RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: find out how many positive integers less than 60 are equal to the product of a positive multiple of 5 and an even number?
A.4
B.5
C.9
D.10
Answer: B.5
Explanation: Number of positive multiples of 5 less than 60 = 11
5*1=5
5*2=10
5*3=15
5*4=20
5*5=25
5*6=30
5*7=35
5*8=40
5*9=45
5*10=50
5*11=55
Only 5 of the above are a product of a positive multiple of 5 and an even number - 10,20,30,40,50
Answer B
Question: A side of beef lost 35 percent of its weight in processing. If the side of beef weighed 580 pounds after processing, how many pounds did it weigh before processing?
A. 191
B. 355
C. 737
D. 892
Answer: D. 892
Explanation: Let weight of side of beef before processing = x
(65/100)*x = 580
=> x = (580 * 100)/65 = 892
Answer D
Question: Cindy has her eye on a sundress but thinks it is too expensive. It goes on sale for 15% less than the original price. Before Cindy can buy the dress, however, the store raises the new price by 25%. If the dress cost $78.2 after it went on sale for 15% off, what is the difference between the original price and the final price?
A.$0.00
B.$5.75
C.$3.40
D.$5.00
Answer: B.$5.75
Explanation: 0.85*{Original Price} = $78.2 --> {Original Price} = $92.
{Final Price} = $78.2*1.25 = $97.75.
The difference = $97.75 - $92 = $5.75
Answer: B.
Question: The area of a triangle is with base 4m and height 5m?
A.10
B.20
C.30
D.15
Answer: A.10
Explanation: The area of a triangle=1/2*bh
=1/2 * 4 * 5 = 10 m^2
ANSWER:A
Question: Three coworkers P , J , R meet for Dinner. P had 5 sandwiches, J had 3 and R had none. Both PJ share their sandwiches with R such that each one got the same amount. If R paid $ 8 to PJ, how much of $ 8 should P get? Assume both sandwiches and Dollars can be split.
A.a) 5$
B.b) 3 $
C.c) 7 $
D.d) 4 $
Answer: C.c) 7 $
Explanation: we got total 8 sandwiches ....we are dividing equally in 3 people.
per person: 8/3
initially
p:8
J:3
r:0
now since r ate 8/3 so he is paying 8 dollars for 8/3 sandwiches.
now p also ate 8/3 of his 5 sandwiches = so he gave 5-8/3 to r ==>7/3 to r
ok we have 8 dollars for 8/3 sandwich
therefore for 7/3 sandwich we will get 7 dollars.
hence p should get 7 dollars.
hence C
Question: A certain league has two divisions. The respective divisions had 7 and 9 teams qualify for the playoffs. Each division held its own double-elimination tournament -- where a team is eliminated from the tournament upon losing two games -- in order to determine its champion. The four division champions then played in a single-elimination tournament -- where a team is eliminated upon losing one game -- in order to determine the overall league champion. Assuming that there were no ties and no forfeits, what is the maximum number of games that could have been played in order to determine the overall league champion?
A. 30
B. 31
C. 34
D. 36
Answer: B. 31
Explanation: Overall, there can be 31 minuses. Tus, it is B.
Question: Jill is dividing her eight-person class into two teams of equal size for a basketball game. If no one will sit out, how many different match-ups between the two teams are possible?
A.10
B.35
C.126
D.252
Answer: B.35
Explanation: With 8 players, the process of figuring out how many groups of 4 can be formed is pretty straight-forward....
8C4 = 8!/(4!4!) = 70 possible groups of 4
Once forming that first group of 4, the remaining 4 players would all be placed on the second team by default.
The 'twist' is that the two teams of 4 canshow upin either order:
B
Question: Ram can do a piece of work in 8 days which Shyam can finish in 12 days. If they work at it on alternate days with Ram beginning, in how many days, the work will be finished?
A.9 1/3
B.9 1/2
C.9 1/4
D.10 1/3
Answer: B.9 1/2
Explanation: (ram+shyam)'s 2 days work = (1/8+1/12) = 5/24
work done in 4 pair of days = (5/24)*4 = 5/6; remaining work = 1-(5/6) = 1/6
work done by ram on 9th day = 1/8; Remaining work = (1/6)-(1/8)= 1/24
On 10th day it is shyam's turn
1/12 work is done by shyam in 1 day
1/24 work is done by shyam in 12*(1/24) = 1/2
total time = (9 + 1/2) day
ANSWER:B
Question: A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1.8 cm when a man gets on it. The mass of man is
A.12 kg
B.60 kg
C.108 kg
D.96 kg
Answer: C.108 kg
Explanation: Solution
Volume of water displaced	= (3 x 2 x 0.018)m3
= 0.108m3.
Mass of man	=Volume of water displaced ×Density of water
= (0.108×1000) kg
= 108 kg.
Answer C
Question: John has on his shelf four books of poetry, four novels, and three reference works. Suppose from these ten books, we were to pick two books at random. What is the probability that we pick one novel and one reference work?
A.1/2
B.12/55
C.3/10
D.7/20
Answer: B.12/55
Explanation: When we are picking two books, one novel and one reference work, we could either pick a novel first and then a reference book or pick a reference book and then a novel. Therefore the answer is 4/11*3/10 + 3/11*4/10 = 12/55.
Answer: B.
Question: What is the sum of all 5 digit numbers which can be formed with the digits 0,1,2,3,4 without repetation?
A.2599980
B.235500
C.923580
D.765432
Answer: A.2599980
Explanation: 10(11111)*4! - 10(1111)3! = 2599980
ANSWER:A
Question: The arithmetic mean of set P is zero. If Q = {-2.22; -1.96; -1.68; 1.62; 1.94; 2.16} is the subset of P consisting of all those elements in P which are more than two but less than three standard deviations away from the arithmetic mean of P, what could be equal to the standard deviation of P?
A.0.54
B.0.77
C.0.82
D.0.97
Answer: B.0.77
Explanation: This is a fairly straightforward question that can be solved quickly by just applying the options
We are provided with Mean, m= 0
and Q = {-2.22; -1.96; -1.68; 1.62; 1.94; 2.16} is the subset of P
Q consists of all those elements in P that are more than 2 but less than 3 SDs away from the arithmetic mean of P
If an element is 1 PD away from the mean, we can write it as either m + PD or m - PD
Similarly, if an element is 2 PDs away from the mean, we can write it as either m + 2*PD or m - 2*PD
So, if these elements lie within 2 and 3 PDs of mean, m=0
we can find which one of these values of PD satisfies each value within Q
Only PD = 0.77 does
Answer : B
Question: A train 360 m long passed a pole in 30 sec. How long will it take to pass a platform 780 m long?
A.76 sec
B.89 sec
C.87 sec
D.95 sec
Answer: D.95 sec
Explanation: Speed = 360/30 = 12 m/sec.
Required time = (360 + 780)/12
= 95 sec.
Answer:D
Question: The following questions are based on the information given below:
1)A cuboid shaped wooden block has 4 cm length, 3 cm breadth and 5 cm height.
2)Two sides measuring 5 cm x 4 cm are coloured in red.
3)Two faces measuring 4 cm x 3 cm are coloured in blue.
4)Two faces measuring 5 cm x 3 cm are coloured in green.
5)Now the block is divided into small cubes of side 1 cm each.
How many small cubes will have will have three faces coloured ?
A.14
B.8
C.10
D.12
Answer: B.8
Explanation: Such cubes are related to the corners of the cuboid and in the cuboid there are 8 corners.
Hence, the required number of small cubes is 8.
Answer :B
Question: A fort of 2000 soldiers has provisions for 50 days. After 10 days some of them left and the food was now enough for the same period of 40 days as before. How many of them left?
A.100
B.0
C.200
D.400
Answer: B.0
Explanation: 2000 ---- 50
2000 ---- 40
x ----- 40
x*40 = 2000*40
x=2000
2000
-------
0
ANSWER:B
Question: If the order of the letter in the English alphabet is reversed which letter will be the seventh to right of the twelfth letter from the right?
A.E
B.V
C.F
D.U
Answer: A.E
Explanation: Lkjihgfedcba
So ans wiil be
E
ANSWER:A
Question: The proportion of copper and zinc in the brass is 3:7. How much zinc will there be in 100 kg of brass?
A.70
B.50
C.40
D.270
Answer: A.70
Explanation: 7/10 * 100 = 70
ANSWER:A
Question: A meal cost $ 36.50 and there was no tax. If the tip was more than 10 pc but less than 15pc of the price, then the total amount paid should be:
A.40-42
B.39-41
C.38-40
D.37-39
Answer: A.40-42
Explanation: 10%(36.5) = 3.65
15%(36.5) = 5.475
total amount could have been 36.5+3.65 and 36.5+5.475
=> could have been between 40.15 and 41.975
=> approximately between 40 and 42
Answer is A.
Question: If a square mirror has a 20-inch diagonal, what is the approximate perimeter Q of the mirror, in inches?
A. 40
B. 60
C. 80
D. 100
Answer: B. 60
Explanation: if you draw the square and diagonal inside the square. u can see square becomes part of two triangles opposite to each other.
And We know the property of the triangle, addition of two sides of triangle must be greater than its diagonal in order to complete the triangle. And each side must be less than 20 and perimeter Q must be less than 80, so we can eliminate answer choice C, D and E.
so Side 1 + side 2 > 20, that means Side 1 or Side 2 must be > 10. so we can eliminate the answer choice A.
Now we are left with is B
Question: The cost price of a radio is Rs.2550 and it was sold for Rs.2130, find the loss %?
A.18
B.10
C.15
D.66
Answer: C.15
Explanation: 2550 ---- 400
100 ---- ? => 15%
Answer: C
Question: Walking across campus, a student interviewed a group of students. 25% of the students took a finance class last semester, 50% took a marketing class last semester, and 40% took neither a finance nor a marketing class last semester. What percent of the students in the group took both a finance and a marketing class?
A.60%
B.50%
C.25%
D.15%
Answer: D.15%
Explanation: {Total} = {finance} + {marketing} - {both} + {neither}
100 = 25 + 50 - {both} + 40
{both} = 15%.
Answer: D.
Question: n is a whole number which when divided by 4 gives 3 as remainder. What will be the remainder when 2n is divided by 4?
A.3
B.2
C.1
D.0
Answer: B.2
Explanation: Let n=4q+3.
2n=8q+6=4(2q+1)+2
Thus, when 2n is divided by 4, the remainder is 2.
Correct Option: B
Question: The area of a rectangular plot is 21 times its breadth. If the difference between the length and the breadth is 10 metres, what is its breadth?
A.10 metres
B.5 metres
C.11 metres
D.Data inadequate
Answer: C.11 metres
Explanation: L × B = 21 × B
∴ L = 21 m
and L – B = 10
∴ B = 21 – 10 = 11 m
Answer C
Question: Find the remainder when 6^50 is divided by 215
A.36
B.99
C.27
D.99
Answer: A.36
Explanation: Ans: 650=(63)16.62=21616.62650=(63)16.62=21616.62
So this expression gives a remainder of 36
Answer:A
Question: Lionel left his house and walked towards Walt's house, 48 miles away. Four hours later, Walt left his house and ran towards Lionel's house. If Lionel's speed was 3 miles per hour and Walt's 6 miles per hour, how many miles had Lionel walked when he met Walt?
A.12
B.16
C.20
D.24
Answer: D.24
Explanation: In the first 4 hours Lionel at the rate of 3 miles per hour covered distance=rate*time=4*3=12 miles. So, the distance between him and Walt was 48-12=36 miles when Walt left his house. Now, their combined rate to cover this distance was 3+6=9 miles per hour, hence they will meet (they will cover that distance) in time=distance/rate=36/9=4 hours. Total time that Lionel was walking is 4+4=8 hours, which means that he covered in that time interval distance=rate*time=3*8=24 miles.
Answer: D.
Question: A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.80 less, he could have gained 25%. What is the cost price?
A.372
B.375
C.278
D.400
Answer: D.400
Explanation: CP1 = 100 SP1 = 120
CP2 = 80 SP2 = 80 * (125/100) = 100
20 ----- 100
80 ----- ? => 375
Answer:D
Question: Which of the following is not a prime number ?
A.743
B.740
C.751
D.757
Answer: B.740
Explanation: Clearly, 740 is not a prime number.
Answer : B
Question: a1, a5, a13 (terms of AP) are in GP and a6 + a15 =63. Find a23
A.181/3
B.182/3
C.183/3
D.184/3
Answer: B.182/3
Explanation: a1
a5= a1+ 4d
a13= a1+12d
Now a5/a1 = a13/a5---->>a1=4d........(1)
Given a6 + a15=63
----> a1+5d + a1+14d=63
---->2a1+ 19d = 63
---->8d+ 19d=63 from (1)
----> d=63/27= 7/3
so a=4d=4*7/3=28/3 from (1)
a23= a1+ 22d =28/3 +22*7/3
=182/3
ANSWER:B
Question: If 3x – 5y = 5 and x/x+y=5/7, then what is the value of x – y?
A.9
B.6
C.4
D.3
Answer: D.3
Explanation: 3x – 5y = 5...(i)
And xx+y=57xx+y=57
⇒ 7x = 5x+ 5y
⇒ 2x = 5y... (ii)
From (i) and (ii), x = 5 and y = 2
∴ x – y = 3
Answer D
Question: In shop contains 500 articles each of a cost of $10. He sold them at a price of $13. If the shop keeper has a order of 200 articles, how much profit he will get?
A.A)200
B.B)2000
C.C)1500
D.D)600
Answer: D.D)600
Explanation: Total money after selling articles = 200*13 = 2600
cost price = 200*10 = 2000
profit = 600
correct option is D
Question: The speed of a boat in still water in 18 km/hr and the rate of current is 6 km/hr. The distance travelled downstream in 14 minutes is:
A.11.4 km
B.10.9 km
C.10.4 km
D.6.06 km
Answer: D.6.06 km
Explanation: Explanation:
Speed downstream = (18 + 6) = 24 kmph
Time = 14 minutes = 14/60 hour = 7/30 hour
Distance travelled = Time × speed = (7/30)×26 = 6.06 km
Answer: Option D
Question: If x + y + z + w = 15, then at least k of the numbers x, y, z, w must be positive, where k is :
A.0
B.1
C.2
D.3
Answer: B.1
Explanation: straight forward question if you realize that 4 negative numbers when added can NEVER give you a positive sum. This directly eliminates A.
As we are given that x+y+z+w=15 and we need to find what is the least number of variables out of the 4 given (x,y,z,w) that need to be positive to adhere to x+y+z+w=15 ,
Consider any large value for x = 45 and -15,-10 and -5 for y,z,w respectively to give you x+y+z+w=15.
Thus k =1 for 'k' value to be the least.
ANSWER:B
Question: A rectangular table seats 5 people on each of two sides, with every person directly facing another person across the table. If 10 people choose their seats at random, what is probability that person P directly faces person Q?
A.1/10
B.1/9
C.1/8
D.1/7
Answer: B.1/9
Explanation: Person P will be seated somewhere at the table.
Each of the other 9 people has an equal chance of sitting opposite person P.
The probability that person Q sits across is 1/9.
The answer is B.
Question: In a race of 1000 m, A can beat by 100 m, in a race of 800m, B can beat C by 100m. By how many meters will A beat C in a race of 600 m?
A.187.5 m
B.127.5 m
C.277.5 m
D.727.5 m
Answer: B.127.5 m
Explanation: Explanation:
When A runs 1000 m, B runs 900 m and when B runs 800 m, C runs 700 m.
When B runs 900 m, distance that C runs = (900 * 700)/800 = 6300/8 = 787.5 m.
In a race of 1000 m, A beats C by (1000 - 787.5) = 212.5 m to C.
In a race of 600 m, the number of meters by which A beats C = (600 * 212.5)/1000 = 127.5 m.
Answer: B
Question: In an objective test, a correct answer scores 4 marks, and a wrong answer scores 2 marks. A student scores 480 marks from 150 questions. how many answers are correct?
A.90
B.80
C.70
D.60
Answer: A.90
Explanation: if all ans. right the marks=4*150=600
but score=480
wrong attempt marks=600-480=120
wrong ans.=120/2=60
right ans.=150-60=90.
ANSWER:A
Question: By using the numbers 1, 2, 5, 7 and 9 only once, how many five digit numbers can be made that are divisible by 25?
A.11
B.12
C.5
D.10
Answer: B.12
Explanation: A number to be divisible by 25 must end with 00, 25, 50, or 75.
So, there are the following cases possible:
179-25 --> the first three digits can be arranged in 3=6 ways.
129-75 --> the first three digits can be arranged in 3=6 ways.
Total = 6 + 6 = 12.
Answer: B.
Question: What percent of 120 are 90?
A.78%
B.85%
C.75%
D.72%
Answer: C.75%
Explanation: (?% /100) * 120 = 90
? = 75%
Answer:C
Question: If p=125×243×16/405, how many digits are in p?
A.1
B.2
C.3
D.4
Answer: D.4
Explanation: p = 125 * 243 * 16 / 405
p= 5^3 * 3 * 9^2 * 4^2 / (5 * 9^2)
p= 5^2 * 3 * 4^2
p = 20^2 * 3 = 1200
answer D
Question: If x<0, y>0, and |x| < |y|, which of the following must be true?
A.x > y
B.y^2 > x^2
C.x^3 > y^2
D.–x > y
Answer: D.–x > y
Explanation: Correct Answer: (E)
Let’s go through each answer choice: (A) can never be true, since no negative is greater than a positive. (B) doesn’t have to be true – consider what would happen if x = -2 and y = 1. (C) can never be true, as x^3 must be negative, and y^2 must be positive. (D) can never be true, since if x < 0, -x is the same thing as |x|, and |x| > y. (E) can be manipulated by multiplying both sides by -1, which gives us –x > y. Remember that x < 0, so –x = |x|, and y is positive, so |y| = y. Thus –x > y is the same statement as |x| > |y|, and (D) must be true.
Question: The amount of water (in ml) that should be added to reduce 9 ml. Lotion, containing 50% alcohol, to a lotion containing 30% alcohol, is?
A.8 ml
B.6 ml
C.3 ml
D.4 ml
Answer: B.6 ml
Explanation: 4.5 4.5
30% 70%
30% ----- 4.5
70% ------? => 10.5 - 4.5 = 6 ml
Answer: B
Question: A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 6 : 7 : 8 : 9 : 10. In all papers together, the candidate obtained 60% of the total marks. Then the number of papers in which he got more than or equal to 60% marks is
A.4
B.3
C.2
D.1
Answer: B.3
Explanation: Here we can assume that one subject is of 100 marks so total there are 5 subjects => 100*5 = 500.
Now according to the question he secured 60 % of those which is 60%of 500 = 300 marks in total.
The ratio between the marks is given as 6 : 7 : 8 : 9 : 10 , so now we can distribute 300 marks according to the ratio.
Total ratio = 40
For 6 : (300/40)*6 = 45
Similarly , we will get for others as 52.5 , 60 , 62.5 , 75.
Hence , there are 3 subject where he secured more that 60 %.
The answer is 3.
B
Question: 9, 16, 19, 25, 36,49
A.9
B.16
C.19
D.25
Answer: C.19
Explanation: Each of the numbers except 19, is perfect square.
Answer: Option C
Question: Prizes totaling $ 55,000 were awarded unequally between 3 contestants. Which of the following choices could be the highest prize?
A.(a) $5,000
B.(b) $10,000
C.(c) $15,000
D.(d) $20,000
Answer: D.(d) $20,000
Explanation: The highest prize cannot possibly be less than 1/3rd of 55,000 (because in this case the sum of 3 prizes would be less than 55,000) and cannot be more than 55,000.
Answer: D.
Question: Let f(x) = x4 – 8x3 + 16x2 – 19 and g(x) = x - 5. Find f(x)/g(x)
A.4
B.5
C.6
D.7
Answer: C.6
Explanation: Solution:
f(x) = x4 – 8x3 + 16x2 – 19
g(x) = x – 5
f(x)/g(x) = (x4 – 8x3 + 16x2 – 19)/(x - 5)
We first need to rearrange all the terms of the dividend according to descending powers of x. The dividend then becomes x4 – 8x3 + 16x2 – 19, with 1 understood as the coefficient of the first term. No x term is there in the polynomial, but we take a zero as a place holder in the x position, so the dividend is written as x4 – 8x3 + 16x2 + 0x – 19.
We solved the division in both the ways;
(x4 – 8x3 + 16x2 + 0x – 19) ÷ (x - 5) by using synthetic division
Quotient = x3 - 3x2 + x + 5
Remainder = 6
Answer C
Question: A circular wire of radius 42cm is cut and bent into the form of a rectangle whose sides are in the ratio of 6:5. The smaller side of the rectangle is:
A.30cm
B.60cm
C.72cm
D.132cm.
Answer: B.60cm
Explanation: Length of wire= circumference of circle of radius 42cm= (2* 22/7* 42)= 264cm.
Therefore, perimeter of rectangle= 264 cm.
Let, length= 6x cm & breadth= 5x cm.
Therefore, 2 (6x+5x)= 264 or x=12.
Therefore, smaller side= 60 cm
ANSWER:B
Question: In how many different ways can 5 girls and 5 boys form a circle such that the boys and the girls alternate?
A.2880
B.1400
C.1200
D.3212
Answer: A.2880
Explanation: Explanation :
In a circle, 5 boys can be arranged in 4! ways
Given that the boys and the girls alternate.
Hence there are 5 places for girls which can be arranged in 5! ways
Total number of ways = 4! x 5! = 24 x 120 = 2880. Answer : Option A
Question: Less than half of a committee that is to be formed out of certain group, are to be men. If there are 100 possible ways of forming the committee, then the number of men in the committee can be,
A.2
B.3
C.4
D.5
Answer: A.2
Explanation: 1. Let there be m men and w women out of which the committee is formed.
2. mCn * wCr = 100, where n is the number of men chosen and r is the number of women chosen
3. The possible products for LHS of (2) are, 100 * 1, 50 * 2, 25 * 4, 20 * 5, 10 * 10
4. Since the number of women is greater than the number of men, the first three products in (3) can be rejected as they would not satisfy this condition.
5. In the case of the fourth product, 20 * 5 may be given by 6C3 * 5C1. Though this may satisfy the condition with 3 women and 1 man, 1 man is not in the choices given.
6. The last product 10 * 10 may be given by 5C2 * 5C3 with 2 men and 3 women. This satisfies the condition and also 2 men is one of the choices given.
Therefore the answer is choice A.
Question: A housewife saved Rs. 2.50 in buying an item on sale. If she spent Rs. 25 for the item, approximately how much percent she saved in the transaction?
A.8%
B.9%
C.10%
D.11%
Answer: B.9%
Explanation: Solution
Actual price	= Rs. (25 + 2.50)
= Rs. 27.50
Therefore, saving	= (2.50 / 27.50 ×100)%
= 100 / 11%
= 9×1/11%
= 9%.
Answer B
Question: If n is a positive integer and the product of all integers from 1 to n, inclusive, is a multiple of 840, what is the least possible value of n?
A.5
B.11
C.12
D.13
Answer: A.5
Explanation: 840 = 2 * 2 * 2 * 3 * 5
so the least value forNcan be 5.
A
Question: a clock hangs on the wall of a railway station,71ft 9in long and 10ft 4in high.those are the dimension of the wall,not the clock!while waiting for a train we noticed that the hands of the clock were pointing in opposite directions,and were parallel to one of the diagonals of the wall,what was the exact time ?
A.7:15
B.7:5
C.7:25
D.7:45
Answer: B.7:5
Explanation: it can have four possiblities
time could be
7:5
1:35
11:25
5:55
ANSWER:B
Question: A rectangular plot measuring 90 meters by 50 meters is to be enclosed by wire fencing. If the poles of the fence are kept 5 meters apart. How many poles will be needed?
A.46m
B.66m
C.26m
D.56m
Answer: D.56m
Explanation: Perimeter of the plot = 2(90+50) = 280m
no of poles =280/5 =56m
Answer: D
Question: The sector of a circle has radius of 21 cm and central angle 90o. Find its perimeter?
A.91.5
B.75
C.93
D.94
Answer: B.75
Explanation: Perimeter of the sector = length of the arc + 2(radius)
= (90/360 * 2 * 22/7 * 21) + 2(21)
= 75 cm
Answer: Option B
Question: The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles.
A.4192 sq m
B.4304 sq m
C.4312 sq m
D.4360 sq m
Answer: C.4312 sq m
Explanation: Let the radii of the smaller and the larger circles be s m and l m respectively.
2∏s = 264 and 2∏l = 352
s = 264/2∏ and l = 352/2∏
Difference between the areas = ∏l2 - ∏s2
= ∏{1762/∏2 - 1322/∏2}
= 1762/∏ - 1322/∏
= (176 - 132)(176 + 132)/∏
= (44)(308)/(22/7) = (2)(308)(7) = 4312 sq m
ANSWER:C
Question: Tom bought 2 shares and sold them for $55 each. If he had a profit of 25% on the sale of one of the shares but a loss of 45% on the sale of the other share, then on the sale of both shares Tom had
A. a profit of $44
B. a loss of $44
C. a profit of $34
D. a loss of $34
Answer: D. a loss of $34
Explanation: total CP = 5500/125 + 5500/55 = 44 + 100=144
SP=55*2=110
loss= Rs 34/-
Answer: D
Question: Mary and Mike enter into a partnership by investing $600 and $400 respectively. At the end of one year, they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business. If Mary received $1000 more than Mike did, what was the profit made by their business in that year?
A.$8500
B.$9500
C.$7000
D.$7500
Answer: D.$7500
Explanation: Explanatory Answer
Let the profit made during the year be $3x
Therefore, $x would have been shared equally and the remaining $2x would have been shared in the ratio 6 : 4.
i.e., 60% of 2x would go to Mary and 40% of 2x would go to Mike.
Hence, Mary would get (60 - 40)% of 2x more than Mike
Or20% of 2x = $1000
i.e.,(20/100)*2x = 1000
or 2x = 5000.
Hence, the profit made by the company during the year $3x = $7500.
Answer : D