divelab/Sys2Bench huggingface dataset:
Question: A company has 15 managers and 75 associates. The 15 managers have an average salary of $120,000. The 75 associates have an average salary of $30,000. What is the average salary for the company?
Options:
A)$35,000
B)$45,000
C)$55,000
D)$65,000
E)$75,000
Rationale: The 15 managers have an average salary of $120,000. The sum of their salaries is:
sum = (average)*(number of salaries) = $120,000*15 = $1,800,000
The 75 associates have an average salary of $30,000. The sum of their salaries is:
sum = (average)*(number of salaries) = $30,000*75 = $2,250,000
When we add those two sums, we get the total payroll of all 90 employees.
$1,800,000 + $2,250,000 = $4,050,000
So, we have 90 employees, and together they earn $4,050,000, so the average is
average = $4,050,000 ÷90 = $45,000
Answer: B.
Answer: B
Question: The marks obtained by Vijay and Amith are in the ratio 4:5 and those obtained by Amith and Abhishek in the ratio of 3:2. The marks obtained by Vijay and Abhishek are in the ratio o
Options:
A)6:5
B)4:7
C)3:5
D)5:7
E)8:9
Rationale: 4:5
3:2
-------
12:15:10
12:10
==>6.5
ANSWER A
Answer: A
Question: A certain list consists of 21 different numbers. If n is in the list and n is 4 times the average(arithmetic mean) of the other 20 numbers in the list, then n is what fraction Q of the sum of the 21 numbers in the list?
Options:
A) 1/20
B) 1/6
C) 1/5
D) 4/21
E) 5/21
Rationale: This is how I used to calculate which I think works pretty well:
if you let the average of the 20 other numbers equal a, can you write this equation for sum of the list (S)
n + 20a = S
the question tells us that
n = 4a
plug this back into the first equation and you get that the sum is 24a
4a + 20a = 24a
therefore fraction Q of n to the total would be
4a/24a or 1/6
answer B
Answer: B
Question: A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: Speed downstream = d/t = 85/(2 1/2) = 34 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (34 - 18)/2
= 8 kmph
Answer: D
Answer: D
Question: If p is the sum of consecutive even integers w, x, y, and z, where w < x < y < z, all of the following must be true EXCEPT
Options:
A)z - w = 3(y - x)
B)p is divisible by 8
C)The average of w, x, y, and z is odd
D)p is divisible by 4
E)w + x + 8 = y + z
Rationale: Just assume that the numbers are 2a, 2a+2, 2a+4 and 2a+6.
p = 2a + 2a+2 + 2a+4 + 2a+6 = 8a + 12
Focus on the easiest options first. You see that p is not divisible by 8. Answer (B)
Answer: B
Question: Find √? /18 = 4 ?
Options:
A)76
B)5776
C)304
D)5184
E)None
Rationale: Answer
Let √N/18= 4
Then √N = 18 x 4 = 72
∴ N = 72 x 72 = 5184.
Correct Option: D
Answer: D
Question: A wildlife preserve is being planned for 8,000 rhinoceroses. The preserve is to contain a total of 10,000 acres of watering area, plus 100 acres of grazing area for each rhinoceros. If the number of rhinoceroses is expected to increase by 10 percent, how many thousand acres should the preserve have in order to provide for the increased population?
Options:
A) 340
B) 330
C) 320
D) 310
E) 890
Rationale: Number of rhinos = 8000
Watering area = 10,000 acres
Number of rhino to increase by 10 percent ,then number of rhino = 8800
Grazing area for a rhino = 100
Total grazing area for 8800 rhinos= 8800 * 100 = 8,80,000
Total area required for the wildlife preserve = 8,80,000 + 10,000 = 8,90,000 = 890 * 1000
Answer E
Answer: E
Question: A train 560 m long, running with a speed of 63 km/hr will pass a tree in?
Options:
A)15
B)16
C)17
D)28
E)32
Rationale: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 560 * 2/35 = 32 sec
Answer: Option E
Answer: E
Question: An old priest fell on a bottom of the well of a church.
The well is 17 inches deep.
At day time, the old priest climbs 5-inches but when at dark he slip back 4 inches.
In how many days priest will come out of the well ?
Options:
A)13-days
B)14-days
C)11-days
D)19-days
E)10-days
Rationale: A
13-days
In 12-days, he will climb 12-inch and when he climbs 5 inch more, he will be out of the well :-)
Answer: A
Question: Sam purchased 20 dozens of toys at the rate of Rs. 375 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit?
Options:
A)5.8%
B)5.5%
C)5.6%
D)2.6%
E)5.3%
Rationale: C.P. of 1 toy = 375/12 = Rs. 31.25
S.P of 1 toy = Rs. 33
Profit = 1.75/31.25 * 100 = 28/5 = 5.6%
Answer: C
Answer: C
Question: A piece of cloth cost Rs 35. if the length of the piece would have been 4m longer and each meter cost Re 1 less , the cost would have remained unchanged. how long is the piece?
Options:
A)5 mtrs
B)10 mtrs
C)12 mtrs
D)15 mtrs
E)18 mtrs
Rationale: If length of piece is x and cost per mtr is C, then
x*C = 35 or C =35/x
(x+4)*(C-1) = 35 or x*C +4C-x -4 =35 or 35+4C-x -4 = 35
4C-x =4
4*(35/x)-x =4
x= 10 mtrs
ANSWER:B
Answer: B
Question: I was x years old 5 years ago. How old shall I be 7 years hence ?
Options:
A)x +5
B)x + 7
C)x + 12
D)x + 13
E)None of these
Rationale: given that my age 5 years ago is x years
hence my present age be x+5 years
so my age after 7 years from now = x+5+7
which is equal to x+12
ANSWER:C
Answer: C
Question: What is the lowest possible common multiple of 2 distinct integers, each greater than 64?
Options:
A)68
B)69
C)130
D)68^2
E)68·69
Rationale: In order to get the lowest LCM, we have to take the first number as 65 and the next number as its multiple.
So, I can take 65 and 130 as two distinct numbers, such that Lowest LCM = 130.
Answer should be C.
Answer: C
Question: By selling a bat for Rs.360/- a man loses 10% what is that bat cost price
Options:
A)s.400/-
B)s.630/-
C)s.700/-
D)s.780/-
E)s.800/-
Rationale: 90 % ------> 360 (90 * 4 = 360)
100 % ------>400 (100 * 4 = 400)
Cost price = Rs.400/-
A)
Answer: A
Question: An equity analyst needs to select 3 stocks for the upcoming year and rank these securities in terms of their investment potential. If the analyst has narrowed down the list of potential stocks to 6, in how many ways can she choose and rank her top 3 picks?
Options:
A)210
B)150
C)120
D)420
E)840
Rationale: Number of ways of choosing 3 stocks = 6C3
Number of ways of ranking the chosen stocks = 3!
Hence total ways of chosing and ranking = 6C3 * 3!= 120
Correct Option: C
Answer: C
Question: A car finishes a journey in ten hours at the speed of 65 km/hr. If the same distance is to be covered in five hours how much more speed does the car have to gain?
Options:
A)8 km/hr
B)10 km/hr
C)65 km/hr
D)16 km/hr
E)None of these
Rationale: Distance covered by the car = 65 × 10 = 650 km
\ Speed = 650⁄5 = 130 km/hr
\ Speed gain = 130 – 65 = 65 km/hr
Answer C
Answer: C
Question: In what ratio should a variety of rice costing Rs. 6 per kg be mixed with another variety of rice costing Rs. 8.75 per kg to obtain a mixture costing Rs. 7.50 per kg?
Options:
A)5/6
B)4/9
C)5/7
D)5/2
E)5/8
Rationale: Let us say the ratio of the quantities of cheaper and dearer varieties = x : y
By the rule of allegation, x/y = (87.5 - 7.50) / (7.50 - 6) = 5/6
Answer:A
Answer: A
Question: An amount of money is to be distributed among Faruk, Vasim and Ranjith in the ratio 3 : 5 : 6. If Vasims share is Rs. 1500, what is the difference between Faruk's and Ranjith's shares?
Options:
A)s 1200
B)s 1500
C)s 1600
D)s 1900
E)s 900
Rationale: Explanation :
Let P = Faruk, Q = Vasim, R = Ranjith
Let P = 3x, Q = 5x and R = 6x.
Then, 5x = 1500 ? x = 300. P=900,Q=1500 and R = 1800.
Hence, (R - p) = (1800 - 900) = 900
Answer : E
Answer: E
Question: In a mixture of milk and water, the proportion of milk by weight was 80%. If, in a 180 gm mixture, 36 gms of pure milk is added, what would be the percentage of milk in the mixture formed?
Options:
A)84.33%
B)83.39%
C)83.93%
D)83.93%
E)83.33%
Rationale: Explanation:
Percentage of milk in the mixture formed = [80/100 (180) + 36] / (180 + 36) * 100% = (144 + 36)/216 * 100% = 5/6 * 100% = 83.33%.
Answer: Option E
Answer: E
Question: A bag contains 4 red and 3 green balls. Another bag contains 4 red and 6 green balls. If one ball is drawn from each bag. Find the probability that one ball is red and one is green.
Options:
A)19/20
B)17/20
C)3/5
D)8/10
E)9/40
Rationale: Let A be the event that ball selected from the first bag is red and ball selected from second bag is green.
Let B be the event that ball selected from the first bag is green and ball selected from second bag is red.
P(A) = (4/7) x (3/5) =12/35.
P(B) = (3/7) x (2/5) = 6/35.
Hence, the required probability is P(A) + P(B) which is nothing but 3/5.
ANSWER:C
Answer: C
Question: P and Q can complete a work in 20 days and 12 days respectively. P alone started the work and Q joined him after 4 days till the completion of the work. How long did the work last?
Options:
A)5 days
B)10 days
C)14 days
D)22 days
E)26 days
Rationale: Explanation :
Work done by P in 1 day = 1/20
Work done by Q in 1 day = 1/12
Work done by P in 4 days = 4 × (1/20) = 1/5
Remaining work = 1 – 1/5 = 4/5
Work done by P and Q in 1 day = 1/20 + 1/12 = 8/60 = 2/15
Number of days P and Q take to complete the remaining work = (4/5) / (2/15) = 6
Total days = 4 + 6 = 10
Answer : Option B
Answer: B
Question: A painting crew painted 80 houses. They painted the first y houses at a rate of x houses per week. Then more painters arrived and everyone worked together to paint the remaining houses at a rate of 5.25x houses per week. How many weeks did it take to paint all 80 houses, in terms of x and y?
Options:
A)(320 - y)/(5x)
B)(y +200)/(5x)
C)5(80 - y)/(4x)
D)(y + 400)/(4x)
E)(4y + 320)/(5x)
Rationale: Ans B
Plug some numbers
Let y = 40 houses and x = 20
then they painted 20 houses per week
as painters were added to the group , the rate of the group increased to 5.25 x => 5.25 * 20 = 105 houses per week
total time they took = (40/20) + (40/1055) = 2.4 weeks
Putting the values of x and y in equation B
(y +200)/(5x) = (40+200)/5*20 = 240/100 = 2.4
Answer: B
Question: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
Options:
A)2345
B)3456
C)2334
D)3456
E)5184
Rationale: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62
E
Answer: E
Question: On dividing a number by 357, we get 42 as remainder.On dividing the same number by 17, what will be the remainder ?
Options:
A)4
B)5
C)8
D)7
E)2
Rationale: Let x be the number and y be the quotient.Then,
x=357*y+42
=(17*21*y)+(17*2)+8
=17*(21y+2)+8.
Required number =8.
Answer is C
Answer: C
Question: A can do a piece of work in 80 days. He works at it for 10 days B alone finishes the remaining work in 42 days. In how much time will A and B working together, finish the work?
Options:
A)25
B)30
C)20
D)32
E)None of them
Rationale: Work done by A in 10 days =(1/80*10)=1/8
Remaining work = (1- 1/8) =7/ 8
Now,7/ 8 work is done by B in 42 days.
Whole work will be done by B in (42 x 8/7) = 48 days.
A’s 1 day's work = 1/80 and B's 1 day's work = 1/48
(A+B)'s 1 day's work = (1/80+1/48)=8/240=1/30
Hence, both will finish the work in 30 days.
Answer is B.
Answer: B
Question: X can do a piece of work in 40days. He works at it for 8days and then Y finished it in 16days. How long will Y take to complete the work?
Options:
A)10
B)12
C)15
D)18
E)20
Rationale: Work done by X in 8days = 8*1/40 = 1/5
Remaining work = 1 - 1/5 = 4/5
4/5 work is done by Y in 16days
Whole work will be done by Y in 16*5/4 = 20days
Answer is E
Answer: E
Question: It has 20L mixutre conatins milk and water in the ratio 3:5,replace 4 litres of mixture with 4 litres of water what is the final ratio of milk and water.
Options:
A)2:7
B)3:7
C)4:7
D)5:7
E)6:7
Rationale: Full mixture has 7.5L milk 12.5L water if we fetch 4L mixture according to ratio it will be 1.5L milk & 2.5L water,replace this mixture from the water then it will be 6L milk and 14L water then ratio will be 6/14=3:7.
ANSWER:B
Answer: B
Question: Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is
Options:
A)Rs.1550
B)Rs.1650
C)Rs.1750
D)Rs.2000
E)None
Rationale: Solution
C.I.	=Rs[4000x(1+10/100)²-4000]
Rs.(4000x11/10x11/10-4000)	= Rs.940.
Sum	=Rs. [420x100 /3x8]
= Rs.1750.
Answer C
Answer: C
Question: The radius of a semi circle is 35 cm then its perimeter is?
Options:
A)32.8
B)180
C)32.1
D)32.2
E)32.9
Rationale: Diameter 70 cm
1/2 * 22/7 * 70 +70 = 180
Answer : B
Answer: B
Question: The maximum number of students among them 1001 pens and 910 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is:
Options:
A)91
B)37
C)99
D)277
E)19
Rationale: Explanation:
Required number of students = H.C.F of 1001 and 910 = 9
Answer: A) 91
Answer: A
Question: A and B start a business with Rs.10000 and Rs.5000 respectively. Hoe should they share their profits at the end of one year?
Options:
A)1:2
B)3:4
C)2:5
D)3:7
E)2:1
Rationale: They should share the profits in the ratio of their investments.
The ratio of the investments made by A and B =
10000 : 5000 => 2:1
ANSWER:E
Answer: E
Question: How many possible ways are there to select 2 stocks at random from 9 stocks?
Options:
A)36
B)38
C)40
D)42
E)44
Rationale: 9C2 = 36
The answer is A.
Answer: A
Question: The salary of a typist was at first raised by 10% and then the same was reduced by 5%. If he presently draws Rs.1045.What was his original salary?
Options:
A)900
B)950
C)1000
D)1050
E)1100
Rationale: X * (110/100) * (95/100) = 1045
X * (11/10) * (1/100) = 11
X = 1000
ANSWER:C
Answer: C
Question: The total car population in a Chennai is 9000 out of which 5000 are made by Honda. Out of every 100 Honda cars, 90 are red in color, but only 60% of the total car population is red. Find the % of non-Honda cars that are red
Options:
A)22.5%
B)21.5%
C)20.5%
D)12.5%
E)10.5%
Rationale: Total Honda brand red cars = 90/100 *5000 = 4500
Total red cars = 60/100*9000 = 5400
No. of Non-Honda cars = 9000-5000 = 4000
No. of Non-Honda red cars = 5400 - 4500 = 900
% of Non-Honda red cars = 900/4000*100 = 22.5%
Answer : A
Answer: A
Question: in a rectangle 8 vertical and 4 horizontal lines are drawn find the number of rectangle formed
Options:
A)674
B)675
C)676
D)677
E)679
Rationale: 8 vertical lines plus the 2 lines of the existing rectangle(as its mentioned in the question "in a rectangle") accordingly 4 plus 2 horizontal lines.
therefore
10C2*6C2= 675 and if its asked for the new rectangle formed than
675-1=674
ANSWER:A
Answer: A
Question: A fisherman has 18 fish, then he catches 3 more fish. Now how many fish does he have?
Options:
A)A)21
B)B)15
C)C)17
D)D)23
E)E)4
Rationale: 18+3=21. Answer is A
Answer: A
Question: Find the next number in the Sequence
6, 10, 22, 42, ?
Options:
A)76
B)70
C)67
D)74
E)72
Rationale: +4 =>10
+12 =>22
+20 =>42
+28 =>70
Answer is B
Answer: B
Question: The length of a rectangular garden is three times its width. If the area of the rectangular garden is 768 square meters, then what is the width of the rectangular garden?
Options:
A)16
B)17
C)18
D)19
E)20
Rationale: Let x be the width of the garden.
3x^2 = 768
x^2 = 256
x = 16
The answer is A.
Answer: A
Question: A certain sum of money doubles itself in 10 years in how much many years will it trible itself at the same rate?
Options:
A)20 years
B)26 years
C)88 years
D)66 years
E)12 years
Rationale: 100 ---- 100 --- 10
100 --- 10
--------------------
300 ---- 20 years
Answer: A
Answer: A
Question: Two trains travelling in the same direction at 40 kmph and 22 kmph completely pass each other in 1 minutes. If the length of first train is 125 m, what is the length of second train ?
Options:
A)125 m
B)150m
C)175 m
D)200m
E)none of these
Rationale: Let the length of the second train be X.
Speed of both the trains = (40 - 22) x 5/18 = 5 m/s
Thus, (125 + X)/5 = 60 sec
or, 125 + X = 300
or, X = 175m
ANSWER:C
Answer: C
Question: Raman mixed 24 kg of butter at Rs. 150 per kg with 36 kg butter at the rate of Rs. 125 per kg. At what price per kg should he sell the mixture to make a profit of 40% in the transaction?
Options:
A)Rs.129
B)Rs.120
C)Rs.189
D)Rs.178
E)Rs.126
Rationale: CP per kg of mixture = [24(150) + 36(125)]/(24 + 36)
= Rs. 135
SP = CP[(100 + profit%)/100]
= 135 * [(100 + 40)/100]
= Rs.189.
Answer:C
Answer: C
Question: AMOUNT OF BACTERIA PRESENT
Time Amount
1:00 P.M. 16.0 grams
4:00 P.M. x grams
7:00 P.M. 20.4 grams
Data for a certain biology experiment are given in the table above. If the amount of bacteria present increased by the same fraction during each of the two 3-hour periods shown, how many grams of bacteria were present at 4:00 P.M.?
Options:
A)12.0
B)18.1
C)12.2
D)12.3
E)18.0
Rationale: The question says that bacteria increased by same fraction, not by same amount in 2 intervals of 3 hours.
Let X represent the amount of bacteria present at 4:00 PM. Since the fractional increase must remain constant from 1 to 4pm as it is from 4pm to 7pm:
Fractional increase from 1 PM to 4 PM = X / 16.0
Fractional increase from 4 PM to 7 PM = 20.4 / X
X \ 16 = 20.4 \ X
X^2 = 20.4 * 16
X = 18
answer : E
Answer: E
Question: What is the place value of 7 in the numeral 51468?
Options:
A)100
B)10
C)1
D)1000
E)11
Rationale: place value of 1 = 1 * 1000 = 1000
Answer is D
Answer: D
Question: There are three foam generators in the factory, each of the first two can generate 14 liters of foam in one hour and the third can generate 18 liters in an hour. The three generators start working together at the same time and after one hour and a half one of the first generators stops working and two hours after that the third generator stops working and only one generator is left. If 5 hours after they all started to work the last generator stops working, how many liters of foam were generated?
Options:
A)120.
B)132.
C)146.
D)154.
E)166
Rationale: Let the foam generators capacity be -
A = 14 lit/hr
B = 14 lit/hr
C = 18 lit/hr
Total foam generation in 1 hour will be 46 lit ( 14 + 14 + 18 ) ; since in 1 and 1/2 hr they will generate 46 + 23 => 69 litres...
Now one of the first generators stops working ( Say A stops working ) , so we have -
B = 14 lit/hr
C = 18 lit/hr
Total foam generation in 2 hour will be 64 litres {2 (14+18)}
The third generator stops working and now only B works for the remaining time 1 and 1/2 ( 5 - 1 and 1/2 - 2 )...
Foam generated by B will be 3/2 * 14 => 21 litres
So, total foam generated will be 154 Litres ( 69 + 64 + 21 ) ; hence answer will be (D)
Answer: D
Question: If A lends Rs.1000 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)112.5
B)122.5
C)132.5
D)114.5
E)45
Rationale: (1000*1.5*3)/100 => 45
ANSWER:E
Answer: E
Question: The difference of and its reciprocal is equal to :
Options:
A)105/302
B)305/309
C)105/312
D)105/304
E)105/309
Rationale: Explanation:
Required difference = 19/16 - 16/19 = = 105/304..
Answer: D) 105/304
Answer: D
Question: A and B started a business in partnership. A invested Rs. 40000 for 6 months. A received Rs.6000 as his share out of the total profit of Rs. 9000, What was the amount invested by B for the whole year?
Options:
A)Rs. 8000
B)Rs. 10000
C)Rs. 5000
D)Rs. 6000
E)None of these
Rationale: Explanation:
Profits of A and B are distributed in the same ratio of their investment and period of investments.
Investment of A/ Investment of B = Profit of A/ Profit of B = 6000/3000
(40000*1/2)/X*1 = 2/1
Therefore, X = B's investment amount = Rs. 10,000
ANSWER IS B
Answer: B
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Options:
A)297
B)269
C)240
D)258
E)298
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 36 = 15
x + 300 = 540
x = 240 m.
Answer:C
Answer: C
Question: How many keystrokes are needed to type the numbers from 1 to 800?
Options:
A)1804
B)1978
C)2176
D)2292
E)2456
Rationale: There are 9 one-digit numbers from 1 to 9.
There are 90 two-digit numbers from 10 to 99.
There are 701 three-digit numbers from 100 to 800.
9 + 90(2) + 701(3) = 2292
The answer is D.
Answer: D
Question: An army’s recruitment process included N rounds of selection tasks. For the first A rounds, the rejection percentage was 60 percent per round. For the next B rounds, the rejection percentage was 50 percent per round and for the remaining rounds, the selection percentage was 70 percent per round. If there were 10000 people who applied for the army and 98 were finally selected, what was the value of N?
Options:
A)4
B)5
C)6
D)7
E)10
Rationale: step(1) 4000 accepted.
step(2) another 40%of 40000=1600 accepted.
here it is quiet observable that if we further deduct candidate by 60% it would change our probablity of easy going 2000 candidate.
so i would get to second stage of recruitment where 50 % is accepted
step(3) 50% of 1600=800
step(4) 50% of 800=400
Step(5) 50% of 400=200...here we are done with total 5 steps
70% of 200=140
and last step of accepting 70% of 140 =98(our target)
total 7 steps required.
Ans D
Answer: D
Question: A person walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 14 minutes earlier. How far is the office from his house?
Options:
A)4 2/5 Km
B)4 1/7 Km
C)3 1/5 Km
D)3 1/7 Km
E)3 2/5 Km
Rationale: Formula = S1*S2/S2-S1 * T1+T2/60
= 4*6/2 * 22/6
= 24/2 * 22/60
= 11 * 2/5
= 22/5 = 4 2/5 Km
A)
Answer: A
Question: If a child flips a coin five times in a row, what is the probability that she will receive at least one head and one tail?
Options:
A)3/4
B)11/12
C)15/16
D)31/32
E)63/64
Rationale: The coin is flipped 5 times in a row.
So there are 2*2*2*2*2 = 32 different outcomes possible such as HHTHH, HTHHT, TTHTH etc
Look for the reverse probability - when will there is no heads or no tails?
There will be no heads when you get all tails. There is only 1 such case TTTTT
There will be no tails when you get all heads. There is again only 1 such case HHHHH
So, out of 32, there are only 2 cases in which there are either no heads or no tails. In all other 30 cases, there is at least one heads and at least one tails.
Required probability = 30/32 = 15/16
Answer (C)
Answer: C
Question: Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 25 hours respectively. The ratio of their speeds is?
Options:
A)4:6
B)5:3
C)4:9
D)4:4
E)4:2
Rationale: Let us name the trains A and B.
Then, (A's speed) : (B's speed)
= âˆšb : âˆša = âˆš25 : âˆš9 = 5:3.Answer: B
Answer: B
Question: A goods train runs at the speed of 72 kmph and crosses a 260 m long platform in 26 seconds. What is the length of the goods train?
Options:
A)260 m
B)270m
C)643m
D)832m
E)270m
Rationale: Speed =	(72 x	5/18)m/sec	= 20 m/sec.
Time = 26 sec.
Let the length of the train be x metres.
Then,	x + 260/26	= 20
x + 260 = 520
x = 260.
Answer:A
Answer: A
Question: 10, 1000, 100000, 10000000....
Options:
A)100,000,000
B)1,000,000,000
C)1,000,000,000,000
D)100
E)1,000,000
Rationale: Each number in this sequence is multiplied by 100. With multiples of ten, it is easiest to remember that you can just transfer all the zeroes on the end of the end of any number. Example: 10 x 100 = 1,000.
Add two digits to the end of 10,000,000 and you get 1,000,000,000.
Answer is B
Answer: B
Question: In a 400 m race,A covers the distance in 60 seconds and B in 100 second.In this race A beats B by :
Options:
A)20 m
B)125 m
C)120 m
D)160 m
E)None of these
Rationale: Solution
Distance covered by B in 40 sec. = (400/100x40)m =160m.
∴ A beats B by 160 metres.
Answer D
Answer: D
Question: In the exam the average was found to be p mark. After deducting typographical error the average marks of 64 student reduced from 82 to 62 . Due to this the average came down by 16 marks. What was the number of students who took the exam?
Options:
A)100
B)80
C)90
D)60
E)160
Rationale: Explanation :
Number of student = (82-62) * 64/16 = 80
Answer : B
Answer: B
Question: The ratio between the sale price and the cost price of an article is 7:5. What is the ratio between the profit and the cost price of that article?
Options:
A)3:5
B)5:5
C)2:5
D)1:6
E)2:6
Rationale: C
2:5
Let C.P. = $ 5x and S.P. = $ 7x.
Then, Gain = $ 2x
Required ratio = 2x : 5x = 2:5
Answer: C