RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: The average wages of a worker during a fortnight comprising 15 consecutive working days was $90 per day. During the first 7 days, his average wages was $87 per day and the average wages during the last 7 days was $95 per day. What was his wage on the 8th day?
A.$76
B.$90
C.$92
D.$97
Answer: A.$76
Explanation: Average daily wage of a worker for 15 consecutive working days = 90$
During the first 7 days , the daily average daily wage = 87$
During the last 7 days , the daily average daily wage = 95$
Wage on 8th day = 90*15 -( 87*7 + 95 *7)
= 1350 - (609 + 665)
=1350 - 1274
= 76
Answer A
Question: Walking 6/7th of his usual speed, a man is 12 minutes too late. The usual time taken by him to cover that distance is :
A.1 hr 20 min
B.1 hr 11 min
C.1 hr 12 min
D.1 hr 30 min
Answer: C.1 hr 12 min
Explanation: Explanation :
New speed = 6/7 of usual speed.
New time = 7/6 of usual time
=> [7/6 of usual time] - (usual time) = 1/5 hr.
=> 1/6 of usual time = 1/5 hr
=> usual time = 6/5 hr = 1 hr 12 min.
Answer : C
Question: U is a set containing 8 different positive odd numbers. V is a set containing 7 different numbers, all of which are members of U. Which of the following statements CANNOT be true?
A.The range of V is even.
B.The mean of U is even.
C.The mean of V is even.
D.The range of U is equal to the range of V.
Answer: C.The mean of V is even.
Explanation: Given: U is a set containing 8 different positive odd numbers
Easily inferred: V is a set containing 7 differentoddnumbers
(A) The range of V is even. - Always even, since it is a difference of two odd numbers
(B) The mean of U is even. - can be. suppose 8 numbers consist of 4 pairs of (16n-1,16n+1) for different values of n. Adding these will give a multiple of 16, which when divided by 8 (to arrive at mean), will give an even number
(C) The mean of V is even. - Cannot be. Mean = (sum of 7 odd numbers)/7 = Odd number/odd number thus cannot be even.
(D) The range of U is equal to the range of V.
(E) The median of V is equal to the mean of V
Option C.
Question: Tanks A and B are each in the shape of a right circular cylinder. The interior of tank A has a height of 10 meters and a circumference of 7 meters, and the interior of tank B has a height of 7 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B?
A.70%
B.80%
C.100%
D.120%
Answer: A.70%
Explanation: The radius of tank A is 7/(2*pi).
The capacity of tank A is 10*pi*49 / (4*pi^2) = 245 / (2*pi)
The radius of tank B is 10 / (2*pi).
The capacity of tank B is 7*pi*100 / (4*pi^2) = 350 / (2*pi)
Tank A / Tank B = 245/350 = 7/10 = 70%
The answer is A.
Question: A circular jogging track forms the edge of a circular lake that has a diameter of 2 miles. Johanna walked once around the track at the average speed of 4 miles per hour. If t represents the number of hours it took Johanna to walk completely around the lake, which of the following is a correct statement?
A.0.5< t < 0.75
B.1.75< t < 2.0
C.1 < t < 2
D.2.5 < t < 3.0
Answer: C.1 < t < 2
Explanation: D=2, and R=1
circumference thus is 2pi miles
we know that she walked 4mph
knowing the formula rt=D, we can deduce that t= D/r
D is 2pi miles and r is 4mph
t = 2pi/4
pi can be rewritten as 22/7
2*22/7 = 44/7 and multiply this by 1/4 = 44/28. This is greater than 1, but less than 2, therefore, 1<t<2. Answer choice C.
Question: How much interest can a person get on Rs. 8200 at 10.5% p.a. simple interest for a period of six years and six months?
A.5596.5
B.5596.55
C.5596.54
D.3587.51
Answer: A.5596.5
Explanation: I = (8200 * 6.5 * 10.5)/100
= (8200 * 13 * 21)/(100 * 2 * 2)
= Rs. 5596.5
Answer: A
Question: Two brother X and Y appeared for an exam. The probability of selection of X is 1/5 and that of B is 2/7. Find the probability that both of them are selected.
A.2/35
B.2/30
C.2/63
D.2/29
Answer: A.2/35
Explanation: Explanation:
Let A be the event that X is selected and B is the event that Y is selected.
P(A) = 1/5, P(B) = 2/7.
Let C be the event that both are selected.
P(C) = P(A) Ã— P(B) as A and B are independent events:
= (1/5) Ã— (2/7) = 2/35
Answer: A) 2/35
Question: Divide Rs. 1500 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?
A.337
B.299
C.375
D.662
Answer: C.375
Explanation: A+B+C = 1500
A = 1/3(B+C); B = 2/3(A+C)
A/(B+C) = 1/3
A = 1/4 * 1500 => 375
Answer: C
Question: There is a 4 digit no. in which 3rd digit is twice of first one. Second digit is the sum of first and third. Fourth digit is twice of third. What is the no?
A.1224
B.1324
C.1444
D.1524
Answer: B.1324
Explanation: Let the 4-digit no. be "abcd"
c = 2*a
b=a+c
d = 2*c => d=4a
abcd => (a)(a+c)(2a)(4a)
Possible values of a ll be 1 nd 2... Bcozzz a>2 implies d>10....Digits should ranges between 0 nd 9...
If a=1, then c=2,d=4, b=3... The no. is 1324
If a=2, then c=4,d=8, b=6... The no. is 2648
Ans : 1324 (or) 2648
ANSWER:B
Question: Find the circumference and area of radius 11 cm.
A.124 cm²
B.144 cm²
C.380 cm²
D.284 cm²
Answer: C.380 cm²
Explanation: Area of circle = πr²
= 22/7 ×11 ×11 cm²
= 154 cm²
ANSWER:C
Question: A student gets 55% in one subject, 65% in the other. To get an overall of 55% how much should get in third subject.
A.75%
B.25%
C.45%
D.55%
Answer: C.45%
Explanation: Let the 3rd subject % = x
55+65+x = 3*55
120+x =165
x = 165-120=45
Answer :C
Question: A train 385 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
A.5
B.21
C.7
D.8
Answer: B.21
Explanation: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr
[66 * 5/18] m/sec = [55/3] m/sec.
Time taken to pass the man = [385 * 3/55] sec = 21 sec
Answer: Option B
Question: A tap can fill a tank in 6 hours. After half the tank is filled then 3 more similar taps are opened. What will be total time taken to fill the tank completely.
A.2 hours 30 mins
B.2 hours 45 mins
C.3 hours 30 mins
D.3 hours 45 mins
Answer: D.3 hours 45 mins
Explanation: Explanation:
Half tank will be filled in 3 hours
Lets calculate remaining half,
Part filled by the four taps in 1 hour = 4*(1/6) = 2/3
Remaining part after 1/2 filled = 1-1/2 = 1/2
2/3:1/2::1:X
=>X=(1/2∗1∗32)
=>X=3/4hrs=45 mins
Total time = 3 hours + 45 mins = 3 hours 45 mins
Option D
Question: On a map, 1 centimeter represents 19 kilometers. Two cities 627 kilometers apart would be separated on the map by how many centimeters?
A.15
B.27
C.49
D.33
Answer: D.33
Explanation: X=627/19= 33
Answer: D
Question: If pq = p^6 + q^2 – 2pq, for what value of q is pq equal to p^6 for all values of p?
A.0
B.-1
C.-2
D.1
Answer: A.0
Explanation: p6 + q2 â€“ 2pq = p6
=> q2 - 2pq = 0
=> q (q - 2p) = 0
=> q = 0 or q = 2p
im not following the logic you used here.. how did you replace pq with 0 could someone help explain it in MORE DETAI
A
Question: A 250 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train?
A.250
B.245
C.240
D.235
Answer: A.250
Explanation: Relative speed = 120 + 80 = 200 km/hr.
= 200 * 5/18 = 500/9 m/sec.
Let the length of the other train be x m.
Then, (x + 250)/9 = 500/9 => x = 250.
Answer: Option A
Question: The length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec is?
A.288
B.269
C.245
D.888
Answer: C.245
Explanation: Speed = 45 * 5/18 = 25/2 m/sec.
Time = 30 sec
Let the length of bridge be x meters.
Then, (130 + x)/30 = 25/2
x = 245 m.
Answer: C
Question: The ratio of the earnings of P and Q is 9:10. If the earnings of P increases by one-fourth and the earnings of Q decreases by one-fourth, then find the new ratio of their earnings?
A.2/3
B.3/2
C.4/5
D.5/8
Answer: B.3/2
Explanation: Let the earnings of P and Q be 9x and 10x respectively.
New ratio = [9x + 1/4 (9x)]/[10x - 1/4 (10x)]
=> 9*(1 + 1/4)/10*(1 - 1/4)
=> 9/10 * (5/4)/(3/4) = 3/2
Answer:B
Question: The average of first ten prime numbers which are odd is?
A.22.2
B.22.1
C.15.3
D.15.8
Answer: D.15.8
Explanation: Explanation:
Sum of first 10 prime no. which are odd = 158
Average = 158/10 = 15.8
Answer:D
Question: If it takes a tub 6 minutes to drain 5/7 of its content, how much more time will it take for the tub to be empty?
A.48 seconds
B.1 minute, 12 seconds
C.1 minute, 50 seconds
D.2 minutes, 24 seconds
Answer: D.2 minutes, 24 seconds
Explanation: If 5/7 of tub's content is drained 2/7 th of tub still needs to be drained.
If it takes 6 minutes to drain 5/7 th of tub it takes 6*(7/5) minutes to drain the entire tub and 6*(7/5)*(2/7) min to drain 2/7 th of the tub which is 2.4 minutes or 12/5 minutes or 2 minute 24 seconds
So answer is D
Question: A qualified worker digs a well in 6 hours. He invites 2 apprentices, both capable of working 3/4 as fast and 2 trainees both working 1/5 as fast as he. If the five-person team digs the same well, how much time does the team need to finish the job?
A.1:24
B.1:34
C.1:44
D.1:54
Answer: D.1:54
Explanation: and answer is correct as you have calculated : 100/64 hrs that is 1.82 hrs - 1 hr and 54 minutes, so 1:54, hence, D.
Question: When 15% is lost in grinding wheat, a country can export 30 lakh tons of wheat. On the other hand, if 10% is lost in grinding, it can export 40 lakh tons of wheat. The production of wheat in the country is
A.20 lakh tons
B.80 lakh tons
C.200 lakh tons
D.800 lakh tons
Answer: C.200 lakh tons
Explanation: Sol.
Let the production be x lakh tons.
Then, 15% of x - 10% of x = (40 - 30) lakh tons
⇔ 5% of x = 10 lakh tons
⇔ x = (10 x 100 / 5) = 200 lakh tons.
Answer C
Question: There are 27 different three-digit integers that can be formed using only the digits 1, 2 and 4. If all 27 of the integers were listed, what would their sum be?
A.6693
B.6793
C.6893
D.6993
Answer: D.6993
Explanation: There must be nine 1's in the hundreds place, nine 1's in the tens place, and nine 1's in the units place. This is also true for the 2's and 4's. Then the sum is:
9(111+222+444)=9*(777)=6993.
The answer is D.
Question: What is the probability of rolling tow six-sided dice, and getting a different number on each die?
A.1/12
B.5/6
C.4/9
D.5/9
Answer: B.5/6
Explanation: MAGOOSHOFFICIAL SOLUTION
For the first die, we can roll any one of six numbers. For the second die, we can roll any number save for the number we rolled on the first die, giving us 5 possibilities. For the third die, we can roll four different numbers (we can’t roll the number we rolled on the first or second die.
6 x 5 = 30 possibilities out of 216 total possibilities. (For total possibilities we get 6 x 6 = 36).
30/36 = 5/6
Answer:B.
Question: 0, 5, 15, 30, 50, 75, 105, 140, ?What number should replace the question mark?
A.180
B.185
C.190
D.175
Answer: A.180
Explanation: A 180add 5,10,15,20,25.
Question: In May Mrs Lee's earnings were 60 percent of the Lee family's total income. In June Mrs Lee earned 40 percent more than in May. If the rest of the family's income was the same both months, then, in June, Mrs Lee's earnings were approximately what percent of the Lee family's total income ?
A.64%
B.68%
C.72%
D.76%
Answer: B.68%
Explanation: Let in May Lee family's total income =100
in May Mrs Lee's income =60
in May rest of the family's income = 40
In june Mrs Lees income = 60*140/100 = 84
In june Total income = 84+ 40 = 124
% of Mrs Lee's income = 84/124 =67.74
(B)
Question: Find the odd man out: 111, 133, 143, 155, 188, 200.
A.111
B.143
C.200
D.All of these.
Answer: B.143
Explanation: In each of the numbers the product of the first and the third digit is the middle one except 143.
1*1=1
1*3=3
1*5=5
1*8=8
2*0=0
ANSWER: B
Question: A construction company wants to number new houses using digit plates only. If the company puts an order for 1212 plates, how many houses are to be given numbers? (The numbers of houses are consecutive and the number of the first house is 1).
A.260
B.440
C.556
D.792
Answer: B.440
Explanation: Run the numbers for houses. For the first 9 houses we need 9 signs.
For the next 90 we need 2 signs each or 180.
For the next 900 houses we need 3 signs each.
If we assume 300 homes, we will need 189 signs for the first 99 homes and then 603 signs for the 201 homes. So, we will use 792 signs for the first 300 homes and will have 420 signs remaining, which is enough for 42034203 or another 140 homes.
The total number of homes is 440
Answer: B
Question: If 20% of a = b, then b% of 20 is the same as
A.2% of a
B.3% of a
C.4% of a
D.5% of a
Answer: C.4% of a
Explanation: 20% of a = b
=> b = 20/100a
b% of 20 = (b/100)20 = [(20/100a)/100]20
= (20 × 20 × a)/(100 × 100)
= 4a/100 = 4% of a
C)
Question: Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is
A.60 gallons
B.80 gallons
C.120 gallons
D.160 gallons
Answer: C.120 gallons
Explanation: Solution
Work done by the waste pipe in 1 minute
=1/15-(1/20+1/24)
= (1/15-11/20)
= - 1/40	[ - ve sigh means emptying]
Volume of 1/40 part	= 3 gallons.
Volume of Whole	= (3×40)
=120 gallons.
Answer C
Question: The price of commodity X increases by 45 cents every year, while the price of commodity Y increases by 20 cents every year. In 2001, the price of commodity X was $5.20 and the price of commodity Y was $7.30. In which year will the price of commodity X be 90 cents more than the price of commodity Y?
A.2010
B.2011
C.2012
D.2013
Answer: D.2013
Explanation: The price of commodity X increases 25 cents each year relative to commodity Y.
The price difference is $2.10 and commodity X needs to be 90 cents more than commodity Y.
$3.00 / 25 cents = 12 years
The answer is 2001 + 12 years = 2013.
The answer is D.
Question: An investment yields an interest payment of $216 each month. If the simple annual interest rate is 9%, what is the amount of the investment?
A.$28,300
B.$30,400
C.$28,800
D.$32,500
Answer: C.$28,800
Explanation: Let the principal amount = P
Simple annual interest = 9%
Simple monthly interest = (9/12) = (3/4)%
(3/4)*(P/100) = 216
=>P = (216 *4 * 10^2 )/3
= 72*4*10^2
= 288 * 10^2= 28800
Answer C
Question: A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price?
A.82%
B.52%
C.12%
D.19%
Answer: C.12%
Explanation: Original price = 100
CP = 80
S = 80*(140/100) = 112
100 - 112 = 12%
Answer:C
Question: A river 8m deep and 25 m wide is flowing at the rate of 8 kmph the amount of water that runs into the sea per minute is?
A.26666
B.26166
C.29666
D.22666
Answer: A.26666
Explanation: Rate of water flow-8kmph--8000/60--133.33 m/min
depth of river--8m
width of river--25m
vol of water per min--133.33 *8*25---26666
Answer A
Question: In January of 2016, there were 100 cats and 125 dogs in a town. In January of 2017, there were 115 cats and 150 dogs. By approximately what percent did the ratio of cats to dog decrease from the 2016 to 2017.
A.12.9%
B.11.0%
C.15%
D.18%
Answer: A.12.9%
Explanation: 2016: cats/dogs = 100/125 =660/750
2017: cats/dogs = 115/150 =575/750
ASIDE: It's useful to write both ratios with the same denominator. This allows us to IGNORE the denominator and focus solely on the numerators.
So, our ratio went from 660/750 to 575/750
Ignoring the denominators, we went from 660 to 575
The percent change = 100(difference in values)/(original value)
= (100)(660-575)/660
= (100)(85)/660)
≈ 12.878...
Answer: A
Question: In a rectangular coordinate system, what is the area of a quadrilateral whose vertices have the coordinates (4,-3), (4, 7), (12, 2), (12,-7)?
A.64
B.68
C.72
D.76
Answer: D.76
Explanation: By graphing the points, we can see that this figure is a trapezoid. A trapezoid is any quadrilateral that has one set of parallel sides, and the formula for the area of a trapezoid is:
Area = (1/2) × (Base 1 + Base 2) × (Height), where the bases are the parallel sides.
We can now determine the area of the quadrilateral:
Area = 1/2 × (10 + 9) × 8 = 76.
The answer is D.
Question: Find the H.C.M of the fractions 1/3, 3/5 and 7/12
A.1/30
B.1/60
C.1/15
D.1/20
Answer: B.1/60
Explanation: Explanation:
H.CF = H.C.F of numarator/L.C.M of denominator
H.C.F = H.C.F of 1, 3, 7 / L.C.M of 3, 5, 12
H.C.F = 1/60
Answer: Option B
Question: A school has 4 section of Chemistry in Class X having 70, 35, 45 and 42 students. The mean marks obtained in Chemistry test are 50, 60, 55 and 45 respectively for the 4 sections. Determine the overall average of marks per student.
A.50.9
B.52.9
C.51.9
D.53.25
Answer: C.51.9
Explanation: Required average marks
= 70Ã—50+35Ã—60+45Ã—55+42Ã—45/70+35+45+42
= 3500+2100+2475+1890/192
= 9965â„192 = 51.90
Answer C
Question: A, B and C can do a work in 90, 30 and 45 days respectively. If they work together, in how many days will they complete the work?
A.15
B.66
C.77
D.88
Answer: A.15
Explanation: One days's work of A, B and C = 1/90 + 1/30 + 1/45
= (1 + 3 + 2)/90 = 1/15
A, B and C together can do the work in 15 days.
Answer:A
Question: If shares of two persons in profits are Rs.800 and Rs.600 then ratio of their capitals is
A.3:4
B.2:3
C.4:3
D.1:3
Answer: C.4:3
Explanation: total profit =1000
ratio=800/600
=4:3
ANSWER:C
Question: The ratio, by volume, of soap to alcohol to water in a certain solution is 20:50:80. The solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved. If the altered solution will contain 100 cubic centimeters of alcohol, how many cubic centimeters of water will it contain?
A.520
B.640
C.700
D.750
Answer: B.640
Explanation: soap:alcohol
Initial ratio soap:alcohol: water --> 20:50:80
Initial soap:alcohol = 20/50 =20:50
after doubled soap:alcohol =2* 20/50 = 40:50
Initial soap:water = 20/80=20:80
after halved soap:water: 1/2 * 20/80 = 10/80 = 10:80
After soap: alcohol:water --> 40:50:320-->4:5:32
given alcohol 100 cubic centimeter.
ratio is 80:100:640(4:5:32)
For 100 cubic centimeter of Alcohol --- 640cubic cm water is required.
Answer-B
Question: A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?
A.1/5
B.3/5
C.1/8
D.5/8
Answer: A.1/5
Explanation: Suppose the vessel initially contains 8 litres of liquid.
Let x litres of this liquid be replaced with water.
Quantity of water in new mixture = (3 -(3x/8)+ x)litres
Quantity of syrup in new mixture = (5 - 5x/8) litres
Therefore, (3 - (3x/8)	+ x)	= 5 -	5x/8)
= 5x + 24 = 40 - 5x
= 10x = 16
= x = 8/5
So, part of the mixture replaced = (8/5 x 1/8)= 1/5
Answer is A.
Question: A and B started a partnership business investing some amount in the ratio of 3:5. C joined them after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C?
A.5 : 6 : 10
B.6 : 10 : 5
C.6 : 5 : 10
D.10 : 6 : 5
Answer: B.6 : 10 : 5
Explanation: Sol.
Let the initial investments of A and B be 3x amd 5x.
A : B : C = (3x * 12) : (5x * 12) : (5x * 6) = 36 : 60 : 30 = 6 : 10 : 5.
Answer B
Question: Find the compound ratio of (2:3), (6:11) and (11:5) is
A.3:2
B.2:1
C.1:2
D.4:5
Answer: D.4:5
Explanation: Required ratio = 2/3 * 6/11 * 11/5 = 2/1 = 4:5
Answer is D
Question: 1=1,2=2,3=9,4=16,5=25, then 9=?
A.1
B.255
C.3
D.445
Answer: C.3
Explanation: 1=1,2=2,3=9,4=16,5=25, then 9=?
9=3
check the third eqn.
ANSWER:C
Question: A miniature gumball machine contains 4 blue, 3 green, and 3 red gumballs, which are identical except for their colors. If the machine dispenses three gumballs at random, what is the probability that it dispenses one gumball of each color?
A.2/5
B.3/5
C.3/10
D.7/30
Answer: C.3/10
Explanation: The total number of ways to dispense 3 gumballs is 10C3=120.
The number of ways to choose one of each color is 4*3*3=36.
P(dispensing one of each color)=36/120=3/10.
The answer is C.
Question: The ratio of the arithmetic mean of two numbers to one of the numbers is 3:5. What is the ratio of the smaller number to the larger?
A.1:5
B.1:4
C.1:3
D.1:2
Answer: A.1:5
Explanation: let the numbers be a,b
acc. to problem,
(a+b)/2∗a(a+b)/2∗a = 3/53/5
1/21/2 + b/2∗ab/2∗a = 3/53/5
b/ab/a = 1/51/5
Ans. A
Question: Find the cost of fencing around a circular field of diameter 34 m at the rate of Rs.2 a meter?
A.215
B.212
C.278
D.279
Answer: B.212
Explanation: 2 * 22/7 * 17 = 106
106 * 2
= Rs.212
Answer: B
Question: Entry fee in a zoo is $10. Later this was reduced by 50% which increased the sale by 40%. The percentage increase in the number of visitors is?
A.100%
B.50%
C.180%
D.200%
Answer: C.180%
Explanation: Let the total original sale be $1000
Then original number of visitors = 100
New number of visitors = 1400/5 = 280
Increase % = 180%
Answer is C
Question: If 20% of A is the same as 25% of B, then A : B is :
A.3:4
B.4:3
C.5:4
D.6:7
Answer: C.5:4
Explanation: Expl : 20% of A I= 25% of B =20A/100 = 25B/100 = 5/4 = 5:4
Answer:C
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 R that all three secretary are assigned at least one report?
A.8/9
B.64/81
C.4/9
D.16/81
Answer: C.4/9
Explanation: I got the same answer: Here's my reasoning
First Report you have 3 choices
Second Report you have 2 choices
Third Report you have 1 choice
Fourth report 3 choices again
Then total number of ways is: 3*2*1*3=3^2*2
This is not correct. You have assumed that the 4th report must go to someone who already has a report. There is no such constraint. You can easily give the 1st and 2nd reports to secretary 1, 3rd report to secretary 2 and 4th report to secretary 3. But you have ignored all such cases.
The number of ways of ensuring at least one report goes to each secretary is 4C2 (select 2 reports out of 4 which go to the same person)*3C1 (select the person who must type 2 reports)*2! (since you have 2 reports left which you must distribute to the 2 remaining people such that each person gets one) = 36
Required probability R= 36/81.C
Question: In a certain sequence of numbers, a1, a2, a3, ..., an, the average (arithmetic mean) of the first m consecutive terms starting with a1 is m, for any positive integer m. If a1=1, what is a12?
A.100
B.55
C.23
D.19
Answer: C.23
Explanation: As stated above, (a1+a2+a3......+a12)/12=12
therefore a1+a2+a3.......a12=144 (1)
using the same logic, we got a1+a2+a3..........+a11=121 (2)
(2)-(1) we got a12=23
C
Question: The number of female students in a college in the previous year was 350. If in the current year the number of male students in the college doubled over that of the previous year but the proportion of male students halved, then what is the number of female students in the college in the current year?
A.1000
B.1200
C.1400
D.1600
Answer: C.1400
Explanation: Let x be the number of male students last year. The number of male students this year is 2x.
Let y be the number of female students this year.
x/350 = 2(2x/y)
y = 1400
The answer is C.
Question: Tough and Tricky questions: Word Problems.
It takes Sarah 12 minutes to do one oil change, and it takes Alice 8 minutes. If Sarah and Alice both begin doing oil changes at exactly 9:00 a.m. without pausing, when is the first time at which they will finish changing the oil of a car simultaneously?
A.09:24 a.m.
B.10:42 a.m.
C.12:00 a.m.
D.1:00 p.m.
Answer: A.09:24 a.m.
Explanation: LCM of 812
8 = 2 * 2 * 2
12 = 2 * 2 * 3
LCM = 2 * 2 * 2 * 3 = 24 minutes
924AM
A