divelab/Sys2Bench huggingface dataset:
Question: P can do a work in 72 days. Q can do the same work in 9 days and R can do the same in 12 days. Q and R start the work and leave after 3 days. P finishes the remaining work in --- days.
Options:
A)7
B)8
C)9
D)10
E)30
Rationale: Work done by P in 1 day = 1/72
Work done by Q in 1 day = 1/9
Work done by R in 1 day = 1/12
Work done by Q and R in 1 day = 1/9 + 1/12 = 7/36
Work done by Q and R in 3 days = 3Ã—7/36 = 7/12
Remaining work = 1 â€“ 7/12 = 5/12
Number of days in which P can finish the remaining work = (5/12) / (1/72) = 30
Option E
Answer: E
Question: If the radius of a cylinder is made 3 times and so is the height, what is the new volume of the cylinder divided by the old one?
Options:
A)27.
B)2.
C)6.
D)4.
E)10.
Rationale: let v and v' be the original and the changed volume
now
v=pir^2h
v'=pi(3r)^2(3h)
v'=27v
A) 27
Answer: A
Question: Find the compound interest on $1200 for 3 years at 20% p.a. if CI is component yearly?
Options:
A)$120
B)$150
C)$874
D)$250
E)$300
Rationale: A = P(1 + R/100)^T
= 1200(1 + 20/100)^3
=$2074
CI = $874
Answer is C
Answer: C
Question: Find 40 % of 320
Options:
A)96
B)94
C)128
D)74
E)110
Rationale: We know that R % of m is equal to R/100 × m.
So, we have 40 % of 320
40/100 × 320
= 128
Answer:C
Answer: C
Question: Two trains are moving in opposite directions with speed of 70 km/hr and 90 km/hr respectively. Their lengths are 1.10 km and 0.9 km respectively. the slower train cross the faster train in --- seconds
Options:
A)56
B)45
C)47
D)26
E)25
Rationale: Explanation:
Relative speed = 70+90 = 160 km/hr (Since both trains are moving in opposite directions)
Total distance = 1.1+.9 = 2km
Time = 2/160 hr = 1/80 hr = 3600/80 seconds = = 45 seconds
Answer: Option B
Answer: B
Question: Statement : A large majority of the work force in India is unorganised. Most of them earn either the minimum or uncertain wages while others are engaged in sundry jobs.
Conclusions :
I. The workers in the organised sector get better facilities and stay longer in their jobs.
II. Some workers in the unorganised sector of the work force have a regular and fixed income.
Options:
A)Only conclusion I follows
B)Only conclusion II follows
C)Either I or II follows
D)Neither I nor II follows
E)Both I and II follow
Rationale: Explanation:
Conclusion I is not stated in the statement.
Only Conclusion II follows.
Option B
Answer: B
Question: When 1 is added to half of one-third of one-fifth of a number, the result is one-fifteenth of the number. Find the number?
Options:
A)30
B)81
C)60
D)27
E)11
Rationale: Explanation:
Let the number be
1 + 1/2[1/3(a/5)] = a/15
=> 1 = a/30 => a = 30
Answer:A
Answer: A
Question: The flow of water through a drainage pipe was monitored for a 3-hour period. In the second hour, the rate of flow was 18 gallons per hour, which was 50 percent faster than the rate of flow for the first hour. If 25 percent more water flowed through the pipe in the third hour than it did in the second, how many gallons of water flowed through the pipe during the entire three hours?
Options:
A)51.25
B)52.5
C)53.75
D)55.0
E)55.5
Rationale: Rate of flow of water in second hour = 18 gallons per hour
Rate of flow of water in first hour = 18/(3/2) = 12 gallons per hour
Rate of flow of water in third hour = (125/100)* 18 = (5/4) * 18 = 22.5 gallons per hour
Number of gallons of water that flowed through the pipe during the entire 3 hours = 12+18+22.5 = 52.5 gallons
Answer B
Answer: B
Question: A school has 4 section of Chemistry in Class X having 60, 35, 45 and 42 students. The mean marks obtained in Chemistry test are 50, 60, 55 and 45 respectively for the 4 sections. Determine the overall average of marks per student.
Options:
A)50
B)52
C)51
D)53
E)None of the above
Rationale: Required average marks
= 60Ã—50+35Ã—60+45Ã—55+42Ã—45/60+35+45+42
= 3000+2100+2475+1890/182
= 9465â„182 = 52
Answer B
Answer: B
Question: A man has Rs.700 in the denominations of five-rupee notes,ten-rupee notes and 20-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
Options:
A)20
B)70
C)60
D)90
E)80
Rationale: Let number of notes of each denomination be x.
Then 5x +10x + 20x = 700
35x = 700
x = 20.
Hence, total number of notes = 3x = 60.
Answer is C
Answer: C
Question: A man engaged a servant on the condition that he would pay him Rs.500 and a uniform after one year service. He served only for 9 months and received uniform and Rs.300, find the price of the uniform?
Options:
A)s.80
B)s.85
C)s.90
D)s.300
E)s.120
Rationale: 9/12 = 3/4 * 500 = 375
300
-------------
75
1/4 -------- 75
1 --------- ? => Rs.300
ANSWER:D
Answer: D
Question: P and Q invested in a business. They earned some profit which they divided in the ratio of 2:3. If P invested Rs.60, 000, the amount invested by Q is:
Options:
A)Rs. 65,000
B)Rs. 70,000
C)Rs. 80,000
D)Rs. 90,000
E)Rs. 60,000
Rationale: Suppose Q invested Rs.y. Then, y = 60,000/y = 2/3
or y = 60000/2 * 3
= 90,000.
ANSWER:D
Answer: D
Question: The arithmetic mean of the scores of a group of students in an exam was 61. The brightest 20% of them secured a mean score of 80 and the dullest 25% a mean score of 31. The mean score of the remaining 55% is:
Options:
A)45
B)50
C)67.72 approximately
D)74.6 approximately
E)None of these
Rationale: Let the required mean score be x. Then, 20 x 80 + 25 x 31 + 55 x x = 61 x 100
1600 + 775 + 55x = 6100
55x = 3725
x = 3725/55 = 67.72
Answer : C
Answer: C
Question: A box contains 12 mangoes out of which 4 are spoilt. If four mangoes are chosen at random, find the probability that Not all the mangoes are spoiled.
Options:
A)1/495
B)394/395
C)494/495
D)1/395
E)4/395
Rationale: Required probability = 1 – 1/495
= 494/495.
ANSWER:C
Answer: C
Question: How many integers between 100 and 160, inclusive, cannot be evenly divided by 3 nor 5?
Options:
A)32
B)27
C)25
D)35
E)29
Rationale: The total numbers between 100 and 160, inclusive, is 61.
3*34=102 and 3*53=159 so the number of multiples of 3 is 20.
5*20=100 and 5*32=160 so the number of multiples of 5 is 13.
However, the multiples of 15 have been counted twice.
15*7=105 and 15*10=150 so the number of multiples of 15 is 4.
Thus the total number is 61-20-13+4=32.
The answer is A.
Answer: A
Question: A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water?
Options:
A)12.8 kmph
B)12.7 kmph
C)12.6 kmph
D)12.5 kmph
E)12.3 kmph
Rationale: Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph.
Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7
Solving the equation, the speed of man in still water is 12.5 kmph.
Answer:D
Answer: D
Question: On January 12, 1980, it was Saturday. The day of the week on January 12, 1979 was –
Options:
A)Saturday
B)Friday
C)Sunday
D)Thursday
E)None of these
Rationale: The year 1979 being an ordinary year, it has 1 odd day.
So, the day on 12th January 1980 is one day beyond on the day on 12th January, 1979.
But, January 12, 1980 being Saturday.
∴ January 12, 1979 was Friday.
Answer B
Answer: B
Question: In 100 litres mixture milk and water are in the ratio 3:2. After adding how many liters of water its ratio will become 3:4
Options:
A)48
B)50
C)62
D)78
E)100
Rationale: Milk quantity = 3/5 * 60 = 36
water quantity = 100-36 = 64
new ratio of M:W = 36:64+x = 3:4
192+3x = 144
x = 48
Answer is A
Answer: A
Question: On multiplying a number by 7, the product is a number each of whose digits is 3. The smallest such number is:
Options:
A)47619
B)47719
C)48619
D)47649
E)47659
Rationale: By hit and trail, we find that
47619 * 7 = 333333.
7) 333333 (47619
333333
----------------
0
ANSWER:A
Answer: A
Question: The angle between the minute hand and the hour hand of a clock when the time is 8.30, is:
Options:
A)10º
B)75º
C)180º
D)270º
E)360º
Rationale: Angle traced by hour hand in 17/2 hrs =(360/12	x 17/2)º = 255.
Angle traced by min. hand in 30 min. = (360/60	x 30)º = 180.
Required angle = (255 - 180)º = 75º.
Answer B
Answer: B
Question: A person P takes 4 hrs time to complete a job and Q takes 6 hrs to complete the same job if they work together how much time will they require to complete the job?
Options:
A)1.2 hrs
B)1.8 hrs
C)2.4 hrs
D)3.0 hrs
E)None of these
Rationale: Explanation:
P’s 1 hr work =1/4
Q’s 1 hr work =1/6
(P+Q)’s 1 hr work= 1/4 +1/6 =5/12=> time = 12/5 =2.4 hrs
Answer: Option C
Answer: C
Question: Amit, Sumit and Pramit go to a seaside town to spend a vacation there and on the first day everybody decides to visit different tourist locations. After breakfast, each of them boards a different tourist vehicle from the nearest bus-depot. After three hours, Sumit who had gone to a famous beach, calls on the mobile of Pramit and claims that he has observed a shark in the waters. Pramit learns from the local guide that at that time of the year, only eight sea-creatures (including a shark) are observable and the probability of observing any creature is equal. However, Amit and Pramit later recall during their discussion that Sumit has a reputation for not telling the truth five out of six times. What is the probability that Sumit actually observed a shark in the waters?
Options:
A)1/36
B)1/30
C)5/36
D)1/24
E)1/28
Rationale: Explanation :
The probability that Sumit actually sees a Shark, given that he claimed to have seen one.
=>P(He actually sees the shark and reports truth) / P(He claims of seeing a shark).
=>P(Sees the shark)P(Reports Truth)/(P(He sees a shark)P(reports truth)+P(Doesn't see) P(reports false).
=>(1/8×1/6)/(1/8×1.6+7/8×5/6)
=>1/36.
Answer : A
Answer: A
Question: what is the sum of first 8 natural no.
Options:
A)30
B)24
C)36
D)33
E)35
Rationale: the formula for first n natural no. are=n(n+1)/2
here value of n=8
8(8+1)/2
=36
answer C
Answer: C
Question: The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is:
Options:
A)2/3
B)4/5
C)4/8
D)9/2
E)3/7
Rationale: Explanation:
Let the required fraction be x. Then 1/x-x=9/20
1-x^2/x=9/20
20 - 20x^2 = 9x
20x^2 + 9x - 20 = 0
20x^2 + 25x - 16x - 20 = 0
5x(4x + 5) - 4(4x + 5) = 0
(4x + 5)(5x - 4) = 0
x =4/5
ANSWER B
Answer: B
Question: Find the highest value of 'a' so that 365a24 is divisible by 8.
Options:
A)9
B)8
C)0
D)2
E)1
Rationale: Explanation:
Given, number is divisible by 8 only if 'a24' is divisible by 8.
.: highest value of a is '8'.
Answer: Option B
Answer: B
Question: What is the scope including 1/61+1/62+1/63+......+1/70?
Options:
A)1/7~1/6
B)1/5~1/4
C)1/4~1/3
D)1/3~1/2
E)1/2~1
Rationale: For Maximum value : It should be less than 1/61 + 1/61 +1/61... 10 times = 10/61 ~ 1/6
For Minimum Value : It should be greater than 1/70+ 1/70+ 1/70 .. 10 times = 10/70 = 1/7
Thus, the answer should lie between 1/7 and 1/6. Correct ans : A.
Answer: A
Question: All of the stocks on the over-the-counter market are designated by either a 4-letter or a 5-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be designated with these codes?
a.
b.
c.
d.
e.
Options:
A)2(26^5)
B)26(26^4)
C)27(26^4)
D)26(26^5)
E)27(26^5)
Rationale: no of different stocks for 4-letter code = 26^4
no of different stocks for 4-letter code = 26^5
total = 26^4 + 26^5 = 26^4(26+1) = 27(26^4)
ANS:C
Answer: C
Question: At what rate percent per annum will a sum of money double in 16 years.
Options:
A)2.45%
B)5.62%
C)5.35%
D)6.9%
E)6.25%
Rationale: Let principal = P
then S.I. = P
T= 16yrs
Rate = (100*P)/(p*16) = 25/4 = 6.25% p.a.
Answer is E
Answer: E
Question: Two boards are being cut for a construction project. If the total length of the boards is 100 inches and the shorter board is 5 inches less than half the length of the longer board, what is the length of the shorter board?
Options:
A)25 inches
B)30 inches
C)35 inches
D)65 inches
E)70 inches
Rationale: There are two boards...let it be T1(bigger) and T2(shorter one)
Now given total is T1 + T2 = 100..
also given that T2 = T1/2 -5 ..sub this value in the above eq
We get T1 + (T1-10)/2 = 200
=> 3 T1 = 210 => T1 = 70..and T2 = 30...
Answer: option B is correct answer
Answer: B
Question: The Royal Hawaiian Hotel decorates its Rainbow Christmas Tree with non-flashing white lights and a series of colored flashing lights - red, blue, green, orange, and yellow. The red lights turn red every 20 seconds, the blue lights turn blue every 30 seconds, the green lights turn green every 45 seconds, the orange lights turn orange every 60 seconds, and yellow lights turn yellow every 1 minute and 20 seconds. The manager plugs the tree in for the first time on December 1st precisely at midnight and all lights begin their cycle at exactly the same time. If the five colored lights flash simultaneously at midnight, what is the next time Q all five colored lights will all flash together at the exact same time?
Options:
A)0:03 AM
B)0:04 AM
C)0:06 AM
D)0:12 AM
E)0:24 AM
Rationale: Time taken by each light to on
Red = 20 secs
Blue = 30 secs
Green = 45 secs
Orange = 60 secs
Yellow = 80 secs
We need to take LCM to find the time all five colored lights will flash together.
LCM = 720 secs
=12 mins
=0.12 AM
Ans = D
Answer: D
Question: Suresh started a business with Rs.20,000. Kiran joined him after 4 months with Rs.30,000. After 2 more months, Suresh withdrew Rs.5,000 of his capital and 2 more months later, Kiran brought in Rs.20,000 more. What should be the ratio in which they should share their profits at the end of the year?
Options:
A)21:32
B)32:21
C)12:17
D)17:12
E)11:10
Rationale: Explanation:
Here capital is not the same.
Suresh invested 20000 for initial 6 months and 15000 for the next 6 months. Hence his term of ratio
=(20000Ã—6+15000Ã—6)=(20000Ã—6+15000Ã—6)
Kiran invested Rs.30000 for 4 months and Rs.50000 for next 4 months. Hence his term of ratio
=(30000Ã—4+50000Ã—4)=(30000Ã—4+50000Ã—4)
Suresh : Kiran
=(20000Ã—6+15000Ã—6)=(20000Ã—6+15000Ã—6) :(30000Ã—4+50000Ã—4):(30000Ã—4+50000Ã—4)
=(20Ã—6+15Ã—6):(30Ã—4+50Ã—4)=(20Ã—3+15Ã—3):(30Ã—2:50Ã—2)=105:160=21:32
ANSWER IS A
Answer: A
Question: On his first 4 tests, Rajeev received an average score of X points. If on his fifth test, he exceeds his previous average score by 25 points, what is his average score for his first 5 tests?
Options:
A)X+6
B)X+7
C)X
D)X+5
E)X+2
Rationale: Total of 1st 4 tests= 4X
5th test score = X + 25
Total of all 5 tests = 5X + 25
Average = X + 5
Answer : D
Answer: D
Question: A sum of money lent out at S.I. amounts to Rs. 720 after 2 years and to Rs. 1020 after a further period of 5 years. The sum is?
Options:
A)600
B)288
C)2768
D)287
E)191
Rationale: S.I for 5 years = (1020 - 720) = Rs. 300.
S.I. for 2 years = 300/5 * 2 = Rs. 120.
Principal = (720 - 120) = Rs. 600.
Answer: A
Answer: A
Question: If a and b are integers and (a*b)^5 = 32y, y could be:
Options:
A)16
B)1
C)8
D)12
E)24
Rationale: Distribute the exponent.
a^5 * b^5 = 32 y
Find the prime factorization of 32. This is 2^5 *1.
we need 1
The answer is B.
Answer: B
Question: A boat can travel with a speed of 22 km/hr in still water. If the speed of the stream is 5 km/hr, find the time taken by the boat to go 108 km downstream
Options:
A)5 hours
B)4 hours
C)3 hours
D)2 hours
E)None of these
Rationale: Explanation :
Speed of the boat in still water = 22 km/hr
speed of the stream = 5 km/hr
Speed downstream = (22+5) = 27 km/hr
Distance travelled downstream = 108 km
Time taken = distance/speed = 108/27 = 4 hours. Answer : Option B
Answer: B
Question: A bag contains 12 white and 18 black balls. 2balls are drawn in succession. What is the probability that first is white and second is black?
Options:
A)21/145
B)36/145
C)23/141
D)21/132
E)None of these
Rationale: The probability that first ball is white:
=12C130C1=12C130C1
=1230=1230
=25=25
Since, the ball is not replaced; hence the number of balls left in bag is 29.
Hence, the probability the second ball is black:
=18C129C1=18C129C1
=1829=1829
Required probability,
=(25)×(1829)=(25)×(1829)
=36/145
B
Answer: B
Question: An electric motor makes 2,800 revolutions per minutes. How many degrees does it rotate in one second?
Options:
A)18.000 d/sec
B)16.800 d/sec
C)38.000 d/sec
D)26.000 d/sec
E)35.000 d/sec
Rationale: 2800 revolutions / minute
= 2800*360 degrees / 60 seconds
= 16,800 degrees / second
B
Answer: B
Question: Four of the following five parts (a), (b), (c), (d) and (e) are exactly equal. The number of the part which is not equal to the other four parts is your answer.
Options:
A)30 × 14 ÷ 7 × 5
B)10 3 – 100 × 7
C)5√3600
D)450 ÷ 50 × 50 – 5 × 30
E)10 × 3 + 120 × 2
Rationale: Other parts are equal to 300.
Answer E
Answer: E
Question: If x and y are positive numbers and z = xy^2, a 40 percent increase in x and a 20 percent decrease in y would result in which of the following changes in z?
Options:
A)decrease of 6.5%
B)decrease of 10.4%
C)increase of 4.3%
D)increase of 12.8%
E)increase of 16.7%
Rationale: After the changes, z = 1.4x*(0.8y)^2 = (1.4*0.64)xy^2 = 0.896*z
The answer is B.
Answer: B
Question: Total of ages of A,B and C at present is 80 years. If ratio of this ages is 2 : 2 : 4 what will be the age of C after 3 years?
Options:
A)43 years
B)42 years
C)40 years
D)37 years
E)None of the above
Rationale: 2+2+4=9
4*(80/8)=40yrs
after 5yrs=43
ANSWER:A
Answer: A
Question: The average runs scored by a batsman in 20 matches is 40. In the next 10 matches the batsman scored an average of 13 runs. Find his average in all the 30 matches?
Options:
A)31
B)34
C)46
D)47
E)57
Rationale: Total score of the batsman in 20 matches = 800.
Total score of the batsman in the next 10 matches = 130.
Total score of the batsman in the 30 matches = 930.
Average score of the batsman = 930/30 = 31.
Answer:A
Answer: A
Question: A reduction of 50% in the price of apples would enable a man to obtain 50 more for Rs.50, what is reduced price per dozen?
Options:
A)1
B)3
C)6
D)7
E)10
Rationale: C
50*(50/100) = 25 --- 50
? --- 12 => Rs.6
Answer: C
Question: A bowl contains pecans, cashews, and almonds in a ratio of 5 : 8 : 12, respectively. If some of the nuts of one of the three types are removed, which of the following could be the ratio of pecans to cashews to almonds remaining in the bowl?
i. 1 : 2 : 3
ii. 2 : 3 : 4
iii. 4 : 7 : 10
Options:
A)II only
B)I only
C)III only
D)II,III only
E)I,III only
Rationale: i. The ratio 2 : 3 is the same as the given ratio 8 : 12. If one pecan were removed, the new ratio would be 4 : 8 : 12, or 1 : 2 : 3.
ii. None of the nuts currently have a ratio of 3 : 4. The cashews and almonds do have a ratio of 2 : 3, but there are not enough pecans in the bowl to complete the ratio.
iii. The ratio 4 : 10 is the same as the given ratio 6 : 15. To see this, multiply the ratio by 3/2 . The new ratio is 6 : 10.5 : 15. Unfortunately, this means that there are fewer cashews that this ratio would require. Removing cashews won’t create the desired ratio.
Answer : B
Answer: B
Question: The edges of a cuboid are 6 cm, 5 cm and 6 cm. Find the volume of the cuboid?
Options:
A)120
B)160
C)210
D)368
E)180
Rationale: 6*5*6
= 180
Answer: E
Answer: E
Question: The time on a clock is 20 minutes past 4. What is the angle between the hands of the clock?
Options:
A)60 degrees
B)20 degrees
C)45 degrees
D)50 degrees
E)10 degrees
Rationale: The hour hand rotates 360 degrees in twelve hours.
The hour hand rotates 30 degrees in one hour.
The hour hand rotates 5 degrees in ten minutes.
At this time, the hour hand has rotated 130 degrees.
The minute hand rotates 360 degrees in 60 minutes, or 60 degrees in ten minutes.
At this time, the minute hand has rotated 120 degrees.
The difference is 130 - 120 = 10 degrees.
The answer is E.
Answer: E
Question: The length of a rectangular landscape is 8 times its breadth. There is a playground in it whose area is 1200 square mtr & which is 1/6rd of the total landscape. What is the length of the landscape?
Options:
A)180
B)270
C)340
D)140
E)240
Rationale: Sol. x * 8x = 6 * 1200
x = 30
Length = 8 * 30 = 240
E
Answer: E
Question: a and b are positive integers less than or equal to 9. If a and b are assembled into the six-digit number ababab, which of the following must be a factor of ababab
Options:
A)2
B)4
C)5
D)6
E)none of the above
Rationale: 464646 when divided by 2 gives the result 232323
CONCEPT: Rule of Divisibility of 2 isIf sum of the digits of the Number is divisible by 2 then the number will be divisible by 2
SUm of the digits of No. which is divisible by 2 hence the Number 464646 will be divisible by 2
A
Answer: A
Question: A can do a piece of work in 30 days. He works at it for 5 days and then B finishes it in 20 days. In what time can A and B together it?
Options:
A)16 2/3 days
B)13 1/3 days
C)17 1/3 days
D)16 1/2 days
E)18 1/2 days
Rationale: Explanation:
5/30 + 20/x = 1
x = 24
1/30 + 1/24 = 3/40
40/3 = 13 1/3 days
Answer: B
Answer: B
Question: If the radius of a circle that centers at the origin is 5, how many J points on the circle have integer coordinates?
Options:
A) 4
B) 8
C) 12
D) 15
E) 20
Rationale: I understand this might not be required but I used the equation of a circle.
Since the origin is at 0, x^2+y^2=5^2.
X,Y could be +/- (0,5 or 5,0) - 4 possibilities.
X,Y could be +/- (3,4 or 4,3) - 8 possibilities.
Ans: J=C
Answer: C
Question: The scoring system in a certain football competition goes as follows: 3 points for victory, 1 point for a draw, and 0 points for defeat. Each team plays 20 matches. If a team scored 8 points after 5 games, what is the least number of the remaining matches it has to win to reach the 40-point mark by the end of the tournament?
Options:
A)6
B)7
C)8
D)9
E)10
Rationale: To get 40 points as end of season we need another 32 points or more from remaining 15 matches:
Option A= 6*3+9*1=27
Option B=7*3 + 8*1=29
Option C=8*3+7*1=31
Option D=9*3+6*1=33
hence option D-9
Answer: D
Question: For the past n days, the average (arithmetic mean) daily production at a company was 70 units. If today's production of 90 units raises the average to 75 units per day, what is the value of n ?
Options:
A)30
B)18
C)10
D)9
E)3
Rationale: (average production for n days) * n = (total production for n days) --> 70n=(total production for n days);
(total production for n days) + 90 = (average production for n+1 days) * (n+1) --> 70n + 90 = 75 * (n+1) --> n=3.
Answer: E.
Answer: E
Question: Pens are bought at a rate of 8 for Rs 100.To make a profit of 60%,these must be sold at
Options:
A)5 for Rs100
B)6 for Rs 100
C)9 for Rs 200
D)8 for Rs 100
E)None
Rationale: C.P. of 8 Pens = Rs100
S.P. of 8 Pens = 160% of Rs 100 = Rs160
For Rs.160 , Pens sold = 8.
For Rs. 100,Pens sold=(8/160)*100=5
Answer: Option A
Answer: A
Question: If s and t are positive integers such that s/t = 36.42, which of the following could be the remainder when s is divided by t ?
Options:
A)42
B)43
C)83
D)20
E)45
Rationale: s/t= 36.42
s = 36.42t
s = (36 + 0.42)t
s = 36t + (42/100)t
s = 36t + (21/50)t
So remainder will be multiple of 21. The only multiple of 21 is 42.
Ans. A
Answer: A
Question: The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half yearly is
Options:
A)6.06%
B)6.07%
C)6.08%
D)6.09%
E)None
Rationale: Solution
Amount of Rs.100 for 1 year when compounded half yearly
= Rs.[100 x (1+3/100)2]
= Rs. 106.09%.
Effective rate	= (106.09 - 100)%
= Rs. 6.09%.
Answer D
Answer: D
Question: A pipe can fill a cistern in 44 minutes. Find the time in which 1/11 part of the cistern will be filled?
Options:
A)4min
B)2min
C)3min
D)1min
E)10min
Rationale: Full cistern filled in = 44 minutes
1/11 part filled in = 44*1/11 = 4minutes
Answer is A
Answer: A
Question: In how many different ways can the letters of the word 'SENDING' be arranged in such a way that the vowels always come together?
Options:
A)A)360
B)B)480
C)C)720
D)D)5040
E)of these
Rationale: The word 'SENDING' has 7 different letters.
When the vowels EI are always together, they can be supposed to form one letter.
Then, we have to arrange the letters SNDNG (EI).
Now, 6 (5 + 1 = 6) letters can be arranged in 6! = 720 ways.
The vowels (EI) can be arranged among themselves in 2! = 2 ways.
Required number of ways = (720 x 2) = 1440.
ANSWER:B
Answer: B