RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Triangle ATriangle B are similar triangles with areas 1792 units square and 2527 units square respectively. The ratio of there corresponding height would be
A.9:10
B.17:19
C.23:27
D.16:19
Answer: D.16:19
Explanation: Let x be the height of triangle A and y be the height of triangle of B.
since triangles are similar, ratio of area of A and B is in the ratio of x^2/y^2
Therefore, (x^2/y^2)=1792/2527
(x^2/y^2)=(16*16*7)/(19*19*7)
(x^2/y^2)=16^2/19^2
x/y=16/19
Ans=D
Question: Find the H.C.F. and L.C.M. of 2/3, 8/9, 16/81 and 10/27.
A.2/81 and 80/3
B.1/80 and 70/2
C.1/90 and 60/3
D.1/75 and 40/5
Answer: A.2/81 and 80/3
Explanation: H.C.F. of given fractions = H.C.F. of 2,8,16,10/L.C.M. of 3,9,81,27 = 2/81
L.C.M of given fractions = L.C.M. of 2,8,16,10/H.C.F. of 3,9,81,27 = 80/3
Answer is A.
Question: A, B and C started a business with a total investment of Rs. 90000. A invests Rs. 6000 more than B and B invests Rs. 3000 less than C. If the total profit at the end of a year is Rs. 8640, Find A's share.
A.Rs. 3168
B.Rs. 2520
C.Rs. 2880
D.Rs. 3360
Answer: A.Rs. 3168
Explanation: Explanation:
Let C's investment = Rs. x
B's investment = Rs. (x - 3000)
A's investment = Rs. (x - 3000 + 6000) = Rs. (x + 3000)
Now, (A + B + C)'s investment = Rs. 90000
=> x + (x - 3000) + (x + 3000) = 90000
=> 3x = 90000
=> x = 30000
Hence, A's investment = Rs. 33000
B's investment = Rs. 27000
C's investment = Rs. 30000
Ratio of the capitals of A, B and C
= 33000 : 27000 : 30000
= 11 : 9 : 10
A's share = Rs. [(11/30) Ã— 8640] = Rs. 3168
Answer: Option A
Question: If the wheel is 14 cm then the number of revolutions to cover a distance of 1056 cm is?
A.27
B.28
C.20
D.12
Answer: D.12
Explanation: 2 * 22/7 * 14 * x = 1056 => x = 12
Answer: D
Question: Out of 15 consecutive numbers, 2 are chosen at random. The probability that they are both odds or both primes is
A.1/7
B.1/5
C.1/9
D.1/2
Answer: B.1/5
Explanation: A leap year has 52 weeks and two days
Total number of cases = 7
Number of favourable cases = 1
i.e., {Saturday, Sunday}
Required Probability = 1/7
Answer: B
Question: Five men and five women have to sit around a circular table so that no 2 women are together. In how many ways can that be done?
A.4!*5!
B.6!*6!
C.5!*7!
D.6!*7!
Answer: A.4!*5!
Explanation: The number of arrangements of n distinct objects in a row is given by n!.
The number of arrangements of n distinct objects in a circle is given by (n-1)!.
The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have: n!/n=(n-1)!
Now, 5 men in a circle can be arranged in (5-1)! ways and if we place 5 women in empty slots between them then no two women will be together. The # of arrangement of these 5 women will be 5! and not 4! because if we shift them by one position we'll get different arrangement because of the neighboring men.
So the answer is indeed 4!*5!.
A
Question: There are 200 cats in Cat-City. Out of the 200, 70 are street cats and the rest are domestic cats. 110 cats are gray, 35 out of the gray cats are NOT domestic ones. How many domestic cats are there which are not gray in Cat-City?
A.90.
B.55.
C.50.
D.40.
Answer: B.55.
Explanation: STREET-CAT DOMESTIC-Cat
70 130
(35gray+35other) 75gray+55other
Answer:B
Question: Rs.400 at 5% p.a compound interest will amount to Rs.441 in ________ years (interest compounded yearly).
A.1 year
B.2 years
C.3/2 year
D.5 years
Answer: B.2 years
Explanation: 1st year compound interest is =400*5/100 = 20
2nd year compound interest is = first year CI + 5%of first year CI= 20 + 20*5/100=>20+1=>21
total CI= first year CI + second year CI= >20+21=21
so total amount to paid = 400 +41=441
so answer is 2 years
ANSWER:B
Question: A student needs 30% of the marks on a test to pass the test. If the student gets 80 marks and fails the test by 10 marks, find the maximum marks set for the test.
A.240
B.300
C.360
D.420
Answer: B.300
Explanation: 30% = 90 marks
1% = 3 marks
100% = 300 marks
The answer is B.
Question: Hammers and wrenches are manufactured at a uniform weight per hammer and a uniform weight per wrench. If the total weight of 1 hammers and three wrenches is one-third that of 8 hammers and 5 wrenches, then the total weight of one wrench is how many times that of one hammer?
A.1/2
B.2/3
C.1
D.5/4
Answer: D.5/4
Explanation: x be the weight of a hammer and y be the weight of a wrench.
(1x+3y)=1/3*(8x+5y)
3(1x+3y)=(8x+5y)
3x+9y=8x+5y
4y=5x
y=5x/4
Ans - D
Question: If the speed of Y meters per second is equivalent to the speed of X meters per hour, what is X in terms of Y? (1 kilometer=1000 meters)
A.15y/18
B.6y/5
C.18y/5
D.3600y
Answer: D.3600y
Explanation: If the speed of Y meters per second is equivalent to the speed of X kilometers per hour, what is X in terms of Y? (1 kilometer=1000 meters)
We need to find an equation with y in the answer...
convert all measurements so they are alike (i.e. convert km to m, seconds to hours, etc)
Speed = y/t
y meters/second
(3600) x meters/hour
Speed = x/t
x KM/hour
Speed = x/hour
x/hour = (3600) x meters/hour
x/1hour = y(3600) / 1 hour
x = y(3600)
x = 3600y
Answer: D.
Question: If x−log48+3log2=log125/3−log3, what is the value of x?
A.2
B.1
C.3
D.5
Answer: B.1
Explanation: Explanation:
1/3 log 125= log (125^1/3) = log 5
3 log 2= log (2^3)= log 8
log a + log b= log (a*b)
Utilizing the same,
LHS= x -log 48 +log 8= x - log 6 - log 8 + log 8 = x - log 6
RHS= log 5 - log 3
=> x= log 5 - log 3 + log 6 = log 5 - log 3 + log 2 + log 3
=> x= log 10 = 1
Answer B
Question: If the product of two positive integers is 50, which of the following could be the LCM and HCF of the two numbers? a. LCM 50 : HCF 1 b. LCM 25 : HCF 2 c. LCM 10 : HCF 5
A.c only
B.a only
C.b only
D.a, b only
Answer: A.c only
Explanation: The right answer is c only
Answer : A
Question: If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 60, what is the average marks of all the students?
A.54.68
B.54
C.45.68
D.45
Answer: A.54.68
Explanation: Average marks of batch1 = 50
Students in batch1 = 55
Total marks of batch1 = 55 × 50
Average marks of batch2 = 55
Students in batch2 = 60
Total marks of batch2 = 60 × 55
Average marks of batch3 = 60
Students in batch3 = 45
Total marks of batch3 = 45 × 60
Total students = 55 + 60 + 45 = 160
Average marks of all the students
=((55×50)+(60×55)+(45×60))/160
=(275+330+270)/16
=875/16
=54.68
Answer is A.
Question: Let Q be any number less than 200 which leaves remainder 2 when divisible by 5 or 7. What is the sum of all those numbers of Q?
A.535
B.545
C.555
D.565
Answer: A.535
Explanation: least number which gives remainder of 2 when divided by 5 or 7 is the LCM of 5 and 7 plus 2 i.e 35+2=37.
now,second number will 72 and by this way,we can say that sum all number less than 200 is
37+72+107+142+177=535
ANSWER:A
Question: A magician has five animals in his magic hat: 3 doves and 2 rabbits. If he pulls two animals out of the hat at random, what is the chance Z that he will have a matched pair?
A.Z=2/5
B.Z=3/5
C.Z=1/5
D.1/2
Answer: A.Z=2/5
Explanation: P(both doves) + P(both rabbits) = p (matched pair)
(3/5)*(2/4) + (2/5)*(1/4) = 2/5
Hi How did you get the probability 2/4 and 1/4???
You have 3 doves and 2 rabbits i.e. a total of 5 animals.
The probability that you pick a dove on your first pick is 3/5 (since there are 3 doves)
The probability that you pick a dove on your second pick too is 2/4 (because now only 2 doves are left after we picked a dove in the first pick. ALso only 4 animals are left to choose from)
Similarly,
The probability that you pick a rabbit on your first pick is 2/5 (since there are 2 rabbits)
The probability that you pick a rabbit on your second pick too is 1/4 (because now only 1 rabbit is left after we picked a rabbit in the first pick. Also only 4 animals are left to choose from)
Probability of picking a matched pair = 3/5 * 2/4 + 2/5 * 1/4 = 2/5
Question: Find the least number which when divided by 20,25,35 and 40 leaves remainders 14,19,29 and 34 respectively.
A.1934
B.1394
C.1943
D.1493
Answer: B.1394
Explanation: Here,(20-14) = 6,(25 – 19)=6,(35-29)=6 and (40-34)=6.
Required number = (L.C.M. of 20,25,35,40) – 6 =1394.
Answer is B.
Question: A bread merchant declares a 15% discount after 8 P.M. Ana goes before 8 P.M. with Rs.50 in her pocket to buy 3 pieces of bread and got some change. Tom goes after 8 P.M. with Rs.40. How many pieces of bread can Tom buy at the most?
A.1
B.2
C.3
D.4
Answer: B.2
Explanation: At the most, a piece of bread costs 50/3 = 16.67 before 8 P.M.
After 8 P.M., each piece of bread will now cost (1 - 15%) * 16.67 = 0.85 * 16.67 = 14.17
Since Tom has Rs.40, 40 / 14.17 = 2.82
Since you cannot buy half pieces of bread, at the most, Tom can buy 2 pieces of bread after 8 P.M.
Correct Option: B
Question: The “z-number” of a number x is defined as the ones digit of 2^x. Antony rolls a die with 6 sides labeled with the integers from 1 to 6, each of which has an equal probability of landing face-up. He then takes 3^z, where z is the z-number of the result of his die roll, and plots 3^z on a number line as the point A. Finally, he repeats this entire process, this time plotting the result as the point B. What is the probability that the distance between A and B is greater than the value of B?
A. 3/8
B. 13/36
C. 17/36
D. 19/36
Answer: B. 13/36
Explanation: If you calculate 3^z for 1st roll, all 6 results will be 9, 81, 6561, 729, 9, 81. This result is the same for 2nd roll. 9, 81, 6561, 729, 9, 81.
About distance: If the first result is 9 and the second is also 9, the distance is 9-9=0 which is smaller than 9. If the first result is 9 and the second is 81, the distance is 81-9=72 which is also smaller than B which has the value of 81. If the first result is 81 and the second is 9, the distance will be greater than B. Distance 81-9=72>9.
On the first roll, the probability of getting result 9 is 2/6. In this case no other alternative values for second roll which would make the distance greater than B. So probability is 0. So next estimations are:
probability of getting 81 on the first roll (2/6) * probability of getting 9 on the second roll (2/6) = 1/9
probability of getting 729 on the first roll (1/6) * probability of getting 9, 81 on the second roll (4/6) = 1/9
probability of getting 6561 on the first roll (1/6) * probability of getting 9, 81, 729 on the first roll (5/6) = 5/36
All together: 1/9 + 1/9 + 5/36 = 13/36=B
Question: How many methods are possible for arranging 5 boys and 4 girls in such a way that no 2 girls could sit together?
A.43200
B.43700
C.44200
D.53200
Answer: A.43200
Explanation: The arrangement can be done as below
X..B..X..B...X..B...X..B...X..B..X
where b is the position of Boys and 4 girls can be placed at any of 6 positions marked as X.
so Number of arrangements will be
5! * 6p4 = 120*360 = 43200
ANSWER:A
Question: Lagaan is levied on the 60 percent of the cultivated land. The revenue department collected total Rs. 3,54,000 through the lagaan from the village of Mutter. Mutter, a very rich farmer , paid only Rs.480 as lagaan. The percentage of total land of Mutter over the total taxable land of the village is:
A.0.22598
B.0.14544
C.0.25632
D.0.35466
Answer: A.0.22598
Explanation: Total land of Sukhiya = \inline \frac{480x}{0.6} = 800x
\therefore Cultivated land of village = 354000x
\therefore Required percentage = \inline \frac{800x}{354000}\times 100 = 0.22598
A
Question: A mathematics teacher tabulated the marks secured by 35 students of 8th class. The average of their marks was 72. If the marks secured by Reema was written as 46 instead of 56 then find the correct average marks up to two decimal places.
A.73.41
B.72.28
C.72.43
D.73.43
Answer: B.72.28
Explanation: Total marks = 35 x 72 =2520
Corrected total marks = 2520 - 46 + 56 =2530
Correct Average = 2530/35 = 72.28
Answer : B
Question: Tickets for all but 100 seats in a 10,000-seat stadium were sold. Of the tickets sold, 20% were sold at half price and the remaining tickets were sold at the full price of $2. What was the total revenue from ticket sales?
A.$15,840
B.$17,820
C.$18,000
D.$19,800
Answer: B.$17,820
Explanation: 10000 seats --> Full Price : Half Price = 8000 : 2000
Price when all seats are filled = 16000 + 2000 = 18000
100 seats are unsold --> Loss due to unfilled seats = 20 + 2*80 = 180
Revenue = 18000 - 180 = 17820
Answer: B
Question: John must arrange 3 different physics books and 2 different mathematics books on one shelf. If the first book on the leftmost side is a mathematics book and no physics book is next to another physics book. How many different arrangements exist?
A.6
B.9
C.36
D.12
Answer: D.12
Explanation: First Place, is reserved for Math book. There are 3 Math books which can be arranged in3 ways
Restriction comes into playhysics book cannot be together. Hence, the maththe physics books take alternate places
Second Place, Physics Book - in 2 ways
Third Place, Math Book - in 2 ways (only 2 books left)
Fourth Place, Physics - in 2 ways (only 2 Physics book left)
Rest two places can be arranged in one way only.
Total no of ways =3*2*2*1*1 = 12 ways
D
Question: A can do a piece of work in 4 hours ;B and C together can do it in 3 hours,while A and C together can do it 2 hours.How long will B alone take to do it ?
A.8 hours
B.10 hours
C.12 hours
D.24 hours
Answer: C.12 hours
Explanation: Solution
A’s 1 hour’s work = 1/4; (B + C)'s 1 hour’s work=1/3; (A + C)'s 1 hour’s work = 1/2
(A+B+C)’s 1 hour’s work =(1/4 +1/3) =7/12
B’s 1 hour’s work = (7/12-1/2)=1/12
∴ B alone will take 12 hours to do the work.
Answer C
Question: A $84.95 lawn chair was sold for $59.95 at a special sale. By approximately what percent was the price decreased?
A.15%
B.20%
C.25%
D.29%
Answer: D.29%
Explanation: Listed selling price of chair = 84.95 $
Discounted selling price of chair = 59.95 $
Discount = 84.95 - 59.95 = 25 $
% decrease in price of chair = (25/84.95) * 100% = 29 % approx
Answer D
Question: A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is:
A.5%
B.25%
C.45%
D.75%
Answer: A.5%
Explanation: C.P. of 56 kg rice = Rs. (26 x 20 + 30 x 36) = Rs. (520 + 1080) = Rs. 1600.
S.P. of 56 kg rice = Rs. (56 x 30) = Rs. 1680.
Gain =80/1600 x 100% = 5%
Answer: A
Question: What is the smallest number which, when increased by 9, is divisible by 7, 8, and 24?
A.143
B.150
C.159
D.168
Answer: C.159
Explanation: LCM(7,8,24)=24x7=168
So the least divisible number is 168, and the number we are looking for is 168-9=159.
The answer is C.
Question: The difference between a two digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2?
A.4
B.8
C.12
D.16
Answer: B.8
Explanation: Sol.
Since the number is greater than the number obtained on reversing the digits, so the ten's is greater than the unit's digit.
Let the ten's and units digit be 2x and x respectively.
Then, (10× 2x + x) - (10x + 2x) = 36
⇔ 9x = 36
⇔ x = 4.
∴ Required difference = (2x+x)-(2x-x) = 2x = 8.
Answer B
Question: Valentine day 14 Feb. 2005 was celebrated by Anand and shilpa on Sunday. They were very happy. What day of the week would come on 14 Feb. 2010?
A.monday
B.tuesday
C.saturday
D.wednesday
Answer: C.saturday
Explanation: feb 14 2005 - sunday
feb 14 2006 - monday
feb 14 2007 - tuesday
feb 14 2008 - wednesday
feb 14 2009 - friday[since 2008 is leap year , 2 days ll go forward]
feb 14 2010 - saturday
ANSWER:C
Question: A bill for Rs. 3000 is drawn on 14th July at 5 months. It is discounted on 5th October at 10%. What is the Banker's Discount?
A.Rs. 60
B.Rs. 82
C.Rs. 90
D.Rs. 120
Answer: A.Rs. 60
Explanation: Explanation :
F = Rs. 3000
R = 10%
Date on which the bill is drawn = 14th July at 5 months
Nominally Due Date = 14th December
Legally Due Date = 14th December + 3 days = 17th December
Date on which the bill is discounted = 5th October
Unexpired Time
= [6th to 31st of October] + [30 Days in November] + [1st to 17th of December] = 26 + 30 + 17
= 73 Days
=73/365 year=1/5 year
BD = Simple Interest on the face value of the bill for unexpired time
=FTR/100=[3000×(1/5)×10]/100=30×1/5×10 = Rs. 60 Answer : Option A
Question: A train 500m long takes 10 sec to cross a man walking at 4kmph in a direction opposite to that of the train. Find the speed of the train?
A.A)174kmph
B.B)150kmph
C.C)162kmph
D.D)145kmph
Answer: A.A)174kmph
Explanation: Let the speed of the train be x kmph
Speed of the train relative to man = x+4 = (x+4)*5/18 m/sec
500/[(x+4)*5/18] = 10
10(x+4) = 1800
x = 174kmph
Answer is A
Question: If a, q, and c are consecutive even integers and a < q < c, all of the following must be divisible by 4 EXCEPT
A.a + c
B.q + c
C.ac
D.(bc)/2
Answer: B.q + c
Explanation: I did get the correct answer within 80 seconds and it was not by luck either. I did not pick numbers but just used the concept stated by Ian.
The 3 numbers can be written as
a, (a + 2)(a + 4).
If 'a' is divisible by 4, then even 'c' or 'a + 4' is divisible by 4. However, is 'b' is divisible by 4, then both 'a' and 'a + 4' are still divisible by 2.
A - (a + c) = a + (a + 4) = 2a + 4 = 2(a + 2) = 2q. 2q will always be divisible by 4 even if 'b' is not divisible by 4. Reason: 'q' already has a prime factorization of at least a '2'. Hence '2q' has two 2s.
C - ac = a(a+4). If, as stated above, one of them is divisible by 4, then the product is divisible. If both of them are not divisible by 4, then the product is still divisible by 4 because of the presence of two 2s again in the prime factorization.
D - qc/2 = (a + 2)(a + 4)/2. Either q or c is divisible by 2. Hence, if we assume that b is divisible by 2 and not divisible by 4, then it leaves us just one possibility. Is c divisible by 4? It has to be because c is the next consecutive even integer.
E - aqc/4 = a(a + 2)(a + 4)/4. One of these integers is divisible by 4 already. If we again assume 'q' to be that integer divisible by 4, then we are left with the question - Is a(a + 4) divisible by 4? This is the same as option C.
B - q + c = (a + 2) + (a + 4) = 2a + 6 = 2(a + 3). (a + 3) will never be divisible by 2 because it is an odd integer. Hence, 2(a + 3), although divisible by 2, will not be divisible by 4 because it has just one 2 in its prime factorization.
As a whole, whether you choose numbers (2, 46 being the easiest) or solve conceptually, the answer is still easily obtainable within 2 minutes.B
Question: Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?
A.3.6
B.6
C.18
D.Cannot be determined
Answer: B.6
Explanation: let rate = R% and time = R years
Then ( 1200 x R x R /100) = 432
=> 12R2= 432
=> R2= 36
=> R= 6
Answer B
Question: A train passes a station platform in 30 seconds and a man standing on the platform in 12 seconds. If the speed of the train is 72 km/hr, what is the length of the platform?
A.320
B.340
C.360
D.380
Answer: C.360
Explanation: The speed of the train is 72 * 5/18 m/s = 20 m/s
The length of the train is 20 x 12 = 240 m
platform + 240 = 20 * 30
platform = 600 - 240 = 360
The answer is C.
Question: What was the day of the week on 24th Feb, 2006?
A.Thursday
B.Friday
C.Saturday
D.Sunday
Answer: B.Friday
Explanation: 28 May, 2006 = (2005 years + Period from 1.1.2006 to 28.5.2006)
Odd days in 1600 years = 0
Odd days in 400 years = 0
5 years = (4 ordinary years + 1 leap year) = (4 x 1 + 1 x 2) 6 odd days
Jan. Feb.
(31 + 24 ) = 55 days
55 days = (7 weeks + 6 day) 1 odd day.
Total number of odd days = (0 + 0 + 6 + 6) = 12 0 odd day.
Given day is Friday.
Answer: Option B
Question: A WORKS TWICE AS FAST AS B. IF B CAN COMPLETE A WORK IN 20DAYS INDEPENDENTLY, THE NUMBER OF DAYS IN WHICH A AND B CAN TOGETHER FINISH THE WORK IS:
A.40/3 DAYS
B.10/3 DAYS
C.20/3 DAYS
D.3/20 DAYS
Answer: C.20/3 DAYS
Explanation: RATIO OF RATES OF WORKING OF A AND B = 2:1. SO, RATIO OF TIME TAKEN = 1:2
A'S 1 DAY'S WORK = 1/10, B'S 1 DAY'S WORK = 1/20
(A+B)'S 1 DAY'S WORK = (1/10+1/20)=3/20=20/3
SO, A AND B TOGETHER CAN FINISH THE WORK IN 20/3 DAYS.
CORRECT OPTION: C
Question: The length of a rectangle is 3 times its width. If the width of the rectangle is 6 inches, what is the rectangle's area, in square inches?
A.30 square inches
B.108 square inches
C.68 square inches
D.89 square inches
Answer: B.108 square inches
Explanation: If the width is 6 in and the length is 3 times the width, then the length is
3 * 6 = 18 in
The area is given by
6 * 18 = 108 square inches
correct answer B
Question: c, q, and r are positive integers. If c, q, and r are assembled into the six-digit number cqrcqr, which one of the following must be a factor of cqrcqr?
A. 23
B. 19
C. 17
D. 7
Answer: D. 7
Explanation: One short way -
cqrcqr = 1000cqr + cqr = (1000+1)cqr = 1001cqr
Therefore any factor of 1001 is a factor of cqrcqr
7 is a factor of 1001
So D
Question: Given two cylindrical containers--A and B. Cylinder A has a diameter of 12 meters and a height of 10 meters. Cylinder B has a radius of 2 meters and a height of 4 meters. If cylinder A is filled to capacity with water, how many cylinder B will be filled to capacity with the content of cylinder A?
A.23
B.22
C.21
D.25
Answer: B.22
Explanation: Calculate the volume of the larger cylinder and divide it by the volume of the smaller cylinder.
volume of cylinder =πr2h
Cylinder A volume=1130.97
Cylinder B volume=50.27
therefore the number of cylinders B that can be filled to capacity=1130.97/50.27=22.5
Answer is B only 22 Cylinders B can be filled to capacity.
Question: A container contains 30 liters of milk. From this container 5 liter of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container?
A.18.45 liter
B.23.44 liter
C.17.36 liter
D.21.87 liter
Answer: C.17.36 liter
Explanation: ANSWER: 17.36 liter
Option:C
Question: If 10 people contributed a total of $20.00 toward a gift and each of them contributed at least $1.00, then the maximum possible amount any one person could have contributed is
A. $11.00
B. $1.25
C. $5.00
D. $6.00
Answer: A. $11.00
Explanation: A for me
9 people with 1$ each -> maximum = 11
Question: A man, a woman and a boy can together complete a piece of work in 3 days. If a man alone can do it in 6 days and a boy alone in 18 days, how long will a woman take to complete the work?
A.9 days
B.21 days
C.24 days
D.27 days
Answer: A.9 days
Explanation: Explanation:
(1 Man + 1 woman + 1 boy)’s 1day’s work = 1/3
1 man’s 1 day work = 1/6
1boy’s 1 day’s work = 1/18
(1 Man + 1 boy) ‘s 1 day’s work = 1/6 + 1/18 = 2/9
Therefore, 1 woman’s 1 day’s work = 1/3 – 2/9 = 3-2/9 = 1/9
Therefore, the woman alone can finish the work in 9 days.
Answer: Option A
Question: If ab - 2c = a(b - c), which of the following must be true?
A. a=2 and c=0
B. a=1/2 and b=2
C. b=1 and c=0
D. a=1 or b=0
Answer: A. a=2 and c=0
Explanation: ab-2c = a (b-c)
ab - 2c = ab - ac
2c= ac
ac-2c = 0
c(a-2) = 0
Either c = 0; or a = 2
A is the answer
Question: A number x is 8 times another number y. The percentage that y is less than x is
A.12.5%
B.87.5%
C.80%
D.11%
Answer: B.87.5%
Explanation: Say y=1 and x=8.
Then y=1 is less than x=8 by (8-1)/8*100=7/8*100=87.5%.
Answer: B.
Question: If xy > 0, 1/x + 1/y = 6, and 1/xy = 12, then (x+y)/6 = ?
A.1/12
B.1/6
C.1/5
D.5
Answer: A.1/12
Explanation: (1/X+1/Y)=6 canbe solved as {(x+y)/xy}=12. Substituting for 1/xy=12, we get
x+y=6/12
==> (x+y)/6= 6/(12*6)=1/12.
A
Question: What is the measure of the radius of the circle that circumscribes a triangle whose sides measure 2, 3 and 5?
A.2.5
B.3
C.4
D.4.5
Answer: A.2.5
Explanation: Some of pyhtagron triplets we need to keep it in mind.
Like {( 2,3,5) , ( 5,12,13) ,( 7, 24,25), ( 11, 60,61).
So now we know the triangle is an right angle triangle. The circle circumscribes the triangle.
The circumraduis of the circle that circumscribes the right angle triangle = hypotanse / 2 = 5 / 2 = 2.5
Ans. A