RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: During the first week of performances of a certain play, 5,400 tickets were sold, all at reduced price. During the remaining weeks of performances, 5 times as many tickets were sold at full price as were sold at reduced price. If the total number of tickets sold T was 25,200, how many of them were sold at full price?
A.21,000
B.19,800
C.16,500
D.15,800
Answer: C.16,500
Explanation: Given:
The question tells us about the number of tickets sold in the first week at reduced price = 5,400. It also tells us that during the remaining weeks, the number of tickets sold at full price was 5 times the no. of tickets sold at reduced price. The total tickets sold was 25,200, and we are asked to find the number of tickets that where sold at full price.
Approach:
The question asks us to find the number of ticket sold at full price. We know that the number of tickets sold at full price was 5 times the no. of tickets sold at reduced price in remaining weeks. Hence, assuming tickets sold at reduced price in remaining weeks to be x would give us the no. of tickets sold at full price to be 5x.
Tickets sold in first week + Tickets sold in remaining weeks = Total no. of tickets soldi.e.
Tickets sold in first week + Tickets sold at full price in remaining weeks + Tickets sold at reduced price in remaining weeks = Total no. of tickets sold
We know the no. of tickets sold during first week and the total no. of tickets sold. We will use this relation to get to our answer.
Working Out:
Tickets sold in first week + Tickets sold at full price in remaining weeks + Tickets sold at reduced price in remaining weeks = Total no. of tickets sold
Substituting values in the equation, we get
5,400 + 5x + x = 25,200
x= 3,300
Tickets sold at full price = 5x = 16,500
Answer: Option C
Question: If 55 percent of congress are Democrats and the rest are Republicans. In a vote on a new law , if 40 percent of the members who are Democrats and 20 percent of the members who are Republicans are expected to vote for the new law , what percent of the members are expected to vote for the new law ?
A. 30%
B. 31%
C. 33%
D. 35%
Answer: B. 31%
Explanation: Say there are total of 100 members in the congress . Thus 55 are Democrats and 45 are Republicans.
55*0.4=22 Democrats are expected to vote for the new law ;
45*0.20=9 Republicans are expected to vote for the new law.
Thus total of 22+9=31 members are expected to vote for the new law, which is 31% of the total number of congress members .
Answer: B.
Question: In a competitive examination in a state A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each state?
A.8000
B.7540
C.6500
D.9100
Answer: A.8000
Explanation: Let the number of candidates appeared be x
then, 7% of x - 6% of x = 80
1% of x = 80
x = 80*100 = 8000
Answer is A
Question: If one person completes a journey in 10 hrs. He travels 1st half of the journey at the rate of 21 km/hr and 2nd half at therate of 24 km/hr. Find the total journey in km.
A.200 km
B.220 km
C.224 km
D.230 km
Answer: C.224 km
Explanation: distance = speed x time
Let time taken to travel the first half = x hr
then time taken to travel the second half = (10 - x) hr
Distance covered in the the first half = 21x
Distance covered in the the second half = 24(10 - x)
But distance covered in the the first half = Distance covered in the the second half
=> 21x = 24(10 - x)
=> 21x = 240 - 24x
=> 45x = 240
=> 9x = 48
=> 3x = 16
⇒x=163Hence Distance covered in the the first half = 21x=21×163=7×16=112 kmTotal distance = 2×112=224 km
C
Question: Train X crosses a stationary train Y in 60 seconds and a pole in 25 seconds with the same speed. The length of the train X is 300 m. What is the length of the stationary train Y?
A.228
B.420
C.882
D.661
Answer: B.420
Explanation: Let the length of the stationary train Y be LY
Given that length of train X, LX = 300 m
Let the speed of Train X be V.
Since the train X crosses train Y and a pole in 60 seconds and 25 seconds respectively.
=> 300/V = 25 ---> ( 1 )
(300 + LY) / V = 60 ---> ( 2 )
From (1) V = 300/25 = 12 m/sec.
From (2) (300 + LY)/12 = 60
=> 300 + LY = 60 (12) = 720
=> LY = 720 - 300 = 420 m
Length of the stationary train = 420 m
Answer:B
Question: Two persons start at the same point, walk in opposite directions with 6 km/hr and 4 km/hr respectively.
What is the distance separated after 4 and half hrs?
A.45 km
B.48 km
C.50 km
D.29.250 km
Answer: A.45 km
Explanation: As the two persons are moving in the opposite direction, so they will be separateed in 1 hour = 6 + 4 = 10 km.
They will be separated in 4.5 hours = 10 * 4.5 = 45 km
ANSWER:A
Question: Simple interest on a sum at 4% per annum for 2 years is Rs.80. The C.I. on the same sum for the same period is?
A.81.6
B.88.6
C.81.1
D.81.5
Answer: A.81.6
Explanation: SI = 40 + 40
CI = 40 + 40 + 1.6 = 81.6
Answer: A
Question: In a BCCI meeting there are 11 people. All shake hands with each other once. How many handshakes will be there altogether?
A.28
B.10
C.11
D.19
Answer: B.10
Explanation: There will be n-1 handshakes as A person will shake hands with all the other members.
=11-1=10
Answer:B
Question: A train moves fast a telegraph post and a bridge 260 m long in 8 sec and 20 sec respectively. What is the speed of the train?
A.79.5
B.39.5
C.79.9
D.78.0
Answer: D.78.0
Explanation: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 8 => x = 8y
(x + 260)/20 = y
y = 21.67
Speed = 21.67m/sec = 21.67 * 18/5 = 78 km/hr.
Answer:D
Question: 20 is subtracted from 60% of a number, the result is 88. Find the number?
A.120
B.300
C.180
D.170
Answer: C.180
Explanation: (60/100) * X â€“ 20 = 88
6X = 1080
X = 180
Answer:C
Question: The sum of the ages of a father and son is 45 years. Five years ago, the product of their ages was four times the father’s age at that time. The present age of father and son, repectively are
A.25 years , 10 years
B.36 years, 9 years
C.39 years, 6 years
D.40 years, 6 years
Answer: B.36 years, 9 years
Explanation: Let son’s age = x years. The father’s age = (45 - x) years
we have (x - 5)(45 - x - 5) = 4(45 - x - 5)
=>x - 5 = 4
=> x = 9
Thus, ages are 36 years and 9 years.
ANSWER:B
Question: A tank can supply water to a village for 80 days. If a leak at the bottom of the tank drains out 10 liters per day, the supply lasts for 60 days only. For how many days will the supply last if the leak drains out 20 liters per day?
A.42
B.45
C.48
D.50
Answer: C.48
Explanation: Losing 10 liters per day results in a loss of 600 liters in 60 days. So, those 600 liters were for 20 days, making daily consumption of the village 30 liters per day. Thus the capacity of the tank is 30*80 = 2400 liters.
Losing 20 liters plus 30 liters gives 50 liters per day. At this rate the supply will last 2400/50 = 48 days.
The answer is C.
Question: The rate of spin of a certain gyroscope doubled every 10 seconds from the moment a particular stopwatch started. If after a minute and a half the gyroscope reached a speed of 1600 meters per second, what was the speed, in meters per second, when the stopwatch was started?
A.25/3
B.25/4
C.25/8
D.25/16
Answer: C.25/8
Explanation: Let x be the original speed when the stopwatch was started.
In 90 seconds, the speed doubled 9 times.
2^9 * x = 1600
x = (2^6 * 25) / 2^9 = 25/8
The answer is C.
Question: In a market, a dozen eggs cost as much as a pound of rice, and a half-liter of kerosene costs as much as 8 eggs. If the cost of each pound of rice is $0.33, then how many E cents does a liter of kerosene cost? [One dollar has 100 cents.]
A. 0.33
B. 0.44
C. 0.55
D. 44
Answer: D. 44
Explanation: Main thing to remember is answer is asked in cents, however when we calculate, it comes up as 0.44 $
Just multiply by 100, Answer E= 44.D
Question: If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is ?
A.1/9
B.1/2
C.1/6
D.3/2
Answer: B.1/2
Explanation: The number of exhaustive outcomes is 36.
Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2
P(E) = 1 - 1/2 = 1/2.
Answer: B
Question: Students of three different classes appeared in common examination. Pass average of 10 students of first class was 55%, pass average of 15 students of second class was 60% and pass average of 25 students of third class was 80% then what will be the pass average of all students of three classes?
A.74%
B.75%
C.69%
D.72%
Answer: C.69%
Explanation: Solution:
Sum of pass students of first, second and third class,
= (55% of 10) + (60% of 15)+ (80% of 25)
= 5.5+9+20 = 34.5
Total students appeared,
= 10+15+25 = 50
Pass average,
= 34.5*100/50 = 69%.
Answer: Option C
Question: If a farmer sells 5 of his chickens, his stock of feed will last for 4 more days than planned, but if he buys 20 more chickens, he will run out of feed 1 day earlier than planned. If no chickens are sold or bought, the farmer will be exactly on schedule. How many chickens does the farmer have?
A.15
B.20
C.20/3
D.25
Answer: C.20/3
Explanation: Let x = total feed required for the planned period
n= number of chicken
t = total time of the planned feed
x = nt
1) x = (n-5) * (t+4)
2) x = (n+20) * (t-1)
equating 1 &2
(n-5) * (t+4) = (n+20) * (t-1)
5n = 25t
n =5t
x= n * n/5
substituting this value in 1
n * n/5 = (n-5) * (n/5+4)
15n = 100
n =20/3
C
Question: A can do a piece of work in 20 days which B can do in 12 days. B worked at it for 9 days. A can finish the remaining work in ?
A.3 days
B.5 days
C.6 days
D.7 days
Answer: B.5 days
Explanation: B's 9 day's work = 9 x (1/12) = 3/4
Remaining work = (1 - 3/4) = 1/4
1/4 work is done by A in = 20 x (1/4) = 5 days.
answer : B
Question: If xy+3z = x(y+z), which of the following must be true?
A.1. x=3 and z=0
B.2. x=1 and y=1
C.3. y=1 and z=0
D.4. x=1 or y=0
Answer: A.1. x=3 and z=0
Explanation: xy+3z=x(y+z)
xy+3z=xy+xz
3z=xz
it means x=3 or z=0
Answer A
Question: The difference between the local value and the face value of 4 in the numeral 98625147 is
A.36
B.63
C.34
D.30
Answer: A.36
Explanation: Explanation:
(Local value of 4) - (Face value of 4) = (40 - 4) = 36
A)
Question: 3 buffaloes eat as much as 4 cows or 2 oxen. At a farm there are 15 buffaloes, 8 oxen and 24 cows. The fodder for these cattle is available for 24days. If 8 more cows & 9 more buffaloes are brought in, how long will the fodder last?
A.10
B.13
C.15
D.18
Answer: D.18
Explanation: Sol. 2 oxen = 3 buffaloes = 4 cows 8 oxen = 16 cows and 15 buffaloes = 20 cows 16 cows + 20 cows + 24 cows = 60 cows Since fodder is available for 60 cows for 24 days
So fodder will be available for (60 + 8 + 12) = 80 cows c 24x60 .0 .
for-^—=18 days.
D
Question: If two dice are thrown together, the probability of getting a doublet on the dice is
A.1/6
B.1/5
C.1/4
D.1/3
Answer: A.1/6
Explanation: The number of exhaustive outcomes is 36.
Let E be the event of getting doublet on the dies is 6/36 = 1/6
P(E) = 1/6.
A)
Question: The number obtained by interchanging the two digits of a two-digit number is less than the original number by 45. If the sum of the two digits of the number so obtained is 13, then what is the original number?
A.22
B.94
C.27
D.19
Answer: B.94
Explanation: Explanation:
Let the number be in the form of 10a + b
Number formed by interchanging a and b = 10b + a.
a + b = 13 --- (1)
10b + a = 10a + b - 45
45 = 9a - 9b => a - b = 5 --- (2)
Adding (1) and (2), we get
2a = 18 => a = 9 and b = 4
The number is: 94.
Answer:B
Question: An office manager must choose a five-digit lock code for the office door. The first and last digits of the code must be odd, and no repetition of the digits is allowed. How many different lock codes are possible.?
A.3120
B.3250
C.3275
D.3860
Answer: A.3120
Explanation: However, I think 6720 (the answer given in MGMAT) is wrong. Here's my reasoning. If you have (an) odd number(s) for your 2nd, 3rd and/or 4th digits, you cannot repeat that(those) numbers for the last digit. Therefore, this problem needs to be partitioned into 4 groups.
1) ODD (1st digit); 3 EVENs (2nd, 3rd, 4th digits); ODD (5th digit)
5 x 5x 4 x 3 x 4 = 1200
2) ODD (1st digit); 2 EVEN, 1 ODD (2nd, 3rd, 4th digits); ODD (5th digit)
5 x 5 x 4 x 4 x 3 = 1200
3) ODD (1st digit); 1 EVEN, 2 ODDs (2nd, 3rd, 4th digits); ODD (5th digit)
5 x 5x 4 x 3 x 2 = 600
4) ODD (1st digit); 3 ODDs (2nd, 3rd, 4th digits); ODD (5th digit)
5 x 4 x 3 x 2 x 1 = 120
Then the total # of combinations would be 1200 + 1200 + 600 + 120 = 3120.
ANS:A
Question: For an employee to qualify for early retirement at a certain company, the sum of the employee’s age and years of service must be at least 78, If Sue was K years old when she was hired by the company, what is the minimum age at which she could possibly qualify for early retirement?
A.K+39
B.2K+39
C.(78+K)/2
D.(78-K)/2
Answer: C.(78+K)/2
Explanation: Let y be the years of service at the company.
After y years of service, Sue's age will be K + y.
Sue can retire when (K+y) + y = 78
y = (78 - K)/2
Then Sue's age will be K + y = K + (78 - K)/2 = (78+K) / 2
The answer is C.
Question: A dealer offers a cash discount of 20% and still makes a profit of 20% when he further allows 10 articles to be sold at the cost price of 9 articles to a particular sticky bargainer. How much percent above the cost price were his articles listed?
A.50%
B.55%
C.60%
D.66+(2/3)%
Answer: D.66+(2/3)%
Explanation: Given
Cash Discount - 20%
Profit - 20%
Items Sold - 10
Price Sold at = List Price of 9
Assume List price = $10
Total Invoice = $90
-20% Cash Discount = $72
Let cost price of 10 items be x
So total cost = 10*x
Given the shopkeeper had a profit of 20%
10 * x * 120/100 = 72
or x = $6
Which means his products were listed at $10 which is a 66+(2/3)% markup over $6
Answer D
Question: Juan is a gold medalist in athletics. In the month of May, if Juan takes 8 seconds to run y yards, how many seconds will it take him to run x yards at the same rate?
A.8x/y
B.11x/y
C.9x/y
D.12x/y
Answer: A.8x/y
Explanation: velocity=distance/time;
since he ran at same rate both d tyms,
y/8=x/t
so t=8x/y
ANSWER:A
Question: Two pipes P and Q can fill a cistern in 11 and 15 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill?
A.1/8
B.1/4
C.2/4
D.10/11
Answer: D.10/11
Explanation: 3/11 + x/15
= 1
x= 10 10/11
Answer: D
Question: Find the average of all even numbers upto 75.
A.35
B.36
C.38
D.34
Answer: C.38
Explanation: Average of all even numbers upto 75 = [ 35/2* ( first even number +
greatest even number before 75) ]/35
= ½ *(2 +74 )
= 76/2
= 38.
ANSWER:C
Question: The weights of three boys are in the ratio 4 : 5 : 6. If the sum of the weights of the heaviest and the lightest boy is 45 kg more than the weight of the third boy, what is the weight of the lightest boy?
A.39 kg
B.36 kg
C.32 kg
D.31 kg
Answer: B.36 kg
Explanation: Let the weights of the three boys be 4k, 5k and 6k respectively.
4k + 6k = 5k + 45
=> 5k = 45 => k = 9
Therefore the weight of the lightest boy
= 4k = 4(9) = 36 kg.
Answer:B
Question: The simple interest and the true discount on a certain sum for a given time and at a given rate are Rs. 88 and Rs. 80 respectively. The sum is:
A.880
B.1450
C.1600
D.1800
Answer: A.880
Explanation: Sol.
Sum = S.I. * T.D. / (S.I)-(T.D.) = 88 * 80 / (88 - 80) = Rs.880.
Answer A
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 21 seconds. The ratio of their speeds is?
A.3/6
B.3/2
C.2/3
D.3/5
Answer: C.2/3
Explanation: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train
= 27 x meters, and length of the second train
= 17 y meters. (27 x + 17 y) / (x + y) = 21 ==> 27 x + 17 y = 21 x + 21 y
==> 6 x = 4 y ==> x/y
= 2/3.
Answer:C
Question: 6 letters have to be put into their 6 respective envelopes. If the letters are inserted randomly into the envelopes, what is the probability that all the letters go into their respective envelopes?
A.1/720
B.1/60
C.1/120
D.1/240
Answer: A.1/720
Explanation: A-B-C-D-E (envelopes)
a-b-c-d-e (letters)
6 letters (a, b, c, d, and e) can be assigned to 6 envelopes (arranged) in 6! ways, out of which only one will be correct, thus the probability is 1/6! = 1/720.
Answer: A
Question: In a bag there are coins of 50 paisa, 25 paisa and one rupee in the proportion 5:6:2. If there are in all Rs.34, the number of 25 paisa coins is?
A.30
B.31
C.32
D.34
Answer: D.34
Explanation: 5x 6x 2x
50 25 100
250x + 150x + 200x = 3400
600x = 3400
x = 5.66 => 6x = 34
ANSWER:D
Question: The expression (11.98 × 11.98 + 11.98 × x + 0.02 × 0.02) will be a perfect square for x equal to
A.0.02
B.0.2
C.0.04
D.0.4
Answer: C.0.04
Explanation: Solution
Given expression = (11.98)2 + (0.02)2 + 11.98 × x.
For the given express to be a perfect square, we must have
11.98 × x = 2 × 11.98 × 0.02 or x = 0.04. Answer C
Question: The owner of a furniture shop charges his customer 15% more than the cost price. If a customer paid Rs. 8325 for a computer table, then what was the cost price of the computer table?
A.Rs.6725
B.Rs.7239.13
C.Rs.6908
D.Rs.6725
Answer: B.Rs.7239.13
Explanation: CP = SP * (100/(100 + profit%))
= 8325(100/115) = Rs.7239.13.
Answer: B
Question: Sam took a loan from his local bank to support his small business. He is expected to double the amount he paid the previous month till he repays a total of $128000. His first payment is $250.
A.10
B.14
C.12
D.13
Answer: D.13
Explanation: First payment--$250
Total amount to be repaid--$128000
First month payment--$250
Second month payment--$250*2=$500
Third month payment--$500*2=$1000
Fourth month payment--$1000*2=$2000
Fifth month payment--$2000*2=$4000
Sixth month payment--$4000*2=$4000
Seventh month payment--$4000*2=$8000
Eight month payment--$8000*2=$16000
Ninth month payment--$16000*2=$32000
Tenth month payment--$32000*2=$64000
Eleventh month payment--$32000*2=$64000
Twelfth month payment--$32000*2=$64000
Thirteenth month payment--$64000*2=$128000
Answer is D
Question: What is the smallest number which when increased by 3 is divisible by 18, 70, 100 and 84?
A.5307
B.5647
C.5927
D.6297
Answer: D.6297
Explanation: When increased by 3, the number must include at least 2^2*3^2*5^2*7 = 6300
The answer is D.
Question: Tough and Tricky questions: Statistics.
Set X consists of prime numbers {3, 11, 7, G, 17, 19}. If integer Y represents the product of all elements in set X and if 11Y is an even number, what is the range of set X?
A. 14
B. 16
C. 17
D. 20
Answer: C. 17
Explanation: Since 11Y = Even therefore Y has to beEVENsince 11 is a odd integer (Even * Odd = Even)
Similarly, Y is the product of all integers in set X But all integers in Set X are odd except the unknown G and since X contains only prime numbers, G has to equal to 2... ( 2 is the only even prime number and the product of all prime numbers in set X has to be Even, Even * Odd = Even)
Since you know value of G you can calculate the range = Largest integer in the set minus Smallest integer in the set = 19-2 =17
Answer is C
Question: The C.P of 30 books is equal to the S.P of 40 books. Find his gain% or loss%?
A.23%
B.24%
C.25%
D.50%
Answer: C.25%
Explanation: explanation:
30 CP = 40 SP
40 --- 10 CP loss
100 --- ? => 25% loss
Answer: C
Question: How many keystrokes are needed to type numbers from 1 to 200?
A.400
B.500
C.492
D.200
Answer: C.492
Explanation: Explanatory Answer
While typing numbers from 1 to 200, there are 9 single digit numbers: from 1 to 9.
Each of these numbers requires one keystroke.
That is 9 key strokes.
There are 90 two-digit numbers: from 10 to 99.
Each of these numbers requires 2 keystrokes.
Therefore, 180 keystrokes to type the 2-digit numbers.
There are 101 three-digit numbers: from 100 to 200.
Each of these numbers requires 3 keystrokes.
Therefore, 303 keystrokes to type the 3-digit numbers.
Totally, therefore, one requires 9 + 180 + 303 = 492 keystrokes.
Choice C is the correct answer.
Question: Three people who work full-time are to work together on a project, but their total time on the project is to be equivalent to that of only one person working full-time. If one of the people is budgeted for 1/2 of his time to the project and a second person for 1/3 of her time, what part of the third worker's time should be budgeted to this project?
A.1/3
B.1/4
C.1/6
D.1/8
Answer: A.1/3
Explanation: Explanation:
One-half (1/2) plus one-third (1/3) equals five-sixths (5/6), so one-sixth (1/6) of the third worker's time should be budgeted to the project in order for the total time to be equivalent to that of one person working full-time.
If x 2 - x - 6 = 0, then (x + 2)(x - 3) = 0, so x = -2 or x = 3.
Correct answer : A
Question: A rectangular grassy plot 110m by 65cm has a gravel path .5cm wide all round it on the inside. Find the cost of gravelling the path at 80 paise per sq.mt
A.680
B.378
C.267
D.299
Answer: A.680
Explanation: Explanation:
area of theplot = 110 * 65 = 7150 sq m
area of the plot excluding the path = (110-5)* (65-5) = 6300 sq m
area of the path = 7150 - 6300 =850 sq m
cost of gravelling the path = 850 * 80/100 = 680 Rs
Answer: A) 680rs
Question: Two pipes can fill a tank in 15 minutes and 15 minutes. An outlet pipe can empty the tank in 45 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank?
A.1/15
B.1/16
C.1/11
D.1/9
Answer: D.1/9
Explanation: Part of the filled by all the three pipes in one minute
= 1/15 + 1/15 - 1/45 = 1/9
So, the tank becomes full in 9 minutes.
Answer:D
Question: How many litres of pure acid are there in 15 litres of a 20% solution
A.4
B.5
C.2
D.3
Answer: D.3
Explanation: Explanation:Question of this type looks a bit typical, but it is too simple, as below... It will be 15 * 20/100 = 3 Answer: Option D
Question: We have 20 thousand dollars that must be invested among 4 possible
mutual funds. Each investment must be in units of 1 thousand dollars,
and there are minimal investments that need to be made if one is to
invest in these funds. The minimal investments are 2, 2, 3 and 4 thou-
sand dollars. How many dierent investment strategies are available if
an investment must be made in each mutual fund?
A.220
B.240
C.260
D.280
Answer: A.220
Explanation: Since minimal investments must be made for 2, 2, 3, and 4 thousand dollars into
the four mutual funds, this leaves 20-2-2-3-4 = 9 thousand dollars to invest as one
pleases. Thus, we want to determine the number of ways of dividing up 9 thousand dollars
among 4 different mutual funds. Consider 12 different boxes aligned as shown and check
three of them:Here, we have checked the first, fifth, and tenth boxes. Each such diagram corresponds to
a way of investing the remaining money as follows. We order the mutual funds. Count
the number of unchecked boxes to the left of the first checkmark. Call this number k1.
In the illustration above, k1 = 0. Next, count the number of unchecked boxes between
the first two checkmarks. Call this number k2. In the illustration, k2 = 3. Next, call
k3 the number of unchecked boxes between the second and third checkmarks, and call k4
the number of unchecked boxes after the third checkmark. Thus, k3 = 4 and k4 = 2.
Observe that k1 + k2 + k3 = 9, the total number of unchecked boxes. Make additional
investments (beyond the required minimal investments) of k1 thousand dollars in the first
fund, k2 thousand dollars in the second fund, k3 thousand dollars in the third fund, and
k4 thousand dollars in the fourth fund. Thus, the total number of dierent investments is
the same as the number of ways of choosing three blocks (to check) from among 12 blocks.
This number is(12 3)=12/3*9=12*11*10/3*2*1=220
correct answer A
Question: A rectangular courtyard, the sides of which are in the ratio of 4:3, cost Rs.600 for paving at 50 p per m2; find the length of the diagonal of the courtyard?
A.17 m
B.45 m
C.54 m
D.77 m
Answer: B.45 m
Explanation: 1 m2 ---- 1/2
? ----- 600 => 1200 m2
4x * 3x = 1200 => x = 10
Answer: B