mathewhe/aqua_rat huggingface dataset:
Question: At what time between 4 and 5 o'clock the hands are in opposite direction?
(A) 10 2/11 minutes past 4 o'clock
(B) 3 2/11 minutes past 4 o'clock
(C) 3 5/11 minutes past 4 o'clock
(D) 10 10/11 minutes past 4 o'clock
(E) 12 10/11 minutes past 4 o'clock
Rationale: hands are opposite,angle=180 deg
so,
angle=11/2(min)-30(h)
=> 180=11/2(min)-30(4)
=> 180+120=11/2(min)
=> (300*2)/11=min
=> min=54 6/11min past 4
ANSWER:E
Answer: (E) 12 10/11 minutes past 4 o'clock
Question: A certain game pays players in tokens, each of which is worth either m points or n points, where m and n are different positive integers whose greatest common factor is 1. In terms of m and n, what is the greatest possible sum, in points, that can be paid out with only one unique combination of these tokens? (For example, if m = 2 and n = 3, then a sum of 5 points can be created using only one combination, m + n, which is a unique combination. By contrast, a sum of 11 points can be created by 4m + n or by m + 3n. This solution does not represent a unique combination; two combinations are possible.)
(A) 2mn
(B) 2mn – m – n
(C) 2mn – m – n – 1
(D) mn + m + n – 1
(E) mn – m – n
Rationale: Multiple combinations are created when you can “exchange” a set of m tokens worth n points each for a set of n tokens worth m points each. In the example given in the problem, the first solution uses 4 m’s (worth 8 points total) and one n (worth 3 points) to reach 11 points. The second solution is created when 3 m’s (worth 2 points each, for a total of 6 points) are exchanged for 2 n’s (worth 3 points each, for a total of 6 points), leading to the new solution m + 3n.
The question asks for a sum with a unique solution, or a solution for which such an “exchange” is not possible. What must be true of this kind of solution?
The payout may include no more than (n – 1) m-point tokens. (If there were n of them, they could be exchanged to make a different combination.)
The payout may include no more than (m – 1) n-point tokens. (If there were m of them, they could be exchanged to make a different combination.)
The question asks for the greatest possible such sum, so use the maximum possible number of m and n tokens, as determined above:
(n – 1)(m) + (m – 1)(n)
= mn – m + mn – n
= 2mn – m – n.
Alternatively, try plugging in numbers. For instance, if m = 2 and n = 3, then you’re looking for the greatest possible sum that can be paid with a unique combination of 2- and 3-point tokens. That sum must be one of the answer choices, so check the sums in the answer choices and stop at the highest one with a unique payout combination.
With m = 2 and n = 3, the answer choices are (A) 12 points, (B) 7 points, (C) 6 points, (D) 10 points, (E) 1 point. Try them in decreasing order (because the problem asks for the greatest sum):
(A) A sum of 12 points can be paid out in three ways: six 2-point tokens; three 2-point tokens and two 3-point tokens; and four 3-point tokens. This answer is not correct.
(D) A sum of 10 points can be paid out in two ways: five 2-point tokens, or two 2-point tokens and two 3-point tokens. This answer is not correct.
(B) A sum of 7 points can be paid out only as two 2-point tokens and one 3-point token. This answer is the largest one left with a unique combination, so it is the correct answer.
The correct answer is (B)
Answer: (B) 2mn – m – n
Question: In how many different number of ways 5 men and 4 women can sit on a shopa which can accommodate persons?
(A) 2051
(B) 3024
(C) 2058
(D) 3020
(E) 4200
Rationale: 9p4 =9 x 8 x 7 x 6 = 3024
B)
Answer: (B) 3024
Question: Among the members of the Malmo family, there are three times as many members who do not wear glasses as members who do. Half of the Malmo family members have blue eyes, and 4/5 of the family members who have blue eyes do not wear glasses. What percent of the Malmo family members wear glasses and do not have blue eyes?
(A) 10
(B) 15
(C) 20
(D) 25
(E) 35
Rationale: Number in black are given and in red are calculated.
Now, since x+3x=100, then x=25 and therefore =25−10=15
Answer: B.
Answer: (B) 15
Question: A boy wants to make cuboids of dimension 5m, 6m and 7m from small cubes of .03 m3. Later he realized he can make same cuboids by making it hollow. Then it takes some cubes less. What is the number of the cubes to be removed?
(A) 1000
(B) 2000
(C) 3000
(D) 4000
(E) 5000
Rationale: volume of the small cube = 0.03 m^3
so side of this cube = cubic root of 0.03 m^3 = .312 m
so after removing the outermost layer the dimensions for the inner cuboid will be (5-2*0.312), (6-2*0.312), (7-2*0.312)
so total volume will be (4.376)*(5.376)*(6.376) = 150 m^3
so no of cubes will be 150/0.03 = 5000
so we can remove 5000 inner cubes
ANSWER:E
Answer: (E) 5000
Question: A fish tank contains orange fish and silver fish. After k more orange fish and 2k more silver fish are added, the probability of choosing an orange fish at random is 1313 . What was the probability of choosing a silver fish before any more fish were added?
(A) 1/4
(B) 1/3
(C) 1/2
(D) 2/3
(E) 3/4
Rationale: Equation (1): o+k=1xo+k=1x
Equation (2): s+2k=2xs+2k=2x
Multiplying the first Equation by 2: 2o+2k=2x2o+2k=2x. Let´s call this last equation, Equation (3): 2o+2k=2x2o+2k=2x
We can subtract Eq (3) −− Eq (2): 2o−s=02o−s=0, and then s=2os=2o.
Then, s/s+o=2o/3o=2/3
The correct answer is letter (D).
Answer: (D) 2/3
Question: A can do 1/4th part of the work in 10 days, B can do 40% of the work in 40 days and C can do 1/3rd of the work in 13 days. Who will complete the work first?
(A) A
(B) B
(C) C
(D) A and C both
(E) None of these
Rationale: Explanation:
The whole work is done by A in 4 × 10 = 40 days
B can do the whole work in 40/40 × 100 days = 100 days
C can do the whole work in 3 × 13 = 39 days.
Therefore, the 1st person to complete the work is C.
Answer: Option C
Answer: (C) C
Question: Find the length of the wire required to go 15 times round a square field containing 69696 m^2.
(A) 1250
(B) 2489
(C) 6398
(D) 15840
(E) 2487
Rationale: Explanation:
a2 = 69696 => a = 264
4a = 1056
1056 * 15 = 15840
Answer: D
Answer: (D) 15840
Question: Roses can be purchased individually for $5.30, one dozen for $36, or two dozen for $50. What is the greatest number of roses that can be purchased for $680?
(A)  156
(B)  162
(C)  317
(D)  324
(E)  325
Rationale: Buy as many $50 deals as possible. We can by 650/50=13 two dozen roses, thus total of 13*24 = 312 roses.
We are left with 680 - 650 = $30. We can buy 30/5.3 = ~5 roses for that amount.
Total = 312 + 5 = 317.
Answer: C.
Answer: (C)  317
Question: If x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year, the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $65. If $2,000 is the total amount invested, how much is invested at 8 percent?
(A) $550
(B) $650
(C) $750
(D) $850
(E) $950
Rationale: 0.1x = 0.08(2000-x)+65
0.18x = 225
x = 1250
Then the amount invested at 8% is $2000 - $1250 = $750
The answer is C.
Answer: (C) $750
Question: 62 small identical cubes are used to form a large cube. How many more cubes are needed to add one top layer of small cube all over the surface of the large cube ?
(A) 64
(B) 128
(C) 152
(D) 154
(E) 256
Rationale: 62 small cube will make a large cube with 4 cubes in each line i.e.
Adding one layer will require one cube at each end and hence new cube will have 6 cubes in each line.
Total number of small cubes in new cube = 6^3 = 216
Extra cube required = 216 - 62 = 154
Hence, D is the answer.
Answer: (D) 154
Question: If a book is sold at 9% profit instead of 9% loss, it would have brought Rs 9 more. Find out the cost price of the book
(A) 75
(B) 72
(C) 50
(D) 70
(E) 80
Rationale: Let C.P. of the book be Rs. ’X’
Given, 1.09 X - 0.91X = 9
=> 0.18 X = 9 = 9/0.18 = Rs 50
ANSWER:C
Answer: (C) 50
Question: Divide $600 among C,D in the ratio 9:6. How many $ that D get?
(A) $44
(B) $40
(C) $36
(D) $32
(E) $28
Rationale: Sum of ratio terms = 9+6 = 15
D = 600*6/15 = $40
Answer is B
Answer: (B) $40
Question: What are the number of ways to select 3 men and 2 women such that one man and one woman are always selected?
(A) 20
(B) 30
(C) 40
(D) 45
(E) 50
Rationale: The number of ways to select three men and two women such that one man and one woman are always selected = Number of ways selecting two men and one woman from men and five women
= ⁴C₂ * ⁵C₁ = (4 * 3)/(2 * 1) * 5
= 30 ways.
B
Answer: (B) 30
Question: Set A consists of all the prime numbers between 10 and 25. What is the range of set A?
(A) 12
(B) 13
(C) 16.6
(D) 17
(E) 23
Rationale: The range of a set of data is the difference between the highest and lowest values in the set
In this set,
Highest number = 23
Lowest number = 11
Range = Highest - Lowest = 23 - 11 = 12
Option A
Answer: (A) 12
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. 6 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?
(A) s.4538
(B) s.4518
(C) s.4518
(D) s.4530
(E) s.5436
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 * 6 = Rs.5436
Answer: E
Answer: (E) s.5436
Question: In a race of 300 m A beats B by 15 m and C by 9 m. In a race of 450 m C will beat B by
(A) 381 m
(B) 429 m
(C) 441 m
(D) 439 m
(E) 449 m
Rationale: A:B=300:285 (Bcoz A beats b by 15 m)
B:C=300:291 (Bcoz A beats C by 9 m)
C:B=291:285 (It means C beats by B 6 m in race of 291m)
then C beats by B in race of 450 m = (6/291)*450=9m
so, 450-9=441m
ANSWER:C
Answer: (C) 441 m
Question: The average of 10numbers is 60. Out of 10numbers the average of first 6no. is 68, and last 6numbers is 75 then find 7th number?
(A) A)78
(B) B)65
(C) C)258
(D) D)62
(E) E)48
Rationale: 7th number = sum of 1st 6no.s + sum of last 6no.s - sum of 11no.s
answer = 6*68+6*75-10*60 = 258
Answer is C
Answer: (C) C)258
Question: A painter intends to mixed two jars of paint to create a new color. He chooses one paint jar randomly from a display containing 2 red and 2 blue samples, and a second jar is chosen at random from a different display containing 4 red and 2 blue samples. If he plans on mixing the two chosen jars together, what is the probability that when mixed together, the result will be purple paint? (The color purple is created with 1 part red and 1 part blue.)
(A) 1/5
(B) 1/2
(C) 2/3
(D) 4/5
(E) 6/5
Rationale: Painter has two buckets he has to randomly pick from 2 different lists ... Let these Lists be A and B ... He has to choose the first bucket from List A , and the second bucket from List B
FOR THE FIRST BUCKET ...
Red color - 2
Blue color - 2
FOR THE SECOND BUCKET
Red color - 3
Blue color -2
In order to get Purple he has to mix red with blue .. Both the LISTS contain either blue or red , therefore we have two scenarios :
Scenario I - He picks Red color from List A and Blue color from List B
Scenario II - He picks Blue color from List A and Red color from List B
Scenario I - Odds for red color from List A are 1/2 .. and for Blue color from List B are 2 /5 .. Multiplying them (because we have to find the odds that both colors are selected from their respective lists together (this is a AND not an OR problem) we get 1/5
Scenario II - Odds for blue color from List A are 1/2 , and for Red color from List B are 3/5 ... Multiplying them we get 3/10 ...
Both the scenarios are equally possible therefore we must ADD the two (not multiply ) because both of them do not have to hold true together (have to independently) for our desired result to be achieved ...
We get 1/5 + 3/10 = 4/5(D)
Answer: (D) 4/5
Question: A ship 450 m long is running at a speed of 24 km/hr. In what time will it pass a bridge 900 m long?
(A) 202.5sec
(B) 205.5 sec
(C) 200 sec
(D) 1350 sec
(E) 900sec
Rationale: total length= 450+900=1350
speed=24 km/h=(24*5)/18= 20/3 m/s
time=(1350*3)/20=202.5 sec.
ANSWER:A
Answer: (A) 202.5sec
Question: At 3:00 pm, a car has driven 30 miles east. It will continue to drive east at 0.5 minutes per mile and then turn around and drive at 0.5 minutes per mile back to its original starting point. How far can it drive before turning around in order to arrive back to its original starting point by 3:40 pm?
(A) a) 10
(B) b) 11
(C) c) 12
(D) d) 13
(E) e) 25
Rationale: 0.8 minutes --> 1 mile
1 minute --> 1/0.5 = 10/5 =2 miles/minute
Distance covered in 40 minutes = 2* 40 =80 miles
Distance covered in the current direction = Distance covered from the opposite direction (since car returns back to starting point)
Let x be the miles driven before turning
30 + x = 80 - x
2x = 50
x = 25
Answer: E
Answer: (E) e) 25
Question: which one is odd?
4377
3954
9860
8454
9831
(A) 4377
(B) 3954
(C) 9860
(D) 8454
(E) None
Rationale: Correct Answer : C
sum of digit of all other number is 21, but sum of digit of 9860 is 23
Answer: (C) 9860
Question: Evaluate 2.5 / .0005
(A) 5000
(B) 500
(C) 50000
(D) 50
(E) 0.5
Rationale: Explanation:
2.5 * 10000 / 5 = 25000/5 = 5000
Option A
Answer: (A) 5000
Question: Rodrick mixes a martini that has a volume of 'n' ounces having 40% Vermouth and 60% Gin by volume. He wants to change it so that the martini is 25% Vermouth by volume. How many ounces of Gin must he add?
(A) n/6
(B) n/3
(C) 3n/5
(D) 5n/6
(E) 8n/5
Rationale: Note that after we add pure Gin, the volume of Vermouth will remain the same. Based on this set the equation:
0.4n=0.25(n+g) --> g=3n/5
Answer: C.
Answer: (C) 3n/5
Question: A certain city with a population of 192,000 is to be divided into 11 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district What is the minimum possible population that the least populated district could have ?
(A) a) 10,700
(B) b) 16,000
(C) c) 10,900
(D) d) 11,000
(E) e) 11,100
Rationale: Let x = number of people in smallest district
x*1.1 = number of people in largest district
x will be minimised when the number of people in largest district is maximised
10*x*1.1 = 11x = total number of people in other districts
So we have 11x + x = 192k
x = 16,000
Answer : B
Answer: (B) b) 16,000
Question: A certain bus driver is paid a regular rate of $16 per hour for any number of hours that does not exceed 40 hours per week. For any overtime hours worked in excess of 40 hours per week, the bus driver is paid a rate that is 75% higher than his regular rate. If last week the bus driver earned $1116 in total compensation, how many total hours did he work that week?
(A) 36
(B) 57
(C) 44
(D) 48
(E) 52
Rationale: For 40 hrs = 40*16=640
Excess = 1116-640=476
For extra hours =.75(16)=12+16=28
Number of extra hrs =476/28=17
Total hrs =40+17=57
Answer B 57
Answer: (B) 57
Question: A dog chases a cat 3 hours after the cat runs. dog takes 6 hours to reach the cat. If the average speed of the dog is 72 kmph, what s the average speed of the cat?
(A) 48kmph
(B) 47kmph
(C) 46kmph
(D) 38kmph
(E) 37kmph
Rationale: cat take 9 hours and dog take 6 hours...then Distance chased by them is 72*6.so speed of cat is (72*6)/9=48kmph.
ANSWER IS A
Answer: (A) 48kmph
Question: In one hour, a boat goes 11 km along the stream and 5 km against the stream. The speed of the boat in still water in ( km/hr) is
(A) 3
(B) 5
(C) 8
(D) 9
(E) 7
Rationale: Solution
Speed in still water	= 1/2(11+5) km/hr
= 8 km/hr.
Answer C
Answer: (C) 8
Question: The H.C.F. of two numbers is 25 and the other two factors of their L.C.M. are 14 and 16. The larger of the two numbers is
(A) 276
(B) 299
(C) 312
(D) 400
(E) None
Rationale: Solution
Clearly, the numbers are (25 x 14) and (25 x 16).
Larger number = (25 x 16)	= 400.
Answer D
Answer: (D) 400
Question: If (2 to the x) - (2 to the (x-2)) = 3 (2 to the 12), what is the value of x?
(A) 9
(B) 11
(C) 13
(D) 15
(E) 14
Rationale: I am guessing the question is:
(2 to the power x) - (2 to the power (x-2)) = 3 (2 to the power 12)
2^x - 2^(x-2) = 3. 2^12
Hence x = 14.
Answer is E
Answer: (E) 14
Question: Evaluate:57- 12*3*2 =?
(A) 42
(B) 49
(C) 62
(D) 72
(E) 82
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
57 - 12*3*2 = 57- 8 = 49
correct answer B
Answer: (B) 49
Question: The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 6 units?
(A) 140
(B) 84
(C) 88
(D) 72
(E) 12
Rationale: Given that the area of the square = 1225 sq.units
=> Side of square = √1225 = 35 units
The radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35 = 14 units
Given that breadth = 6 units
Area of the rectangle = lb = 14 * 6 = 84 sq.units
Answer: B
Answer: (B) 84
Question: In a certain math department, students are required to enroll in either Calculus or Trigonometry, each of which is offered in beginner and advanced courses. The number of students enrolled in Trigonometry is 50% greater than the number of students enrolled in Calculus, and 70% of Calculus students are enrolled in the beginner course. If 4/5 of students are in the beginner courses, and one student is selected at random, what is the probability that a beginner Trigonometry student is selected?
(A) 40%
(B) 44%
(C) 48%
(D) 52%
(E) 56%
Rationale: Let x be the number of students in calculus.
Then the number of students in trigonometry is 1.5x
The number of students on beginner calculus is 0.7x
The number of students in beginner trigonometry is 4/5*(2.5x) - 0.7x = 1.3x
The percentage in beginner trigonometry is 1.3x / 2.5x = 52%
The answer is D.
Answer: (D) 52%
Question: The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 11 years, son's age will be:
(A) 12 years
(B) 14 years
(C) 18 years
(D) 20 years
(E) 25 years
Rationale: Explanation:
Let the present ages of son and father be x and (60 -x) years respectively.
Then, (60 - x) - 6 = 5(x - 6)
54 - x = 5x - 30
6x = 84
x = 14.
Son's age after 11 years = (x+ 11) = 25 years..
Answer: E
Answer: (E) 25 years
Question: In how many ways 5 Indians and 2 Englishmen can be seated in a row so that they are alternate?
(A) 240
(B) 96
(C) 144
(D) 202
(E) 256
Rationale: number of ways = 5!*2! = 240
Answer is A
Answer: (A) 240
Question: f a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance travelled by him is:
(A) 5 km
(B) 50 km
(C) 10 km
(D) 25 km
(E) 30 km
Rationale: Explanation:
Let the actual distance travelled be x km.
Then, x/10=x+20/14
14x = 10x + 200
4x = 200
x = 50 km.
ANSWER:B
Answer: (B) 50 km
Question: Mangala completes a piece of work in 10 days, Raju completes the same work in 50 days. If both of them work together, then the number of days required to complete the work is?
(A) 8 days
(B) 10 days
(C) 12 days
(D) 50/6 days
(E) 16 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 10 Ã— 50/60 = 50/6 days
D)
Answer: (D) 50/6 days
Question: 9 partners bought a restaurant for 1 million dollars. If they want to pay the same amount and none of them have bills smaller than $1, how much money would they have to pay?
(A) $2,000,001
(B) $2,000,003
(C) $2,000,005
(D) $2,000,006
(E) $2,000,008
Rationale: In order to divide the sum in 9 parts, the amount must be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 1,000,000 = 1 and 9 is divisible by 9.
Hence, we need to add 8 to this number for it to be divisible by 9
Correct Option: E
Answer: (E) $2,000,008
Question: If x is less than y by 40% then y exceed x by:
(A) 33.33%
(B) 25%
(C) 75%
(D) 66.66%
(E) None of these
Rationale: Using formula (x/(100-x)*100) where x is Percentage decrease (here it is 40%)
=> 40/(100-40)*100
=66.66%
ANSWER:D
Answer: (D) 66.66%
Question: A triangle has sides 10, 17, and 21. A square is inscribed in the triangle. One side of the square lies on the longest side of the triangle. The other two vertices of the square touch the two shorter sides of the triangle. What is the length of the side of the square?
(A) 148/29
(B) 168/29
(C) 168/26
(D) 158/29
(E) 198/29
Rationale: By Heron's Formula, the area, A, of a triangle with sides a, b, c is given by A = square root[s(s − a)(s − b)(s − c)], where s = ½(a + b + c) is the semi-perimeter of the triangle.
Then s = ½(10 + 17 + 21) = 24, and A = 84.
A square inscribed in a 10 by 17 by 21 triangle, with perpendicular dropped onto the side of length 21.
Now drop a perpendicular of length h onto the side of length 21.
We also have A = ½ × base × perpendicular height.
Hence A = 21h/2 = 84, from which h = 8.
Notice that the triangle above the square is similar to the whole triangle. (This follows because its base, the top of the square, is parallel to the base of the whole triangle.)
Let the square have side of length d.
Considering the ratio of altitude to base in each triangle, we have 8/21 = (8 − d)/d = 8/d − 1.
Therefore the length of the side of the square is 168/29.
ANSWER:B
Answer: (B) 168/29
Question: A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length?
(A) 66
(B) 11
(C) 40
(D) 21
(E) 23
Rationale: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (2/25) = 40 seconds.Answer: C
Answer: (C) 40
Question: When E is divided by 5, the remainder is 3. When y is divided by 5, the remainder is 4. What is the remainder when E + y is divided by 5?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: In my view the answer should be C
E/5 has Remainder=3 -> E = 5 x Q + 3
Y/5 has a Remainder=4 -> Y = 5 x Q + 3
Combining both
((5 x Q1 + 3) + (5 x Q2 + 3))/5 =
5(Q1+Q2)/5 + 7/5 =
Q1+Q2 + 7/5
7/5 = 1+ 2/5 => Remainder 2
Answer C
Answer: (C) 2
Question: David spends $350 buying his favorite dolls. If he buys only small LemonHead dolls, which are $2 cheaper than the large LemonHead dolls, he could buy 20 more dolls than if he were to buy only large LemonHead dolls. How much does a large LemonHead doll cost?
(A) $5
(B) $7
(C) $6
(D) $8
(E) $9
Rationale: If large doll costs $5, then he can buy 350/5 = 70 large dolls and 350/3 =116 small dolls. Difference is more than 20. Discard.
If large doll costs $7, then he can buy 350/7 = 50 large dolls and 350/5 =70 small dolls.
Difference is 20, which is we wanted.
Answer B.
Answer: (B) $7
Question: There are three secretaries who work for four departments. If each of the four departments have one report to be typed out, and the reports are randomly assigned to a secretary, what is the probability Z that all three secretary are assigned at least one report?
(A) 8/9
(B) 64/81
(C) 4/9
(D) 16/81
(E) 5/9
Rationale: For each report there are three possible outcomes: Secretary A, Secretary B, Secretary C
Total outcome: 3^3=27
Total outcome that three secretary are assigned at least one report: P(3,3)=3!=6
Probability Z= 6/27=2/9=C
Answer: (C) 4/9
Question: A certain hospital has a policy that for every 50 patients there should be 2 doctors. If the number of patients visiting the hospital every day is 400, how many doctors are there in the hospital?
(A) 4
(B) 16
(C) 5
(D) 14
(E) 11
Rationale: 2/50=x/400
x=16
Answer is B
Answer: (B) 16