divelab/Sys2Bench huggingface dataset:
Question: A tank is filled in eight hours by three pipes A, B and C. Pipe A is twice as fast as pipe B, and B is twice as fast as C. How much time will pipe B alone take to fill the tank?
Options:
A)16 hours
B)28 hours
C)18 hours
D)19 hours
E)10 hours
Rationale: 1/A + 1/B + 1/C = 1/8 (Given)
Also given that A = 2B and B = 2C
=> 1/2B + 1/B + 2/B = 1/8
=> (1 + 2 + 4)/2B = 1/8
=> 2B/7 = 8
=> B = 28 hours.
Answer:B
Answer: B
Question: How many positive integers P less than 20 are either a multiple of 2, an odd multiple of 9, or the sum of a positive multiple of 2 and a positive multiple of 9 ?
Options:
A)19
B)18
C)17
D)16
E)15
Rationale: We're asked to deal with the positive integers LESS than 20. There are only 19 numbers in that group (1 to 19, inclusive). We're asked to find all of the numbers that fit one (or more) of the given descriptions. Looking at the answer choices, we have every value form 15 to 19, inclusive, so most (if not all) of the numbers from 1 to 19 fit one (or more) of the descriptions. How long would it take you to find the ones that DON'T fit.....?
The first several should be pretty easy to find - the prompt wants us to focus on multiples of 2 and 9 (and sums of those multiples). So what ODD numbers are less than 9?
1, 3, 5, 7
None of these values fit the given descriptions. That's 4 out of 19 that we know for sure do NOT fit. 19 - 4 = 15 = E
Answer: E
Question: In Town X, 64 percent of the population are employed, and 38 percent of the population are employed males. What percent of the employed people in Town X are females?
Options:
A)16%
B)25%
C)32%
D)40%
E)52%
Rationale: We are asked to find the percentage of females in employed people.
Total employed people 64%, out of which 38 are employed males,hence 26% are employed females.
(employed females)/(total employed people)=26/64=40%
Answer: D.
Answer: D
Question: A family has two children. find the probability that both the children are girls given that at least
one of them is a girl?
Options:
A)1/3
B)2/3
C)2/5
D)3/7
E)3/11
Rationale: Let b stand for boy and g for girl. The sample space of the experiment is
S = {(g, g), (g, b), (b, g), (b, b)}
Let E and F denote the following events :
E : ‘both the children are girls’
F : ‘at least one of the child is a girl’
Then E = {(g,g)} and F = {(g,g), (g,b), (b,g)}
Now E n F = {(g,g)}
Thus P(F) = 3/4
and P (E n F )= 1/4
Therefore P(E|F) = P(E ∩ F)/P(F) = (1/4)/(3/4) = 1/3
A
Answer: A
Question: The speed of a boat in upstream is 70 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?
Options:
A)10 kmph
B)67 kmph
C)5 kmph
D)88 kmph
E)12 kmph
Rationale: Speed of the boat in still water
= (70+80)/2
= 75 kmph. Speed of the stream
= (80-70)/2
= 5 kmph.
Answer:C
Answer: C
Question: While driving from A-ville to B-town, Harriet drove at a constant speed of 100 kilometers per hour. Upon arriving in B-town, Harriet immediately turned and drove back to A-ville at a constant speed of 150 kilometers per hour. If the entire trip took 5 hours, how many minutes did it take Harriet to drive from A-ville to B-town?
Options:
A)138
B)148
C)150
D)162
E)180
Rationale: 5hr = 300min.
If harriet spend equal hrs on each leg she will spend 150min on each. Since speed A-B is less than speed B-A and distance on each leg is the same, time spent on A-B is more than 150min, which mean we can eliminate ans. A, B and C.
Now let plug in ans. D or E and verify which one give same distance on each leg.
E. t= 180min
* leg A-B ---> d = 100.180/60 = 18000/60
* leg B-A ----> d = 150*120/60 = 18000/60
so the correct ans. isE
Answer: E
Question: If x, y, and z are positive integers, and 2x = 5y = 6z, then the least possible value of x + y + z is
Options:
A)15
B)26
C)37
D)42
E)60
Rationale: Take LCM of 2,5 and 6 = 30
Now 2x = 30 => x =15
5y = 30 => y = 6
6z = 30 => z =5
15+6+5 = 26.
Option B.
Answer: B
Question: Two trains of length 120 m and 280 m are running towards each other on parallel lines at 42 kmph and 36 kmph respectively. In what time will they be clear of each other from the moment they meet?
Options:
A)18.4 sec
B)77 sec
C)76 sec
D)20 sec
E)66 sec
Rationale: Relative speed = (42 + 36) * 5/18 = 21.7 mps.
Distance covered in passing each other = 120 + 280 = 400 m.
The time required = d/s = 400/21.7 = 18.4 sec.
Answer:A
Answer: A
Question: P,Q and R enter into a partnership in the ratio 7/2 : 4/3 : 6/5. After 4 months, A increases his share by 50%. If the total profit at the end of one year be Rs.21600, then B’s share in the profit is:
Options:
A)Rs.2100
B)Rs 2400
C)Rs.3600
D)Rs.4000
E)Rs.3000
Rationale: Ratio of initial investments = 105 : 40 : 36.
Let the initial investments be 105x, 40x & 36x.
Therefore, P : Q : R = 105x * 4 + 150/100 x 105x * 8 : 40x * 12 : 36x * 12
= 1680x : 480x : 432x = 35 : 10 : 9.
Therefore, Q’s share = Rs. 21600 * 10/54
= Rs.4000.
ANSWER:D
Answer: D
Question: What will be the remainder when 8-3 + 3^5 + 2^10 is divided by 4?
Options:
A)12
B)3
C)16
D)0
E)9
Rationale: The multiplication(e.g. 2^10) is done first and then the sum(e.g. 15+20) and
subtraction (e.g. 8-3), and after all this expression it should be divided by 4 and the answer is 0, option D.
Answer: D
Question: A and B invests Rs.3000 and Rs.4000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit?
Options:
A)9:7
B)9:8
C)9:1
D)9:2
E)9:9
Rationale: (3*6 + 6*6): (4*12)
54:48 => 9:8
Answer:B
Answer: B
Question: Find the numbers which are in the ratio 3:2:4 such that the sum of the first and the second added to the difference of the third and the second is 28?
Options:
A)4,3,22
B)4,4,22
C)12,6,16
D)9,6,12
E)9,2,23
Rationale: Let the numbers be a, b and c.
a:b:c = 3:2:4
Given, (a + b) + (c - b) = 21
=> a + c = 28
=> 3x + 4x = 28 => x = 4
a, b, c are 3x, 2x, 4x
a, b, c are 12, 8, 16.
Answer:C
Answer: C
Question: In a city the doors of buildings where numbered from 1 to 100. How many 3’s are there as the door number?
Options:
A)10
B)20
C)30
D)40
E)50
Rationale: We will have the 3’s as follows 3,13,23,30,31,32,33,34,35,36,37,38,39,43,53,63,73,83,93.
In 33 we have 2 3’s. So we get 20 3’s from 1 to 100.
Note: for any numbers from 1 to 9 we’ll get 20 as answer.
Answer B
Answer: B
Question: The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
Options:
A)200 m
B)225 m
C)245 m
D)250 m
E)300 m
Rationale: Explanation:
Speed =45 X 5/18 m/sec =25/2 m/sec
Time = 30 sec.
Let the length of bridge be x metres.
Then,	130 + x	/30=25/2
2(130 + x) = 750
x = 245 m.
ANSWER IS C
Answer: C
Question: If 0.75: x :: 5:8, then x is equal to:
Options:
A)1.12
B)1.16
C)1.20
D)1.3
E)None of these
Rationale: Explanation:
(x * 5) = (0.75 *8)
X=6/5 = 1.20
Answer: C
Answer: C
Question: Find the number of different prime factors of 25650
Options:
A)4
B)2
C)3
D)5
E)6
Rationale: Explanation:
L.C.M of 25650 = 2 x 3 x 3 x 3 x 5 x 5 x 19
3, 2, 5,19
Number of different prime factors is 4.
Answer: Option A
Answer: A
Question: If y = x^2 + ux + v, y is minimum when x is:
Options:
A)u/u
B)-u/u
C)-u/2
D)-v/2
E)v/u
Rationale: We're given the equation Y = X^2 + uX + v.
IF.. we use a simple Classic Quadratic....
u = 2
v = 1
Y = X^2 + 2X + 1
We can then go about finding the answer that yields the MINIMUM result when X = ...
Answer A: u/v = 2/1 = 2 --> 4+4+1 = +9
Answer B: -u/v = -2/1 = -2 --> 4-4+1 = +1
Answer C: -u/2 = -2/2 = -1 --> 1-2+1 = 0
Answer D: -v/2 = -1/2 -->(1/4)-1+1 = +1/4
Answer E: v/u = 1/2 --> (1/4)+1+1 = +2 1/4
From these results, we can see the minimum result:
C
Answer: C
Question: 164 pencils are distributed to children with the same number. What can’t be the range including the number of children?
Options:
A)1~10
B)10~20
C)50~60
D)20~30
E)70~80
Rationale: In 164=1*164=2*82=4*41=6*24, you can come up with 4 cases. Amongst these cases, what is not included is C. 50~60. Therefore, the answer is C.
Answer: C
Question: How many three digit even numbers M can be formed that are divisible by 9 such that both M and M^2 have the same units digits?
Options:
A) 20
B) 21
C) 22
D) 23
E) 24
Rationale: For an even number to have the same units digit as its square, it must have the units digit of 0 (0^2 = 0) or 6 (6^2 = 6). Thus the units digit of M must be 0 or 6.
For a number to be divisible by 9, the sum of its digit must be divisible by 9.
If the units digit of M is 0, then M could be:
900;
810, 180;
720, 270;
630, 360;
540, 450;
990.
10 numbers.
If the units digit of M is 0, then M could be:
306;
216, 126;
936, 396;
846, 486;
756, 576;
666.
10 numbers.
Total = 10 + 10 = 20.
Answer: A.
Answer: A
Question: There are seven pairs of black shoes and 5 pairs of white shoes .Tey all are put into a box and shoes are drawn at a time.To ensure that at leat one pair of black shoes are taken out,What is the minimum number of shoes required to be drawn out so as to get at leat 1 pair of correct shoes.
Options:
A)13
B)14
C)15
D)16
E)17
Rationale: All the one sided (assume only left) white shoes, total draws required: 5
All the one sided (assume only left) black shoes, total draws required: 7
So, total draws are: 5+7=12
Next draw or 13th draw will contain any color right footed shoe, i.e. making at least one correct pair.
So, minimum number of shoes required to be drawn out is: 13
ANSWER:A
Answer: A
Question: The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 5 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?
Options:
A)Rs.4529
B)Rs.4586
C)Rs.4597
D)Rs.4530
E)Rs.4528
Rationale: Area of the four walls = 2h(l + b)
Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.
Total cost = 906 * 5
=Rs.4530
Answer: D
Answer: D
Question: If a 1 mm thick paper is folded so that the area is halved at every fold, then what would be the thickness of the pile after 50 folds ?
Options:
A)100 km
B)1000 km
C)1 million km
D)1 billion km
E)None
Rationale: after 1 hold, thickness will be 2mm
After 2 hold, thich ness will be 4mm
after 50th hold thick ness will be 2^50 mm..converting to km....gives 1 billion km
ANSWER:D
Answer: D
Question: City I City II	City III	City IV	City V	City VI
City I
City II
City III
City IV
City V
City VI
In the table above, what is the least number of table entries that are needed to show the mileage between each city and each of the other five cities?
Options:
A)14
B)15
C)13
D)12
E)11
Rationale: Easy way to go about this problem is we have 6*6 = 36 enteries in table the least number of enteries would be (36 - 6) /2 since 6 enteries represent the distances between same points .
Alternatively this can be solved as combination problem.
Correct Answer B
Answer: B
Question: |-4| (|-25|-|15|)= ??
Source: Preparation Material MBA Center
Options:
A)40
B)–60
C)60
D)75
E)100
Rationale: Absolute value will turn negatives into their positive 'equivalents', and will leave positives unchanged, so |-4| = 4, |-25| = 25, and |15| = 15. Getting rid of our absolute values we have:
|-4| (|-25|-|15|) = (4) (25 - 15) = 4*10 = 40
Answer: A
Question: What distance (in meters) will be covered by a bus moving at 54 km/hr in 20 seconds?
Options:
A)200
B)250
C)300
D)350
E)400
Rationale: 54 km/hr = 54 * 5/18 = 15 m/s
distance = 15 * 20 = 300 meters
The answer is C.
Answer: C
Question: A watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?
Options:
A)Rs.1000
B)Rs.1028
C)Rs.1029
D)Rs.1030
E)Rs.1028
Rationale: 90%
104%
--------
14% ---- 140
100% ---- ? => Rs.1000
Answer: A
Answer: A
Question: A bicycle wheel has a diameter of 0.75m. How many complete revolutions does it make in 1km?
Options:
A)424
B)448
C)1408
D)710
E)223
Rationale: 1 revolution = 3.14 * diameter.
Number of revolutions in 1km = 1000m / ( 3.14 * 0.75m ) = 424.6. Hence 424 complete revolutions.
Answer A
Answer: A
Question: If 2x +3y = 30 and (x+y)/y = 11/8, then find the value of 5y + 6x
Options:
A)72
B)58
C)64
D)29
E)34
Rationale: Explanation:
The given equations are :
2x + 3y = 30 --------- (i)
and, (x+y)/y = 11/8
8x + 8y = 11y
8x – 3y =0 ----(ii)
Adding (i) & (ii), we get : 10 x = 30 or x = 3.
Put x = 3 in (i), we get : y = 8
Therefore, 5y + 6x = (5 * 8 + 6 * 3) = 40 + 18 = 58.
ANSWER: B
Answer: B
Question: A cycle is bought for Rs.1500 and sold for Rs.1620, find the gain percent?
Options:
A)11
B)8
C)10
D)20
E)12
Rationale: 1500 ---- 120
100 ---- ? =>8%
Answer: B
Answer: B
Question: One-sixth of the attendees at a certain convention are female students, two-thirds of the attendees are female, and one-third of the attendees are students. If 250 of the attendees are neither female nor students, what is the total number of attendees at the convention?
Options:
A)600
B)300
C)1200
D)1500
E)1600
Rationale: Let no. of Attendee are A.
Now As per the condition of the problem stated above .
We have following population in the convention as Attendee.
Total no. of females = [2/3]*A
Total no. of females as student : [1/6]*A
Total no. of students = [1/3]*A
Total no. of male as student = [1/6]*A
Total no. of males = A - [2/3]*A = [1/3]A
No. of males which are not student = [1/3]A - [1/6]*A = 250
Hence A = 1500
Total no of males who are not student will be the answer as it states it should be neither female nor student
So Answer is D
Answer: D
Question: A basketball is dropped from a height of 20 feet. If it bounces back up to a height that is exactly half of its previous height, and it stops bouncing after hitting the ground for the fourth time, then how many total feet will the ball have traveled after 2 full bounces.
Options:
A)50
B)55
C)60
D)75
E)80
Rationale: Initial distance = 20 feet
first bounce = 10 feet up + 10 feet down = 20 feet
second bouche = 5 feet up + 5 feet down = 10 feet
total distance covered = 20+20+10+ = 50
ANSWER IS A
Answer: A
Question: A man completes of a job in 10 days. At this rate, how many more days will it takes him to finish the job?
Options:
A)6
B)12
C)7
D)15
E)5
Rationale: Work done =5/8
Balance work =	(1 -5/8)=3/8
Let the required number of days be x.
Then,	(5/8):(3/8)= :: 10 : x
(5/8)* x =	(3/8)* 10
x =(3/8) * 10 *(8/5)
x = 6.
Answer is A.
Answer: A
Question: How many three digit numbers R are divisible by 78 or 91?
Options:
A)17
B)19
C)20
D)21
E)22
Rationale: The answer will be 19.
Explanation:
78= 2*3*13 now multiples of 78, 156 ....780, now 1000-780 = 220 only two more muktiples of 78 can exists. So total number of 3 digit Multiples of 78 are 9+2=11
91= 13*7--Total number of three digit multiples --9
No remember we have a common multiples as well-- 13*7*6=91*6=546
So total number of multiples R--11+9 -1 =19.
Hence Answer is 19.B
Answer: B
Question: The HCF of two numbers is 42 and the other two factors of their LCM are 10 and 20. What is the largest number.
Options:
A)462
B)450
C)840
D)504
E)555
Rationale: Explanation:
HCF of the two numbers = 42
HCF will be always a factor of LCM
42 is factor of LCM
other two factors are 10 & 20
Then the numbers are (42 *10) and (42 x 20)
= 420 and 840
Answer: Option C
Answer: C
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is?
Options:
A)1 : 3
B)3 : 2
C)3 : 4
D)4 : 3
E)3 : 5
Rationale: Explanation:
Let the speeds of the two trains be x m/sec and y m/sec respectively.
Then, length of the first train = 27x metres,
and length of the second train = 17y metres.
( 27x + 17y ) / (x+ y )= 23
=> 27x + 17y = 23x + 23y
=> 4x = 6y
=> ( x/y ) = ( 3/2 )
Answer: Option B
Answer: B
Question: Solution X is 10 percent alcohol by volume, and solution Y is 30 percent alcohol by volume. How many milliliters of solution Y must be added to 200 milliliters of solution X to create a solution that is 14 percent alcohol by volume?
Options:
A)50
B)100
C)150
D)200
E)250
Rationale: 14% is 4%-points higher than 10% but 16%-points lower than 30%.
Thus there should be 4 parts of solution X for 1 part of solution Y.
We should add 50 ml of solution Y.
The answer is A.
Answer: A
Question: NHAI employs 100 men to build a highway of 2km in 50 days working 8 hours a day. If in 25 days, they completed 1/3 part of work. than how many more employees should NHAI hire to finish it in time working 10 hours a day?
Options:
A)55
B)60
C)70
D)50
E)65
Rationale: Explanation:
The given problem can be written in a tabular form like below: -
Men	Days	Hour	Work
Planned	100	50	8	1
Actual	100	25	8	1/3
Remaining	?	25	10	2/3
We can apply chain rule now.
Total men required to complete the remaining work = 100× (25/25) × (8/10) × (2/3)/ (1/3) = 160.
So additional men required = 160 - 100 = 60.
ANSWER IS B
Answer: B
Question: John had a stock of 1000 books in his bookshop. He sold 75 on Monday, 50 on Tuesday, 64 on Wednesday, 78 on Thursday and 135 on Friday. What percentage of the books were not sold?
Options:
A)59.8%
B)23.8%
C)66.5%
D)34.9%
E)43.5%
Rationale: Let N be the total number of books sold. Hence
N = 75 + 50 + 64 + 78 + 135 = 402
Let M be the books NOT sold
M = 1000 - N = 1000 - 402 = 598
Percentage
Books not sold / total number of books = 598/1000 = 59.8 = 59.8%
correct answer A
Answer: A
Question: The number of sailors on a ship is 78% more than the number of officers. The ratio of sailors to officers would be
Options:
A)33:25
B)47:20
C)47:25
D)89:50
E)97:50
Rationale: Sailor = 1.78 * Officer
Sailor/Officer = 1.78/1 = 178/100 = 89/50
Answer will be D
Answer: D
Question: The cost of 100 articles is equal to selling price of 90. Find the gain or loss percent?
Options:
A)11%
B)20%
C)27%
D)32%
E)49%
Rationale: C.P. of each article be $1
C.P. of 90 articles = 100
gain% = 10/90*100 = 11% approximately
Answer is A
Answer: A
Question: A farm has chickens, cows and sheep. There are eight times the number of chickens and cows than sheep. If there are more cows than chickens or sheep, and together, cows and chickens have a total of 100 feet and heads, how many sheep live at the farm?
Options:
A)5
B)8
C)10
D)14
E)3
Rationale: Chicken - ch
Cows - C
Sheep -S
ch+C=8S
C> ch and c>s
Each cow has 4 legs and 1 head
Each chicken has 2 legs and 1 head
So 5c+3ch=100 (sum of legs and head)
There are 2 possible solutions to this equation
c=22 and ch=30 or
c=14 and ch=10
Since from first equation where ch+c=8s
The sum of ch and c should be divisbile by 8. 20 is not so the only possible solution is c=14 and ch=10. So s=3
Answer : E
Answer: E
Question: On June 1 a bicycle dealer noted that the number of bicycles in stock had decreased by 4 for each of the past 5 months. If the stock continues to decrease at the same rate for the rest of the year, how many fewer bicycles will be in stock on September 1 than were in stock on January 1?
Options:
A)8
B)12
C)20
D)32
E)36
Rationale: Jan 1 = C
Feb 1 = C - 4
March 1 = C - 8
April 1 = C - 12
May 1 = C - 16
June 1 = C - 20
July 1 = C - 24
Aug 1 = C - 28
Sept 1 = C - 32
Difference between stock on September 1 than were in stock on January 1 will be -
C - ( C - 32 )= 32
Hence answer will be (D)
Answer: D
Question: Out of 8 consonants and 5 vowels, how many words of 4 consonants and 3 vowels can be formed?
Options:
A)15000
B)352800
C)25200
D)214000
E)None of these
Rationale: Solution
Number of ways of selecting (4 consonants out of 8) and (3 vowels out of 5)
nCr=n!/r!(n-r)!
8c4 x 5c3= (8x7x6x5/4x3x2x1)x(5x4x3/3x2x1) =70x10=700
Number of group,each having 4 consonants and 3 vowels = 700
Each group contains 7 letter.
Number of ways of arranging 7 letters among themselves
= 7 ! = (7 x 6 x 5 × 4 × 3 × 2 × 1) = 5040 .
So, Required number of words = (5040 × 700) = 352800 .Answer B
Answer: B
Question: The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?
Options:
A)18/35
B)18/39
C)18/36
D)18/33
E)18/32
Rationale: If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 3/5 * 4/7 + 2/5 * 3/7
= 12/35 + 6/35 = 18/35
Answer: A
Answer: A
Question: In how many different number of ways a combination of 3 persons can be selected from 4 men and 2 women?
Options:
A)160
B)180
C)200
D)210
E)220
Rationale: 6C3 × 5C2
6C3
= 6!/(3! . 3!)
= (6 × 5 × 4)/(3 × 2)
= 5 × 4 = 20.
5C2
= 5!/(3! . 2!)
= 5 × 2 = 10
= 20 × 10 = 200.
C)
Answer: C
Question: A canteen requires 112 kgs of wheat for one week. How many kgs of wheat will it require for 69 days?
Options:
A)1,204kgs
B)1,401kgs
C)1,104kgs
D)1,014kgs
E)None
Rationale: Quantity of wheat for 7 days = 112kg
quantity of wheat for one day = 112/7 kg
quantity of wheat for 69 days= 112/7 * 69 = 1104 kg
Answer C
Answer: C
Question: The value of a "Tin-Rin" stock in the stock market decreased by 15% in the last two years. The economic experts believe that the value of the stock will increase by 7% during the following year, which will make the value $440. What was the approximate price of the stock two years ago?
Options:
A)$473.
B)$464.
C)$455.
D)$445
E)$430.
Rationale: Let the stock value was x.
x* 0.85 * 1.07= 440
x= 440/0.85*1.07= 490 (approximately)
A is the answer
Answer: A
Question: A contractor undertakes to complete the construction of a tunnel 720 meters long in 240 days and employs 60 men for the purpose. After 120 days, he finds that only 240 meters of the tunnel is complete. How many more men should be employ in order to complete the work in time?
Options:
A)22
B)27
C)60
D)88
E)12
Rationale: In 120days, only 240m of the tunnel is constructed by 60 men.
The remaining 120days, 480m of the tunnel can be constructed by 120 men.
Additional number of men required = 120 - 60 = 60 men.
Answer: B
Answer: B
Question: K-numbers are positive integers with only 2's as their digits. For example, 2, 22, and 222 are K-numbers. The K-weight of a number n is the minimum number of K-numbers that must be added together to equal n. For example, the K-weight of 50 is 5, because 50 = 22 + 22 + 2 + 2 + 2. What is the K-weight of 750?
Options:
A)10
B)11
C)12
D)13
E)15
Rationale: 750 = 3*222 + (22*3) + 9*2
K weight of 600 = 3 +3+9 = 15
Answer E
Answer: E
Question: A bag contains 30 red jellybeans and 30 blue jellybeans. If 3 jellybeans are removed one at a time, at random and are not replaced, what is the probability that all 3 jellybeans removed from the bag are blue?
Options:
A)9/100
B)2/19
C)1/8
D)1/20
E)3/10
Rationale: Method-1
10 red jellybeans and 10 blue jellybeans
Total Outcomes = No. of ways to choose 3 Jelly bean at random out of a total 20 jellybeans = 20C3 = 1140
Favourable Outcomes = No. of ways to choose 3 Jelly bean such that they are all Blue out of 10 Blue = 10C3 = 120
Probability = Favourable Outcomes / Total Outcomes = 10C3 / 20C3
Probability = 120 / 1140 = 2/19
Answer: option B
Method-2
Probability of First jelly bean to be Blue = 10/20 [Total 10 Blue out of total 20 jellybeans]
Probability of Second jelly bean to be Blue = 9/19 [Total 9 Blue remaining out of total 19 jellybeans remaining]
Probability of Third jelly bean to be Blue = 8/18 [Total 8 Blue remaining out of total 18 jellybeans remaining]
Required Probability = (10/20)*(9/19)*(8/18) = 1/20
Answer: option D
Answer: D
Question: Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?
Options:
A)57%
B)60%
C)90%
D)65%
E)70%
Rationale: Req percentage = 11628/20400*100 = 57%
ANSWER A
Answer: A