Rs.2000 and Rs.10000 respectively. Hoe should they share their profits at the end of one year?
Options:
A)1:2
B)1:3
C)1:4
D)1:5
E)2:1
Rationale: Explanation:
They should share the profits in the ratio of their investments.
The ratio of the investments made by B and C =
2000 : 10000 => 1:5
Answer:D
Answer: D
Question: A merchant marks his goods up in such a way that the profit made on selling 30 articles is equal to the cost price of 20 articles. What is the % Q profit made by the merchant?
Options:
A)66.67 %
B)50 %
C)200 %
D)100 %
E)33.33 %
Rationale: C.P of 1 article= $30(say)
C.P of 20 articles=30*20=$600
Now, C.P of 20 articles=Profit on 30 articles
Therefore, profit on 1 article=$600/30=$20
Profit Q%=(20/30)*100=66.67%
Answer A
Answer: A
Question: Sreenivas sells a table to Shiva at 10% profit and Shiva sells it to Mahesh at 10% loss. At what price did Sreenivas purchase the table if Mahesh paid Rs. 2178?
Options:
A)Rs. 2100
B)Rs. 2150
C)None of these
D)Rs. 2200
E)Cannot be determined
Rationale: Explanation :
et the cost price of table for Sreenivas be Rs. x and given that, cost price of table for Mahesh = Rs. 2178.=> (90%) of (110%) of x = Rs. 2178.=> (90/100)(110/100)x = 2178=> x = (2178 x 100)/(9 x 11)=> x = Rs. 2200
Answer : D
Answer: D
Question: A dog takes 3 leaps for every 5 leaps of a hare. If one leap of the dog is equal to 3 leaps of the hare,
the raƟo of the speed of the dog to that of the hare is
Options:
A)4:5
B)9:5
C)8:5
D)9:2
E)None of these
Rationale: Explanation:
Dog : Hare = (3*3) leaps of hare : 5 leaps of hare
= 9 : 5
Answer: B
Answer: B
Question: 5 z – 3 < 3 z + 4, which of the following cannot be a value of z3z3 ?
Options:
A)0
B)1
C)8
D)27
E)6
Rationale: 5z - 3z < 4 + 3
2z < 7
z < 3.5
z must be 4 for z^3 to be 64. On the other hand z an be 0, 1, 2, or 3 thus z^3 can be 0, 1, 8, or 27.
ANSWER:D
Answer: D
Question: Two numbers N and 16 have LCM = 48 and GCF = 8. Find N.
Options:
A)12
B)24
C)36
D)48
E)52
Rationale: The product of two integers is equal to the product of their LCM and GCF. Hence.
16 × N = 48 × 8
N = 48 × 8 / 16 = 24
correct answer is B)24
Answer: B
Question: A can do a piece of work in 10 days and B can do the same work in 12 days. A and B worked together for 2 days. How many more days are required to complete the remaining work if they work together?
Options:
A)3 (5/18) days
B)3 (7/11) days
C)3 (5/11) days
D)2 (5/11) days
E)3 (2/11) days
Rationale: A can do 1/10 of the work in a day.
B can do 1/12 of the work in a 1 day.
Both of them together can do (1/10 + 1/12) part of work in 1 day = (6 + 5)/60 = 11/60
They take 60/11 days to complete the work together.
Given that they already worked for 2 days.
The number of days required to complete remaining work => 60/11 - 2 = 38/11 = 3 (5/11) days.
Answer:C
Answer: C
Question: What percent of a week is 3 days?
Options:
A)50%
B)45%
C)42,85%
D)23,33%
E)40%
Rationale: Explanation :
Total days in a week = 7
Required percentage = (3/7) Ã— 100 = 42,85%
Answer : Option C
Answer: C
Question: The price of lunch for 14 people was $207 including a 15% gratuity for service. What was the average price per person, EXCLUDING the gratuity?
Options:
A)11.73
B)12.85
C)13.8
D)14
E)15.87
Rationale: Clearly B is the answer
I used POE here
Lets consider option (B)
14*12.85= 180 now 180(115/100)=207
=> possible ANSWER IMO B
Answer: B
Question: A man buys Rs. 20 shares paying 9 % dividend. The man wants to have an interest of 12% on his money.The market value of each share is :
Options:
A)Rs. 12
B)Rs. 15
C)Rs. 18
D)Rs. 21
E)None
Rationale: Solution
Dividend on Rs. 20 = Rs.(9/100x20) = Rs.9/5
Rs. 12 is an income on Rs. 100.
∴ Rs.9/5 is an income on Rs. (100/12 X9/5)= Rs.15
Answer B
Answer: B
Question: A certain number of machines can do a work in 75 days. If there were 6 machine more it could be finished in 15days less. How many machines are there?
Options:
A)20
B)24
C)25
D)30
E)32
Rationale: Number of machines = 6* (75-15)/15 = 24 machines
Answer is B
Answer: B
Question: A and B walk around a circular track. They start at 9 a.m. from the same point in the opposite directions. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other before 12:00 P.m.?
Options:
A)28
B)27
C)26
D)25
E)20
Rationale: Sol.
Relative speed = (2 + 3) = 5 rounds per hour.
So, they cross each other 5 times in an hour.
Hence, they cross each other 20 times before 12:00 P.m.
Answer E
Answer: E
Question: Diesel costs Rs.4per lit and petrol costs 5.63 per litre. If the price of diesel rise by 10% a month and the price of petrol is unchanged.How many months will it take until a litre of Diesel costs more than a litre of petrol.
Options:
A)9 months
B)5 months
C)6 months
D)4 months
E)2 months
Rationale: Explanation :
=>In the First Month the price of the diesel would be 4*110/100 = 4.4
=>In the Second Month the price of the diesel would be 4.4*110/100 = 4.84
=>In the Third Month the price of the diesel would be 4.84*110/100 = 5.324
=>In the fourth Month the price of the diesel would be 5.324*110/100 = 5.85 which is higher than the
price of the petrol!
Answer : D
Answer: D
Question: The average of first seven multiples of 5 is:
Options:
A)20
B)16
C)15
D)8
E)10
Rationale: Explanation :
(5(1+2+3+4+5+6+7)/7
= 5x28/7
= 20
Answer : A
Answer: A
Question: What day of the week does May 28 2006 fall on
Options:
A)Saturday
B)Monday
C)Sunday
D)Thursday
E)Friday
Rationale: Explanation:
28th May 2006 = (2005 years + period from 1-Jan-2006 to 28-May-2006)
We know that number of odd days in 400 years = 0
Hence the number of odd days in 2000 years = 0 (Since 2000 is a perfect multiple of 400)
Number of odd days in the period 2001-2005
= 4 normal years + 1 leap year
= 4 x 1 + 1 x 2 = 6
Days from 1-Jan-2006 to 28-May-2006 = 31 (Jan) + 28 (Feb) + 31 (Mar) + 30 (Apr) + 28(may)
= 148
148 days = 21 weeks + 1 day = 1 odd day
Total number of odd days = (0 + 6 + 1) = 7 odd days = 0 odd day
0 odd day = Sunday
Hence May 28 2006 is Sunday.
Answer: Option C
Answer: C
Question: A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is?
Options:
A)266
B)298
C)269
D)150
E)277
Rationale: Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 15 => y = x/15
x + 100 / 25 = x / 15
x = 150 m.
Answer: D
Answer: D
Question: The ratio of the present ages of a man and his wife is 6 : 5. Which of the following can't be a possible ratio of their ages 35 years ago?
Options:
A)4: 6
B)5: 6
C)6:6
D)7: 6
E)8: 6
Rationale: 6x-35/5x-35 = 7/6
Therefore x=-35
Age cannot be negative.
Answer: D
Answer: D
Question: A train 110 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
Options:
A)4
B)6
C)5
D)9
E)8
Rationale: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr
[66 * 5/18] m/sec = [55/3] m/sec.
Time taken to pass the man = [110 * 3/55] sec = 6 sec
ANSWER:B
Answer: B
Question: The average height of 40 girls out of a class of 50 is 169 cm. and that of the remaining girls is 167 cm. The average height of the whole class is :
Options:
A)138.9 cms
B)149.2 cms
C)168.6 cms
D)159.2 cms
E)142.5 cms
Rationale: Explanation:
Average height of the whole class =(40×169+10×167/50)=168.6 cms
Answer C
Answer: C
Question: The average monthly salary of 20 employees in an organisation is Rs. 1500. If the manager's salary is added, then the average salary increases by Rs. 100. What is the manager's monthly salary ?
Options:
A)3600
B)3890
C)88798
D)2789
E)2891
Rationale: Explanation:
Manager's monthly salary Rs. (1600 * 21 - 1500 * 20) = Rs. 3600.
Answer: A) 3600
Answer: A
Question: If 10 is added to thrice a number and this sum is multiplied by 5, the result is the same as if the number is multiplied by 5 and 13 is added to the product. What is the number?
Options:
A)-3.5
B)-3.7
C)-5
D)-9
E)11
Rationale: let the number be x;
5(10+3x)=5x+13;
x=-3.7
ANSWER:B
Answer: B
Question: If A's salary is 25% higher than B's salary,then how much percent is B's salary lower than A's?
Options:
A)22%
B)20%
C)25%
D)30%
E)10%
Rationale: If A's salary is 25% higher than B's salary, means A's salary is Rs. 125 if B's salary is Rs 100. Then B 's salary is lower than A by 25*100/125 = 20% .
ANSWER:B
Answer: B
Question: If A lends Rs.3500 to B at 10% per annum and B lends the same sum to C at 11.5% per annum then the gain of B in a period of 3 years is?
Options:
A)157.5
B)157.51
C)157.57
D)157.59
E)157.52
Rationale: (3500*1.5*3)/100 => 157.50
Answer: A
Answer: A
Question: A and B finish the job in 15 days.while A,B and C can finish it in 10 days . C alone will finish the job in
Options:
A)40 days
B)30 days
C)60 days
D)70 days
E)50 days
Rationale: Explanation:
10 = (15 * x)/(15 + x)
150+10x=15x
5x=150
X=30
Answer: Option B
Answer: B
Question: A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 550 m long?
Options:
A)70sec
B)72sec
C)74sec
D)76sec
E)79sec
Rationale: Speed = 240/24 = 10 m/sec.
Required time = (240 + 550)/10 = 79 sec.
Answer:E
Answer: E
Question: A certain company reported that the revenue on sales increased 60 % from 2000 to 2003, and increased 80 % from 2000 to 2005. What was the approximate percent increase in revenue for this store from 2003 to 2005?
Options:
A)50 %
B)40 %
C)35 %
D)32 %
E)13 %
Rationale: Assume the revenue in 2000 to be 100. Then in 2003 it would be 160 and and in 2005 180, so from 2003 to 2005 it increased by (180-160)/160=20/160=13%
Answer: E.
Answer: E
Question: daal is now being sold at rate Rs.20 a kg.During last month its rate was Rs 16 per kg.By How reduce percent should a family its consumption so as to keep the expenditure fixed?
Options:
A)10%
B)20%
C)30%
D)40%
E)50%
Rationale: Last month rate= 16 per kg
this month rate = 20 per kg
if 20=100% then 16= ?
therefore %= (16 * 100)/20=80%
to reduce consumption 100-80=20%
ANSWER:B
Answer: B
Question: From the following choice, what is the equation of a line whose x-intercept is half as that of line 3x+4y=12 and y-intercept twice of same
Options:
A)3x+y=6
B)3x+y=5
C)3x+y=4
D)3x+y=3
E)2x+y=6
Rationale: x/4 +y/3 = 1
x-intecept = 4
y-intecept = 3
new,
x-intecept = 2
y-intecept = 6
x/2 + y/6 = 1
3x+y=6
ANSWER:A
Answer: A
Question: Sachin is younger than Rahul by 7 years. If the ratio of their ages is 5:12, find the age of Sachin
Options:
A)9
B)24.8
C)2
D)3
E)5
Rationale: Explanation:
If Rahul age is x, then Sachin age is x - 7,
so,
12x - 84 = 5x
7x = 84
x = 12
So Sachin age is 12 - 7 = 5
Answer: E) 5
Answer: E
Question: A, B and C enter into a partnership. They invest Rs. 40,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. IN what ratio will the profit be shared at the end of 3 years?
Options:
A)3:4:8
B)3:4:7
C)3:4:4
D)3:4:2
E)3:4:1
Rationale: A:B:C
= (40000 * 36) : (80000 * 12 + 40000 * 24) : (120000 * 24 + 40000 * 12)
= 144:192:336
= 3:4:7
Answer: B
Answer: B
Question: If b> 0, a> 0, and (b^2)a= b,then which of the following MUST equal b?
Options:
A)1/(a^2)
B)B.1/a
C)A
D)A^2
E)A^2 – 2b+1
Rationale: B^2A=B
B^2A-B=0
B(ba-1)=0
Since B>0 then
Ba-1=0
B=1/a
Ans:B
Answer: B
Question: If a train, travelling at a speed of 18 kmph, crosses a pole in 5 sec, then the length of train is?
Options:
A)281 m
B)25 m
C)50 m
D)125 m
E)75 m
Rationale: B
B = 18 * 5/18 * 5 = 25 m
Answer: B
Question: In one hour, a boat goes 15 km/hr along the stream and 11 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
Options:
A)12 kmph
B)13 kmph
C)14 kmph
D)15 kmph
E)16 kmph
Rationale: Explanation:
Let the speed downstream be a km/hr and the speed upstream be b km/hr, then
Speed in still water =1/2(a+b) km/hr
Rate of stream = 1/2(a−b) km/hr
Speed in still water = 1/2(15+11) kmph = 13 kmph.
Answer: Option B
Answer: B
Question: In a class of 140 students, 60% of them passed. By what percent is the number of students who passed more than the number of failed students?
Options:
A)70%
B)90%
C)72%
D)50%
E)53%
Rationale: Number of students passed = 60% of 140 = 60/100 * 140 = 84
Number of students failed = 140 - 84 = 56.
Required percentage = 28/56 * 100 = 50%.
Answer: D
Answer: D
Question: Train X crosses a stationary train Y in 60 seconds and a pole in 25 seconds with the same speed. The length of the train X is 300 m. What is the length of the stationary train Y?
Options:
A)185 m
B)420 m
C)167 m
D)176 m
E)168 m
Rationale: Let the length of the stationary train Y be LY
Given that length of train X, LX = 300 m
Let the speed of Train X be V.
Since the train X crosses train Y and a pole in 60 seconds and 25 seconds respectively.
=> 300/V = 25 ---> ( 1 )
(300 + LY) / V = 60 ---> ( 2 )
From (1) V = 300/25 = 12 m/sec.
From (2) (300 + LY)/12 = 60
=> 300 + LY = 60 (12) = 720
=> LY = 720 - 300 = 420 m
Length of the stationary train = 420 m
Answer:B
Answer: B
Question: A batsman makes a score of 66 runs in the 17th inning and thus increases his averages by 3. What is his average after 17th inning?
Options:
A)25
B)31
C)27
D)29
E)18
Rationale: Let the average after 17 innings = x
Total runs scored in 17 innings = 17x
Average after 16 innings = (x-3)
Total runs scored in 16 innings = 16(x-3)
Total runs scored in 16 innings + 66 = Total runs scored in 17 innings
=> 16(x-3) + 66 = 17x
=> 16x - 48 + 66 = 17x
=> x = 18
Answer is E.
Answer: E
Question: In what ratio must wheat at Rs.3.20 pe rkg be mixed with wheat at Rs.2.90 per kg so that the mixture be worth Rs.3.08 per kg
Options:
A)3:4
B)3:2
C)3:5
D)3:7
E)2:3
Rationale: If 2 ingredients are mixed, then the required ratio is given by, the rule of allegation C.P of a unit quantity of cheaper (c) C.P. of a unit quantity of dearer (d)
Mean Price (m) d-m m-c  Required ratio is cheaper quantity : dearer quantity = (d-m) : (m-c) Answer with Explanation:
Given
i. C.P of a unit quantity of I kind (p) = 3.20 ii. C.P of a unit quantity of II kind (p) = 2.90 iii. Mean price (p) = 3.08 iv. d – m = 3.08 – 2.90 = 0.18 v. m – c = 3.20 – 3.08 = 0.12  Required ratio = 0.18 : 0.12 = 3 : 2
Answer:B
Answer: B
Question: Timothy leaves home for school, riding his bicycle at a rate of 6 miles per hour. Fifteen minutes after he leaves, his mother sees Timothy’s math homework lying on his bed and immediately leaves home to bring it to him. If his mother drives at 36 miles per hour, how far (in terms of miles) must she drive before she reaches Timothy?
I think is a 700 level problem but I tag it as 600/700, let me know. Either way I hope in an explanationThanks
Options:
A)1/3
B)9/5
C)4
D)9
E)12
Rationale: In 15 mins, Timothy travels=6/4 miles.
Now, let his mother takes x hours to reach him, traveling at 36mph.
So, 36x=6x+6/4
x=1/20 hrs.
Thus, the distance traveled by his mother to reach= 36*1/20=9/5 miles. Ans B
Answer: B
Question: A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?
Options:
A)1 kmph
B)2 kmph
C)3 kmph
D)7 kmph
E)8 kmph
Rationale: DS = 6
US = 4
S = ?
S = (6 - 4)/2
= 1 kmph
Answer:A
Answer: A
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(76)-A(75)?
Options:
A)2^22+1
B)2^23+1
C)2^23+1
D)2^24
E)2^75
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 A76-A75= 2^75
E is the answer
Answer: E
Question: A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current?
Options:
A)1.7
B)1.5
C)1.2
D)1.1
E)1.9
Rationale: 72 --- 9 DS = 8
? ---- 1
45 ---- 9 US = 5
? ---- 1 S = ?
S = (8 - 5)/2 = 1.5
Answer: B
Answer: B
Question: By selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 7 p.c?
Options:
A)28000
B)29000
C)37000
D)37200
E)40000
Rationale: Option B
Explanation:
CP + CP/8 = 45000
CP = 40000
SP = 40000*(93/100) = 37200
Option D
Answer: D
Question: The G.C.D. of 1.08, 0.36 and 0.6 is:
Options:
A)0.03
B)0.9
C)0.12
D)0.108
E)0.118
Rationale: Given numbers are 1.08, 0.36 and 0.60. H.C.F. of 108, 36 and 60 is 18,
H.C.F. of given numbers = 0.12.
Answer: Option C
Answer: C
Question: In order to fence a square Manish fixed 48 poles. If the distance between two poles, is 4 metres then what will be the area of the square so formed?
Options:
A)Cannot be determined
B)2600 cm2
C)2500 cm2
D)3025 cm2
E)2304 cm2
Rationale: Let the side of the square be x m.
∴ Perimeter of the square = 48 × 4 = 4x ∴ x = 48 m
∴ Area = (48)2 = 2304 m2
Answer E
Answer: E
Question: If 0.75 : x :: 3 : 8, then x is equal to:
Options:
A)A)2.12
B)B)2.2
C)C)1.25
D)D)1.3
E)E)2.0
Rationale: (x * 3) = (0.75 * 8)
x = 6/3
x = 2
Answer = E
Answer: E
Question: The cost of 3 kg of sugar is $90. What will the cost of 8 kg of sugar be?
Options:
A)120
B)140
C)180
D)220
E)240
Rationale: 3 kg costs $90
1 kg costs $30
8 kg costs $240
The answer is E.
Answer: E
Question: How many 3-digit numbers are completely divisible 6 ?
Options:
A)A)100
B)B)150
C)C)200
D)D)250
E)E)300
Rationale: 3-digit number divisible by 6 are: 102, 108, 114,... , 996
This is an A.P. in which a = 102, d = 6 and l = 996
Let the number of terms be n. Then tn = 996.
a + (n - 1)d = 996
102 + (n - 1) x 6 = 996
6 x (n - 1) = 894
(n - 1) = 149
n = 150
Number of terms = 150.
B)
Answer: B
Question: Nitin borrowed some money at the rate of 4% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of eleven years is Rs. 8160, how much money did he borrow?
Options:
A)Rs. 9451.84
B)Rs. 8014.54
C)Rs. 8000
D)Rs. 8242.42
E)Rs. 8542.54
Rationale: Let the sum be Rs. x. Then,
[(x * 4 * 3)/100] + [(x * 9 * 5)/100] + [(x * 13 * 3)/100] = 8160
12x + 45x + 39x = (8160 * 100)
99x = 816000 => x = 8242.42.
ANSWER:D
Answer: D