RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: The sum of three consecutive multiples of 3 is 117. What is the largest number?
A.45
B.48
C.51
D.42
Answer: D.42
Explanation: Let the numbers be 3x, 3x + 3 and 3x + 6.
Then,
3x + (3x + 3) + (3x + 6) = 117
9x = 108
x = 12
Largest number = 3x + 6 = 42
Answer : D
Question: A train running at the speed of 30 km/hr crosses a pole in 12 seconds. What is the length of the train?
A.70
B.80
C.90
D.100
Answer: D.100
Explanation: Speed=(30 x(5/18)m/sec	=(25/3)m/sec.
Length of the train = (Speed x Time).
Length of the train =	((25/3)x 12)m = 100 m
D
Question: A man sells two articles for Rs.3600 each and he gains 25% on the first and loses 25% on the next. Find his total gain or loss?
A.9% loss
B.6.25% Loss
C.4000
D.324
Answer: B.6.25% Loss
Explanation: (25*25)/100 = 6.25%loss
ANSWER:B
Question: The probability of shooting a target increases after a certain skill is enhanced and is equal to the new probability of NOT shooting the target. Given this fact, which of the following must be false?
A.The new probability of shooting the target is greater than 0.5
B.The original probability of shooting the target is less than 0.5
C.The original probability of NOT shooting the target and the new probability of shooting the target are the same
D.The original probability of shooting the target and that of NOT shooting the target are the same.
Answer: D.The original probability of shooting the target and that of NOT shooting the target are the same.
Explanation: 1. Let p(i), q(i), be the initial probability of shooting and missing the target respectively and let p(n) and q(n) be the new probability of shooting and missing the target respectively.
Given:
1. p(i) + q(i) =1
2. P(n) + q(n) =1
3. p(n) > p(i)
4. p(i) = q(n)
Deductions:
5. q(n) + q(i) =1 ( from (1) and (4) )
6. p(n) + p(i) =1 ( from (2) and (4) ) - ( Choice E always true)
7. From ( 3) and (6), p(i) < 0.5 and p(n) > 0.5 - ( Choice A and Choice B always true)
8. From (1) and (6), q(i) = p(n) - ( Choice C always true)
9. From (3) and (8), q(i) > p(i) - ( choice D always false)
Therefore the answer is Choice D
Question: A man can row downstream at the rate of 32 Kmph and upstream at 17 Kmph. Find the man’s rate in still water and rate of current?
A.7.5
B.8.0
C.9.5
D.9.0
Answer: A.7.5
Explanation: Rate of still water = 1/2 (down stream + upstream)
= 1/2 (32 + 17) = 24.5 Kmph
rate of current = 1/2 (down stream - upstream)
= 1/2 (32 - 17)
= 1/2 (15)
= 7.5 kmph
Answer is A.
Question: Edward earns $7.00 per hour for the first 40 hours he works per week, and twice this rate for overtime. If Michael earned $210 last week, how many hours did he work?
A.43
B.44
C.45
D.46
Answer: C.45
Explanation: $7*40 + $12*x = $210 --> x = 5 hours.
Total working hours = 40 + 5 = 45
Answer: C.
Question: Which of the following inequalities is always true for any real number 'a' and 'b'?
A.|a+b| >= |(|a|-|b|)|
B.|a-b| <= |(|a|-|b|)|
C.|a-b| = |(|a|-|b|)|
D.|a-b| >= |(|a|-|b|)|
Answer: D.|a-b| >= |(|a|-|b|)|
Explanation: The answer here is D. One of the fundamental properties of absolute value is subadditivity, and this is a reverse triangle inequality, which is equivalent to subadditivity. So this means that difference of two any elements is something (some number) which is greater than or equal to the difference of the each element taken on itself separately, i.e. |a-b| >= |(|a|-|b|)|
Question: S = {2, 3, 4, 5}
B = {4, 5, 6, 7, 8}
Two integers will be randomly selected from the sets above, one integer from set S and one integer from set B. What is the probability that the sum of the two integers will equal 9 ?
A. 0.15
B. 0.20
C. 0.25
D. 0.30
Answer: B. 0.20
Explanation: The total number of pairs S,B possible is 4*5=20. Out of these 20 pairs only 4 sum up to 9: (2, 7); (3, 6), (4, 5) and (5, 4). The probability thus is 4/20=0.2.
Answer: B.
Question: What will come in place of the x in the following Number series? 5,28,57,88,125
A.123
B.143
C.166
D.190
Answer: C.166
Explanation: 28=23+5
57=29+28
88=31+57
125=37+88
166=41+125
=166
C
Question: The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is:
A.40%
B.44%
C.50%
D.54%
Answer: B.44%
Explanation: Let original length = x metres and original breadth = y metres.
Original area = (xy) m2.
New length = 120 x m = 6 x m.
100 5
New breadth = 120 y m = 6 y m.
100 5
New Area = 6 x x 6 y m2 = 36 xy m2.
5 5 25
The difference between the original area = xy and new-area 36/25 xy is
= (36/25)xy - xy
= xy(36/25 - 1)
= xy(11/25) or (11/25)xy
Increase % = 11 xy x 1 x 100 % = 44%.
25 xy
B
Question: Find the unit's digit in 264^102 +264^103
A.zero 0
B.1
C.2
D.4
Answer: A.zero 0
Explanation: Required unit's digit = unit's digit in 4102+4103.4102+4103.
Now, 4242 gives unit digit 6.
⇒ 41024102 gives unit digit 6.
⇒ 41034103 gives unit digit of the product 6×46×4 i.e., 4.
Hence, unit's digit in 264102+264103264102+264103
= unit's digit in (6+4)=0
A
Question: If a square and a rhombus stand on the same base, then the ratio of the areas of the square and the rhombus is:
A.1:1
B.1:9
C.1:2
D.1:5
Answer: A.1:1
Explanation: Explanation:
A square and a rhombus on the same base are equal in area
Answer: A) 1:1
Question: You had a math quiz at class. The quiz had 5 questions; three of them have 3 marks each, and the other two have 4 marks each. You managed to correctly solve 2 questions with the 3 marks and one question with the 4 marks. What is the percentage of the marks that you got in this quiz?
A.48.8%
B.58.8%
C.38.8%
D.28.8%
Answer: B.58.8%
Explanation: Solution:
The total marks = 3x3 + 2x4 = 17 marks
Marks obtained = 2x3 + 4 = 10 marks
Percent of marks obtained = 10/17 x 100 = 58.8%
Answer B
Question: There are 660 male and female participants in a meeting. Half the female participants and one-quarter of the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female?
A.75
B.110
C.125
D.175
Answer: B.110
Explanation: female = x
Male = 660-x
x/2 + 660-x/4 = 1/3* (660)= 220
x= 220
x/2 = 110 is supposed to be the answer
M is missing something
Correct Option B
Question: For any positive number x, the function [x] denotes the greatest integer less than or equal to x. For example, [1] = 1, [1.367] = 1 and [1.988] = 1. If k is a positive integer such that k^2 is divisible by 45 and 80, what is the units digit of k^3/4000 ?
A.0
B.1
C.27
D.54
Answer: A.0
Explanation: It cannot be determined.As we do not know the actual value of K.
however minimum value of k is sq.rt of 3^2*4^2*5^2 = 60 * any integer
K=[lCM of 80 and 45] * (any integer)
for value of k(60) * any integer unit value will be always zero .
A
Question: Isabelle decided to go on an 8 mile run in which she ran from home to the school four miles away and then back the same route. The first four miles took her 40 minutes to complete, and the returning four miles took her 24 mins to complete. What was the wind speed in mph?
A.1 mph
B.2 mph
C.3 mph
D.4 mph
Answer: B.2 mph
Explanation: Explanation:
Speed from home to school: (4/40) X 60 = 6 mph
Speed from school to home: (4/24) X 60 = 10 mph
Wind speed: 1/2 (10 - 6) = 4/2= 2 mph
Answer: Option B
Question: Four of the following five numbered parts (a), (b), (c), (d) and (e) are equal. The number of the part which is not equal to the other four parts is the answer.
A.115 × 8 ÷ 10 + 8
B.425 ÷ 17 × 4
C.36 × 5 ÷ 6 + 17 × 4
D.2(6) + √256 + 20
Answer: C.36 × 5 ÷ 6 + 17 × 4
Explanation: All others are equal to 100. But option (c) gives a value equal to 98.
Answer C
Question: A rectangular Box 60 m long and 40 m wide has two concrete crossroads running in the middle of the box and rest of the box has been used as a lawn. The area of the lawn is 2109 sq. m. what is the width of the road?
A.3 m
B.4 m
C.5 m
D.6 m
Answer: A.3 m
Explanation: Total area of cross roads=60x+40x−x2
But total area of the cross roads =291 m2
Hence,
60x+40x−x2=291
⇒100x−x2=291
⇒x2−100x+291=0
⇒(x−97)(x−3)=0
⇒x=3
ANSWER:A
Question: Pump A can fill a tank of water in 5 hours. Pump B can fill the same tank in 8 hours. How long does it take the two pumps working together to fill the tank?(round your answer to the nearest minute).
A.3 hours 5 minutes
B.4 hours 5 minutes
C.5 hours 5 minutes
D.6 hours 5 minutes
Answer: A.3 hours 5 minutes
Explanation: In 1 hour pump A can fill 1/5 of a tank and pump B can fill 1/8 of the same tank. So in 1 hour the two pumps working together can fill
1/5 + 1/8 = 13 / 40 of a tank
Since the rate of the two pumps working together is 13/40, the time t needed to fill the tank by the two pumps is found by solving
(13/40) t = 1
t = 40 / 13 = 39/13 + 1/13 hours
= 3 hours and (1/13)*60 minutes
= 3 hours 5 minutes (rounded to the nearest minute)
correct answer A
Question: Tough and Tricky questions: Word Problems.
AK Car Company wants to manufacture a new car known as Model X, and it is trying to determine how many cars it needs to sell in order to make an annual profit of $30,500,000. The annual fixed costs for Model X total $50,200,000. In addition, each Model X car has an average cost of $5,000 per vehicle to manufacture. If the Company forecasts it will sell 20,000 Model X cars this year, at what price must the Company sell the car to achieve the desired annual profit?
A.$4,035
B.$4,036
C.$9,035
D.$16,140
Answer: C.$9,035
Explanation: The AK company plans to make a profit of $30,500,000 and it needs to earn the fixed costs of $50,200,000, so it needs to earn $80,700,000 on top of the costs for the production of the 20,000 cars.
Therefore, price of each car needs to be the unit costs plus $80,700,000/20,000. After removing the 0's, we end with the unit costs plus $8,070/2, which is $5,000 plus $4,035. Therefore, Answer C is correct.
Question: How many consonants are present between the first and third vowel in the sequence of English alphabet ?
A.12
B.13
C.6
D.10
Answer: C.6
Explanation: Explanation:
Ref : A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
The first and third vowels are A and I respectively. There are 7 letters between A and I; out of which 'E' is a vowel. Thus, there are 6 consonants between A and I.
ANSWER C
Question: In how many ways the word "PACK" can be arranged?
A.14
B.24
C.28
D.None
Answer: B.24
Explanation: Explanation :
The required number of ways = 4!
= 24
Answer : B
Question: Andrew travelling to 7 cities. Gasoline prices varied from city to city. $1.75, $1.61, $1.79, $2.11, $1.96, $2.09, $1.82. What is the median gasoline price?
A.$1
B.$1.82
C.$1.92
D.$2.13
Answer: B.$1.82
Explanation: Ordering the data from least to greatest, we get:
$1.61, $1.75, $1.79, $1.82, $1.96, $2.09, $2.11
The median gasoline price is $1.82. (There were 3 states with higher gasoline prices and 3 with lower prices.)
B
Question: A cat leaps 5 leaps for every 4 leaps of a dog, but 3 leaps of the dog are equal to 4 leaps of the cat. What is the ratio of the speed of the cat to that of the dog?
A.11:15
B.15:11
C.16:15
D.15:16
Answer: D.15:16
Explanation: Solution: Given;
3dog = 4 cat;
Or, dog/cat = 4/3;
Let cat's 1 leap = 3 meter and dogs 1 leap = 4 meter.
Then, ratio of speed of cat and dog = 3*5/4*4 = 15:16.''Answer: Option D
Question: Define A = The sum of digits of the number 7^100 and B = The sum of the digits of A. What is the sum of the digits of B?
A.7
B.16
C.10
D.11
Answer: A.7
Explanation: Following approach will take you only couple of sec.
\(7^{100} = (7^{50})^2\)
The sum of digits (digital root) of a PERFECT SQUARE can only be 1, 4, 7 or 9.
For example \(7^2=49\) => DR=4+9=13 => 1+3=4 and etc.
Checking available options.
Answer A.
Question: A small, experimental plane has three engines, one of which is redundant. That is, as long as two of the engines are working, the plane will stay in the air. Over the course of a typical flight, there is a 1/4 chance that engine one will fail. There is a 75% probability that engine two will work. The third engine works only half the time. What is the probability that the plane will crash in any given flight?
A. 7/12
B. 1/4
C. 1/2
D. 7/24
Answer: A. 7/12
Explanation: In probability questions the trap answer is just the multiple of the numbers in the question.
i.e. if you multiply 1/3 * 1/4 * 1/2 = 1/24 is trap answer
The other trap answer could be 2/3 * 3/4 * 1/2 = 6/24 is trap answer
So lets say you have30 secsand you want to guess the answer then B, C are ruled out because they can be traps. You best guess is A, D, E. So you have 33% chances of being correct.
A
Question: A departmental store charges the commission of 25 percent on the first sale of items worth $50,000 and then an additional 10 percent on any sale price that exceeds the initial $50,000. If the department store earned $24,000 in commissions for the sale of a series of diamonds, what was the sale price of the diamond set?
A. $215,000
B. $165,000
C. $115,000
D. $240,000
Answer: B. $165,000
Explanation: 24,000 = 0.25 *(50000) + 0.10 (x - 50000)
24000 - 12500 = 0.10 (x-50000)
115000 = x - 50000
x = 1,65,000
Answer : B
Question: The price of an item is discounted 10 percent on day 1 of a sale. On day 2, the item is discounted another 10 percent, and on day 3, it is discounted an additional 30 percent. The price of the item on day 3 is what percentage of the sale price on day 1?
A.63%
B.40%
C.64.8%
D.70%
Answer: A.63%
Explanation: original price = 100
day 1 discount = 10%,price = 100-10 =90
day 2 discount = 10%,price = 90-9=81
day 3 discount = 30%,price = 81-24.3= 56.7
which is 56.7/90 *100 of the sale price on day 1= ~63%
Answer A
Question: A boat can travel with a speed of 24 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 112 km downstream
A.3 hours
B.4 hours
C.5 hours
D.6 hours
Answer: B.4 hours
Explanation: Explanation:
Speed of the boat in still water = 24 km/hr
speed of the stream = 4 km/hr
Speed downstream = (22+5) = 28 km/hr
Distance travelled downstream = 112 km
Time taken = distance/speed = 112/28 = 4 hours
Answer: Option B
Question: Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar's age at present?
A.14
B.15
C.16
D.17
Answer: C.16
Explanation: Let the ages of Kunal and Sagar 6 years ago be 6x and 5x years respectively.
Then,	((6x + 6) + 4)/ ((5x + 6) + 4)	=	11/10
10(6x + 10) = 11(5x + 10)
5x = 10
x = 2.
Sagar's present age = (5x + 6) = 16 years.
ANSWERS : C
Question: The sum of five consecutive even numbers is 500. Find the middle number of the five?
A.140
B.66
C.100
D.99
Answer: C.100
Explanation: Middle number =500/5
=100
Ans C
Question: One vessel contains a mixture of 4 parts pure wine and 3 parts soda, whereas the other vessel contains a mixture of 9 parts pure wine and 5 parts soda. Compare the strength of the wine.
A.35;36
B.10 : 9
C.7 : 4
D.14 : 5
Answer: B.10 : 9
Explanation: 4/7 : 9/14
LCM of 7,14 = 14
(5/7)*14: (9/14)*14
10:9
Answer is B.
Question: A part-time employee whose hourly wage was decreased by 20 percent decided to increase the number of hours worked per week so that the employee's total income did not change. By what percent W should the number of hours worked be increased?
A.12.5%
B.20%
C.25%
D.50%
Answer: C.25%
Explanation: Correct Answer: C
Solution: C. We can set up equations for income before and after the wage reduction. Initially, the employee earns W wage and works H hours per week. After the reduction, the employee earns .8W wage and works X hours. By setting these equations equal to each other, we can determine the increase in hours worked: WH = .8WX (divide both sides by .8W) 1.25H = X We know that the new number of hours worked W will be 25% greater than the original number. The answer is C.
Question: A and B can do a work in 4 hours and 12 hours respectively. A starts the work at 6AM and they work alternately for one hour each. When will the work be completed?
A.3
B.4
C.5
D.6
Answer: D.6
Explanation: Work done by A and B in the first two hours, working alternately = First hour A + Second hour B = 1/4 + 1/12 = 1/3.
Total time required to complete the work = 2 * 3 = 6 days.Answer:D
Question: A person bought an article and sold it at a loss of 10%. If he had bought it for 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?
A.250
B.277
C.299
D.266
Answer: A.250
Explanation: CP1 = 100 SP1 = 90
CP2 = 80 SP2 = 80 * (140/100) = 112
22 ----- 100
55 ----- ? => Rs.250.Answer: A
Question: The perimeter of an equilateral triangle is 60. If one of the sides of the equilateral triangle is the side of an isosceles triangle of perimeter 70, then how long is the base of isosceles triangle?
A.15
B.20
C.25
D.30
Answer: D.30
Explanation: The base of the isosceles triangle is 70-20-20= 30 units
The answer is D.
Question: In a firm there are men and cows. In all, there are 21 heads and 64 feet. How many men and how many cows are in the firm?
A.8 men and 13 cows.
B.10 men and 11 cows.
C.6 men and 15 cows.
D.5 men and 16 cows.
Answer: B.10 men and 11 cows.
Explanation: 10 men and 11 cows.
Let M = men and C = cows. We can come up with 2 equations.
M + C = 21
2M + 4C= 64
Solving the 2 equations will give 10 men and 11 cows.
Answer B
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 80% 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 an advanced Trigonometry student is selected?
A.8%
B.12%
C.16%
D.20%
Answer: B.12%
Explanation: 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 0.8x
The number of students in beginner trigonometry is 4/5*(2.5x) - 0.8x = 1.2x
The number of students in advanced trigonometry is 0.3x
The percentage in advanced trigonometry is 0.3x / 2.5x = 12%
The answer is B.
Question: If a and b are different positive integers and a + b = a(a + b+1), then which of the following must be true?
I. a = 1
II. b = 1
III. a < b
A.I only
B.II only
C.III only
D.I and II
Answer: C.III only
Explanation: Number picking might not be the best way to solve MUST BE TRUE questions.
The question asks which of the followingMUSTbe true, or which of the following isALWAYStrue no matter what set of numbers you choose. For such kind of questionsif you can prove that a statement is NOT truefor one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.
So the set you chose just proves that II is not always true and hence it's not a part of a correct choice. As for I and III: they might be true for this particular set of numbers but not true for another set, so you can not say that I and III are always true just based on one set of numbers (it just happens to be that I and III are always true).
As forCOULD BE TRUEquestions:
The questions asking which of the followingCOULDbe true are different:if you can prove that a statement is truefor one particular set of numbers, it will mean that this statement could be true and hence is a correct answer.
C
Question: Linda spent 3/4 of her savings on furniture and the rest on a TV. If the TV cost her $450, what were her original savings?
A.$1500
B.$1600
C.$1700
D.$1800
Answer: D.$1800
Explanation: If Linda spent 3/4 of her savings on furnitute, the rest
4 / 4 - 3 / 4 = 1 / 4 on a TV
But the TV cost her $450. So 1 / 4 of her savings is $450. So her original savings are 4 times $450 = $1800
correct answer D
Question: A is thrice as good a work man as B and together they finish a piece of work in 16 days.The number of days taken by B alone to finish the work is :
A.64 days.
B.24 days.
C.52 days.
D.35 days.
Answer: A.64 days.
Explanation: Solution
(A’s 1 day’s work): (B’s 1 day’s work)= 3 : 1.
(A + B)'s 1 day’s work = 1/16
Divide 1/14 in the ratio 3 : 1.
∴ B’s 1 day’s work = (1/16 x1/4)= 1/64
Hence,B alone can finish the work in 64 days.
Answer A
Question: The edges of three iron cubes are 6cm; 8cm; 10cm respectively. A new cube was made by melting them. Find the edge of the new cube?
A.16
B.12
C.17
D.15
Answer: B.12
Explanation: 63 + 83 + 103 = a3
=> a = 12
Answer: B
Question: Thirty five percent of the portfolios managed by the Crocodile Brokers company (C.B.C.) hold Hatsopoulos stocks. Forty percent of the portfolios managed by C.B.C. hold McQuarrie stocks and do not hold Hatsopoulos stocks. Fifteen percent of the portfolios managed by C.B.C. hold Hatsopoulos stocks and do not hold McQuarrie stocks. What percent of the portfolios managed by C.B.C. do NOT hold McQuarrie stocks?
A.20
B.25
C.40
D.60
Answer: C.40
Explanation: H represent those portfolios holding Hatsopoulos stocks
M represent those portfolios holding McQuarrie stocks
35% hold H => z+x=35z+x=35
40% hold M and do not hold H => y = 40
15% hold H and not M => z = 15
We have , x = 20
x+y+z=20+40+15=75 x+y+z=20+40+15=75
There are 25% portfolios holding neither H nor M.
Portfolios that do not hold M = z+(neither H nor M)z+(neither H nor M)
= 15+25
=40
ANSWER:C
Question: The population of a town increased from 1,75,000 to 2,45,000 in a decade. The average percent increase of population per year is
A.4%
B.5%
C.6%
D.8.75%
Answer: A.4%
Explanation: Solution
Increase in 10 years	= (245000 - 175000)
= 87500.
Increase%	= (70000/175000Ã—100)%
= 40%.
Required average	= (40/10)%
= 4%.
Answer A
Question: Find the value of x from the below equation? : 3x^2+5x+2 = 0
A.-1
B.-2
C.1
D.2
Answer: A.-1
Explanation: a = 3, b = 5, c = 2
x1,2 = (-5 ± √(52 - 4×3×2)) / (2×3) = (-5 ± √(25-24)) / 6 = (-5 ± 1) / 6
x1 = (-5 + 1)/6 = -4/6 = -2/3
x2 = (-5 - 1)/6 = -6/6 = -1
A
Question: 3 candidates in an election and received 3000, 5000 and 20000 votes respectively. What % of the total votes did the winningcandidate got in that election?
A.45.12%
B.50%
C.57%
D.71.42%
Answer: D.71.42%
Explanation: Total number of votes polled = (3000 + 5000 + 20000) = 28000
So, Required percentage = 11628/20400 * 100 = 71.42%
D
Question: C and D started a business by investing Rs.1000/- and Rs.1500/- respectively. Find the D’s share out of a total profit of Rs.500:
A.400
B.300
C.200
D.100
Answer: D.100
Explanation: C = Rs.1000/-
D = Rs.1500/-
C share 2 parts & D share 3 parts
Total 5 parts -----> Rs.500/-
----> 1 part -------> Rs.100/-
D share = 3 parts -----> Rs.300/-
D
Question: Ayesha’s father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
A.2 years
B.4 years
C.6 years
D.8 years
Answer: C.6 years
Explanation: EXPLANATION
Mother’s age when Ayesha’s brother was born = 36 years.
Father’s age when Ayesha’s brother was born = (38 + 4) years = 42 years.
Required difference = (42 – 36) years = 6 years.
Answer C
Question: If x,y and z are positive integers, and 30x=35y=42z, then which of the following must be divisible by 3?
I. x
II. y
III. z
A.I
B.II
C.III
D.I & III
Answer: B.II
Explanation: 30X=35y=42z
x=35y/30---now check whether x is divisible by 3--35y/30 is not divisible by 3
y=30X/35---divisible by 3
z=35y/42----not divisible by 3
hence y is only divisible by 3.
Answer:B
Question: Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 2 litres from vessel P is mixed with 6 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?
A.13:1
B.13:3
C.13:8
D.13:5
Answer: B.13:3
Explanation: Quantity of alcohol in vessel P = 62.5/100 * 2 = 5/4 litres
Quantity of alcohol in vessel Q = 87.5/100 * 6 = 21/4 litres
Quantity of alcohol in the mixture formed = 5/4 + 21/4 = 13/2 = 6.5 litres
As 8 litres of mixture is formed, ratio of alcohol and water in the mixture formed
= 6.5 : 1.5 = 13:3.
Answer: B
Question: The dairy condensed milk has only 20% water while the cow milk has 90% water. How many litres of milk maid will be obtained from 72 litres of milk?
A.2
B.7
C.6
D.9
Answer: D.9
Explanation: Explanation:
In this question, Pure milk in condensed milk = Pure milk in cow milk
80% (x) = 10% (72)
Therefore, x = 9 Liters.
Answer:D