mathewhe/aqua_rat huggingface dataset:
Question: If six persons sit in a row, then the probability that three particular persons are always together is?
(A) 1/5
(B) 1/4
(C) 1/9
(D) 1/6
(E) 1/1
Rationale: Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6! = 1/5
Answer:C
Answer: (C) 1/9
Question: Marla is hanging a banner diagonally across a rectangular room. The length of the room is 3 feet shorter than its width. If the total area of the room is 130 square feet, what is the length of the banner (in feet)?
(A) between 16 and 17
(B) between 17 and 18
(C) between 18 and 19
(D) between 19 and 20
(E) between 20 and 21
Rationale: To solve this, we first need to set up an equation for the area of the room. If x is the width, then we have
x(x - 3) = 130. By putting the equation in standard form, we get x^2-3x-130=0. By using the quadratic formula, we get roots of -10 and 13. We know that x is the width, and x-3 is the length, so by using the roots, we get 13 as the width (x), and 10 as the length (x-3).
Once we have this, we can use the Pythagorean Theorem to solve for the diagonal. Plugging in the length and width, we will get d^2=13^2+10^2
=169+100
=269
The square root of 269 is less than 17, since 17^2 = 289. Going down a number, we can compute 16^2 = 256 < 269. Therefore, the length of the diagonal must be between 16 and 17.
The correct answer is A.
Answer: (A) between 16 and 17
Question: S is a set containing 8 different positive odd primes. T is a set containing 8 different numbers, all of which are members of S. Which of the following statements CANNOT be true?
(A)  The median of S is prime.
(B)  The median of T is prime
(C)  The median of S is equal to the median of T.
(D)  The sum of the terms in S is prime.
(E)  The sum of the terms in T is prime.
Rationale: Here is my explanation. The question states:S is a set containing 9 different positive odd primes. T is a set containing 8 different numbers, all of which are members of S. Which of the following statements CANNOT be true?
(A) The median of S is prime.
Thismust be true. If there are an odd number of members of a set, then the median is a member of the set: it's the middle number, when all the numbers are ranked from smallest to biggest. Every number in S is a positive odd prime, so the median is one of them, and is prime.
(B) The median of T is prime.
Thismay or may not be true. If a set has an even number of members, the median is average of the two numbers in the middle, when ranked from smallest to biggest. The average of two odd numberscould beeven (average of 71 and 73 is 72), and hence not prime, or itcould beodd (the average of 71 and 79 is 75). For particularly well chosen odd numbers, the average can be not only odd but also prime -- for example, the average of 89 and 113 is 101, another prime number. If the two middle numbers of T were 89 and 113, the median would be 101, a prime number.
(C) The median of S is equal to the median of T.
Under most configurations for S and T, this wouldn't happen. If you weren't trying to make it happen, it would be unlikely to happen by chance. BUT, if the number dropped going from from S to T was the median of S (say, 101), and if the two middle numbers of T happen to have an average of that number that was dropped (for example, if the two numbers were 89 and 113), then the medians would be equal. In other words, the three middle numbers of S would have to be {. . ., 89, 101, 133, . . .}, and when 101 is dropped in going to T, the median of two would be the average of 89113, which happens to be 101. It's an exceptional case, but itcouldbe true.
(D) The sum of the terms in S is prime.
Thismay or may not be true. The sum of 9 odd numbermustbe an odd number. That odd numbercould beprime. For example, the sum of the first nine odd prime numbers {3, 5, 11, 13, 17, 19, 23, 29} is 127, which is prime. If you drop 3 and include the next prime, 31, the set {5, 11, 13, 17, 19, 23, 29, 31} has a sum of 155, which is clearly not prime.
(E) The sum of the terms in T is prime.
Thismust be false. The sum of eight odd numbers must be an even number. Only 2 is prime, and all other even numbers are not. Therefore, the sum of eight odd prime numbers will be an even number bigger than two, and absolutely cannot be prime.
C
Answer: (C)  The median of S is equal to the median of T.
Question: Triathlete Dan runs along a 3-mile stretch of river and then swims back along the same route. If Dan runs at a rate of 10 miles per hour and swims at a rate of 6 miles per hour, what is his average rate for the entire trip in miles per minute?
(A) 1/8
(B) 2/15
(C) 3/15
(D) 1/4
(E) 3/8
Rationale: Dan travels 6 miles round trip.
Running part: (3/10*60 = 18 minutes)
Swimming Part: (3/6 *60 = 30 minutes)
6 miles in (18+30) minutes
6/48 = 1/8 mile per minute
Answer: 1/8 mile per minute
A
Answer: (A) 1/8
Question: A woodworker normally makes a certain number of parts in 24 days. But he was able to increase his productivity by 5 parts per day, and so he not only finished the job in only 22 days but also he made 80 extra parts. How many parts does the woodworker normally makes per day and how many pieces does he make in 24 days?
(A) 360
(B) 480
(C) 754
(D) 687
(E) 147
Rationale: Let x be the number of parts the woodworker normally makes daily. In 24 days he makes 24⋅x pieces. His new daily production rate is x+5 pieces and in 22 days he made 22⋅(x+5) parts. This is 80 more than 24⋅x. Therefore the equation is:
24⋅x+80=22(x+5)
30=2x3
x=15
Normally he makes 15 parts a day and in 24 days he makes 15⋅24=360 parts.
correct answer is A)360
Answer: (A) 360
Question: If you have 8 New Year greeting cards and you want to send them to 3 of your friends, in how many ways can this be done?
(A) 336
(B) 720
(C) 340
(D) 670
(E) None
Rationale: Solution
We have to find number of permutations of 3 objects out of 8 objects. This number is 8P3=8(8-1)(8-2)=8*7*6=336
Answer A
Answer: (A) 336
Question: 6x − 12 = 6y
4y + 4x = 12
Which of the following is the number of solutions to the system of equations shown above?
(A) More than three
(B) Exactly one
(C) Exactly two
(D) Exactly three
(E) None
Rationale: 6x − 12 = 6y
=> 6x - 6y = 12
=> x- y =2 -- 1
4y + 4x = 12
=>x + y = 3 -- 2
From equation 1 and 2 , we get
2x = 5
=> x=2.5
y=.5
Therefore , the given system will have Exactly one solution
Answer : B
Answer: (B) Exactly one
Question: 115 liters of a mixture of milk and water contains in the ratio 3:2. How much water should now be added so that the ratio of milk and water becomes 3:4?
(A) 12 liters
(B) 32 liters
(C) 46 liters
(D) 50 liters
(E) 34 liters
Rationale: Milk = 3/5 * 115 = 69 liters
Water = 46 liters
69 : (46+P) = 3:4
138 + 3P = 276 => P = 46
46 liters of water are to be added for the ratio become 3:4.
Answer:C
Answer: (C) 46 liters
Question: Let the number which when multiplied by 12 is increased by 198.
(A) 18
(B) 20
(C) 26
(D) 28
(E) 30
Rationale: Solution
Let the number be x .
Then, 12x - x = 198
‹=›11x = 198
x ‹=› 18.
Answer A
Answer: (A) 18
Question: The total age of A and B is 18 years more than the total age of B and C. C is how many year younger than
(A) 14 years
(B) 12 years
(C) 56 years
(D) 66 years
(E) 18 years
Rationale: Given that A+B = 182 + B + C
=> A â€“ C = 18 + B â€“ B = 18
=> C is younger than A by 18 years
Answer:E
Answer: (E) 18 years
Question: The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
(A) 332
(B) 268
(C) 245
(D) 276
(E) 191
Rationale: 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: C
Answer: (C) 245
Question: How many seconds will a train 100 meters long take to cross a bridge 250 meters long if the speed of the train is 36 kmph?
(A) 54 sec
(B) 35 sec
(C) 25 sec
(D) 45 sec
(E) 24 sec
Rationale: D = 100 + 250 = 350
S = 36 * 5/18 = 10 mps
T = 350/10 = 35 sec
Answer:B
Answer: (B) 35 sec
Question: Rs.8000 become Rs.9261 in a certain interval of time at the rate of 5% per annum of C.I. Find the time?
(A) 4 years
(B) 6 years
(C) 2 years
(D) 3 years
(E) 8 years
Rationale: Explanation:
9261 = 8000(21/20)N
(21/20)3 = (21/20)N => N = 3
Answer IS D
Answer: (D) 3 years
Question: In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:
(A) 750 cu.m
(B) 75 cu.m
(C) 4500 cu.m
(D) 500 cu.m
(E) 600 cu.m
Rationale: hectare = 10,000 m^2
so area = (1.5 * 10000) m^2 = 15000 m^2
depth = 5/100m = 1/20m
volume = (area*depth) = 15000 * 1/20 = 750 m^3
ANSWER A
Answer: (A) 750 cu.m
Question: Find the area of a parallelogram with base 30 cm and height 12 cm?
(A) 290 cm2
(B) 360 cm2
(C) 270 cm2
(D) 280 cm2
(E) 260 cm2
Rationale: Area of a parallelogram = base * height = 30 * 12
= 360 cm2
Answer:B
Answer: (B) 360 cm2
Question: a, b, c, d, and e are five consecutive numbers in increasing order of size. Deleting one of the five
numbers from the set decreased the sum of the remaining numbers in the set by 20%. Which one of
the following numbers S was deleted?
(A)  a
(B)  b
(C)  c
(D)  d
(E)  e
Rationale: a+b+c+d+e => 1+2+3+4+5=15
S=20%*15= 3 =>C
Answer: (C)  c
Question: If 2994 Ã· 14.5 = 179, then 29.94 Ã· 1.45 = ?
(A) 17.1
(B) 17.3
(C) 17.5
(D) 17.7
(E) 17.9
Rationale: 29.94/ 1.45 = 299.4/14.5
= (2994/14.5) x 1/10) [ Here, Substitute 179 in the place of 2994/14.5 ]
= 179/10
= 17.9
Answer is E.
Answer: (E) 17.9
Question: Evaluate: 30 - 12*3*2 = ?
(A) 62
(B) 52
(C) 32
(D) 12
(E) 22
Rationale: According to order of operations, 12?3?2 (division and multiplication) is done first from left to right
12**2 = 4* 2 = 8
Hence
30 - 12*3*2 = 30 - 8 = 22
correct answer E
Answer: (E) 22
Question: Tough and Tricky questions: Number Properties.
What is the smallest positive integer x such that 324x is the cube of a positive integer?
(A) 9
(B) 12
(C) 18
(D) 24
(E) 36
Rationale: We want to know the smallest x that will make 324x a CUBE of some number. Let's call that number y.
Let's first figure out what we're working with. The prime factorization of 324 can be visualized:
...........324
......../.......\
......81.......4
...../..\....../...\
...27...3...2.....2
.../..\
..9....3
/\
.3 3
So, we have 3 * 3 * 3 * 3 * 2 * 2 that can be multiplied together to get 324. Now we need to figure out what we need to make 324 * x into a cube of y (y^3=324*x).
We have four 3s, and two 2s. To arrange these numbers in identical triples (2,3,3), we need at least one more 2 and two 3's. Each of these triples will give us the value of y (2*3*3=18), which, multiplied by itself three times, gives us 324 * x.
Looking at the factors we need to complete the triples, we get 3 * 3 * 2 = 18. We know this is the smallest number possible because prime factors by definition cannot be broken down any further.
Therefore, we can go with answer choice C.
If time permits, we can do a sanity check. We calculated that y should be 2 * 3 * 3, or 18. 18 * 18 * 18 = 5832. Also, 324 * 18 = 5832.
Answer: C
Answer: (C) 18
Question: Bag A contains red, white and blue marbles such that the red to white marble ratio is 1:3 and the white to blue marble ratio is 2:3. Bag B contains red and white marbles in the ratio of 1:4. Together, the two bags contain 26 white marbles. How many red marbles could be in bag A?
(A) 1
(B) 3
(C) 4
(D) 2
(E) 8
Rationale: # of Red marbles in Bag A can be either 2 or 6. No 2 in the choices, so 6. D.
Bag A:
R:W:B = 2:6:9
Bag B
R:W = 1:4
6X + 4Y = 26 i.e 3X + 2Y = 13
X has to be odd to make an odd sum from the eq.
X = 1 , Y = 5 OR X = 3, Y = 2
So R can be 2X i.e 2 or 6.
Answer D
Answer: (D) 2
Question: The price of an article has been reduced by 25%. In order to restore the original price the new price must be increased by?
(A) 33 1/3 %
(B) 9 1/11 %
(C) 11 1/9 %
(D) 66 2/3 %
(E) None
Rationale: 100
75
-------
75 ------- 25
100 ------ ? => 33 1/3%
ANSWER:A
Answer: (A) 33 1/3 %
Question: A man sells a horse for Rs.20 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse?
(A) 227
(B) 340
(C) 277
(D) 860
(E) 771
Rationale: CP = SP + 1CP = SP - g
20 + x = 980 - 2x
3x = 960=> x = 320
CP = 320 + 20 = 340
Answer: B
Answer: (B) 340
Question: If x and y are prime numbers, which of the following CAN be the sum of x and y?
(A) 5
(B) 8
(C) 12
(D) 15
(E) 23
Rationale: Answer: A
Answer: (A) 5
Question: Aish started a business investing Rs. 25,000 in 2010, In 2011, he invested an additional amount of Rs. 10,000 and Roshan joined him with an amount of Rs. 35,000. In 2012, Aish invested another additional amount of Rs. 10,000 and Atul joined them with an amount of Rs. 35,000. What will be Roshan’s share in the profit of Rs. 2,10,000 earned at the end of 3 years from the start of the business in 2010?
(A) Rs.45000
(B) Rs.50000
(C) Rs.60000
(D) Rs.70000
(E) None of these
Rationale: Explanation :
Aish : Roshan : Atul
= (25000 x 12 + 35000 x 12 + 45000 x 12) : (35000 x 24) : (35000 x 12)
= 1260000 : 840000 : 420000 = 3 : 2 : 1
Roshan's share = Rs. 210000 x 2/6
= Rs. 70000.
Answer : D
Answer: (D) Rs.70000
Question: Eesha bought 18 sharpeners for Rs.100. She paid 1 rupee more for each white sharpener than for each brown sharpener. What is the price of a white sharpener and how many white sharpener did she buy ?
(A) Rs.6, 19
(B) Rs.6, 10
(C) Rs.6, 16
(D) Rs.6, 11
(E) Rs.6, 12
Rationale: Explanation: Just check the options. If she bought 10 white sharpeners at Rs.6 per piece, She has spent Rs.60 already. And with the remaining Rs.40, she bought 8 brown sharpeners at 40/8 = Rs.5 which is Rs.1 less than White sharpener.
Sol: B
Answer: (B) Rs.6, 10
Question: Ann invested a certain sum of money in a bank that paid simple interest. The amount grew to $240 at the end of 2 years. She waited for another 3 years and got a final amount of $300. What was the principal amount that she invested at the beginning?
(A) $200
(B) $150
(C) $210
(D) $175
(E) Insufficient data
Rationale: Answer
The sum grew to $240 at the end of 2 years.
At the end of another 3 years, the sum grew to $ 300.
i.e. in 3 years, the sum grew by $ 60.
Therefore, each year, it grew by $ 20.
Sum at the end of 2 years = $ 240
Sum grew by $ 20 each year.
Hence, in the first 2 years, sum grew by 2 * 20 = $ 40.
Therefore, sum at the beginning of the period = Sum at the end of 2 years - $40 = $ 240 - $ 40 = $ 200.
choice is (A)
Answer: (A) $200
Question: Tom drives from town A to town B, driving at a constant speed of 60 miles per hour. From town B Tom immediately continues to town C. The distance between A and B is twice the distance between B and C. If the average speed of the whole journey was 36 mph, then what is Tom's speed driving from B to C in miles per hour?
(A) 12
(B) 20
(C) 24
(D) 30
(E) 36
Rationale: Let's assume that it takes 4 hours to go from point A to B.
Then the distance between them becomes 240 which makes distance between B and C 120.
(240+120)/(4+x) gives us the average speed which is 36.
You find x=6. So the question simplifies itself to 120/6=20
Hence the answer is B
Answer: (B) 20
Question: 66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be:
(A) 84
(B) 90
(C) 94
(D) 95
(E) 65
Rationale: Let the length of the wire be h.
RADIUM = 1/2 mm = 1/20 cm then
22/7*1/20*1/20*h = 66
h=(66*20*20*7/22) = 8400 cm = 84m
ANSWER A
Answer: (A) 84
Question: The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 776
(B) 283
(C) 245
(D) 266
(E) 288
Rationale: 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: C
Answer: (C) 245
Question: If x is 20 percent greater than 98, then x =
(A) 68
(B) 70.4
(C) 86
(D) 105.6
(E) 117.6
Rationale: x=98*1.2=117.6
So the answer is E.
Answer: (E) 117.6
Question: Two trains of length 150 m and 250 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 18 kmph and 36 kmph. In how much time will the trains cross each other?
(A) 87/7 sec
(B) 80/7 sec
(C) 100/3 sec
(D) 80/5 sec
(E) 20/7 sec
Rationale: Relative speed = (18 + 36)* 5/18 = 3 * 5 = 15 mps.
The time required = d/s = (100 + 150 + 250)/15
= 500/15 = 100/3 sec.
Answer: C
Answer: (C) 100/3 sec
Question: When 35 per cent of a number is added to another number,the second number increases by its 20 per cent. What is the ratio between the second number and the first number?
(A) 4 : 7
(B) 7 : 4
(C) 8 : 5
(D) Data inadequate
(E) None of these
Rationale: 35% of x + y = 120⁄100y
or 35x+100y/100=120y/100⇒35x=20y
y⁄x = 35⁄20 = 7 : 4
Answer B
Answer: (B) 7 : 4
Question: It is being given that (232 + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?
(A) (216 + 1)
(B) (216 - 1)
(C) (7 x 223)
(D) (296 + 1)
(E) None of these
Rationale: Explanation:
Let 232 = x. Then, (232 + 1) = (x + 1).
Let (x + 1) be completely divisible by the natural number N. Then,
(296 + 1) = [(232)3 + 1] = (x3 + 1) = (x + 1)(x2 - x + 1), which is completely divisible by N, since (x + 1) is divisible by N.
ANSWER IS D
Answer: (D) (296 + 1)
Question: A division of a company consists of seven men and five women. If two of these twelve employees are randomly selected as representatives of the division, what is the probability that both representatives will be female?
(A) 1/6
(B) 2/5
(C) 2/9
(D) 5/12
(E) 5/33
Rationale: First, the denominator. We have twelve different people, and we want a combination of two selected from these twelve. We will use the formula:
nC2 = n(n-1)/2
which, for profound mathematical reasons we need not address here, is also the formula for the sum of the first (n – 1) positive integers. Here
12C2=12(11)/2=6*11=66
That’s the total number of pairs we could pick from the twelve employees. That’s our denominator.
For the numerator, we want every combination of two from the five female employees. That’s
5C2=5(4)/2=5*2=10
That’s the number of pairs of female employees we could pick from the five. That’s our numerator.
probability= 10/66 =5/55
Answer = E
Answer: (E) 5/33
Question: How many pairs of letters are there in the word 'CASTRAPHONE' which have as many letters between them in the word as in the alphabet?
(A) Four
(B) One
(C) Three
(D) Seven
(E) None
Rationale: Looking into the alphabets there are four such pairs namely ON,EH,ST,TO.
ANSWER A
Answer: (A) Four
Question: For arranging a picnic, each student contributed an amount equal to the number of students while the teacher contributed an amount equal to twice the number of students. However, if each student would have contributed an amount equal to twice the number of students and the teacher would have contributed an amount equal to the number of students, they would have generated Rs. 1056 more. Find the number of students in the group?
(A) 54
(B) 56
(C) 33
(D) 18
(E) 19
Rationale: Explanation:
Let the number of students = x. Thus, we get,
[(2x2 + x) – (x2 + 2x)] = 1056
x2 - x - 1056 = 0
Solving the equation, we get, x = 33 or x = - 32.
Since the number of students are to be positive, number of students = x = 33
ANSWER: D
Answer: (D) 18
Question: A room is 5 meters 76 centimeters in length and 4 meters 32 centimeters in Width. Find the least number of square tiles of equal size required to cover the entire floor of the room.
(A) 12
(B) 15
(C) 17
(D) 137
(E) 147
Rationale: Let us calculate both the length and width of the room in centimeters.
Length = 5 meters and 76 centimeters = 576 cm
width = 4 meters and 32 centimeters = 432 cm
As we want the least number of square tiles required, it means the length of each square tile should be as large as possible.Further,the length of each square tile should be a factor of both the length and width of the room.
Hence, the length of each square tile will be equal to the HCF of the length and width of the room = HCF of 576 and 432 = 144
Thus, the number of square tiles required = (576 x 432 ) / (144 x 144) = 4 x 3 = 12
Answer: B
Answer: (B) 15
Question: A can complete a work in 15 days and B can do the same work in 9days. If A after doing 5days, leaves the work, find in how many days B will do the remaining work?
(A) 2days
(B) 4days
(C) 6days
(D) 7days
(E) 10days
Rationale: The required answer = (15-5)*9 / 15 = 40/10 = 6days
Answer is C
Answer: (C) 6days
Question: A Cuban cigar would cost 1 dollar less than 1.5 times a French cigar, had the French cigar cost 0.7 dollar less than it does now. An Arabian cigar costs 50 cents more than 1.5 times the Cuban cigar. The three cigars together cost 74.7 dollars. What is the price of the French cigar?
(A) 16.7$.
(B) 23$.
(C) 25.5$.
(D) 35$.
(E) 37.4$.
Rationale: The three cigars together cost 74.7 dollars. If each cost the same , they would have cost a little less than 25 dollars each.
From the given data we know French cigar < Cuban cigar < Arabic cigar
and each is more expensive 1.5 times. Therefore eliminate options C,D,E straightaway . Since French cigar is at least 1.5 times cheaper we know B cannot be the answer.
Therefore A is the answer
Answer: (A) 16.7$.
Question: (X)+1789+9011-7819=90510. Calculate the value of X
(A) 87501
(B) 87599
(C) 87529
(D) 87520
(E) 87521
Rationale: x+1789+9011-7819=90510
=x+1789+9011=90510+7819
=x+10800=98329
=x=98329-10800
=87529
Answer is C
Answer: (C) 87529
Question: If r is an even integer and q is an odd integer, which of the following must be an odd integer?
(A) r/q
(B) rq
(C) 2r+q
(D) 2(r+q)
(E) 3r/q
Rationale: this is a must question:
A. r/q
can be a non-integer
B.rq
always even
C. 2r+q
2r = even -> even+odd = odd
D. 2(r+q)
always even - r+q = odd *2 -> even
E. 3r/q
might be a non integer.
C
Answer: (C) 2r+q
Question: A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 630 m long?
(A) 22
(B) 89
(C) 277
(D) 278
(E) 87
Rationale: Speed = 240/24 = 10 m/sec.
Required time = (240 + 630)/10 = 87 sec.
Answer: E
Answer: (E) 87
Question: A business executive and his client are charging their dinner tab on the executive's expense account.The company will only allow them to spend a total of 50$ for the meal.Assuming that they will pay 10% in sales tax for the meal and leave a 15% tip,what is the most their food can cost?
(A) 39.52$
(B) 40.63$
(C) 41.63$
(D) 42.15$
(E) 41.15$
Rationale: let x is the cost of the food
1.07x is the gross bill after including sales tax
1.15* 1.10x=50
x=39.52
Hence, the correct option is A
Answer: (A) 39.52$
Question: Meg and Bob are among the 5 participants in a cycling race. If each participant finishes the race and no two participants finish at the same time, in how many different possible orders can the participants finish the race so that Meg finishes ahead of Bob?
(A) 24
(B) 30
(C) 60
(D) 90
(E) 120
Rationale: Let me redeem myself:
JXXXX => Bob can be in any X...Total 4! = 24
XJXXX => Bob can be in the last 3 Xs...Total 3! = 6. However, since the first person can change too and it cannot be Bob, it can only be 3 other people. So Total = 6*3 = 18
XXJBX => 3! = 6 total
XXJXB => 3! = 6 total
So this yields total of 12
XXXJB => 3! = 6
Ans = 24+18+12+6 = 60
answer is C
Answer: (C) 60
Question: In a cricket team, the average of eleven players is 28 years. Out of these, the average ages of three groups of three players each are 31 years, 28 years and 30 years respectively. If in these groups, the captain and the youngest player are not included, and the captain is eleven years older than the youngest player, what is the age of the captain ?
(A) 33 years
(B) 34 years
(C) 35 years
(D) 26 years
(E) 37 years
Rationale: Explanation :
Let the age of youngest player be x.
Then, age of the captain = (x + 11).
=> 3*31 + 3*28 + 3*30 + x + x + 11 = 11*28.
=> 93+84+90+2x+11=308
so 2x = 30
so x = 15.
Age of the captain = (x+11)
= 26 years.
Answer : D
Answer: (D) 26 years