RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: The distance between two cities A and B is 330 Km. A train starts from A at 8 a.m. and travel towards
B at 60 km/hr. Another train starts from B at 9 a.m and travels towards A at 75 Km/hr. At what time do
they meet?
A.10 am
B.11 am
C.12 pm
D.1 pm
Answer: B.11 am
Explanation: Explanation:
Suppose they meet x hrs after 8 a.m.
then
(Distance moved by first in x hrs) + [Distance moved by second in (x-1) hrs]
= 330
So, 60x+75(x-1) = 330
x=3.
So,they meet at (8+3). i.e 11a.m.
Answer: B
Question: A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
A.999
B.279
C.120
D.99
Answer: C.120
Explanation: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 6
= 120 m.
Answer: C
Question: In 2003 there are 28 days in February and 365 days in a year in 2004 there are 29 days in February and 366 days in the year. If the date march 11 2003 is Tuesday, then which one of the following would the date march 11 2004 would be?
A.21
B.2
C.8
D.7
Answer: B.2
Explanation: If 11-3-2003 is Tuesday, Then 11-3 - 2004 is Thursday
The number of odd days between the two dates are [3667]Rem[3667]Rem= 2.
Answer:B
Question: If a light flashes every 6 seconds, how many times will it flash in 1/3 of an hour?
A.101
B.201
C.301
D.401
Answer: B.201
Explanation: In 1/3 of an hour there are 20*60 = 1200 seconds
The number of 6-second intervals = 1200/6 = 200
After the first flash, there will be 200 more flashes for a total of 201.
The answer is B.
Question: If there are 11 containers and 562,156 apples, how many apples should be removed to equally distribute them across the containers?
A.5
B.0
C.1
D.8
Answer: C.1
Explanation: Given:
There are 11 containers
This means, the total number of apples should be divisible by 11
Take the alternating sum of the digits in the number, read from left to right. If that is divisible by 11, so is the original number.
562156 => (5+2+5) - (6+1+6) = 12-13 = -1 which is not divisible by 11
The closest divisible number to -1(or 1) is 0, thus we remove 1 apple
So By removing 1 apple we make the total 562155 => (5+2+5)-(6+1+5) = 0 which is divisible by 11
ANSWER: C
Question: A watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?
A.1000
B.1899
C.7861
D.1229
Answer: A.1000
Explanation: 90%
104%
--------
14% ---- 140
100% ---- ? => Rs.1000
Answer: A
Question: There are 780 male and female participants in a meeting. Half the female participants and one-quarterof the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female?
A.130
B.100
C.125
D.175
Answer: A.130
Explanation: Let m be the number of male participants and f be the number of female articipants in the meeting. Thetotal number of participants is given as 780.
Hence, we have m+f= 780
Now, we have that half the female participants and one-quarter of the male participants are Democrats.
Let d equal the number of the Democrats.
Then we have the equation f/2 + m/4 =d
Now, we have that one-third of the total participants are Democrats. Hence, we have the equation
d = 780/3 = 260
Solving the three equations yields the solution
f = 260,m= 520, and d= 260.
The number of female democratic participants equals half the female participants equals
260/2 = 130.
ANSWER:A
Question: A shopkeeper sold an book offering a discount of 5% and earned a profit of 14%. What would have been the percentage of profit earned if no discount was offered?
A.140
B.120
C.130
D.110
Answer: B.120
Explanation: Let C.P. be $100.
Then, S.P. = $114
Let marked price be $x. Then, 95/100 x = 114
x = 114/95 = $120
Now, S.P. = $120, C.P. = $100
Profit % = 20%.
B
Question: Divide Rs. 1600 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?
A.Rs.800
B.Rs.400
C.Rs.600
D.Rs.500
Answer: B.Rs.400
Explanation: A+B+C = 1600
A = 1/3(B+C); B = 2/3(A+C)
A/(B+C) = 1/3
A = 1/4 * 1600 => 400
ANSWER:B
Question: The population of a town is 176400. If it increase at the rate of 5% per annum. What was its population 3 years ago?
A.152460
B.214560
C.152381
D.210000
Answer: C.152381
Explanation: population 2 years ago = 176400/(1 + 5/100)^3
Answer is C
Question: David purchased a house for Rs.75000 and a site for Rs.15000 respectively, if he sold the house for Rs.83000 and the site for Rs.10000, then find the resultant percentage of gain?
A.30 %
B.330/3 %
C.31/3 %
D.3.33 %
Answer: D.3.33 %
Explanation: Sol.
Total CP = 90000 & total SP = 93000 ⇒ gain = SP/CP = 93000/90000 = 1.0333 = 3.33%.
Answer D
Question: Divide Rs. 1500 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?
A.227
B.268
C.375
D.998
Answer: C.375
Explanation: A+B+C = 1500
A = 1/3(B+C); B = 2/3(A+C)
A/(B+C) = 1/3
A = 1/4 * 1500 => 375
Answer: C
Question: The ratio of ducks and frogs in a pond is 37 : 39 respectively. The average number of ducks and frogs in the pond is 132. What is the number of frogs in the pond ?
A.148
B.134
C.156
D.144
Answer: B.134
Explanation: Solution:
Ratio of Ducks and Frogs in Pond,
= 37 : 39.
Average of Ducks and Frogs in Pond,
= 132.
So, total number of Ducks and Frogs in the Pond,
= 2* 132 = 262.
Therefore,
Number of Frogs, = (262*39)/76 = 134.
Answer: Option B
Question: A and B enter into a partnership with respective capitals of Rs. 20,000 and Rs. 40,000. At the end of the year, the total profit is Rs. 42,000. If A receives Rs. 15,000 as both his salary and profit, then what is his salary?
A.Rs. 1000
B.Rs. 4000
C.Rs. 3500
D.Rs. 3000
Answer: A.Rs. 1000
Explanation: Explanation:
A's capital : B 's capital
20000 : 40000 = 1 : 2
Since, the time period is fixed, the profit is distributed in the ratio of capital 1 : 2
Profit of A = (1/3) * 42,000 = Rs. 14,000
Salary of A = Rs. (15000 – 14000) = Rs. 1000
ANSWER: A
Question: A wheel rotates 10 times every minute and moves 20 cm during each rotation. How many metres does the wheel move in two hour?
A.240 metre
B.12 metre
C.120 metre
D.1200 metre
Answer: A.240 metre
Explanation: Expl : Number of times wheel moves in 2 hour = 10 * 120 = 1200
:. Distance moves = (1200 *20) cm = 24000 cm
In metres = 240 metre
Answer: A
Question: The simple interest on Rs.500 at 6% per annum from May 3rd to July 15th in the same year is
A.Rs. 8
B.Rs. 6
C.Rs. 4
D.Rs. 9
Answer: B.Rs. 6
Explanation: Explanation :
Time from May 3rd to July 15th = 28 days of May + 30 days of June and 15 days of July
= 73 days= 73/365 years = 15 years
Simple interest = PRT/100=500×6×15/100=6
Answer : Option B
Question: 8 liters of a 25 percent solution of alcohol in water are mixed with 2 liters of a 12 percent alcohol in water solution. What is the percentage of alcohol in the new solution?
A.21.2%
B.21.6%
C.22.0%
D.22.4%
Answer: D.22.4%
Explanation: The total amount of alcohol is 0.25(8) + 0.12(2) = 2.24 liters.
The percentage is 2.24 / 10 = 22.4 / 100 which is 22.4%
The answer is D.
Question: 19.19/2000 is equal to:
A.1.01252633
B.0.01262533
C.0.12526333
D.0.012793333
Answer: D.0.012793333
Explanation: 19.19/2000 = 2525/200000
= 0.012793333
ANSWER:D
Question: If 2x+3y=34 and ((x + y)/y)=13/8,then find the value of 5y+7x.
A.75
B.65
C.85
D.95
Answer: A.75
Explanation: The given equations are:
2x+3y=34 …(i) and, ((x + y) /y)=13/8 => 8x+8y=13y => 8x-5y=0 …(ii)
Multiplying (i) by 5,(ii) by 3 and adding, we get : 34x=170 or x=5.
Putting x=5 in (i), we get: y=8.
Therefore, 5y+7x=((5*8)+(7*5))=40+35=75
Answer is A.
Question: Find the value of “n” where 348 + 31996 + 33943 + 33n.
A.1963
B.1964
C.1960
D.1991
Answer: A.1963
Explanation: 3^48 + 3^1996 + 3^3943+3^3n
(3^16 )^3 + 3^1996 + 3^3943 + (3^n)^3
its expansion of (a+b)^3=a^3+3a^2b+3ab^2+b^3
=> 3*(3^16)^2*3^n=3^1996
=> 3^(33+n)=3^1996
=> n = 1963
ANSWER:A
Question: Two trains run in opposite directions on a circular track. Train A travels at a rate of 4π miles per hour and Train B runs at a rate of 6π miles per hour. If the track has a radius of 6 miles and the trains both start from Point R at the same time, how long, in hours, after the trains depart will they again meet at Point R?
A.3
B.6
C.9
D.18
Answer: B.6
Explanation: I don't agree with your solutions, first. And second the answer choices don't seem to contain the right answer.
My solution is as follows, and I ask anyone to correct me if I am wrong.
Solution 1
Let the distance covered by train A be X, thus that covered by the train B will be 12*3.14-X
dA = X dB = 12*3.14 - X
Times taken by A and B are
tA= X/4*3.14 , tB = (12*3.14 - X)/6*3.14 (ii)
Since they have been traveling for the same period of time, then
X/4*3.14 = (12*3.14 - X)/6*3.14
X/2 =(12*3.14 -X)/3
3X = 2(12*3.14 -X)
5X = 24*3.14
X = 24*3.14/5
Plugging that in either equation of (ii) yields t = 6/5
Solution 2
We add the speed of A and B: totalSpeed R= 4*3.14 + 6*3.14 = 10*3.14
Total distance covered = 12*3.14
t ime = distance / speed = 12*3.14/10*3.14 = 6/5.
tA =( X/4*3.14) =(24*3.14/5)/4*3.14 = 6/5=B
Question: what should be multiplied to 2880 to make it a perfect square?
A.2
B.3
C.4
D.5
Answer: D.5
Explanation: Step 1== 288*10
Step 2== 144*2*2*5
Step 3== 12*12*2*2*5 if perfect square===12*12*2*2*5*5
So answer is 5 we have to multiply it by 5 to make it as a perfect square.
ANSWER:D
Question: Pipe A fills a tank of capacity 750 liters at the rate of 40 liters a minute. Another pipe B fills the same tank at the rate of 30 liters a minute. A pipe at the bottom of the tank drains the tank at the rate of 20 liters a minute. If pipe A is kept open for a minute and then closed and pipe B is open for a minute and then closed and then pipe C is open for a minute and then closed and the cycle is repeated, when will the tank be full?
A.45 minutes
B.14 minutes
C.39 minutes
D.40 minutes 20 seconds
Answer: A.45 minutes
Explanation: In one cycle they fill 40+30-20 = 50 liters
750 = 50*n => n = 15
here n = number of cycles.
total time = 15*3 = 45 as in one cycle there are 3 minutes.
thus 45 minutes
ANSWER:A
Question: The distance traveled by Airplane in one year approximately 3,570,000,000 miles.The distance traveled by Airplane in 10 years?
A.10<7>
B.10<5>
C.10<10>
D.10<9>
Answer: D.10<9>
Explanation: The distance traveled by Airplane in one year = 3,500,000,000 miles
The distance traveled by Airplane in 10years = 3,500,000,000 miles * 10 years = 35,000,000,000
= 35*10<9> (exponent miles) Answer : D
Question: In each term of a sequence, 3 is added to get the next term. If the first term is 6, what is the 64th term?
A. 192
B. 154
C. 134
D. 174
Answer: A. 192
Explanation: 1rst term + 63 terms = 6 + 3+3+3+3+3+3+3+...+3 (63 times)
6 + (3 x 63) = 3 + 189 = 192
Answer A
Question: Two pipes A and B can fill a tank in 12 and 24 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?
A.8 min
B.28 min
C.18 min
D.5 min
Answer: A.8 min
Explanation: Explanation :
Part filled by pipe A in 1 minute= 1/12
Part filled by pipe B in 1 minute= 1/24
Part filled by pipe A and pipe B in 1 minute= 1/12+1/24=1/8
i.e., both the pipe together can fill the tank in 8 minutes
Answer is A
Question: X and Y invest Rs.22500 and Rs.17500 respectively in a business. At the end of the year, they make a profit of Rs.26400. What is the share of X in the profit?
A.Rs.14850
B.Rs.26400
C.Rs.12000
D.Rs.12500
Answer: A.Rs.14850
Explanation: Ratio of the investment=22500:17500=9:7
Share of X in the profit=(26400×9)/16=
=14850
ANSWER:A
Question: The average weight of a group of persons increased from 48 kg to 51 kg, when two persons weighing 78 kg and 93 kg join the group. Find the initial number of members in the group?
A.34
B.21
C.23
D.25
Answer: C.23
Explanation: Let the initial number of members in the group be n.
Initial total weight of all the members in the group = n(48)
From the data,
48n + 78 + 93 = 51(n + 2) => 51n - 48n = 69 => n = 23
Therefore there were 23 members in the group initially.
Answer: C
Question: Dhoni bought 5 shirts with the average cost of $60. If David also buys the sixth shirt with the price of $ 72, what is the average (arithmetic mean) price of those 6 toys?
A.$63
B.$64
C.$65
D.$62
Answer: D.$62
Explanation: 5 shirts-> Total cost = 5 * Avg cost = 5*60 = 300
Sixth toy cost = 72
Total cost for 6 toys= 300+72 = 372
AM = 372/6= 62
Hence D
Question: How many natural numbers are there which give a remainder of 41 after dividing 1997?
A.2
B.4
C.6
D.None of these
Answer: C.6
Explanation: Solution
Let us assume that the quotient is Q and divisor is D.
Using the condition given in question,
1997 = QD + 41
⇒ QD = 1956.
Now we will factorize 1956 in two parts such that D (divisor) is more than 41. Answer C
Question: 40% of a number is more than 20% of 650 by 190. Find the number?
A.600
B.700
C.800
D.900
Answer: C.800
Explanation: Explanation:
(40/100) * X â€“ (20/100) * 650 = 190
2/5 X = 320
X = 800
ANSWER IS C
Question: A man spends Rs. 1400 per month on an average for the first three months, Rs 1550 for next four months and Rs. 1800 per month for the last five months and saves Rs . 5200 a year. What is his average monthly income?
A.2050
B.2100
C.2200
D.2300
Answer: A.2050
Explanation: Explanation:
Total expenditure for the first 3 months = 3 Ã— 1400 = 4200
Total expenditure for 4 months = 4 Ã— 1550 = 6200
Total expenditure for 5 months = 5 Ã— 1800 = 9000
Total expenditure and saving (which is income for one year)
= 4200 + 6200 + 9000 + 5200 = Rs. 24600
So, Average monthly income = 25200/12 = Rs. 2050
Answer A
Question: A particular parking garage is increasing its rates by 15 percent per month. Bob decides to reduce the number of days he uses the garage per month so that the amount he spends at the garage per month remains unchanged. Which of the following is closest to Bob’s percentage reduction in the number of days he uses the garage each month?
A.10%
B.11%
C.12%
D.13%
Answer: D.13%
Explanation: Let parking rate = 100
=(15/100+15)*100
=13.04%
ANSWER:D
Question: Sabrina is contemplating a job switch. She is thinking of leaving her job paying $85,000 per year to accept a sales job paying $45,000 per year plus 20 percent commission for each sale made. If each of her sales is for $1,500, what is the least number of sales she must make per year if she is not to lose money because of the job change?
A.57
B.177
C.178
D.133
Answer: C.178
Explanation: Lets say she sales x items so her commission will be : x * 1500*20 /100 = 300x
Salary difference is: 85000 - 45000 = 40000
So commission must at least be equal to salary difference i.e. x = 40000/300= 133 (Approx).
Hence answer is C
Question: If the average (arithmetic mean) of five consecutive negative integers is 2k – 1, what is the difference V between the greatest and least of the five integers?
A.4K
B.4k^2 -4k
C.4-4k
D.4
Answer: D.4
Explanation: (n-2 + n - 1 + n + n + 1 + n + 2)/5 = 2k - 1
=> n = 10k - 5
Greatest = n + 2 = 10k - 5 + 2 = 10k - 3
Least = n - 2 = 10k - 5 - 2
=> Difference V= 10k - 3 - (10k - 7)
= 4
Answer - D
Question: Of the 200 math majors at a certain university, 20 percent will be assigned to advanced calculus on Monday and Wednesday and the remaining 70 percent will be assigned to advanced calculus on Tuesday and Thursday. However, 40 percent of the math majors prefer Tuesday and Thursday and 60 percent prefer Monday and Wednesday. What is the lowest possible number of math majors who will NOT be assigned to the days they prefer?
A. 15
B. 20
C. 30
D. 45
Answer: B. 20
Explanation: 30% of students are assigned to Monday and Wednesday = 0.3*200 = 60
70% of students are assigned to Tuesday and Thursday = 0.7*200 = 140
60% of students prefer Monday and Wednesday = 0.6*200 = 120
40% of students prefer Tuesday and Thursday = 0.4*200 = 80
Since we need theleastnumber of students who will not be assigned to their preferred days, we shall fit in themaximumpossible students as per their preference:
All of the 40% of students who prefer Tuesday and Thursday can be accommodated to their preferred days, whereas only 60 out of 120 students who prefer Monday and Wednesday can be accommodated to their preferred days.
The remaining 60 students who prefer Monday and Wednesday will be allocated to Tuesday and Thursday by default, which is not their choice.
Answer is B.
Question: A motorcyclist goes from Bombay to Pune, a distance of 160 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 ½ hours after the first, and reaches Pune ½ hour earlier. What is the ratio of the speed of the motorcycle and the car?
A.1:2
B.2:5
C.1:4
D.1:1
Answer: B.2:5
Explanation: T = 160/32 = 5 h
T = 5 - 3 = 2
Time Ratio = 5:2 = 5:2
Speed Ratio = 2:5
Answer: B
Question: According to a 2010 census, China's population was 1.34 billion people. If the ratio of male's to females is 1.052:1, respectively, then how many women are there? Answer in terms of (M = women).
A.W = M - 1.052
B.W = (M)(1.052)
C.W = M + 1.052
D.W = M/1.052
Answer: D.W = M/1.052
Explanation: The ratio of M to W, where
M = the number of males, and
W = the number of females.
Population = 1.34 billion people.
M/W:M/M = 1.052:1, so
M/W = 1.052
W = M/1.052
Answer is D
Question: A can do a piece of work in 28 days and B alone can do it in 10 days. B works at it for 5 days and then leaves. A alone can finish the remaining work in
A.5days
B.6days
C.7.5days
D.14days
Answer: D.14days
Explanation: Explanation:
B's 5 days work =
1/10∗5=1/2
Remaining work =1−1/2=1/2
A can finish work =28∗1/2=14days
Option D
Question: A certain number when divided by 50 leaves a remainder 25, what is the remainder if the same no.be divided by 15?
A.4
B.5
C.6
D.8
Answer: B.5
Explanation: Explanation:
50 + 25 = 75/15 = 5 (Remainder)
B
Question: In the biology lab of "Jefferson" High School there are 5.4*10^6 germs, equally divided among 10,800 Petri dishes. How many germs live happily in a single dish?
A.100
B.200
C.500
D.1000
Answer: C.500
Explanation: 5.4*10^6/ 10800==> 54*10^3/108==> 54000/108= 500
ANSWER:C
Question: The cost price of a radio is Rs.1900 and it was sold for Rs.1330, find the loss %?
A.18%
B.31%
C.30%
D.45%
Answer: C.30%
Explanation: 1900 ---- 570
100 ---- ? => 30%
Answer:C
Question: A WORKS TWICE AS FAST AS B. IF B CAN COMPLETE A WORK IN 10 DAYS INDEPENDENTLY, THE NUMBER OF DAYS IN WHICH A AND B CAN TOGETHER FINISH THE WORK IS:
A.11/3 DAYS
B.10/3 DAYS
C.12/3 DAYS
D.3/12 DAYS
Answer: B.10/3 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 = 1/5, B'S 1 DAY'S WORK = 1/10
(A+B)'S 1 DAY'S WORK = (1/5+1/10)=3/10=10/3
SO, A AND B TOGETHER CAN FINISH THE WORK IN 10/3 DAYS.
CORRECT OPTION: B
Question: In a simultaneous throw of pair of dice. Find the probability of getting the total more than 7.
A.5/19
B.5/12
C.5/28
D.5/10
Answer: B.5/12
Explanation: Explanation:
Here n(S) = (6 x 6) = 36
Let E = event of getting a total more than 7
= {(2,6),(3,5),(3,6),(4,4),(4,5),(4,6),(5,3),(5,4),(5,5),(5,6),(6,2),(6,3),(6,4),(6,5),(6,6)}
Therefore,P(E) = n(E)/n(S) = 15/36 = 5/12.
Answer: B) 5/12
Question: The price of 3 tables and 4 chairs is Rs. 3300. With the same money one can buy 2 tables and 10 chairs. If one wants to buy 1 table and 1 chair, how much does he need to pay?
A.940
B.1050
C.1100
D.1240
Answer: B.1050
Explanation: Let price of a table = t
and price of a chair = c
3t + 4c = 3300 ---(Equation 1)
2t + 10c = 3300
=> t + 5c = 1650 ---(Equation 2)
(Equation 2) × 3 => 3t + 15c = 4950 ---(Equation 3)
(Equation 3) - (Equation 1) => 11c = 1650
=> c = 150
Substituting the value of c in equation 1, we get
3t + (4 × 150) = 3300
=> 3t = 3300 – 600 = 2700
=>t = 2700/3 = 900
Cost of 1 table and 1 chair = c + t = 150 + 900 = 1050
Answer : Option B
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 16%?
A.20%
B.26%
C.42%
D.27%
Answer: B.26%
Explanation: SP2 = 2/3 SP1
CP = 100
SP2 = 84
2/3 SP1 = 84
SP1 = 126
100 --- 26 => 26%
Answer: B
Question: The arithmetic mean and standard deviation of a certain normal distribution are 12 and 1.2, respectively. What value is exactly 2 standard deviations less than the mean?
A.9.6
B.11
C.11.5
D.12
Answer: A.9.6
Explanation: Mean = 12
Two standard deviations is 1.2 + 1.2 = 2.4
There could be two calues for this.
Mean + two standard deviations = 14.4
Mean - Two standard deviations = 9.6
Answer choice has 9.6 and so A is the answer.
Question: If X is the sum of first 10 positive even integers and Y is the sum of first 10 positive odd integers, what is the value of x-y?
Please try to explain your answers
A.10
B.25
C.50
D.75
Answer: A.10
Explanation: First even minus first odd = 2-1 = 1;
The sum of first 2 even integers minus the sum of first 2 odd integers = (2+4)-(1+3) = 2;
The sum of first 3 even integers minus the sum of first 3 odd integers = (2+4+6)-(1+3+5) = 3;
We can see the patterns here, so the sum of first 10 positive even integers minus the sum of first 10 positive odd integers will be 10.
Answer: A.
Question: Select Odd number:
6, 9, 15, 21, 24, 28, 30
A.20
B.21
C.24
D.28
Answer: D.28
Explanation: Each of the numbers except 28, is a multiple of 3.
answer D
Question: There is a 4 inch cube painted on all sides. This is cut into no of 1 inch cubes. What is the no of cubes which have no painted sides.
A.7
B.8
C.9
D.10
Answer: B.8
Explanation: The original cube is cut into 64 pieces. Removing all cubes from any two opposite pairs of faces leaves total 32 cubes, as one face contains 16 cubes each. It can be seen that in the remaining two layers, only four each from each layer have no sides painted. So total = 2*4=8 cubes.
ANSWER:B
Question: If m and n are positive integer, and 1800m=n^3, what is the least possible value of m?
A.2
B.3
C.15
D.30
Answer: C.15
Explanation: 1800*m=n^3
m=n^3/1800
=n^3/(3^2*5^2*2^3)
so n has to be 3*5*2 so that n^3 is divisible by 1800.
So m= (2*3*5)^3/(3^2*5^2*2^3)
m=15
ANSWER:C
Question: Worker A takes 8 hours to do a job. Worker B takes 10 hours to do the same job. How long it take both A & B, working together but independently, to do the same job?
A.40/9 days
B.40/7 days
C.7.5 days
D.8.5 days
Answer: A.40/9 days
Explanation: A's one hour work = 1/8.
B's one hour work = 1/10.
(A+B)'s one hour work = 1/8+1/10 = 9/40.
Both A & B can finish the work in 40/9 days
Answer : A.
Question: The difference between the length and breadth of a rectangle is 42 m. If its perimeter is 280 m, then its area is:
A.1520 m2
B.4250 m2
C.4459 m2
D.4092 m2
Answer: C.4459 m2
Explanation: EXPLANATION
We have: (l â€“ b) = 42 and 2(l + b) = 280 or (l + b) = 140.
Solving the two equations, we get: l = 91 and b = 49.
Area = (l x b) = (91x 49) m2 = 4459 m2.
Answer C
Question: Having received his weekly allowance, a student spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $1.00 at the candy store. What is this student’s weekly allowance?
A.$2.75
B.$3.25
C.$3.75
D.$4.25
Answer: C.$3.75
Explanation: Let x be the value of the weekly allowance.
(2/3)(2/5)x = 100 cents
(4/15)x = 100
x = $3.75
The answer is C.