RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: The average (arithmetic mean) of four different positive integers is 12. If the first of these integers in 3 times the second integer and the second integer is 2 less than the third integer, what is the least possible value of the fourth integer?
A.5
B.4
C.3
D.2
Answer: C.3
Explanation: Let the second integer be x and the fourth be a.
Then [3x + x + (x+2) + a]/4 = 12
=> 5x + 2 + a = 48
=> 5x + a = 48
=> a = 48 - 5x
From the above equation we can see that a is minimum when x is maximum, provided both are positive
The maximum value that x can take in the above equation while still keeping a positive is x=9
This gives us a= 48 - 45 = 3
Therefore the minimum value that the fourth integer can have is 3. Option C.
Question: In the country of Celebria, the Q-score of a politician is computed from the following formula:
Q=(41ab^2c^3)/d2, in which the variables a, b, c, and d represent various perceived attributes of the politician, all of which are measured with positive numbers. Mayor Flower’s Q-score is 150% higher than that of Councilor Plant; moreover, the values of a, b, and c are 60% higher, 40% higher, and 20% lower, respectively, for Mayor Flower than for Councilor Plant. By approximately what percent higher or lower than the value of d for Councilor Plant is the corresponding value for Mayor Flower?
A.56% higher
B.25% higher
C.8% lower
D.20% lower
Answer: D.20% lower
Explanation: Let's say M stands for Mayor and P stands for councilor
Then as per given information -
Qm = 2.5*Qp
Am = 1.6 Ap
Bm = 1.4 Bp
Cm = 0.8 Cp
and let
Dm = X* Dp
On substituting these values and solving for X we get X ~ 0.8 ....
Hence it is lower by 20%
Ans - D
Question: Eleven bags are bought for Rs.1000 and sold at 10 for Rs.1100. What is the gain or loss in percentage?
A.29%
B.21%
C.23%
D.28%
Answer: B.21%
Explanation: Explanation:
As selling price is Rs.1100 for 10 bags, each bag is sold at Rs.110.
Hence, the profit is Rs.100 after selling 10 bags plus the selling price of 1 bag = 100 + 110 = Rs.210.
%profit = 210/1000 *100
= 21%
ANSWER: B
Question: The prices of tea and coffee per kg were the same in june. In july the price of coffee shot up by 20% and that of tea dropped by 20%. if in july , a mixture containing equal quantities of tea and coffee costs 90/kg. how much did a kg of coffee cost in june ?
A.50
B.60
C.80
D.90
Answer: D.90
Explanation: Let the price of tea and coffee be x per kg in June.
Price of tea in July = 1.2x
Price of coffee in July = 0.8x .
In July the price of 1/2 kg (900gm) of tea and 1/2 kg (900gm) of coffee (equal quantities) = 90
1.2x(1/2) + 0.8x(1/2) = 90
=> x =90
Thus proved...option D.
Question: The maximum gap between two successive leap year is?
A.2
B.8
C.9
D.6
Answer: B.8
Explanation: Explanation:
This can be illustrated with an example.
Ex: 1896 is a leap year.The next leap year comes in 1904 (1900 is not a leap year).
Answer: B) 8
Question: What is the greatest integer that will always evenly divide the sum of four consecutive integers?
A.2
B.3
C.4
D.6
Answer: C.4
Explanation: Let the three consecutive even integers be x , x + 4 , x+8 , x+12
Sum = x + x + 4 + x + 8 + x + 12
= 4x+24 = 4(x+6)
Therefore , 4 will always be a factor .
Answer C
Question: For any function Fn(x)=Fn−1(F(x))Fn(x)=Fn−1(F(x)) if for n > 1 also g(x) = 1/x, h(x) = x−−√x and k(x) = x2x2 then what is the value of g(h3(k2(x)))?
A.1
B.8
C.7
D.6
Answer: A.1
Explanation: Given Fn(x)=Fn−1(F(x));Fn(x)=Fn−1(F(x)); g(x) = 1/x; h(x) = x−−√x; k(x) = x−−√x
Then, k(k(x)) = (x2)2=x4(x2)2=x4
And, h3(k2(x))=h(h(h(k2(x))))=h(h(x2))=h(x)=x−−√.h3(k2(x))=h(h(h(k2(x))))=h(h(x2))=h(x)=x.
And, g(h3(k2(x)))=g(x−−√)=1/x−−√.g(h3(k2(x)))=g(x)=1/x.
Hence answer is option (A).
Question: Which of the following must be subtracted from 2^526 so that the resulting integer will be a multiple of 3?
A.1
B.2
C.3
D.5
Answer: A.1
Explanation: 2^12 is definitely NOT a multiple of 3 as 2^12 will only have 2s in it.
Coming back to the question,
2^1 leaves a remainder of 2 when divided by 3
2^2 leaves a remainder of 1 when divided by 3
2^3 leaves a remainder of 2 when divided by 3
2^4 leaves a remainder of 1 when divided by 3... etc. and the cyclicity continues.
Thus, 2^526 will leave a remainder of 1 when divided by 3. Thus you must subtract 1 from 2^526 to make it divisible by 3.
A is thus the correct answer.
Question: 28 buckets of water fill a tank when the capacity of each bucket is 13.5 litres. How many buckets will be required to fill the same tank if the capacity of each bucket is 9 litres?
A.30
B.42
C.60
D.Data inadequate
Answer: B.42
Explanation: Capacity of the tank = 28 Ã— 13.5= 378 litres
When the capacity of each bucket = 9 litres, then the required no. of buckets
= 378â„9 = 42
Answer B
Question: What is the are of an equilateral triangle of side 16 cm?
A.64√6 cm2
B.84√3 cm2
C.64√9 cm2
D.64√3 cm2
Answer: D.64√3 cm2
Explanation: Area of an equilateral triangle = √3/4 S2
If S = 16, Area of triangle = √3/4 * 16 * 16
= 64√3 cm2;
Answer: D
Question: There is a plane contains 32 points.all the 32 points have equal distance from point x. which of the following is true .
A.ll 32 points lie in circle
B.the distance from x to all 32 points is less than the distance between each other c. both a and b
C.both a and b
D.32
Answer: C.both a and b
Explanation: Option 3
X must be the center of the circle and 32 points are on the circumference. So Option A is correct
Number of diagnols of a regular polygon = n(n−3)2n(n−3)2
So for a polygon of 32 sides, Number of diagnols = 464. Now the minimum distance between any two points = 2πr32=1156r2πr32=1156r
Now total lengh of all the distances from 32 points = 2πr2πr + Sum of the lengths of all the 464 diagnols.
Sum of the lengths of x to all the 32 points = 32 radius = 32r
But the 464 diagnols have 16 diameters connecting 2 oposite points connecting via center. So Sum of the lengths of distances from point to point is clearly greater than sum of the length from x to all 32 ponts. Option B is correct
Answer:C
Question: In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can?
A.40
B.44
C.48
D.52
Answer: B.44
Explanation: Let the capacity of the can be T litres.
Quantity of milk in the mixture before adding milk = 4/9 (T - 8)
After adding milk, quantity of milk in the mixture = 6/11 T.
6T/11 - 8 = 4/9(T - 8)
10T = 792 - 352 => T = 44.
ANSWER:B
Question: If X:Y is 1:5 and Y:Z is 5:7 then X:Z is equal to
A.1:6
B.1:5
C.1:4
D.1:7
Answer: D.1:7
Explanation: The two ratios given are having the same number 5 for Y in both the ratios.
Hence- X:Y = 1:5 Y:Z = 5:7
=> X:Z = 1:7
Answer D
Question: If two integers x,y (x>y) are selected from -5 to 5 (inclusive), how many cases are there?
A.55
B.60
C.65
D.70
Answer: A.55
Explanation: There are 11 integers from -5 to 5 inclusive.
11C2 = 55.
The answer is A.
Question: If 100 microns = 1 decimeter, and 1,000angstroms = 1 decimeter, how many angstroms equal 1 micron?
A.1.0e-05
B.0.0001
C.10
D.10,000
Answer: C.10
Explanation: 100 microns = 1 decimeter
1,000 angstroms = 1 decimeter
100 microns = 1,000 angstroms
1 micron = 1,000/100 = 10
Answer : C
Question: A military camp has a food reserve for 250 personnel for 40 days. If after 15 days 50 more personnel are added to the camp, find the number of days the reserve will last for?
A.20
B.36
C.25
D.42
Answer: C.25
Explanation: Explanation:
As the camp has a reserve for 250 personnel that can last for 40 days, after 10 days the reserve left for 250 personnel is for 30 days. Now 50 more personnel are added
in the camp.
Hence, the food reserve for 300 personnel will last for:
250:300::x:30 ……..(it is an indirect proportion as less men means more days)
x = (250*30)/300
x = 25 days
ANSWER C
Question: A man can row with a speed of 15 kmph in still water. If the stream flows at 4 kmph, then the speed in downstream is?
A.33
B.77
C.20
D.19
Answer: D.19
Explanation: M = 15
S = 4
DS = 15 + 4 = 19
Answer: D
Question: If a fisherman catches 203128 shrimp while out and has to evenly split the catch between 9 restaurants, how many shrimp would he have left over?
A.4
B.7
C.2
D.1
Answer: B.7
Explanation: In order to find the answer you need to find a number that is divisible by 9.
The sum of 203128 16. 9 is divisible by 9 therefore you would subtract 7. 16-7=9
There would be 7 shrimp leftover. Answer B.
Question: A 15% item yields 30%. The market value of the item is:
A.Rs. 45
B.Rs. 55
C.Rs. 50
D.Rs. 60
Answer: C.Rs. 50
Explanation: Let the face value of the item is Rs.100
It yields Rs.15
Market value of the stock=(15/30)*100=Rs.50
ANSWER:C
Question: Three-twentieths of the members of a social club are retirees who are also bridge players, Four-twentieths of the members are retirees, and one-half of the members are bridge players. If 110 of the members are neither retirees nor bridge players, what is the total number of members in the social club?
A.200
B.300
C.360
D.400
Answer: A.200
Explanation: {Total} = {Retirees} + {Bridge players} - {Both} + {Neither}
x = 4/20*x + x/2 - 3/20*x + 110
20x = 4x + 10x - 3x + 110*20 (multiply by 20)
11x = 110*20
x = 200.
Answer: A
Question: The radius of a semi circle is 5.2 cm then its perimeter is?
A.32.52
B.32.48
C.26.74
D.32.9
Answer: C.26.74
Explanation: 36/7 r = 5.2 = 26.74
Answer:C
Question: The ratio of two numbers is 3:4 and their sum is 42. The greater of the two numbers is?
A.12
B.14
C.24
D.17
Answer: C.24
Explanation: 3:4
Total parts = 7
= 7 parts --> 42 (7 Ã— 6 = 42)
= 1 part ---->6 (1 Ã— 6 = 6)
= The greater of the two number is = 4
= 4 parts ----> 24 (6 Ã— 4 = 24)
C)
Question: In a particular year, the month of january had exactly 4 thursdays, and 4 sundays. On which day of the week did january 1st occur in the year.
A.sunday
B.monday
C.tuesday
D.wednesday
Answer: B.monday
Explanation: series of days may be either one of two:
(i)sun-4,mon-4,tue-4,wed-4,thu-4,fri-3 or 5,sat-3 or 5
(ii)thu-4,fri-4,sat-4,sun-4,mon-3or5,tue-3or5,wed-3or5
Lets check through option,
sun=1,8,15,22,29 jan ... which is not satisfies // wrong
Mon=1,8,15,22,29 jan,,,This satisfy option(ii) with thu-4,fri-4,sat-4,sun-4,mon-5,tue-5,wed-5
ANSWER:B
Question: If 2 men or 3 women can reap a field in 12 days how long will 4 men and 5 women take to reap it?
A.12/16
B.11/36
C.14/24
D.18/36
Answer: B.11/36
Explanation: Explanation:
2 men reap 1/12 field in 1 day
1 man reap 1/(2 x 12)
3 women reap 1/12 field in 1 day
1 woman reap 1/(12 x 3)
4 men and 5 women reap (4/(2 x 12)+ 5/(3 x 12) =11/36 in 1 day
4 men and 5 women will reap the field in 11/36 days
Answer: Option B
Question: A boy has 11 trousers and 12 shirts. In how many different ways can he select a trouser and a shirt?
A.120ways
B.138ways
C.140ways
D.132ways
Answer: D.132ways
Explanation: The boy can select one trouser in 11 ways.
The boy can select one shirt in 12 ways.
The number of ways in which he can select one trouser and one shirt is 11 * 12
= 132 ways.
Answer: D
Question: If y = 30p, and p is prime, what is the greatest common factor of y and 12p, in terms of p?
A.p
B.5p
C.6p
D.7p
Answer: C.6p
Explanation: Y=30p
other number is 12p
then GCF(30p,12P)=6P; C is the correct answer
Question: The unit digit in the product (445 * 534 * 999 * 234) is:
A.2
B.0
C.6
D.5
Answer: B.0
Explanation: Explanation:
Unit digit in the given product = Unit Digit in (5*4*9*4) = 0
ANSWER: B
Question: A pair of articles was bought for $360 at a discount of 10%. What must be the marked price of each of the article?
A.$200
B.$500
C.$350
D.$400
Answer: A.$200
Explanation: S.P. of each of the article = 360/2 = $180
Let M.P = $x
90% of x = 360
x = 180*100/90 =$200
Answer is A
Question: Jim bought edging to go around a circular garden with a radius of 5 feet. Later he decided to
double the diameter of the garden. How many more feet of edging must he buy?
A.28.84' additional edging
B.48.84' additional edging
C.31.40' additional edging
D.18.84' additional edging
Answer: C.31.40' additional edging
Explanation: circumference of small garden = 2 x 3.14 x 5 = 31.40'
double of the circumference of small garden = 2 x 31.40' = 62.80'
More feet to be buy = 62.80 - 31.40 = 31.40
Answer : C
Question: The difference between the local value and the face value of 7 in the numeral 32675149 is
A.75142
B.64851
C.5149
D.69993
Answer: D.69993
Explanation: (Local value of 7) - (Face value of 7) = (70000 - 7) = 69993
Answer: Option D
Question: The average age of boys in a class is 16 years and that of the girls is 15 years. What is the average age for the whole class?
A.15
B.16
C.15.5
D.Insufficient Data
Answer: D.Insufficient Data
Explanation: Explanation:
We do not have the number of boys and girls. Hence we cannot find out the answer.
Answer: Option D
Question: A and B start a business with investments of Rs. 5000 and Rs. 4500 respectively. After 4 months, A takes out half of his capital. After two more months, B takes out one-third of his capital while C joins them with a capital of Rs. 7000. At the end of a year, they earn a profit of Rs. 5080. Find the share of each member in the profit.
A.A - Rs. 1600, B - Rs. 1800, C - Rs. 1680
B.A - Rs. 1680, B - Rs. 1600, C - Rs. 1800
C.A - R,s. 1800, B - Rs. 1500, C - Rs. 1780
D.A - Rs. 1400, B - Rs. 1900, C - Rs. 1780
Answer: A.A - Rs. 1600, B - Rs. 1800, C - Rs. 1680
Explanation: Explanation:
A:B:CA:B:C =(5000Ã—4+2500Ã—8)=(5000Ã—4+2500Ã—8) :(4500Ã—6+3000Ã—6):(4500Ã—6+3000Ã—6) :(7000Ã—6):(7000Ã—6)
=40000:45000:42000=40000:45000:42000 =40:45:42=40:45:42.
A's share = Rs. 5080Ã—401275080Ã—40127 = Rs. 1600.
B's share = Rs. 5080Ã—451275080Ã—45127 = Rs. 1800.
C's share = Rs. 5080Ã—421275080Ã—42127 = Rs. 1680.
ANSWER IS A
Question: Four different objects 1,2,3,4 are distributed at random in four places marked 1,2,3,4. What is the probability that none of the objects occupy the place corresponding to its number?
A.17/24
B.3/8
C.1/2
D.5/8
Answer: C.1/2
Explanation: Explanation :
Let a particular number (say) number 2 occupies position 1.
Then all possible arrangement are given as:
=>(2,1,3,4), (2,1,4,3), (2,3,4,1), (2,4,1,4), (2,4,1,3), (2,4,3,1).
Out of these six, three (2,1,3,4), (2,3,1,4), (2,4,3,1) are not acceptable because numbers 3 and 4 occupy the correct positions.
Hence, the required probability = 3/6 = 1/2.
Answer : C
Question: Of the families in City X in 1991, 60 percent owned a personal computer. The number of families in City X owning a computer in 1993 was 20 percent greater than it was in 1991, and the total number of families in City X was 9 percent greater in 1993 than it was in 1991. what percent of the families in City X owned a personal computer in 1993?
A.59%
B.55%
C.63%
D.66%
Answer: D.66%
Explanation: Say a 100 families existed in 1991 then the number of families owning a computer in 1991 - 60
Number of families owning computer in 1993 = 60 * 120/100 = 72
Number of families in 1993 = 109
The percentage = 72/109 * 100 = 66%.
ANSWER:D
Question: A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 35600
. What percentage of profit did he make?
A.80%
B.49%
C.40%
D.60%
Answer: D.60%
Explanation: The total CP = Rs. 16000 + Rs. 6250
= Rs. 22250 and SP = Rs. 35600
Profit(%) = (35600 - 22250)/22250 * 100
= 60%
Answer:D
Question: John had a stock of 1200 books in his bookshop. He sold 75 on Monday, 50 on Tuesday, 64 on Wednesday, 78 on Thursday and 135 on Friday. What percentage of the books were not sold?
A.36.5%
B.46.5%
C.66.5%
D.76.5%
Answer: C.66.5%
Explanation: Let N be the total number of books sold. Hence
N = 75 + 50 + 64 + 78 + 135 = 402
Let M be the books NOT sold
M = 1200 - N = 1200 - 402 = 798
Percentage
Books not sold / total number of books = 798/1200 = 0.665 = 66.5%
correct answer C
Question: A and B can do a piece of work in 7 days. With the help of C they finish the work in 4 days. C alone can do that piece of work in?
A.33
B.9 1/3
C.30
D.88
Answer: B.9 1/3
Explanation: C = 1/4 â€“ 1/7 = 3/28 => 28/3 = 9 1/3 days
Answer: B
Question: A committee of three students has to be formed. There are six candidates: Jane, Joan, Paul, Stuart, and Jessica. If Paul and Stuart refuse to be in the committee together and Jane refuses to be in the committee without Paul, how many committees are possible?
A.3
B.4
C.5
D.6
Answer: D.6
Explanation: Let's try a different problem with your approach. There are five people: A, B, C, D, E. Need to chose 3 for a committee. A and B cannot be chosen together. B and C cannot be chosen together. How many options?
Your approach: total 10 options, 5c3.
Now, assume the wrong scenario where A and B are chosen together. There are three such scenarios. (A and B are chosen, just need one more person.) So we have to subtract the three wrong options. Similarly, there are three wrong scenarios where B and C are chosen together.
This gives us 10-3-3=4 as the answer.
Yet this answer is wrong. There are five possibilities: ACD, ACE, ADE, BDE, CDE.
D
Question: The simple interest on Rs. 10 for 4 months at the rate of 3 paise per rupeeper month is
A.1.2
B.1.4
C.2.25
D.3.21
Answer: A.1.2
Explanation: Sol.
S.I. = Rs. [10 * 3/100 * 4] = Rs. 1.20
Answer A
Question: If n is a positive integer, which of the following is a possible value of |36 - 5n|?
A.7
B.14
C.12
D.15
Answer: B.14
Explanation: When 36>5n, then |36- 5n| = 71- 5n = (36-5n) + 1 = {multiple of 5} + 1
When 36<=5n, then |36- 5n| = -(71- 5n) = (36-70) - 1 = {multiple of 5} - 1
So, the correct answer must be 1 greater or 1 less than a multiple of 5. Only B fits.
Answer: B
Question: TOM traveled the entire 50 miles trip. If he did the first 15 miles of at a constant rate 20 miles per hour and the remaining trip of at a constant rate 45 miles per hour, what is the his average speed, in miles per hour?
A.60.40mph
B.60.20mph
C.55.32mph
D.65.50mph
Answer: A.60.40mph
Explanation: avg speed = total distance/ total time = (d1+d2)/(t1+t2) = (15+35) / ((15/20)+(35/45)) = 50*180/149 = 60.40mph
A
Question: A train traveled the first d miles of its journey it an average speed of 60 miles per hour, the next d miles of its journey at an average speed of y miles per hour, and the final d miles of its journey at an average speed of 160 miles per hour. If the train’s average speed over the total distance was 90 miles per hour, what is the value of y?
A. 68
B. 84
C. 90
D. 110
Answer: D. 110
Explanation: Average speed=Total distance traveled /Total time taken
3d/d/60+d/y+d/160=90
Solving for d and y,
15y=11y+480
4y=440
y=110
Answer D
Question: The size of a television screen is given as the length of the screen's diagonal. If the screens were flat, then the area of a square 20-inch screen would be how many square inches greater than the area of a square 18-inch screen?
A.2
B.4
C.16
D.38
Answer: D.38
Explanation: Pythogoras will help here!
let the sides be x and diagonal be d
Then d ^2 = 2x^2
and
Area = x^2
Now plug in the given diagonal values to find x values
and then subtract the areas
Ans will be 20^2/2 - 18^2 /2 = 76 /2 = 38
Ans D.
Question: how many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?
A.5
B.10
C.15
D.20
Answer: D.20
Explanation: Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it.
The tens place can now be filled by any of the remaining 5 digits (2, 3, 6, 7, 9). So, there are 5 ways of filling the tens place.
The hundreds place can now be filled by any of the remaining 4 digits. So, there are 4 ways of filling it.
Required number of numbers = (1 x 5 x 4) = 20.
ANSWER D 20
Question: Two cars are 500 cm apart. each is moving forward for 100 cm at a velocity of 50 cm/s and receding back for 50 cm at 25cm/s at what time they will collide with each other.
A.11 sec
B.14 sec
C.12 sec
D.13 sec
Answer: B.14 sec
Explanation: each car is moving forward for 100 cm with velocity 50cm/s
so time to cover 100cm is=100/50=2 sec
again receding back for 50 cm at 25cm/s velocity
so time to cover 50 cm is=50/25=2 sec
actually they individually cover (100-50)=50 cm in (2+2)=4 sec
so in 12 sec they together cover (150+150)=300 cm
and after that both move 100 cm in 2 sec
so after (12+2)=14 sec they cover (300+200)=500cm
so they collide after 14 sec
ANSWER:B
Question: What is the % change in the area of a rectangle when its length increases by 30% and its width decreases by30%?
A.0%
B.20% increase
C.20% decrease
D.9% decrease
Answer: D.9% decrease
Explanation: (13/10)*(7/10) =91/100 of original area
91/100 is a 9% decrease from 100/100 ->D
Question: Find the area of the quadrilateral of one of its diagonals is 20 cm and its off sets 9 cm and 6 cm?
A.150 cm2
B.196 cm2
C.189 cm2
D.146 cm2
Answer: A.150 cm2
Explanation: 1/2 * 20(9 + 6)
= 150 cm2
Answer:A
Question: If the cost of 12 apples is $20. What would be the cost of 20 apples?
A.25.5
B.29.36
C.33.33
D.35.56
Answer: B.29.36
Explanation: The cost of one apple=20/12=1.67
The cost of twenty apples= 1.67x20= $ 33.33
Answer: B
Question: Income and expenditure of a person are in the ratio 10 : 8. If the income of the person is Rs. 10000, then find his savings?
A.2003
B.2002
C.2000
D.2001
Answer: C.2000
Explanation: Let the income and the expenditure of the person be Rs. 10x and Rs. 8x respectively.
Income, 10x = 10000 => x = 1000
Savings = Income - expenditure = 10x - 8x = 2x = 2(1000)
So, savings = Rs. 2000.
Answer:C
Question: The banker's gain on a bill due 1 year hence at 10% per annum is Rs. 20. What is the true discount?
A.Rs. 200
B.Rs. 100
C.Rs. 150
D.Rs. 250
Answer: A.Rs. 200
Explanation: Explanation :
TD = (BG ×100)/TR = (20×100)/(1×10) = Rs. 200 Answer : Option A
Question: The first train leaves the station at 6:00 am with a speed of 60 km/hr. The second train leaves at 7:00 am, in the same direction from the same station, with a speed of 75 km/hr. What time will the second train catch the first train?
A.10:00 am
B.11:00 am
C.12:00 noon
D.1:00 pm
Answer: B.11:00 am
Explanation: In sixty minutes, the first train travels 60 km.
The second train catches the first train with a relative speed of 15 km/h.
The second train will catch the first train in 4 hours.
The second train will catch the first train at 11:00 am.
The answer is B.
Question: The area of a square field is A square feet and the perimeter is p feet. If 6A=6(2p+9), what is the perimeter of the field, in feet? (Here A=a^2)
A.28
B.36
C.40
D.56
Answer: B.36
Explanation: You can also solve this via using the given numbers in the answer choices!
Of course you need to be aware of the basic properties as outlined by the other posts above (a = x^2 and p = 4x)
Starting with D you will notice that x=14 is way too big for your area (14^2) and will not satisfy: 6A=6(2p+9) or a=2p+9
--> Eliminate D and E
Now pick B (its either too big, then its A, or too small then you know its C or it is B itsself)
And picking B indeed solves the problem! (36/4 --> 9; a= 9^2 = 81 and 81=2x36+9)
Question: A is two years older than B who is twice as old as C.If the total of the ages of A,B nd C be 27,then how old is B ?
A.7
B.8
C.9
D.10
Answer: D.10
Explanation: Solution
Let C's age be x years .Then,B's age =2x years.A's age =(2x +2) years.
∴ (2x +2) +2x + x =27 ⇔ 5x =25 ⇔ x =5.
Hence,B's age =2x = 10 years. Answer D
Question: if 12401 is divided by any no. then quotient is 76 and remainder is 13.what is divisor?
A.154
B.124
C.153
D.163
Answer: D.163
Explanation: divisor=(dividend-remainder)/quotient=(12401-13)/76=12388/76=163
divisor = 163
answer D
Question: Find the value of x from the below equation:
x^2−7x+10=0
A.5 or 2
B.3 or 5
C.3 or 7
D.4 or 6
Answer: A.5 or 2
Explanation: Here we need to find out a and b such that a + b = -7 and ab = +10
a = -5 and b = -2 satisfies the above condition.
Hence
x^2−7x+10=(x−5)(x−2)
x2−7x+10=(x−5)(x−2)
x^2−7x+10
=0
⇒(x−5)(x−2)
=0
x2−7x+10=0⇒(x−5)(x−2)=0
Step 3: Equate each factor to 0 and solve the equations
(x−5)(x−2)
=0
⇒(x−5)
=0or (x−2)=0
⇒x= 5 or 2
A
Question: A jar of 180 marbles is divided equally among a group of marble-players today. If 2 people joined the group in the future, each person would receive 1 marble less. How many people are there in the group today?
A.16
B.18
C.20
D.22
Answer: B.18
Explanation: 180 = 18*10 = 20*9
There are 18 people in the group today.
The answer is B.