divelab/Sys2Bench huggingface dataset:
Question: A tank can supply water to a village for 100 days. If a leak at the bottom of the tank drains out 10 liters per day, the supply lasts for 75 days only. For how many days will the supply last if the leak drains out 20 liters per day?
Options:
A)50
B)60
C)65
D)70
E)72
Rationale: Losing 10 liters per day results in a loss of 750 liters in 75 days. So, those 750 liters were for 25 days, making daily consumption of the village 30 liters per day. Thus the capacity of the tank is 30*100 = 3000 liters.
Losing 20 liters plus 30 liters gives 50 liters per day. At this rate the supply will last 3000/50 = 60 days.
The answer is B.
Answer: B
Question: In a party every person shakes hands with every other person. If there were a total of 120 handshakes in the party then what is the number of persons present in the party ?
Options:
A)15
B)16
C)17
D)18
E)19
Rationale: Explanation :
Let the number of persons be n
∴ total handshakes = nC2 = 120
n(n-1)/2 = 120 ∴ n = 16
Answer : Option B
Answer: B
Question: √(36)^2
Options:
A)6
B)14
C)36
D)21
E)None of these
Rationale: explanation
√(36)^2 =?
or, ? = 36
Answer C
Answer: C
Question: A car travelling with of its actual speed covers 42 km in 1 hr 40 min 48 sec. Find the actual speed of the car.
Options:
A)17 6/7 km/hr
B)25 km/hr
C)30 km/hr
D)35 km/hr
E)40 km/hr
Rationale: Time taken = 1 hr 40 min 48 sec = 1 hr40 4/5min = 1 51/75hrs= 126/75hrs
Let the actual speed be x km/hr.
Then,5/7x X 126/75 =42
x = [42x7x75/5x126] = 35 km/hr
Answer is D
Answer: D
Question: Sonika bought a V.C.R. at the list price of 18,700. If the rate of sales tax was 8%, find the amount she had to pay for purchasing the V.C.R.
Options:
A)20,196
B)19,780
C)19,680
D)19,380
E)None of these
Rationale: Sol. List price of V.C.R. =18,700
Rate of sales tax = 8%
∴ Sales tax = 8% of 18,700
= 8⁄100 × 18700 = 1496
So, total amount which Sonika had to pay for purchasing the V.C.R. = 18,700 + 1496
= 20,196. Answer A
Answer: A
Question: 4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 12 mat-weavers in 12 days?
Options:
A)25
B)19
C)39
D)61
E)36
Rationale: Let the required number of bottles be x.
More weavers, More mats (Direct Proportion)
More days, More mats (Direct Proportion)
Wavers	4	:	12 :: 4 : x
Days	4:12
4 * 4 * x = 12 * 12 * 4
x =	(12 * 12 * 4)/(4 x 4)
x = 36.
Answer is E.
Answer: E
Question: A grocer buys apples for 63¢ per pound. If 10% of the apples goes bad and he still wants to make a 20% profit over his purchase price, what should be the sales price?
Options:
A)66¢
B)70¢
C)75¢
D)77¢
E)84¢
Rationale: for making calculation simple let us consider he buys 10 pounds @ 63/pound=630¢ in total .
10% apples lost...means 9 pounds left.
further he wants 20% profit on 630 ¢
means he wants to earn 756¢
sales price should be 756/9==¢ 84
ANSWER:E
Answer: E
Question: A grocer has a sale of Rs. 7435, Rs. 7920, Rs. 7855, Rs. 8230 and Rs. 7560 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 7500?
Options:
A)500
B)2000
C)5000
D)6000
E)7000
Rationale: Total sale for 5 months = Rs. (7435 + 7920 + 7855 + 8230 + 7560) = Rs. 39000.
Required sale = Rs. [ (7500 x 6) - 39000 ]
= Rs. (45000 - 39000)
= Rs. 6000
Answer: Option D
Answer: D
Question: Only a single rail track exists between stations A and B on a railway line. One hour after the north bound super fast train N leaves station A for station B, a south-bound passenger train S reaches
station A from station B. The speed of the super fast train is twice that of a normal express train E, while the speed of a passenger train S is half that of E. On a particular day, N leaves for B from A, 20 min behind the normal schedule. In order to maintain the schedule, both N and S increased their speeds. If the super fast train doubles its speed, what should be the ratio (approximately) of the speeds of passenger train to that of the super fast train so that the passenger train S reaches exactly at the scheduled time at A on that day?
Options:
A)1 : 3
B)1 : 4
C)1 : 5
D)1 : 6
E)1 : 7
Rationale: Explanation :
If speed of N = 4, speed of S = 1.
=> Average speed = (2 X 4 x 1) / ( 4 + 1) = 1.6.
Because time available is 2/3, speed = 3/2.
Now Average speed = 2.4
Now speed of N = 8.
Speed of S = y.
=> (2 x 8 x y) / (8+y) = 2.4
=> y = 1.3
The required ratio is 1.3 : 8 i.e 1 : 6.
Answer : D
Answer: D
Question: A cyclist covers a distance of 750 meter in 2 minutes 40 seconds. What is the speed in km/hr of cyclist
Options:
A)16 km/hr
B)16.85 km/hr
C)18 km/hr
D)19 km/hr
E)20 km/hr
Rationale: Explanation:
Speed=Distance/Time
Distance=750meter
Time=2 min 40sec=160sec
Speed=750/160=4.68m/sec
=>4.68âˆ—18/5km/hr=16.85km/hr
Option B
Answer: B
Question: Two same glasses are respectively 1/4th 1/5th full of milk. They are then filled with water and the contents mixed in a tumbler. The ratio of milk and water in the tumbler is?
Options:
A)9:39
B)9:31
C)9:37
D)9:32
E)9:33
Rationale: 1/4 : 3/4 = (1:3)5 = 5:15
1/5 : 4/5 = (1:4)4 = 4:16
------
9:31
Answer: B
Answer: B
Question: If the ratio of x to y is 2 to 6, then (y-x)/(x+y)?
Options:
A)-7/3
B)-3/7
C)1/2
D)1/4
E)7/3
Rationale: I believe this problem can be solved using algebra.
The ratio of x to y is 2 to 6 means
(x/y)=(2/6)
Cross-multiply
2x = 6y or 1x=3y
x = (1/3)*y
Then, substitute x in the original equation in the problem with the value we just found.
(y - (1/3)*y) / ((1/3)*y + y)
= ((2/3)*y) / ((4/3)*y)
Simplify by canceling the y in the numerator with the y in the denominator.
(2/3) / (4/3)
= (2/3) * (4/3)
The 3s cancel each other out, and you are left with 2/4 to 1/2.
Answer: C
Question: Find the ones digit of 73^350
Options:
A)3
B)5
C)6
D)7
E)9
Rationale: 3,9,7,1 repeats after every four times
therefore 350/4 = 87 + 2 remainder
9 is the ones digit
so E is correct
Answer: E
Question: Today is Thursday. The day after 59 days will be
Options:
A)Monday
B)Tuesday
C)Saturday
D)Sunday
E)None of these
Rationale: Explanation :
59 days = 8 weeks 3 days = 3 odd days
Hence if today is Thursday, After 59 days, it will be = (Thursday + 3 odd days)
= Sunday. Answer : Option D
Answer: D
Question: In how many ways letters of the word PRESS be arranged?
Options:
A)10
B)20
C)60
D)80
E)40
Rationale: PRESS has 5 letters, out of which S repeated 2 time. Hence total ways = 5! / (2!) = 60 ways
C
Answer: C
Question: The average age of 16 persons in a office is 15 years. Out of these, the average age of 5 of them is 14 years and that of the other 9 persons is 16 years. The age of the 15th person is?
Options:
A)9
B)11
C)15
D)12
E)26
Rationale: Age of the 15th student = 16*15 - (14*5+16*9) = 240-214 = 26 years
Answer is E
Answer: E
Question: At what time between 4 and 5 o'clock will the hands of a watch point in opposite directions?
Options:
A)(54 + 6/11) past 00
B)(54 + 6/11) past 29
C)(54 + 6/11) past 19
D)(54 + 6/11) past 4
E)(54 + 6/11) past 12
Rationale: 4 o'clock, the hands of the watch are 20 min. spaces apart.
To be in opposite directions, they must be 30 min. spaces apart.
Minute hand will have to gain 50 min. spaces.
55 min. spaces are gained in 60 min
50 min. spaces are gained in min. or
Required time = min. past 4
Answer: D)
Answer: D
Question: Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 66900. What is his profit percent?
Options:
A)22
B)77
C)18
D)21.6
E)88
Rationale: Total CP = Rs. 42000 + Rs. 13000 = Rs. 55000 and SP = Rs. 66900
Profit(%) = (66900 - 55000)/55000 * 100 = 21.6%
Answer: D
Answer: D
Question: Determine the equation for the line parallel to r ≡ 3x + 2y − 4 = 0 that passes through the point A = (2, 3).
Options:
A)2x + 3y +12= 0
B)2x + 3y -12= 0
C)3x + 2y − 12= 0
D)3x + 2y +12= 0
E)x + y − 6= 0
Rationale: the equation for the line parallel to r ≡ 3x + 2y − 4 = 0 is
3x + 2y + K= 0
3 • 2 + 2• 3 + k = 0
k = −12
3x + 2y − 12= 0
ANSWER C 3x + 2y − 12= 0
Answer: C
Question: Graph G has a line of symmetry of x = –3. Graph G passes through the point (3, 3). What is the x-coordinate of another point that must have a y-coordinate of 3?
Options:
A) –9
B) –7
C) –5
D) –4
E) 2
Rationale: Line of symmetry is X=-3; one point is (3,3)
Right side distance =3+3(distance from origin) = 6; therefore Left side distance should be same from line of symmetry =6;
therefore left side co-ordinate=6+ 3(distance from origin) = 9; as the X coordinate is in 2nd quadrant hence -9
Therefore answer is A
Answer: A
Question: 170kg of an alloy A is mixed with 250 kg of alloy B. If alloy A has lead and tin in the ratio 1:3 and alloy B has tin and copper in the ratio 3:5, then the amount of tin in the new alloy is?
Options:
A)210.6kg
B)221.3kg
C)229.5kg
D)110.8kg
E)114kg
Rationale: Quantity of tin in 170kg of A = 170*3/4 = 127.5kg
Quantity of tin in 250kg of B = 250*3/8 = 93.75kg
Quantity of tin in the new alloy = 127.5+93.75 = 221.25kg
Answer is B
Answer: B
Question: A sum of money becomes triple itself in 5 years at simple interest. How many years will it become six times at the same rate?
Options:
A)12 1/2
B)12 1/6
C)12 1/9
D)12 1/5
E)12 1/1
Rationale: 100 ---- 200 ---- 5
200 ---- 5
100 ---- 2 1/2
------------------
600 ---- 12 1/2 years
Answer: A
Answer: A
Question: Ram sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles?
Options:
A)3000
B)4000
C)5000
D)4000
E)2000
Rationale: (10*10)/100 = 1%loss
100 --- 99
? --- 1980 => Rs.2000
ANSWER E
Answer: E
Question: If 4/p=8 & 6/q=18 then p-q=?
Options:
A)5/24
B)6/24
C)7/24
D)1/6
E)9/24
Rationale: p=4/8 , q=6/18=>q=1/3
therefore
p-q=(1/2)-(1/3)=1/6
ANSWER:D
Answer: D
Question: Birbal is a witty trader who trade of a mystical fruit grown far in north. He travels from one place to another with three sacks which can hold 30 fruits each. None of the sack can hold more than 30 fruits. On his way, he has to pass through thirty check points and at each check point, he has to give one fruit for each sack to the authorities.
How many mystical fruits remain after he goes through all the thirty check points?
Options:
A)25
B)29
C)48
D)26
E)54
Rationale: A
25 Fruits
Remember we told you that Birbal is a witty trader. So his sole motive is to get rid of the sacks as fast as he can.
For the first sack:
He must be able to fill fruits from one sack to other two sacks. Assume that he is able to do that after M check points. Now to find M,
(Space in first sack) M + (Space in second sack) M = (Remaining fruits in Third Sack) 30 – M
M = 10
Thus after 10 checkpoints, Birbal will be left with only 2 sacks containing 30 fruits each.
Now he must get rid of the second sack.
For that, he must fill the fruits from second sack to the first sack. Assume that he manages to do that after N checkpoints.
(Space in First Sack) N = (Remaining fruits in second sack) 30 – N
N = 15
Thus after he has crossed 25 checkpoints, he will be left be one sack with 30 fruits in it. He has to pass five more checkpoints where he will have to give five fruits and he will be left with twenty five fruits once he has crossed all thirty check points.
Answer: A
Question: If x is a number such that x^2 + 5x - 6 = 0 and x^2 - 5x + 4 = 0, then x =
Options:
A)-1
B)1
C)4
D)-6
E)6
Rationale: x^2 + 5x - 6 = (x+6)(x-1) = 0
Then x=-6 or x=1.
x^2 - 5x + 4 = (x-4)(x-1) = 0
Then x=4 or x=1.
Thus x=1.
The answer is B.
Answer: B
Question: An association of mathematics teachers has 1,500 members. Only 525 of these members cast votes in the election for president of the association. What percent of the total membership voted for the winning candidate if the winning candidate received 40 percent of the votes cast?
Options:
A)75%
B)58%
C)42%
D)34%
E)14%
Rationale: Total umber of members = 1500
Number of members that cast votes = 525
Since , winning candidate received 40 percent of the votes cast
Number of votes for winning candidate = (40/100)*525 = 210
Percent of total membership that voted for winning candidate = (210/1500)*100 = 14%
Answer E
Answer: E
Question: A starts business with Rs.3500 and after 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is B’s contribution in the capital?
Options:
A)6000
B)9000
C)9500
D)12000
E)None
Rationale: Sol.
Let B’s capital be Rs. x. Then, 3500 * 12 / 7x = 2/3 ⇔ 14x = 126000 ⇔ x = 9000.
Answer B
Answer: B
Question: What is the sum Y of all 3 digit numbers that leave a remainder of '2' when divided by 3?
Options:
A)897
B)164,850
C)164,749
D)149,700
E)156,720
Rationale: The series is => 101+...998
Number of terms => 300
sum => 300/2 * [101+998]
hence sum Y=> 164850 i.e. option B
Answer: B
Question: 210 reputed university students were asked in a survey if they preferred Windows or Mac brand computers. 60 Students claimed that they preferred Mac to Windows brand computers. One third as many of the students who preferred Mac to Windows, equally preferred both brands. 90 of the students had no preference. How many of the students in the survey preferred Windows to Mac brand computers?
Options:
A)25
B)40
C)50
D)60
E)75
Rationale: We are told that60 Students claimed that they preferred Mac to Windows, which means that 60 preferred Mac but NOT Windows, so # of students who preferred Mac (P(A) as you wrote), does not equal to 60, it equals to 60+20 (20 is # of students who equally preferred both brands). Also we are asked to find # of the students who preferred Windows to Mac, so if you denote x as those who prefer Windows then you should calculate x-20.
So, if we use your formula it should be: 210={Mac}+{Windows}-{Both}+{Neither}=(60+20)+x-20+90 --> x=60 (# of student who prefer Windows) --> # of the students who preferred Windows to Mac is x-20=40.
Answer: B
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. After how much time will the trains meet?
Options:
A)21/9 sec
B)32/3 sec
C)20/7 sec
D)32/3 sec
E)53/2 sec
Rationale: They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed = (54 + 72)*5/18 = 7*5 = 35 mps.
The time required = d/s = 100/35 = 20/7 sec.
Answer:C
Answer: C
Question: Two identical machines have the ability to produce both nuts and bolts. However, it takes 3 second to produce a bolt but 2 seconds to produce a nut. What is the fastest the two machines, working together, can produce 1,000 nuts and 1,000 bolts?
Options:
A)1,250 seconds
B)1,500 seconds
C)1,750 seconds
D)2,500 seconds
E)3,000 seconds
Rationale: To minimize the amount of time, we should make both machines work all the time while producing 1,000 nuts and 1,000 bolts.
Two machines to produce 1,000 bolts will need (1,000*3)/2 = 1500 seconds.
Two machines to produce 1,000 nuts will need (1,000*2)/2 = 1,000 seconds.
Total = 1500 + 1,000 = 2,500.
Answer:D.
Answer: D
Question: The average of four numbers is 27. If one number is excluded, the average becomes 25. The excluded number is
Options:
A)25
B)27
C)30
D)33
E)40
Rationale: Sol.
Therefore excluded number
= (27 × 4) - ( 25 × 3)
= 108– 75
= 33.
Answer D
Answer: D
Question: Which of the following functions f(x) satisfies the condition f(y-z) = f(y)-f(z) for all possible values of y and z?
Options:
A)f(x) = x2
B)f(x) = x + (x−1)^2
C)f(x) = x-1
D)f(x) = 5/x
E)f(x) = x/5
Rationale: E. f(x) = x/5
Now for LHS x=y-z
so F(x) = F(y-z)
put x as Y-Z in X/5
f(y-z)=y-z/5= y/5-z/5---------1
similarly RHS
F(Y) = y/5---
F(Z)=Z/5 ---
F(Y)-F(Z)=Y/5 - Z/5------------2
we can see LHS =RHS ..so E remains.
ANSWER:E
Answer: E
Question: In how many different ways can the letters of the word 'DETAIL' be arranged such that the vowels must occupy only the even positions?
Options:
A)None of these
B)64
C)120
D)36
E)360
Rationale: OEOEOE
3 vowels EAI can be arranged on even places in 3!=6 ways. Similarly 3 consonants can be arranged on odd places in 3!=6 ways.
Total = 6*6 = 36.
Answer: D.
Answer: D
Question: A boy rides his bicycle 10 km at an average sped of 12 km/hr and again travels 12 km at an average speed of 10 km/hr. His average speed for the entire trip is approximately.
Options:
A)10.2 kmph
B)10.4 kmph
C)10.8 kmph
D)11.8 kmph
E)None
Rationale: Sol.
Total distance travelled = (10+12) km/hr = 22 km/hr.
total time taken = [10/12 + 12/10] hrs = 61/30 hrs
∴ Average speed = [22*30/61] km/hr = 10.8 km/hr.
Answer C
Answer: C
Question: If 0 < y < 1, what is the median of the values y, y^-1, y^2, y^1/2 and y^3?
Options:
A)y
B)y^-1
C)y^2
D)y^1/2
E)y^3
Rationale: A. To make the problem less confusing, I picked a number between 0 and 1 such as y = 1/4 and calculate:
y = 1/4
y^-1 = 4
y^2 = 1/16
y^(1/2) = 1/2
y^3 = 1/8.
From this, rearrange the number and the median is 1/4, which is y. Answer A
Answer: A
Question: A man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream?
Options:
A)30/18
B)30/19
C)30/15
D)30/13
E)30/11
Rationale: Speed downstream = 20 + 6 = 26 kmph.
Time required to cover 60 km downstream = d/s = 60/26
= 30/13 hours.
Answer: D
Answer: D
Question: In a certain city, 60% of the registered voters are congress supporters and the rest are BJP supporters. In an assembly election, if 75% of the registered congress supporters and 20% of the registered BJP supporters are expected to vote for candidate A, what percent of the registered voters are expected to vote for candidate A?
Options:
A)53
B)66
C)77
D)89
E)11
Rationale: let the people in the city be 100
Congress supporters = 60% of 100 = 60
40% are BJP=40% of 100 = 40
out of 60,75% voted for congress=75%(60)=45
out of 40%,20% voted for congress=20%(40)=8
Total=45 + 8 = 53
Total percent= 53%
Answer:A
Answer: A
Question: In a certain match all the teams were to play with each other. If there are 8 teams, how many matches will have to be played?
Options:
A)40
B)28
C)60
D)90
E)None of the above
Rationale: 8c2
=28
ANSWER:B
Answer: B
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. 2772?
Options:
A)2277
B)2669
C)2200
D)2800
E)2998
Rationale: Let the cost price of table for Sreenivas be Rs. x and given that, cost price of table for Mahesh = Rs. 2772.
=> (90%) of (110%) of x = Rs. 2772.
=> (90/100)(110/100)x = 2772
=> x = (2772 * 100)/(9 * 11)
=> x = Rs. 2800
Answer: D
Answer: D
Question: The function F(n) is defined as the product of all the consecutive positive integers between 1 and n^2, inclusive, whereas the function G(n) is defined as the product of the squares of all the consecutive positive integers between 1 and n, inclusive. The exponent on 3 in the prime factorization of F(3)/G(3) is
Options:
A)	1
B)	2
C)	3
D)	4
E)	5
Rationale: F(3)/G(3)
=product(1 to 3 ^2) / 1.2^2.3^2
=1.2.3.4.5.6.7.8.9/1.4.9
=1.2.3.(2^2).5.(2.3).7.(2^3).9/1.(2^2).9
=1.(2^7).3.5.7.9/1.(2^2).9
Loof for 2^7/2^2=2^5 ----Exponent 1
Answer: A
Answer: A
Question: In the quiet town ofNothintodothere are 500 inhabitants, 300 are unemployed and 300 are somnambulists. If half of the somnambulists are unemployed, how many are employed and are not somnambulists?
Options:
A)50.
B)100.
C)150.
D)200.
E)300.
Rationale: Total = 500
unemployed=300
employed=500-300=200
som=300
unemployed som = 300/2=150
employed som = 150
employed that are not som = 200-150=50
Answer:A
Answer: A
Question: At what price must an Book costing $47.50 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price?
Options:
A)72.5
B)55.5
C)62.5
D)82.5
E)60.5
Rationale: C
$62.50
CP = 47.50
SP = 47.50*(125/100) = 59.375
MP*(95/100) = 59.375
MP = 62.5
Answer: C
Question: In how many ways can 5 boysand 2 girls be arranged at a table if 2 girls are never together?
Options:
A)400
B)420
C)430
D)450
E)480
Rationale: Total ways of arranging 7 person in a circle = 6! = 720 ways
If we consider two women as one, then we have 5+1=6 persons. Arranging these six persons in circle will take = 5! = 120 ways
And two women can arrange themselves in 2! ways
Total ways in which two women sit together in circle = 5!*2! = 240 ways
Total ways in which two women doesn’t sit together in circle = 6! - 5!*2! = 720 - 240 = 480 ways
E
Answer: E
Question: The C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%?
Options:
A)16 2/3% loss
B)16 2/8% loss
C)16 8/3% loss
D)18 2/3% loss
E)26 2/3% loss
Rationale: 15 CP = 18 SP
18 --- 3 CP loss
100 --- ? => 16 2/3% loss
Answer:A
Answer: A
Question: On decreasing the price of a Computer by 10%, its sale is increased by 40%. The effect on the revenue is?
Options:
A)4% decrease
B)28% increase
C)16% decrease
D)26% increase
E)none of these
Rationale: Net% change in revenue
= ( x + y + xy/100) %
= [-10 + 40 + ( -10 x 40)/100]% or 26%
ANSWER:D
Answer: D
Question: How many keystrokes are needed to type numbers from 56 to 200?
Options:
A)310
B)391
C)270
D)289
E)None of these
Rationale: Explanatory Answer
While typing numbers from 56 to 200, there are 44 two-digit numbers: from 56 to 99.
Each of these numbers requires 2 keystrokes.
Therefore, 88 keystrokes to type the 2-digit numbers.
There are 101 three-digit numbers: from 100 to 200.
Each of these numbers requires 3 keystrokes.
Therefore, 303 keystrokes to type the 3-digit numbers.
Totally, therefore, one requires 88 + 303 = 391 keystrokes.
Choice B is the correct answer.
Answer: B
Question: A group of workers was put on a job. From the second day onwards, one worker was withdrawn each day. The job was finished when the last worker was withdrawn. Had no worker been withdrawn at any stage, the group would have finished the job in 55% of the time. How many workers were there in the group?
Options:
A)33
B)38
C)23
D)10
E)27
Rationale: Explanation:
It can be solved easily through option.
\inline \left ( 10+9+8+....+1 \right )=10\left ( 10\times \frac{55}{100} \right )
55 = 55 Hence correct
Alternatively:
\inline \frac{n(n+1)}{2}=n\times \frac{55n}{100}
=> n= 10
In Both cases total work is 55man-days.
Answer: D) 10
Answer: D
Question: What approximate value should come in place of question mark (?) in the following equations ?
(0.0078 ÷ 0.00012) x 77.88 = ?
Options:
A)5010
B)5040
C)5070
D)5100
E)5400
Rationale: Explanation :
? = 65 x 78 = 5070
Answer : Option C
Answer: C
Question: In how many ways can the letters of the word MANIFOLD be arranged so that the vowels are separated ?
Options:
A)14400
B)36000
C)18000
D)24000
E)22200
Rationale: We have 3 vowels: AIO and 5 consonants: MNFLD.
Consider the following case: *M*N*F*L*D* If we place vowels in any 3 empty slots (*) then all vowels will be separated by at least one consonant:
The # of ways to choose 3 empty slots out of 6 for 3 vowels = C36=20C63=20;
The # of ways to arrange the vowels: 3! (or instead of these two steps we could use P36)P63);
The # of ways to arrange MNFLD = 5!.
Total = 20*3!*5! = 14,400.
Answer: A
Answer: A
Question: There are n members in a certain department, including Michael. Two representatives are to be selected to attend a company conference. If there are 28 possible combinations in which Michael is not selected, what is the value of n?
Options:
A)7
B)8
C)9
D)10
E)11
Rationale: The combinations of two people, in which Michael was not selected = 28
The number of ways two people can be selected from m people = m*(m-1)/2
Let m be the number of people excluding Michael.
Then m*(m-1) = 56 = 8*7
Thus, n = m + 1(Michael) = 9
The answer is C.
Answer: C
Question: A bag contains 6 white and 4 black balls .2 balls are drawn at random. find the probability that they are of same colour.
Options:
A)6/7
B)15/7
C)8/9
D)7/15
E)4/3
Rationale: .let S be the sample space
Then n(S)=no of ways of drawing 2 balls out of (6+4)=10c2=(10*9)/(2*1)=45
Let E=event of getting both balls of same colour
Then n(E)=no of ways(2 balls out of six) or(2 balls out of 4)
=(6c2+4c2)=(6*5)/(2*1)+(4*3)/(2*1)=15+6=21
P(E)=n(E)/n(S)=21/45=7/15
Ans: D
Answer: D