divelab/Sys2Bench huggingface dataset:
Question: The five sides of a pentagon have lengths of 2, 3, 4, 5 and 6 inches. five pentagons are considered different only when the positions of the side lengths are different relative to each others. What is the total number of different possible pentagons that could be drawn using these five side lengths ?
Options:
A) 5
B) 12
C) 24
D) 32
E) 120
Rationale: CONCEPT: The number of ways to arrange n elements around a circular Manner is (n-1)!.
But the number of ways to arrange n elements in circular manner where the arrangement can be flipped around (e.g. Necklace, Garland, Bracelet) = (n-1)!/2.
The pentagon in the problem above can be flipped over (Clockwise Arrangement of Sides = Counter-clockwise arrangement), the number of distinct ways to arrange the 5 sides = (5-1)!/2 = 32.
Answer: option D
Answer: D
Question: At a speed of 60 miles per hour, a certain car uses 1 gallon of gasoline every 30 miles. If the car starts with a full 12 gallon tank of gasoline and travels for 5 hours at 60 miles per hour, the amount of gasoline used would be what fraction of a full tank?
Options:
A)3/25
B)11/36
C)7/12
D)2/3
E)5/6
Rationale: Gas used = (5 hours)*(60 miles/hour)*(1 gallon/30 miles) = 10 gallons
Portion used = (10) / 12 = 5/6
Ans E
Answer: E
Question: Aman started a business investing Rs. 70,000. Rakhi joined him after six months with an amount of Rs.. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business?
Options:
A)7 : 6 : 10
B)12 : 15 : 16
C)42 : 45 : 56
D)Cannot be determined
E)None
Rationale: EXPLANATION
Aman : Rakhi : Sagar = (70,000 x 36) : (1,05,000 x 30) : (1,40,000 x 24) = 12 : 15 : 16.
Answer B
Answer: B
Question: If a quarter kg of onions costs 70 paise, how many paise will 100 gm cost?
Options:
A)28 paise
B)65 paise
C)56 paise
D)87 paise
E)15 paise
Rationale: Explanation:
Let the required cost be x paise.
Less weight, Less cost (Direct proportion)
250 : 100 : : 70 : x
250 * x = (100 * 70)
x = (100 * 70) / 250
x = 28
ANSWER: A
Answer: A
Question: If 16^y = 2^16, what is y?
Options:
A)2
B)4
C)8
D)10
E)12
Rationale: 16^y = 2^4y = 2^16
4y=16
y = 4
The answer is B.
Answer: B
Question: At what rate percent on simple interest will a sum of money double itself in 40 years?
Options:
A)3 1/3%
B)2 1/2%
C)3 9/3%
D)3 2/3%
E)3 6/3%
Rationale: P = (P*40*R)/100
R = 2 1/2%
Answer: B
Answer: B
Question: Two bike riders ride in opposite directions around a circular track, starting at the same time from the same point. Biker A rides at a speed of 16 kmph and biker B rides at a speed of 14 kmph. If the track has a diameter of 40 km, after how much time (in hours) will the two bikers meet?
Options:
A)8.18 hrs.
B)6.18 hrs.
C)4.18 hrs.
D)1.18 hrs.
E)7.18 hrs.
Rationale: Explanation:
Distance to be covered = = 40 km
Relative speed of bikers = 16 + 14 = 30 kmph.
Now, = = 4.18 hrs.
Answer:C
Answer: C
Question: Water man has 2 cans of water. The 1st contains 25% water and the rest milk. The 2ndcontains 50% water. How much milk should he mix from each of the containers so as to get 12ltr of water such that the ratio of milk to water is 3 : 5?
Options:
A)4 ltr
B)5 ltr
C)6 ltr
D)7 ltr
E)9 ltr
Rationale: Let the cost of 1 litre milk be Re. 1
Milk in 1 litre mix. in 1st can =	3	litre, C.P. of 1 litre mix. in 1st can Re.	3
4	4
Milk in 1 litre mix. in 2nd can =	1	litre, C.P. of 1 litre mix. in 2nd can Re.	1
2	2
Milk in 1 litre of final mix. =	5	litre, Mean price = Re.	5
8	8
By the rule of alligation, we have:
C.P. of 1 litre mixture in 1st can C.P. of 1 litre mixture in 2nd can
3
4
Mean Price
5
8
1
2
1
8
1
8
Ratio of two mixtures =	1	:	1	= 1 : 1.
8	8
So, quantity of mixture taken from each can = 1	x 12 = 6 ltr.
2
C
Answer: C
Question: Of the three-digit integers greater than 600, how many have two digits that are equal to each other and the remaining digit different from the other two?
Options:
A) 90
B) 81
C) 80
D) 45
E) 36
Rationale: To satify the given condition,
required no. of cases = total numbers - numbers with all digits different - numbers when all three digits are same,
number greater than 600;
total numbers = 1*10*10 = 100
numbers with all digits different = 1*9*8 = 72
numbers when all three digits are same (777) = 1
req. = 100- 72 - 1 = 27
considering the numbers between 700999 = 27*3=82
Answer is 81 ('cause 700 can't be included)
Answer (B).
Answer: B
Question: A man whose bowling average is 12.4, takes 7 wickets for 26 runs and there by decreases his average by 0.4. the number of wickets taken by him before his last match is?
Options:
A)143
B)144
C)145
D)146
E)147
Rationale: 12.4*x+26=(7+x)12
solve equation x=145
ANSWER:C
Answer: C
Question: The average age of husband, wife and their child 3 years ago was 24 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is
Options:
A)22
B)40
C)38
D)21
E)31
Rationale: Explanation:
Sum of the present ages of husband, wife and child = (24 x 3 + 3 x 3) years = 81 years.
Sum of the present ages of wife and child (20 x 2 + 5 x 2) years = 50 years.
Husband's present age = (81 - 50) years = 31 years.
Answer: E
Answer: E
Question: If two numbers, a and b, are to be chosen from a set of 4 consecutive integers starting with 1 and a set of three consecutive even integers starting with 4, respectively, what is the probability that b/a will not be an integer?
Options:
A)1/6
B)1/4
C)1/3
D)1/2
E)2/3
Rationale: a is from the following set {1,2,3,4}
b is from the following set {4,6,8}
Total number of ways of choosing 2 integers, one from each set is = 4* 3 = 12 ways
Now the number of possibilities where b/a is not an integer is for the following outcomes
{b,a} => {4,3},{6,4},{8,3} = 3 ways
Hence probability is = 3/12 = 1/4
ans is B
Answer: B
Question: 16384, 8192, 2048, 256, 16, ?
Options:
A)1
B)8
C)2
D)0.5
E)3
Rationale: Explanation :
Terms are continuously divided by 2,4,8,16, and so on
16384
16384 ÷ 2 = 8192
8192 ÷ 4 = 2048
2048 ÷ 8 = 256
256 ÷ 16 = 16
16 ÷ 32 = 0.5
Answer : Option D
Answer: D
Question: Sari and Ken climb up a mountain. At night, they camp together. On the day they are supposed to reach the summit, Sari wakes up at 06:00 and starts climbing at a constant pace. Ken starts climbing only at 08:00, when Sari is already 600 meters ahead of him. Nevertheless, Ken climbs at a constant pace of 500 meters per hour, and reaches the summit before Sari. If Sari is 50 meters behind Ken when he reaches the summit, at what time did Ken reach the summit?
Options:
A)13:00
B)11:15
C)14:00
D)15:00
E)15:30
Rationale: Both Sari and Ken climb in the same direction.
Speed of Sari = 600/2 = 300 meters/hr (since she covers 700 meters in 2 hrs)
Speed of Ken = 500 meters/hr
At 8:00, distance between Ken and Sari is 600 meters. Ken needs to cover this and another 50 meters.
Time he will take = Total distance to be covered/Relative Speed = (600 + 50)/(500 - 300) = 3.25 hrs
Starting from 8:00, in 5 hrs, the time will be 11:15
Answer (B)
Answer: B
Question: If 1.5x=0.04y then the value of (y-x)/(y+x) is
Options:
A)730/77
B)73/77
C)7.3/77
D)7.3/770
E)7.3/77
Rationale: x/y=0.04/1.5
y/x=1.5/0.04
by componendo dividendo rule
(y+x)/(y-x)=1.54/1.46
(y-x)/(y+x)=1.46/1.54=73/77
ANSWER:B
Answer: B
Question: 5 OUT OF 1500 PARTS OF EARTH IS SULPHUR. WHAT IS THE PERCENTAGE OF SULPHUR IN EARTH
Options:
A)11/50
B)2/9
C)1/45
D)1/3
E)NONE OF THESE
Rationale: REQUIRED PERCENTAGE=(5/1500*100)%=1/3%
CORRECT OPTIONS: D
Answer: D
Question: The speed of a car is 100 km in the first hour and 30 km in the second hour. What is the average speed of the car?
Options:
A)50 kmph
B)65 kmph
C)75 kmph
D)85 kmph
E)65 kmph
Rationale: Explanation:
S = (100 + 30)/2 = 65 kmph
E)
Answer: E
Question: In how many different W ways can 4 ladies and 4 gentlemen be seated at a round table so that all ladies sit together?
Options:
A)70
B)288
C)576
D)10,080
E)20,160
Rationale: Treat the 4 ladies as one object, now you have 5 objects to arrange around a table (m1,m2,m3,m4,women). This can be done in (5-1)! ways
And there are 4! ways to arrange ladies among themselves
Answer W= (4!)^2 = 576 or C
Answer: C
Question: In a certain appliance store, each model of television is uniquely designated by a code made up of a particular ordered pair of letters. If the store has 40 different models of televisions, what is the minimum number of letters that must be used to make the codes?
Options:
A)6
B)7
C)7
D)9
E)10
Rationale: If n is the number of distinct letters used to create the two lettered codes, then a total of n∗n=n^2 different codes can be created. We need n2≥40. The smallest n which fulfills this condition is n = 7.
Answer C
Answer: C
Question: Walking with 3/5 of my usual speed, I miss the bus by 5 minutes. What is my usual time?
Options:
A)16 min
B)26 min
C)34 min
D)20 min
E)15 min
Rationale: Speed Ratio = 1:3/5 = 5:3Time Ratio
= 3:5 1 -------- 5 3 --------- ? è 15
Answer: E
Answer: E
Question: A car covers a distance of 780 km in 6 ½ hours. Find its speed?
Options:
A)104 kmph
B)187 kmph
C)164 kmph
D)130 kmph
E)106 kmph
Rationale: 780/6
= 130 kmph
Answer: D
Answer: D
Question: Statements: Prime school-going children in urban India have now become avid as well as more regular viewers of TV, even in households without a TV. As a result there has been an alarming decline inthe extent of readership of newspapers. Conclusions: 1) Method of increasing the readership of newspapers should be devised. 2) A team of experts should be sent to other countries to study the impact of TV. on the readership of newspapers.
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: The statement concentrates on the increasing viewership of TV. and does not stress either on increasing the readership of newspapers or making studies regarding the same. So, neither I nor II follows.
D
Answer: D
Question: Call a number Guardian if it is composite but not divisible by 2, 3, or 5. The three smallest guardian numbers are 49, 77, and 91. There are 168 prime numbers less than 1000. How many Guardian numbers are there less than 1000?
Options:
A)100
B)102
C)104
D)106
E)108
Rationale: S1 = total number of numbers divisible by 2 from 1-1000 = 500
S2 = total number of numbers divisible by 3 from 1-1000 = 333
S3 = total number of numbers divisible by 5 from 1-1000 = 200
S4 = total number of numbers divisible by 2 and 3 = 166
S5 = total number of numbers divisible by 2 and 5 = 100
S6= total number of numbers divisible by 3 and 5 =66
S7 = total number of numbers divisible by 2,3 and 5 = 33
thus total number of numbers divisible by 2,3 or 5 are = 500 +333+200-166-100-66+33 = 734
now since we have already included 2,3 and 5 while calculating their multiple in the above calculations, hence total number of prime numbers from 1-1000 becomes = 168-3 =165
also, since 1 is neither composite nor prime, hence we will subtract 1 from the final answer.
thus total number of guardian numbers are 1000-734-1-165 = 100
ANSWER:A
Answer: A
Question: add 8% of 24 and 10% of 40.
Options:
A)9.5
B)10.5
C)5.5
D)5.9
E)8.5
Rationale: 8% of 24 + 10% of 40
24*8/100+40*10/100
1.9+4=5.9
answer D
Answer: D
Question: Rajan is sixth from the left end and vinay is tenth from the right end in a row of boys. If there are eight boys between Rajan and Vinay, how many boys are there in the row ?
Options:
A)24
B)66
C)88
D)27
E)91
Rationale: Explanation:
Number of boys in the row = (6 + 10 + 8) = 24
Answer: A) 24
Answer: A
Question: I remember during the school days , the teacher asked the class "can you tell me the sum of the first 50 odd numbers ?".
I ran quickly to the teacher and told her "the answer is 2500". The teacher replied "lucky guess".
She then asked me "can you tell me the sum of first 74 odd numbers ?".
I wait for approx 10 seconds and replied with the correct answer.
How can i answer so quickly and whats the correct answer ?
Options:
A)8715
B)0152
C)3581
D)5476
E)9126
Rationale: D
5476
n^1
74 * 74 = 5476 (sum of first 74 odd numbers).
50 * 50 = 2500 (sum of first 50 odd numbers).
Answer: D
Question: The average (arithmetic mean) of 4 different integers is 68. If the largest integer is 90, what is the least possible value of the smallest integer?
Options:
A)5
B)19
C)29
D)30
E)33
Rationale: Total of Integers=68*4=272
Lowest of the least possible integer is when the middle 2 intergers are at the maximum or equal to the highest possible integer.
But all integers are distinct. So if the largest integer is 90, then the middle 2 will be 88 and 89
Lowest of least possible integer = 272-(90+89+88)=272-267=5
Answer: A
Answer: A
Question: In an examination, it is required to score 32% of the aggregate marks for a student to pass the examination.Raju has scored 250 marks and was declared failed by 22 marks.Find the aggregate marks?
Options:
A)720
B)750
C)800
D)850
E)900
Rationale: 32% of x =272.
x=850
ANSWER:D
Answer: D
Question: The monthly incomes of A and B are in the ratio 5 : 2. B's monthly income is 12% more than C's monthly income. If C's monthly income is Rs. 13000, then find the annual income of A?
Options:
A)Rs. 420000
B)Rs. 180000
C)Rs. 436800
D)Rs. 504000
E)None of these
Rationale: B's monthly income = 13000 * 112/100 = Rs. 14560
B's monthly income = 2 parts ----> Rs. 14560
A's monthly income = 5 parts = 5/2 * 14560 = Rs. 36400
A's annual income = Rs. 36400 * 12 = Rs. 436800
ANSWER:C
Answer: C
Question: How many paying stones, each measuring 2 1/2 m * 2 m are required to pave a rectangular court yard 30 m long and 16 1/2 m board?
Options:
A)99
B)86
C)21
D)26
E)11
Rationale: 30 * 33/2 = 5/2 * 2 * x => x
= 99
A
Answer: A
Question: A can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With help of C, they did the job in 4 days only. Then, C alone can do the job in?
Options:
A)9
B)9 3/5
C)10
D)11
E)None of these
Rationale: (A + B + C)'s 1 day's work =	1	,
4
A's 1 day's work =	1	,
16
B's 1 day's work =	1	.
12
Therefore C's 1 day's work =	1	-	(	1	+	1	)	=	(	1	-	7	)	=	5	.
4	16	12	4	48	48
So, C alone can do the work in	48	= 9	3	days.
5	5
Answer is B
Answer: B
Question: 5,7,11,19,?,67,131
Options:
A)32
B)40
C)30
D)35
E)25
Rationale: The Pattern is + 2, + 4, +8, +16, ...
19+16=35
Answer :D
Answer: D
Question: A ladder was rested along a wall of height 5m. If ladder slides 2m away from the wall then ladder touches the foot of the wall .What is the height of the ladder.
Options:
A)6.25 mtrs
B)7.25 mtrs
C)8.25 mtrs
D)9.25 mtrs
E)5.25 mtrs
Rationale: suppose , earlier foot of ladder was x mtres away from wall, then
length of ladder = x+2 mtrs
hence
(x+2)^2 = x^2+5^2
x= 21/4 = 5.25 mtrs
length of ladder = 5.25+2= 7.25 mtrs
ANSWER:B
Answer: B
Question: From January 1, 2015, to January 1, 2017, the number of people enrolled in health maintenance organizations increased by 12 percent. The enrollment on January 1, 2017, was 45 million. How many million people, to the nearest million, were enrolled in health maintenance organizations on January 1, 2015 ?
Options:
A)38
B)39
C)40
D)41
E)42
Rationale: Soln:-
12x=45 --> 28/25*x=45 --> x=45*25/28=1125/28=~40
Answer: C.
Answer: C
Question: When x is divided by y, the quotient is q with remainder r. Which of the following is y in terms of r, x, and q? (Assume both y and q are nonzero.)
Options:
A)x – r – q
B)(x+r)/q
C)x/q−r
D)(x−r)/q
E)xr – q
Rationale: Given that when x is divided y, the quotient is q and remainder is r. This implies x-r is divisible by y and yq=(x-r) or y = (x-r)/q.
Answer D.
Answer: D
Question: A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 32150. What percentage of profit did he make?
Options:
A)22
B)44.5
C)40
D)26
E)11
Rationale: The total CP = Rs. 16000 + Rs. 6250 = Rs. 22250 and SP = Rs. 32150
Profit(%) = (32150 - 22250)/22250 * 100 = 44.5%.Answer:B
Answer: B
Question: Two persons start running simultaneously around a circular track of length 380 m from the same point at speeds of 24 kmph and 28 kmph. When will they meet for the first time any where on the track if they
are moving in the opposite direction ?
Options:
A)144
B)36
C)124
D)26
E)38
Rationale: Time taken to meet the first time = length of track/relative speed
= 380/ (24 +28) (5/18)
= 380/52 *(18/5) = 26 sec.
Answer : D
Answer: D
Question: The number 341 is equal to the sum of the cubes of two integers. What is the product of those integers?
Options:
A)8
B)15
C)21
D)30
E)39
Rationale: 5^3+6^3= 341 number is 5*6=30
D
Answer: D
Question: 50 is divided into two parts such that the sum of their reciprocals is 1/12. Find the two parts.
Options:
A)40,10
B)22,28
C)25,25
D)35,15
E)30,20
Rationale: Let the two parts be x and (50 - x).
Then, 1 / x + 1 / (50 – x) = 1 / 12 => (50 – x + x) / x ( 50 – x) = 1/12
=> x^2 – 50x + 600 = 0 => (x – 30)( x – 20)=0 => x = 30 or x = 20.
So, the parts are 30 and 20.
Answer E)30,20.
Answer: E
Question: Angelo and Isabella are both salespersons. In any given week, Angelo makes $550 in base salary plus 8 percent of the portion of his sales above $4,000 for that week. Isabella makes 10 percent of her total sales for any given week. For what amount of weekly sales would Angelo and Isabella earn the same amount of money?
Options:
A) 11,500
B) 24,500
C) 25,500
D) 26,500
E) 27,500
Rationale: OFFICIAL SOLUTION:
The problem asks for the amount of weekly sales it takes for Angelo and Isabella to earn the same amount of money. You can write an equation that sets Angelo’s and Isabella’s weekly earnings equal to each other, with x representing weekly sales. Weekly earnings for each salesperson equal base salary plus commission. So Angelo’s earnings are 550 + (0.08)(x – 4,000), and Isabella’s are 0.10x. Set up the equation and solve:
550 + (0.08)(x – 4,000) = 0.10x
Distribute the 0.08:
550 + 0.08x – 320 = 0.10x
Combine terms and subtract 0.08x from both sides:
230 = 0.02x
Divide both sides by 0.02:
11,500 = x
Your answer is A.
Answer: A
Question: What is the 28th digit to the right of the decimal point in the decimal form of 4/11?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: 4/11 = 0.363636...
The even numbered positions in the decimal expansion are all 6.
The answer is D.
Answer: D
Question: What is the value of(a,y) in (13^-20-a*13^y)=168*13^-22?
Options:
A)(1,2)
B)(0,1)
C)(-1,22)
D)(1,-22)
E)(1,-20)
Rationale: (13^-20-a*13^y)=168*13^-22
Divide the LHS and RHS by 13^-22
13^2-a*13^(y+22) =168
168 can be expressed as 13^2 - 1
13^2-a*13^(y+22) =13^2 - 1
a*13^(y+22) =1
Now look at options and substitute .. Its easy for y=-22 . 13^0=1 a also = 1
ANSWER:D
Answer: D
Question: If the sum of the interior angles of a regular polygon measures up to 1080 degrees, then how many sides does the polygon have?
Options:
A)10
B)16
C)8
D)11
E)14
Rationale: one of the interior angle = 180 - 360/n
sum of the interior angles is = n (180 - 360/n)
given
n(180 - 360/n)=1080
180n - 360 = 1080
180n = 1440
n = 1440/180 = 8
ANSWER:C
Answer: C
Question: In an isoscele right angled triangle, the perimeter is 20 metre. Find its area.
Options:
A)9,320 m2
B)8,750 m2
C)7,980 m2
D)6,890 m2
E)None of these
Rationale: In an isoscele right angled triangle,
Area = 23.3 × perimeter2
= 23.3 × 20(2) = 9320 m2
Answer A
Answer: A
Question: In the expression 51840/x^4, for which of the following values of x will the expression NOT be an integer?
Options:
A)1/2
B)1
C)2
D)3
E)5
Rationale: We can straightaway eliminate A & B, since the expression will always yields an integer for those values
Out of C, D, and E. Let us consider option E. 51840 has only one trailing zero and tens digit is not 5, so It has just one 5 in it. But for the expression to be an integer numerator should have 5^4.
ANSWER:E
Answer: E
Question: HCF and LCM two numbers are 12 and 396 respectively. If one of the numbers is 36, then the other number is?
Options:
A)36
B)66
C)132
D)264
E)364
Rationale: 12 * 396 = 36 * x
x = 132
ANSWER:C
Answer: C
Question: Find the number of ways in which 4 letters may be selected from the word "Examination"?
Options:
A)66
B)70
C)136
D)330
E)4264
Rationale: EXAMINATION has 11 letters, and in which 'A', 'I' and 'N', all occur twice. 11C4, would have been fine if all letters were distinct.
So, we have E, X, M, T, O, (AA), (II), (NN). 8 distinct letters.
1. 4 letters selected, which are all distinct: 8C4 = 70
2. 2 letters alike, and 2 distinct (eg: AAEX) = 3C1 x 7C2 = 63
3. 2 letters alike, and 2 letters alike (eg: AAII) = 3C2 = 3
So answer is, 70 + 63 + 3 = 136.
ANSWER:C
Answer: C
Question: By selling a book for 250, 20% profit was earned. What is the cost price of the book?
Options:
A)A)215
B)B)208
C)C)230
D)D)235
E)E)240
Rationale: SP = 120% of CP; :. CP = 250 × 100/120 = 208
Option 'B'
Answer: B
Question: Calculate the ratio between x and y if 90% of x equal to 60% of y?
Options:
A)1 : 2
B)3 : 5
C)3 : 2
D)3 : 4
E)5 : 2
Rationale: Explanation:
90 x = 60 y
x: y = 90: 60 = 3 : 2
Answer:C
Answer: C
Question: There are 8 students. 4 of them are men and 4 of them are women. If 4 students are selected from the 8 students. What is the probability R that the number of men is equal to that of women?
Options:
A)R=18/35
B)16/35
C)14/35
D)13/35
E)12/35
Rationale: METHOD-1:
Favorable outcomes (i.e. No. of Men= No. of Women =2) = 4C2 * 4C2 = 6*6 = 36
Total ways of selecting 4 out of 8 Students = 8C4 = 8! / (4! * 4!) = 70
Probability = 36/70 = 18/35
A
METHOD-2:Also see the mistake done by the person who posted this question
Probability of First selected person being Man = 4/8
Probability of Second selected person being Man = 3/7
Probability of First selected person being Woman = 4/6
Probability of Second selected person being Woman = 3/5
i.e. Probability = (4/8)*(3/7)*(4/6)*(3/5) *[4!/(2!*2!)]= 18/35
The important part for the readers is to understand the reason of multiplying[4!/(2!*2!)]here
When we take the probability of each case like we have have taken in this method then it always include ARRANGEMENTS as well and so we have to take every arrangement of the events as well
The arrangement of these 4 events can be done in 4! ways but since the second man can't be selected before 1st so we have to exclude their arrangement by dividing by 2! and similarly since the second Woman can't be selected before 1st so we have to exclude their arrangement by dividing by 2!
A
Answer: A
Question: Farm Tax is levied on the 60% of the cultivated Land. The tax department collected total $ 4000 through the farm Tax from the village of Mr. willam. Mr. willam paid only $ 500 as farm tax. The percentage of total land of Mr. willam over the total taxable land of the village is :
Options:
A)15%
B)25%
C)12.5%
D)20.83%
E)none
Rationale: Only trick n this question is to ignore 60% information as farm tax is levied uniformly in the village and that includes Mr William's land.
What percentage of tax Mr William paid ? This will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village. That leads to (500/4000)x100 =12.5%in percentage terms.
But the question asks ratio between his total land to total cultivated land. Hence the answer is 12.5%x (100/60) = 20.833% and the answer is not there in the options.
The correct answer is (D).
Answer: D
Question: A train running at the speed of 60 km/hr crosses a pole in 8 seconds. Find the length of the train.
Options:
A)133.33
B)882
C)772
D)252
E)121
Rationale: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 8 = 133.33 meter.Answer: A
Answer: A
Question: If an article is sold at 18% profit instead of 9% profit, then the profit would be $54 more. What is the cost price?
Options:
A)$500
B)$600
C)$700
D)$800
E)$900
Rationale: 9% * cost price = $54
1% * cost price = $54 / 9 = $6
The cost price is $600.
The answer is B.
Answer: B
Question: A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B's share?
Options:
A)1000
B)3000
C)2000
D)4000
E)5000
Rationale: Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively.
Then, 4x - 3x = 1000
x = 1000.
B's share = Rs. 2x = Rs. (2 x 1000) = Rs. 2000.
Answer is C.
Answer: C