mathewhe/aqua_rat huggingface dataset:
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively . If they cross each other in 21 seconds, what is the ratio of their speeds?
(A) 1:3
(B) 3:1
(C) 2:3
(D) 3:2
(E) 3:4
Rationale: Let the speed of the trains be x and y respectively
length of train1 = 27x
length of train2 = 17y
Relative speed= x+ y
Time taken to cross each other = 21 s
= (27x + 17 y)/(x+y) = 21
= (27x + 17 y)/ = 21(x+y)
= 6x = 4y
=x/y = 4/6 = 2/3 i.e 2:3
Answer :C
Answer: (C) 2:3
Question: What is the four-digit number in which the first digit is 1/3 of the second,the third is the sum of the first and second, and the last is three times the second?
(A) 1349
(B) 1347
(C) 1449
(D) 2349
(E) 1399
Rationale: It is given that the first digit is 1/3 of the second. There are 3 such possibilities 1)1 and 3
2)2 and 6
3)3 and 9
Now, the third digit is the sum of the first and second digits.
1)1 + 3 = 4
2)2 + 6 = 8
3)3 + 9 = 12
It is clear that option 3 is not possible. So we are left with only two options.Also, the last digit is three times the second, which rules out the secondoption. Hence, the answer is 1349
ANSWER:A
Answer: (A) 1349
Question: If w is a positive integer and 10^w – 74 in decimal notation has digits whose sum is 440, what is the value of w?
(A) 40
(B) 44
(C) 45
(D) 46
(E) 50
Rationale: Answer E = 50
We have (10^w)-74, where the sum of the digits is 440.
100-74 = 26, so we already have 2+6 = 8 from the 440.
Because we have a power of 10, we will have numbers like 100, 1000, 10000 and so on. This minus 74 rests 26 and a lot of 9s. E.g: 1000-74 = 9926.
So dividing the 432/9 = 48, that`s the number of 9s. and we have 2 other numbers (2 and 6) wich were 00 before the subtraction.
So we have 48 + 2 as an w = 50
Answer: (E) 50
Question: A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train?
(A) 87 Kmph
(B) 97 Kmph
(C) 72 Kmph
(D) 28 Kmph
(E) 19 Kmph
Rationale: Length = Speed * time
Speed = L/T
S = 400/20
S = 20 M/Sec
Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 72 Kmph
Answer: C
Answer: (C) 72 Kmph
Question: What is the area of square field whose side of length 15 m?
(A) 225 sq m
(B) 297 sq m
(C) 167 sq m
(D) 112 sq m
(E) 981 sq m
Rationale: 15 * 15
= 225 sq m
Answer: A
Answer: (A) 225 sq m
Question: Find the value of 72519 x 9999=m?
(A) 678994226
(B) 357900042
(C) 567890900
(D) 725117481
(E) 567788990
Rationale: 72519 x 9999 = 72519 x (10000 - 1)
= 72519 x 10000 - 72519 x 1
= 725190000 - 72519
= 725117481
D
Answer: (D) 725117481
Question: My grandson is about as many days as my son in weeks, and my grandson is as many months as I am in years. My grandson, my son and I together are 100 years. Can you tell my grandson age in years?
(A) 50 years
(B) 20 years
(C) 5 years
(D) 10 years
(E) 90 years
Rationale: Let m be my age in years. If s is my son's age in years, then my son is 52s weeks old. If g is my grandson's age in years, then my grandson is 365g days old. Thus,365g = 52s.Since my grandson is 12g months old,12g = m.Since my grandson, my son and I together are 120 years,g + s + m = 100.The above system of 3 equations in 3 unknowns (g, s and m) can be solved as follows:g + 365g / 52 + 12g = 100 or52g + 365g + 624g = 5,200 org = 5,200 / 1,041 = 5 yearsAnswer : C
Answer: (C) 5 years
Question: A new ram material product $2.67 raw , $0.67 to manufacture, $4.73 to packing and sell price $9.03. How many unit order sold with profit 44000?
(A) 4583.33
(B) 4683.33
(C) 4783.33
(D) 4883.33
(E) 4983.33
Rationale: CP = 2.67 + 0.67 + 4.73 = 8.07
SP =9.03
Profit = 9.03 - 8.07 = 0.96
Unit order sold = 44000/0.96
=4583.33 unit order
ANSWER:A
Answer: (A) 4583.33
Question: In an election between two candidates, 70% of the voters cast their votes, out of which 4% of the votes were declared invalid. A candidate got 65520000 votes which were 75% of the total valid votes. Find the total number of votes enrolled in that election.
(A) 130000000
(B) 12500
(C) 14000
(D) 12000
(E) None of these
Rationale: Explanation :
Solution: let the total number of votes enrolled be x. then, number of votes cast = 70% of x. valid votes = 96% of(70% of x). .'. 75% of(96% of (70% of of x)) = 65520000.
(75/100 * 96/100 * 70/100 * x) = 65520000.
=> x = (65520000*100*100*100)/(75*96*70) = 130000000
Answer : A
Answer: (A) 130000000
Question: City A to city B, Andrew drove for 1hr at 40 mph and for 3 hours at 60 mph. What was the average speed for the whole trip?
(A) 55
(B) 57.5
(C) 61
(D) 61.5
(E) 62.5
Rationale: The total distance is 1×40+3×60=220
And the total time is 4 hours. Hence,
Average Speed=(Total Distance/Total Time)
=220/4=55
A
Answer: (A) 55
Question: You and your friend spent a total of $15 for lunch. Your friend spent $5 more than you. How much did your friend spend on their lunch?
(A) $9
(B) $3
(C) $4
(D) $6
(E) $10
Rationale: My lunch = l, my friends lunch = l+5
(l)+(l+5)=15
l+l+5-5=15-5
2l=10
l=5
My friends lunch l+5 = 5+5=$10, the answer is E
Answer: (E) $10
Question: Machine A produces 100 parts twice as fast as Machine B does. Machine B produces 100 parts in 20 minutes. If each machine produces parts at a constant rate, how many parts does Machine A produce in 8 minutes?
(A) 100
(B) 90
(C) 80
(D) 30
(E) 50
Rationale: Machine B produces 100 part in 20 minutes. Machine A produces 100 parts twice as fast as B, so Machine A produces 100 parts in 20/2=10 minutes.
Now, Machine A produces 100 parts in 10 minutes which is 100/10 = 10 parts/minute.
10 parts X a total of 8 minutes = 80
C
Answer: (C) 80
Question: A boy has to cover a total distance of 300 kms. in 6 hours. He travels at the rate of 60 kmph. for first 90 minutes and next 100 kms. at the rate of 50 kmph. At what average speed must he travel now in order to complete the journey in 6 hours?
(A) 25 kmph.
(B) 32 kmph
(C) 44 kmph
(D) 58 kmph
(E) None of these
Rationale: Explanation:
The boy travels 60 kmph for 90 min, this means he travels 90 km.
Next 100 km at the rate of 50 kmph, this means he travels 100 km.
Total distance traveled till now = 100 + 90 = 190 km
Time spent = 1.5 + 2 = 3.5 hr
Required speed = Remaining distance/ Time
= (300 – 190) /(6 – 3.5)
= 110/ 2.5 = 44 kmph
ANSWER: C
Answer: (C) 44 kmph
Question: On Saturday morning, John will begin a camping vacation and he will return home at the end of the first day on which it rains. If on the first three days of the vacation the probability of rain on each day is 0.2, what is the probability that Malachi will return home at the end of the day on the following Monday?
(A) 0.008
(B) 0.125
(C) 0.128
(D) 0.512
(E) 0.64
Rationale: Re-phrasing the question:
What is the probability of: Saturday: No rain, Sunday: No rain, Monday: Rain
Probability of rain = 0.2
Therefore, probability of no rain = 0.8
0.8*0.8*0.2 = 0.128
Hence C
Answer: (C) 0.128
Question: A family has two children. find the probability that both the children are girls given that at least
one of them is a girl?
(A) 1/5
(B) 1/3
(C) 3/7
(D) 2/7
(E) 3/7
Rationale: Let b stand for boy and g for girl. The sample space of the experiment is
S = {(g, g), (g, b), (b, g), (b, b)}
Let E and F denote the following events :
E : ‘both the children are girls’
F : ‘at least one of the child is a girl’
Then E = {(g,g)} and F = {(g,g), (g,b), (b,g)}
Now E n F = {(g,g)}
Thus P(F) = 3/4
and P (E n F )= 1/4
Therefore P(E|F) = P(E ∩ F)/P(F) = (1/4)/(3/4) = 1/3
B)
Answer: (B) 1/3
Question: A tap can fill a tank in 16 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?
(A) 2 hrs
(B) 1 hrs
(C) 10 hrs
(D) 5 hrs
(E) 4 hrs
Rationale: Explanation:
A tap can fill a tank in 16 hours.
Therefore the tap can fill half the tank in 8 hours.
One tap take time to fill half of the tank = 8 hrs
4 taps take time to fill half of the tank =8/4 hrs = 2 hrs
Total time taken to fill the tank = 8 hr+2 hr = 10 hrs
Answer : C
Answer: (C) 10 hrs
Question: A car gets 30 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 200 kilometers?
(A) 3.5 gallons
(B) 2.7 gallons
(C) 6.7 gallons
(D) 4.5 gallons
(E) 7.5 gallons
Rationale: Each 30 kilometers, 1 gallon is needed. We need to know how many 30 kilometers are there in 200 kilometers?
200 Ã· 30 = 6.7 Ã— 1 gallon = 6.7 gallons
correct answer is C) 6.7 gallons
Answer: (C) 6.7 gallons
Question: In digging a pond 28 m * 10 m * 5 m the volumes of the soil extracted will be?
(A) 3387
(B) 1000
(C) 2866
(D) 2787
(E) 1400
Rationale: 28 * 10 * 5 = 1400
Answer: E
Answer: (E) 1400
Question: The lateral surface area of cube is 100 sq.units. find the volume of cube?
(A) 135
(B) 155
(C) 125
(D) 145
(E) 115
Rationale: Lateral surface = 4 a(power)2 = 100 sq.units
a(power)2 = 25
a = 5.
Cube volume = a(power)3 => 125 m(power)3
Answer is C.
Answer: (C) 125
Question: A statue is being carved by a sculptor. The original piece of marble weighed 300 kg. In the first week 30 percent is cut away. In the second week 30 percent of the remainder is cut away. In the third week the statue is completed when 15 percent of the remainder is cut away. What is the weight of the final statue?
(A) 105 kg
(B) 103 kg
(C) 108 kg
(D) 125 kg
(E) 117 kg
Rationale: D
125 kg
300 Ã— 0.7 Ã— 0.7 Ã— 0.85 = 125 kg.
Answer: (D) 125 kg
Question: A can do a job in 12 days and B can do it in 15 days. A and B working together will finish twice the amount of work in days?
(A) 22 1/6
(B) 22 1/2
(C) 22 1/0
(D) 22 1/9
(E) 13 1/3
Rationale: 1/12 + 1/15 = 9/60 = 3/20
20/3 = 20/3 *2 = 13 1/3 days
Answer: E
Answer: (E) 13 1/3
Question: A number increased by 20% gives 480. The number is
(A) 200
(B) 400
(C) 300
(D) 450
(E) 500
Rationale: Formula = TOTAL=100% ,INCRESE = "+" DECREASE= "-"
A number means = 100 %
That same number increased by 20 % = 120 %
120 % -------> 480 (120 × 4 = 480)
100 % -------> 400 (100 × 4 = 400)
B)
Answer: (B) 400
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.9 km and 2.1 km respectively. The time taken by the slower train to cross the faster train in seconds is?
(A) 99
(B) 277
(C) 48
(D) 96
(E) 22
Rationale: Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 1.9 + 2.1 = 4 km = 4000 m.
Required time = 4000 * 3/125 = 96 sec.
Answer:D
Answer: (D) 96
Question: An office has 6 employees; there are 5 female employees and 1 male employee. In how many ways can a 3-person committee be created if the committee must include the male employee?
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25
Rationale: Total Employees: 6
Female: 5
Male: 1
committee of 3 with inclusion of Male
Number of ways Female can be selected : 5C2 = 10
For male it should be 6C1 or 6C6
6C1= 6
6C6= 1
ANS= 10 B
Answer: (B) 10
Question: A certain number of two digits is three times the sum of its digits and if 45 be added to it, the degits are reversed. The number is.
(A) 23
(B) 27
(C) 32
(D) 72
(E) 46
Rationale: Let the ten's digit be x and unit's digit be y.
Then 10x + y = 3 (x+y) ==> 7x - 2y = 0 ==> 7x - 2y = 0----> (I)
10 + y + 45 = 10y + x ==> y - x = 5 ===> -2x + 2y = 10------(II)
By adding (I) and (II) we get 5x = 10
so x = 2 and y = 7 so the required number is 27.
so the correct option is B) 27.
Answer: (B) 27
Question: You have been given a physical balance and 7 weights of 52, 50, 48, 44, 45, 46, and 78 Kgs.. Keeping weights on one pan and object on the other, what is the maximum you can weigh less than 183 Kgs.?
(A) 178
(B) 180
(C) 181
(D) 182
(E) 183
Rationale: balance=52+50+48+44+45+46+78-183
ANSWER:E
Answer: (E) 183
Question: Two vessels contains equal number of mixtures milk and water in the ratio 4:1 and 7:3. Both the mixtures are now mixed thoroughly. Find the ratio of milk to water in the new mixture so obtained?
(A) 2:1
(B) 4:1
(C) 3:1
(D) 2:3
(E) 4:3
Rationale: The ratio of milk and water in the new vessel is = (4/5 + 7/10) : (1/5 + 3/10)
= 3/2 : 1/2 = 3:1
Answer is C
Answer: (C) 3:1
Question: A train is moving at a speed of 30km/hr and its length is 100m. Find the time taken by it to pass a man standing near the railway line?
(A) 12sec
(B) 10sec
(C) 15sec
(D) 18sec
(E) 22sec
Rationale: Speed of the train = 30*5/18 = 25/3 m/sec
Distance moved in passing the standing man = 100m
Required time taken = 100/(25/3) = 100*3/25 = 12sec
Answer is A
Answer: (A) 12sec
Question: The mean of 50 observations was 32. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is
(A) 35.2
(B) 32.5
(C) 36.5
(D) 39.1
(E) None
Rationale: Sol.
Therefore correct sum
= ( 32 × 50 + 48 – 23)
= 1625.
Therefore correct mean
= 1625 / 50
= 32.5.
Answer B
Answer: (B) 32.5
Question: A vessel of capacity 60 litres is fully filled with pure milk. Nine litres of milk is removed from the vessel and replaced with water. Nine litres of the solution thus formed is removed and replaced with water. Find the quantity of pure milk in the final milk solution?
(A) 23.89
(B) 72.9
(C) 38.3
(D) 43.35
(E) 79.3
Rationale: Explanation:
Let the initial quantity of milk in vessel be T litres.
Let us say y litres of the mixture is taken out and replaced by water for n times, alternatively.
Quantity of milk finally in the vessel is then given by [(T - y)/T]^n * T
For the given problem, T = 60, y = 9 and n = 2.
Hence, quantity of milk finally in the vessel
= [(60 - 9)/60]^2 (60) = 43.35 litres.
Answer: Option D
Answer: (D) 43.35
Question: Last year, Company X paid out a total of $1,050,000 in salaries to its 31 employees. If no employee earned a salary that is more than 20% greater than any other employee, what is the lowest possible salary that any one employee earned?
(A)  $10,000
(B)  $$28,378.37
(C)  $42,000
(D)  $50,000
(E)  $60,000
Rationale: Employee 1 earned $x(say)
Employee 2 will not earn more than $1.2x
Therfore, to minimize the salary of any one employee, we need to maximize the salaries of the other 30 employees
(1.2x*30)+x=1,050,000
Solving for x=$28,378.37
Answer B
Answer: (B)  $$28,378.37
Question: If 3<x<6<y<10, then what is the greatest possible positive integer difference of x and y?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: 3 < x < 6 < y < 10;
3 < x
y < 10
3 + y < x + 10
y - x < 7.
Positive integer difference is 6 (for example y = 9.5 and x = 3.5)
Answer: D.
Answer: (D) 6
Question: A secondhand car was purchased for £8000. After three years the car's value had decreased by 35%.Find the price of the car after three years.
(A) £5100
(B) £5200
(C) £5300
(D) £5400
(E) £5400
Rationale: Solution
We begin by finding 10% of £8000 by dividing by 10. So 10% = £800.
Now 5% is half of 10% so 5% = £400
So 35% = 10% + 10% + 10% + 5% = 800 + 800 + 800 + 400 = £2800
The find the value of the car after three years subtract 35% from the original amount.
£8000 - £2800 = £5200
Answer B
Answer: (B) £5200
Question: If the S.P of Rs. 63 results in a 10% discount on the list price, What S.P would result in a 20% discount on the list price?
(A) s. 55
(B) s. 56
(C) s. 57
(D) s. 58
(E) s. 59
Rationale: Let the list price be Rs. X,
90/100*x = 63, x = 63*100/90 = 70
Required S.P = 80% of Rs. 70
= 80*70/100
=56
ANSWER:B
Answer: (B) s. 56
Question: If -3x > 0, which of the following must be true?
(A) x < -3
(B) x < -2
(C) x > 3
(D) x > -2
(E) x < 0
Rationale: -3x > 0
=> -x > 0
=> x < 0
Answer E
Answer: (E) x < 0
Question: Three seventh of a number is 12 more than 40% of that number. What will be the 60% of that number?
(A) 148
(B) 210
(C) 126
(D) 248
(E) 258
Rationale: 3/7 x – 40/100 x = 12
x = 35 * 12
35 * 12 * 60/100 = 252/2 = 126
ANSWER:C
Answer: (C) 126
Question: Circular gears L and R start to rotate at the same time at the same rate. Gear R makes 10 complete revolutions per minute and gear L makes 40 revolutions per minute. How many seconds after the gears start to rotate will gear L have made exactly 6 more revolutions than gear R?
(A) a) 6
(B) b) 12
(C) c) 10
(D) d) 14
(E) e) 15
Rationale: GearR -- 10 rotations per 60 seconds -- 1 rotation per 6 seconds.
Gear L -- 40 rotations per 60 seconds -- 4 rotations per 6 seconds.
First 6 seconds -- Gear R makes 1 rotation. -- Gear L makes 4 rotations -- Net difference -- 3 rotations
Hence every 6 seconds the difference between the number of rotations of R and L gear is 3 units.
Required net difference should be 6 rotations => 2 (6 seconds later) ==> 12 seconds.
Answer: B
Answer: (B) b) 12
Question: The area of playground is 6000 sq. meters. What will be the cost of covering it with grass sheet 1cm deep, if cost of grass sheet is $2.80 per cubic meter.
(A) a) $144
(B) b) $150.50
(C) c) $168
(D) d) $158.60
(E) e) $160.70
Rationale: total volume * unit cost = total cost
or, 6000 * 0.01 * 2.8 = total cost = 168=C
Answer: (C) c) $168
Question: If the wheel is 14 cm then the number of revolutions to cover a distance of 1056 cm is?
(A) 22
(B) 28
(C) 17
(D) 12
(E) 88
Rationale: 2 * 22/7 * 14 * x = 1056 => x = 12
Answer: D
Answer: (D) 12
Question: Two trains leaving from two station 50 miles away from each other with costant speed of 60 miles per hour, approaches towards each other on diffrent tracks. if lenght of each train is 1/6 mile. when they meet How much time they need to pass each other totally?
(A) 1/6 min
(B) 1/7 min
(C) 1/8 min
(D) 1/9 min
(E) 1/5 min
Rationale: both are approaching each other relative speed=60+60=120m/h
distance=50m
time=50/120=5/12hrs= 25 minutes to meet
now,
relative length of train= 1/6+1/6=1/3m
relative speed = 120m/h
time to cross both the trains= (1/3)/120=1/360 hrs
= 1/6 minutes
ANSWER:A
Answer: (A) 1/6 min
Question: The base of a triangle is 15 cm and height is 12 cm. The height of another triangle of double the area having the base 20 cm is :
(A) 22 cm
(B) 20 cm
(C) 18 cm
(D) 10 cm
(E) None of these
Rationale: Explanation:
Area of triangle, A1 = 1/2∗base∗height
=1/2∗15∗12=90cm2
Area of second triangle =2∗A1=180cm2
1/2∗20∗height=180
=>height=18cm
Option C
Answer: (C) 18 cm
Question: In a can, there is a mixture of milk and water in the ratio 5:3. If the can is filled with an additional 20 liters of milk, the can would be full and the ratio of milk and water would become 3:1. Find the capacity of the can?
(A) 52
(B) 56
(C) 60
(D) 64
(E) 68
Rationale: Let C be the capacity of the can.
(5/8)*(C-20)+20=(3/4)*C
5C-100+160=6C
C=60
The answer is C.
Answer: (C) 60
Question: Company X provides bottled water to its employees in 5 liter bottles, $2 each. At least how many 5L bottles must Company X buy monthly, so that new contract with $100 fixed monthly rate and $1 for 10L bottle each paid off? (Assume that no other costs apply)
(A)  121
(B)  125
(C)  132
(D)  134
(E)  138
Rationale: let the no. of 5 liter bottles be x, so the no. of 10l bottles will be x/2 (to equate the vol.) since the total cost will be equal , 2x= 100+x/2 so x= 133.33 or 134. Answer is (D).
Answer: (D)  134
Question: Sum of two numbers is 30. Two times of the first exceeds by 10 from the three times of the other. Then the numbers will be?
(A) 14, 16
(B) 16, 14
(C) 18, 12
(D) 12, 18
(E) 17, 13
Rationale: Explanation:
x + y = 30
2x Ã¢â‚¬â€œ 3y = 10
x = 16 y = 14
Answer: B
Answer: (B) 16, 14
Question: In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr?
(A) 2.5 sec
(B) 2.8 sec
(C) 3.5 sec
(D) 2.7 sec
(E) 5.5 sec
Rationale: Speed = 144 * 5/18 = 40 m/sec
Time taken = 100/40 = 2.5 sec.
Answer: A
Answer: (A) 2.5 sec
Question: 60 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?
(A) 8 days
(B) 6 days
(C) 7 days
(D) 9 days
(E) 12 days
Rationale: 1 women's 1 day work = 1/420
1 child's 1 day work = 1/140
(5 women + 10 children)'s 1 day work
= (5/420 + 10/140) = 1/12
5 women and 10 children will complete the work in 12 days.
Answer: E
Answer: (E) 12 days
Question: At a local supermarket, a box of cereal usually costs 22 dollars. This week, the supermarket sells the box of cereal for 11 dollars. How much money will you save if you buy this cereal at this supermarket?
(A) 11 dollars
(B) 13 dollars
(C) 14 dollars
(D) 12 dollars
(E) 10 dollar
Rationale: Solution:
In this situation, there is a decrease in the price.
Saving = 22 - 11 = 11 dollars
Option A
Answer: (A) 11 dollars
Question: 243 has been divided into three parts such that half of the first part, one - third of the second part and one - fourth of the third part are equal. The largest part is ?
(A) 12628
(B) 23488
(C) 26688
(D) 26667
(E) 12672
Rationale: Explanation:
Ratio of their shares = (35000 * 8) : (42000 * 10) = 2 : 3.
Reena's share Rs. 31570 * (2 / 5) = Rs. 12628.
Answer: A) 12628
Answer: (A) 12628
Question: 1 + 2 + 3 + ... + 12 = ?
(A) 76
(B) 68
(C) 78
(D) 66
(E) 67
Rationale: 1+2+3+⋯+n=∑n=n(n+1)/2
1+2+3+⋯+12=n(n+1)/2=(12(12+1))/2=(12×13)/2=6×13=78
Answer is C
Answer: (C) 78
Question: In a series of football matches, the probability that Team P wins a match against Team Q is 1/5 and the probability that the match ends in a draw is 2/3. If the two teams play five matches, what is the probability that all five matches end in a draw?
(A) 2/3
(B) 4/9
(C) 8/27
(D) 16/81
(E) 32/243
Rationale: P(5 draws)=(2/3)^5=32/243
The answer is E.
Answer: (E) 32/243
Question: If the sum of a number and its square is 182, what is the number?
(A) 15
(B) 26
(C) 28
(D) 91
(E) none of these
Rationale: Let the number be x. Then,
x + x2 = 182
(x + 14)(x - 13) = 0
x = 13
ANSWER:E
Answer: (E) none of these
Question: A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 5 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?
(A) 7.5
(B) 20
(C) 30
(D) 32
(E) 40
Rationale: Net part filled in 1 hour = (1/4 - 1/5) = 1/20
The cistern will be filled in 20/1 hrs i.e., 20 hrs.Answer: B
Answer: (B) 20
Question: Mr and Mrs A are opposite to each other.The distance between Mr A and Mrs A are 120 km.The speed of Mr A and Mrs A are 30 kmph, 10 kmph respectively.one Bee is running between Mr A nose to Mrs A nose and returning back to Mr A nose.The speed of Bee is 60 kmph. Then How far Bee traveled?
(A) 160km
(B) 170km
(C) 180km
(D) 190km
(E) 130km
Rationale: 30x+10X=120
X= 3 hrs
speed of bee=60kmph
distance traveled by bee=speed * time taken=60*3=180km
ANSWER:C
Answer: (C) 180km
Question: x, y, and z are three positive integers whose average is 10. If x≤y≤z and z-x=3, which of the following could be the median W of x, y, and z?
I. 9
II. 10
III. 11
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
Rationale: Average gives us an idea that 3 nos. are close to 10.
so 10, 10, 10 is an unacceptable option because (z-x =3), but it helps in getting other combinations.
Let us see options.
If 9 has to be median W.
1st term has to less than 9 or equal to 9. (also maintain z-x = 3)
9 9 12 --> satisfies all conditions so 9 can be a median value.
If 11 has to be a median
3rd term has to be 11 or more than 11. (also maintain z-x = 3)
8 11 11 -->satisfies all conditions so 9 can be a median value.
Now for 10 to be median.
z+ x = 20 and z-x = 3, we wont have integer values of z.
10 cannot be a median
E is the answer.
Answer: (E) I and III only
Question: Find the annual income derived by investing $ 6800 in 20% stock at 136.
(A) 550
(B) 1000
(C) 2500
(D) 300
(E) 4000
Rationale: By investing $ 136, income obtained = $ 20.
By investing $ 6800, income obtained = $ [(20/136)*6800] = $ 1000.
Answer B.
Answer: (B) 1000
Question: If 10 gallons of grape juice are added to 40 gallons of a mixture, which contains 20 percent grape juice then what percent of the resulting mixture is grape juice?
(A) 14%
(B) 25%
(C) 28%
(D) 36%
(E) 50%
Rationale: OFFICIAL SOLUTION:
If we start with 40 gallons of a mixture that is 10% grape juice, then we have:
40 × 0.20 = 8 gallons of grape juice.
40 × 0.80 = 32 gallons of other components.
If we add 10 gallons of grape juice, we will end up with 18 gallons of grape juice and 32 gallons of other components, and we will have a total of 50 gallons of the mixture.
So 18/50 of the new mixture is grape juice. Now we convert this to a percent:Percent Grape Juice = 18/50 = 36/100= 36%.
The correct answer is choice (D)
Answer: (D) 36%