RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A password for a computer uses four digits from 0 to 9, inclusive. What is the probability that the digits of the password solely consist of prime numbers or zero?
A.1/32
B.1/16
C.1/8
D.2/5
Answer: B.1/16
Explanation: To calculate all the possibilities, there are 10 choices for each digit. The number of possibilities for five digits is 10 × 10 × 10 × 10 = 10,000 possible combinations.
Prime numbers constitute 2, 3,and 5 . In addition to zero, this is 4 total possibility for each digit. So the number of satisfactory variants is 4 × 4 ×4 × 4 So the probability is 1/2 × 1/2 × 1/2 × 1/2 = 1/16.
The right answer is choice (B).
Question: A couple who own an appliance store discover that if they advertise a sales discount of 10% on every item in the store, at the end of one month the number of total items sold increases 12%. Their gross income from sales for one month increases by what percent?
A.0.4%
B.0.8%
C.2%
D.4%
Answer: B.0.8%
Explanation: Let P be the original price and let x be the number of items sold originally.
The original income is P*x.
After the changes, the income is 0.9P*1.12x = 1.008*(P*x), an increase of 0.8%.
The answer is B.
Question: Arya starts cycling along the boundaries of the squares. She starts from a point A and after 90 minutes she reached to point C diagonally opposite to A. If she is travelling with 18km/hr, then find the area of square field.
A.125
B.182.25
C.325
D.425
Answer: B.182.25
Explanation: Explanation :
D = 18*3/2 = 27 km. So side of square is 13.5km, so area – 182.25km^2
Answer – B
Question: In 10 years, A will be twice as old5as B was 10 years ago. If A is now 11 years older than B, the present age of B is
A.35
B.37
C.39
D.41
Answer: D.41
Explanation: Explanation:
Let B's age = x years.
Then, As age = (x+ 11) years.
(x+11+10)=2(x—10)
hence x=41.
Present age of B = 41 years
Answer: Option D
Question: Company X sells a selection of products at various price points. Listed below are unit sales made for one particular day. How many unit sales on that day were greater than the mean sale price but less than the median sale price?
$50, $50, $97, $97, $97, $120, $125, $155, $199, $199, $209
A.0
B.1
C.2
D.3
Answer: B.1
Explanation: Taking the prices of products in ascending order(already arranged)
$50, $50, $97, $97, $97, $120, $125, $155, $199, $199, $209
we see that median value is the 6th value as there in total 11 values given
Arithmetic mean = total/number of entries = 1398/11 =127.9090
We are asked to find how many unit sales on that day were greater than the mean sale price but less than the median sale price
as we can clearly see that there is one value between $120 and $127.90, answer is 1 unit
Correct Answer - B
Question: A towel, when bleached, lost 20% of its length and 10% of its breadth. What is the percentage decrease in area?
A.26
B.28
C.24
D.20
Answer: B.28
Explanation: Formula for percentage change in area is:
=(−x−y+(xy)/100)%
=(−20−10+(20×10)/100)%=−28%
i.e., area is decreased by 28%
Answer is B.
Question: Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is:
A.48
B.49
C.50
D.51
Answer: C.50
Explanation: Let the length of each train be x metres.
Then, distance covered = 2x metres.
Relative speed = (46 - 36) km/hr
= 10x5/18 m/sec
= 25/9 m/sec
= 2x/36 =25/9
2x =100
X=50
answer :C
Question: A fruit seller had some apples. He sells 30% and still has 420 apples. Originally, he had ?
A.30 apples
B.600 apples
C.420 apples
D.70 apples
Answer: B.600 apples
Explanation: Answer
âˆµ 70% of N = 420
âˆ´ N = (420 x 100)/70 = 600
Correct Option: B
Question: A man, a woman and a boy can together complete a piece of work in 3 days. If a woman alone can do it in 6 days and a boy alone in 18 days, how long will a man take to complete the work?
A.5days
B.8days
C.7days
D.9days
Answer: D.9days
Explanation: Explanation:
(1 Man + 1 woman + 1 boy)’s 1day’s work = 1/3
1wo man’s 1 day work = 1/6
1boy’s 1 day’s work = 1/18
man alone can finish the work in 9 days.
Answer: Option D
Question: 9, 16, 18, 25, 36,49
A.9
B.16
C.18
D.25
Answer: C.18
Explanation: Each of the numbers except 18, is perfect square.
Answer: Option C
Question: A man can row downstream at 22 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?
A.16, 2
B.16, 4
C.16, 8
D.16, 6
Answer: D.16, 6
Explanation: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 22 --- (1)
and x - y = 10 --- (2)
From (1) & (2) 2x = 32 => x = 16, y = 6.
Answer:D
Question: In how many ways 4 Indians and 2 Englishmen can be seated in a row so that they are alternate?
A.120
B.96
C.144
D.48
Answer: D.48
Explanation: number of ways = 4!*2! = 48
Answer is D
Question: A number x is 3 times another number y. The percentage that y is less than x is
A.12.5%
B.66.6%
C.80%
D.11%
Answer: B.66.6%
Explanation: Say y=1 and x=3.
Then y=1 is less than x=3 by (3-1)/3*100=2/3*100=66.6%.
Answer: B.
Question: The volume of the largest right circular cone that can be cut out of a cube of edge 7 cm is:
A.79.8cm3
B.79.4cm3
C.89.8cm3
D.89.4cm3
Answer: C.89.8cm3
Explanation: Explanation:
Volume of the largest cone = Volume of the cone with diameter of base 7 and height 7 cm
Volume of cone =1/3πr2h
=1/3∗22/7∗3.5∗3.5∗7
=269.5/3cm3
=89.8cm3
Note: radius is taken as 3.5, as diameter is 7 cm
Option C
Question: Q' = 3Q - 3, what is the value of (6')' ?
A. 120
B. 150
C. 180
D. 210
Answer: D. 210
Explanation: (6')'=(3*6-3)'=15'=15*15-15=210
Answer D
Question: What is the remainder when 14,453 × 15,654 × 16,788 is divided by 5?
A.2
B.1
C.5
D.4
Answer: B.1
Explanation: Only the unit's digit of the product will decide the remainder when divided by 5.
Hence, 3*4*8= will give units digit as 5
So, whatever be the number, if it ends in 6, the remainder after dividing with 5 will be 1.
OptionB
Question: The ratio of the incomes of Uma and Bala is 8:7 and the ratio of their expenditure is 7:6. If at the end of the year, each saves $2000 then the income of Uma is?
A.$16800
B.$16500
C.$16000
D.$16300
Answer: C.$16000
Explanation: Let the income of Uma and Bala be $8x and $7x
Let their expenditures be $7y and $6y
8x-7y = 2000-------1)
7x-6y = 2000-------2)
From 1) and 2)
x = 1000
Uma's income = 8x = 8*2000 = $16000
Answer is C
Question: A train 110 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.7 sec
B.5 sec
C.4 sec
D.6 sec
Answer: D.6 sec
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
= [110 * 3/55] sec
= 6 sec
Answer:D
Question: 10 People take a history test. The following are the scores:
40, 45, 45, 50, 50, 60, 70, 75, 95, 100
Using the mean and median scores, find the amount of scores that fall in between the range of the two
A.One
B.Three
C.Five
D.Seven
Answer: A.One
Explanation: The median = (the average of two middle terms) = (50 + 60)/2 = 55.
The mean = (the sum)/(# of terms) = 630/10 = 63.
Only 60 is between 55 and 63.
Question: A compact car uses 15 gallons of fuel in traveling 360 miles. In order for the truck to travel the same distance using 12 gallons of fuel, by how many miles per gallon must the car’s fuel mileage be increased?
A.10
B.6
C.15
D.36
Answer: B.6
Explanation: There are two sets 15G1 gallons and 12G2 gallons details given.
15 gallons covering 360 miles
Then 1 G1 is used to cover 24 miles.
Now for 12, G2 covering 360 miles.
then 1 G2 is used to cover 30 miles.
Therefore, 30 - 24 = 6 miles per gallon increment is needed for 12 gallons to improve the mileage to cover 360 miles.
Thus, B is the correct answer.
Question: Mangala completes a piece of work in 12 days, Raju completes the same work in 20 days. If both of them work together, then the number of days required to complete the work is?
A.7.5 days
B.7.6 days
C.7.7 days
D.8.7 days
Answer: A.7.5 days
Explanation: 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 = 12 Ã— 20/32 = 7.5 days.
A)
Question: If selling price is doubled, the profit triples. Find the profit percent:
A.66 2/3
B.100
C.105 1/3
D.120
Answer: B.100
Explanation: Let C.P. be Rs. x and S.P. be Rx. y.
Then, 3(y - x) = (2y - x) => y = 2x
Profit = (y - x) = Rs. (2x - x) = Rs. x
Profit % = x/x * 100 = 100%.
ANSWER:B
Question: X, Y and Z can do a work in 9 , 10 and 15 days respectively. They completed the work and got Rs.600. What is the total amount earned by X and Y?
A.476
B.356
C.456
D.466
Answer: C.456
Explanation: The ratio of their working rates = 1/9 : 1/10 : 1/15 = 10 : 9 : 6.
Since, they work together, the share of X
= 10/25 * 600 = Rs.240
the share of Y = 9/25 * 600 = Rs.216
total amount earned by X and Y = 240 + 216 = Rs.456
Answer: C
Question: How many odd 4-digit positive integers R that are multiples of 5 can be formed without using the digit 3?
A.648
B.729
C.900
D.1296
Answer: A.648
Explanation: I choose A.
Possible n° of 1st digit: 8 (0 can't be the first number, or else it wouldn't have 4 digits. 3 is exlcuded)
Possible n° of 2nd digit: 9 (3 is excluded)
Possible n° of 3rd digit: 9 (3 is excluded)
Possible n° of 4th digit: 1 (a number is a multiple of 5 if it ends in 5 or 0, here we are asked for the odd numbers, hence the last digit can't be 0)
So, R=8*9*9*1=648 (A)
Question: Three pipes of same capacity A,B,C can fill a tank in 6 hours. If there are only two pipes B and C of same capacity, the tank can be filled in?
A.2
B.4
C.9
D.12
Answer: C.9
Explanation: The part of the tank filled by three pipes in one hour
= 1/6
=> The part of the tank filled by two pipes in 1 hour
= 2/3 * 1/6 = 1/9.
The tank can be filled in 9 hours.
Answer:C
Question: A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
A.278
B.276
C.20
D.288
Answer: C.20
Explanation: M = 15
S = 5
DS = 15 + 5 = 20
Answer: C
Question: The speeds of 3 trains in the ratio 4:12:24. The ratio between time taken by them to travel the same distance is?
A.6:2:1
B.1:2:3
C.4:8:9
D.6:5:2
Answer: A.6:2:1
Explanation: Ratio of time taken is = 1/4 : 1/12 : 1/24 = 6:2:1
Answer is A
Question: The ratio of ages of A and B at present is 2:3. After five years the ratio of their ages will be 3:4 What is the present age of A in years?
A.10
B.15
C.25
D.30
Answer: A.10
Explanation: ( 2x+5 ) /( 3x+5) = 3/4
or, 8x+20=9x+15
or,x=5
So, Present age of A = 2x = (2*5) = 10
ANSWER:A
Question: In dividing a number by 585, a student employed the method of short division. He divided the number successively by 5, 9 and 13 (factors 585) and got the remainders 4, 8, 12 respectively. If he had divided the number by 585, the remainder would have been
A.24
B.144
C.292
D.584
Answer: D.584
Explanation: 5 | x z = 13 x 1 + 12 = 25
--------------
9 | y - 4 y = 9 x z + 8 = 9 x 25 + 8 = 233
--------------
13| z - 8 x = 5 x y + 4 = 5 x 233 + 4 = 1169
--------------
| 1 -12
585) 1169 (1
585
---
584
---
Therefore, on dividing the number by 585, remainder = 584.
Answer:D
Question: The cost price of an article is 64% of the marked price. Calculate the gain percent after allowing a discount of 12%.
A.37.5 %
B.38.5 %
C.42 %
D.27.5 %
Answer: A.37.5 %
Explanation: Sol.
Let marked price = Rs. 100. Then, C.P. = Rs. 64. S.P = Rs. 88.
∴ Gain % = [24/64 * 100]% = 37.5%.
Answer A
Question: Combine terms: 12a + 26b -4b – 16a.
A.4a + 22b
B.-28a + 30b
C.-4a + 22b
D.28a + 30b
Answer: C.-4a + 22b
Explanation: 12a + 26b -4b – 16a.
= 12a – 16a + 26b – 4b.
= -4a + 22b.
correct answer C
Question: What least number must be added to the least number of six digits so that the resulting number may be a perfect square.
A.489
B.267
C.278
D.199
Answer: A.489
Explanation: The least number of six digits = 100000 3 10 00 00 317 9 61 100 61 627 3900 4389 – 489 Least number to be added = 489.
Answer:A
Question: what is the remainder when 789456123 is divided by 999
A.349
B.359
C.369
D.379
Answer: C.369
Explanation: there is a simple trick for 99 or 999..u have to add the digits from right side for 99 you will select the last 2 digits and add with next two last digits and go on..similarly for 999 u will add last three digits then its next two last digits and so on..
so you will get 123 + 456 +789 =1368 again select last 3 and add them u will get 368 + 001 i.e 369
ANSWER:C
Question: X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?
A.6 days
B.10 days
C.15 days
D.16 days
Answer: B.10 days
Explanation: Work done by X in 4 days =(1/20)*4=1/5
Remaining work =1 -1/5=4/5	.
(X + Y)'s 1 day's work =1/20+1/12 =	8/60	=	2/15	.
Now,	2/15	work is done by X and Y in 1 day.
So,	4/5	work will be done by X and Y in	(15/2x4/5)= 6 days.
Hence, total time taken = (6 + 4) days = 10 days.
Option B
Question: A toy store sells small, medium, and large toy trucks in each of the colors red, blue, black, green, and yellow. The store has an equal number of trucks of each possible color-size combination. If Paul wants a medium, red truck and his mother will randomly select one the trucks in the store, what is the probability that the truck she selects will have at least one of the two features Paul wants?
A.2/5
B.7/15
C.11/15
D.7/20
Answer: B.7/15
Explanation: Probability of NOT selecting medium out of 3 sizes = 2/3
Probability of NOT selecting red out of 5 colours = 4/5
Total probability of NOT selecting red and medium = (2/3)*(4/5) = 8/15
Required probability = 1 - 8/15 (this will select at least one of red and medium)
= 7/15
The answer is B.
Question: A student scored an average of 60 marks in 3 subjects: Physics, Chemistry and Mathematics. If the average marks in Physics and Mathematics is 90 and that in Physics and Chemistry is 70, what are the marks in Physics?
A.86
B.160
C.76
D.140
Answer: D.140
Explanation: Given M + P + C = 60 * 3 = 180 --- (1)
M + P = 90 * 2 = 180 --- (2)
P + C = 70 * 2 = 140 --- (3)
Where M, P and C are marks obtained by the student in Mathematics, Physics and Chemistry.
P = (2) + (3) - (1) = 180 + 140 - 180
= 140
Answer:D
Question: Find the ratio between whole surfaces of a sphere and a hemisphere?
A.4:8
B.4:3
C.4:2
D.4:1
Answer: B.4:3
Explanation: 4 πr2 : 3 πr2 => 4:3
Answer: B
Question: What least value should be replaced by * in 483*4312 so the number become divisible by 6
A.3
B.4
C.5
D.2
Answer: D.2
Explanation: Explanation:
Trick: Number is divisible by 6, if sum of all digits is divisible by 3 and 2,
Last digit is 2 so it is dividable by 2
so (4+8+3+*+4+3+1+2) = 25+* should be divisible by 6,
15+ will be divisible by ,
so that least number is 2.
Answer: Option D
Question: Marginal cost is the cost of increasing the quantity produced (or purchased) by one unit. If the fixed cost for n products is $10,000 and the marginal cost is $80, and the total cost is $16,000, what is the value of n?
A. 30
B. 50
C. 60
D. 75
Answer: D. 75
Explanation: Total cost for n products = fixed cost for n products + n*marginal cost --> $16,000 = $10,000 + n * $80 --> n = 75.
Answer: D.
Question: If x, y, and z are consecutive positive integers greater than 1, not necessarily in that order, then which of the following is (are) true?
I. x > z
II. 4x+ 4y > 4z
III. yz > xz
IV. xy > y + z
A. I only
B. II only
C. II and III only
D. II and IV only
Answer: B. II only
Explanation: we do not know the values or the relative values but that the three are consecutive..
so the max difference in any two number is 2 and min 1..
lets see the choices..
I. x > z...
we do not know the values or the relative values... need not be true..
II. 4x+ 4y > 4z or x+ y > z
we take the worst case that z is teh largest and x and y are lowest possible..... so 2+3>4.. 5>4.. always true
III. yz > xz
we do not know the values or the relative values between x and y..need not be true
IV. xy > y + z
xy-y>z or y(x-1)>z...
again lets take the worst scenario..
we take the worst case that z is the largest and x and y are lowest possible..... so (2-1)3>4.. 3>4.. not true
only ii is true
ans B
Question: A large delicatessen purchased p pounds of cheese for K dollars per pound. If d pounds of the cheese had to be discarded due to spoilage and the delicatessen sold the rest for s dollars per pound, which of the following represents the gross profit on the sale of the purchase? (gross profitequalssales revenueminusproduct cost)
A.(p − d)(s − c)
B.s(p-d) - Kp
C.c(p − d) − ds
D.d(s − c) − pc
Answer: B.s(p-d) - Kp
Explanation: Total cost price = K*p ............... (1)
Wastage = d pounds
Quantity sold = p-d
Selling price per pound = s
Total selling price = s(p-d) ........... (2)
Profit = (2) - (1)
= s(p-d) - Kp
B
Question: A jogger running at 9 km/hr along side a railway track is 190 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
A.88
B.27
C.36
D.31
Answer: D.31
Explanation: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 190 + 120 = 310 m.
Time taken = 310/10 = 31 sec.
Answer: D
Question: A new basketball cost increased 5% last week. A basketball coach wanted to buy two dozen basketballs in bulk for his team. He was able to negotiate paying only 90% of the posted price for the bulk purchase. How much did the coach save by purchasing in bulk?
A.2.5%
B.3.5%
C.4.5%
D.5.5%
Answer: D.5.5%
Explanation: Quantity X Rate = Price
1 X 1 = 1
0.9 X 1.05 = 0.945
Decrease in price = (0.055/1) Ã— 100 = 5.5%
Answer = Option D
Question: The average age 12 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number?
A.24 years
B.21 years
C.18 years
D.29 years
Answer: A.24 years
Explanation: 12 * 2 = 24 years
Answer:A
Question: 29 persons can repair a road in 16 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?
A.12.88
B.3.88
C.13.88
D.15
Answer: A.12.88
Explanation: Let the required number of days be x
More persons, less days (indirect proportion)
More hours, less days (indirect proportion)
Hence we can write as
(persons)29:30
}::x:16
(hours)5:6
29*5*16=30*6*x
x=12.88
ANSWER:A
Question: If a card is randomly drawn from a well shuffled pack of cards, what is the probability of drawing a black card or a king?
A.6/13
B.7/10
C.4/11
D.7/13
Answer: D.7/13
Explanation: There are 26 black cards and 2 red kings.
P(black card or king) = 28/52 = 7/13
The answer is D.
Question: Jack and Jill are marathon runners. Jack can finish a marathon (42 km) in 5 hours and Jill can run a marathon in 4.2 hours.What is the ratio of their average running speed? (Jack: Jill)
A.14/15
B.15/14
C.4/5
D.21/25
Answer: D.21/25
Explanation: Average Speed of Jack =Distance/ Time
= 42 /5
Average Speed of Jill = 42/(4.2) = 10
Ratio of Average speed of Jack to Jill = (42/5)/10 =42/50 =21/25
Answer D
Question: The dimensions of a room are 10m x 7m x 5m. There are 2 doors and 3 windows in the room. The dimensions of the doors are 1m x 3m. One window is of size 2m x 1.5m and the other 2 windows are of size 1m x 1.5m. The cost of painting the walls at Rs. 3 per sq m is
A.2488
B.378
C.739
D.474
Answer: D.474
Explanation: Explanation:
Area of 4 walls = 2(l+b)h
=2(10+7) x 5 = 170 sq m
Area of 2 doors and 3 windows = 2(1x3)+(2x1.5)+2(1x1.5) = 12 sq m
area to be planted = 170 -12 = 158 sq m
Cost of painting = Rs. 158 x 3 = Rs. 474
Answer:D
Question: In how many ways can the letters of the word AEOGHYI be rearranged such that the vowels always appear together?
A.254
B.576
C.476
D.765
Answer: B.576
Explanation: AEOGHYI
AEOI will come together as a group which can be arranged in 4!=24ways.
AEOI, G,H,Ycan be arranged in 4!=24 ways.
total possible arrangements = 24*24=576 ways
ANSWER:B
Question: In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?
A.50400
B.50420
C.50500
D.50540
Answer: A.50400
Explanation: The word 'CORPORATION' has 11 letters. It has the vowels 'O','O','A','I','O' in it and these 5 vowels should always come together. Hence these 5 vowels can be grouped and considered as a single letter. that is, CRPRTN(OOAIO).
Hence we can assume total letters as 7. But in these 7 letters, 'R' occurs 2 times and rest of the letters are different.
Number of ways to arrange these letters
=
7
!
2
!
=
7
×
6
×
5
×
4
×
3
×
2
×
1
2
×
1
=
2520
=7!2!=7×6×5×4×3×2×12×1=2520
In the 5 vowels (OOAIO), 'O' occurs 3 and rest of the vowels are different.
Number of ways to arrange these vowels among themselves
=
5
!
3
!
=
5
×
4
×
3
×
2
×
1
3
×
2
×
1
=
20
=5!3!=5×4×3×2×13×2×1=20
Hence, required number of ways
=
2520
×
20
=
50400
=2520×20=50400
A)
Question: Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 1/3 were basic and the rest were deluxe. If it takes 7/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?
A.7/17
B.14/31
C.7/15
D.14/19
Answer: D.14/19
Explanation: # of basic stereos was 1/3 of total and # of deluxe stereos was 2/3 of total, let's assume total=15, then Basic=5 and Deluxe=10.
Now, if time needed to produce one Deluxe stereo is 1 unit than time needed to produce one Basic stereo would be 7/5 units. Total time for Basic would be 5*1=5 and total time for Deluxe would be 10*7/5=14 --> total time for both of them would be 5+14=19--> deluxe/total=14/19.
Answer: D.
Question: A corporation that had $10 billion in profits for the year paid out $200 million in employee benefits. Approximately what percent of the profits were the employee benefits? (Note: 1 billion = 10^9)
A.50%
B.20%
C.5%
D.2%
Answer: D.2%
Explanation: required answer = [employee benefit/profit] *100
=[(200 million)/(10 billion)]*100
=[(200*10^6)/(10*10^9)]*100
=(20/1000)*100
=2%
So answer is (D)
Question: What will come in place of the x in the following Number series? 177147 ,59049 ,19683 ,6561, 2187 , x
A.727
B.729
C.726
D.722
Answer: B.729
Explanation: Go on dividing by 3 to the next number
Answer : B
Question: The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is:
A.12
B.16
C.24
D.48
Answer: D.48
Explanation: EXPLANATION
Let the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 4.
So, the numbers 12 and 16.
L.C.M. of 12 and 16 = 48.
Answer D
Question: All the water in container A which was filled to its brim was poured into two containers B and C. The quantity of water in container B was 62.5% less than the capacity of container A. If 148 liters was now transferred from C to B, then both the containers would have equal quantities of water. What was the initial quantity of water in container A?
A.1726 liters
B.1362 liters
C.1280 liters
D.1184 liters
Answer: D.1184 liters
Explanation: B has 62.5% or (5/8) of the water in A. Therefore, let the quantity of water in container A(initially) be 8k.
Quantity of water in B = 8k - 5k = 3k.
Quantity of water in container C = 8k - 3k = 5k
Container: A B C
Quantity of water: 8k 3k 5k
It is given that if 148 liters was transferred from container C to container B, then both the containers would have equal quantities of water.
5k - 148 = 3k + 148 => 2k = 296 => k = 148
The initial quantity of water in A = 8k = 8 * 148 = 1184 liters.
Answer:D
Question: The difference of two numbers is 8 and one-fourth of their sum is 6. Find the numbers.
A.16,8
B.10,2
C.17,6
D.14,10
Answer: A.16,8
Explanation: Let numbers be x and y.
Equation (i): x - y = 8
Equation (ii): (x + y)/4 = 6
Solve system of equations: x=16, y=8
A is the correct answer.