RikoteMaster/aqua-rat-mcqa huggingface dataset:
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 76, 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+38
B.2K+38
C.(76+K)/2
D.(76-K)/2
Answer: C.(76+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 = 76
y = (76 - K)/2
Then Sue's age will be K + y = K + (76 - K)/2 = (76+K) / 2
The answer is C.
Question: In a house a hall is 20 m long, 15m wide and 5m high. Its interior has to be covered with mat. What will be the total expenditure if it costs Rs. 30 per square m?
A.s.28500
B.s.50000
C.s.57000
D.s.60000
Answer: A.s.28500
Explanation: Length (l) = 20 m, Breadth (b) = 15 m and Height (h) = 5 m
Total area of the hall to be covered with mat = 2(lb + bh + hl)
= 2(20 * 15 + 15 * 5 + 5 * 20)
=2(300 + 75 + 100)
= 2 * 475
= 950 sq. m
Total expenditure = 30 * 950
= Rs.28,500
A
Question: A man is 28 years older than his son. In two years, his age will be twice the age of his son. The present age of the son is?
A.16
B.19
C.15
D.26
Answer: D.26
Explanation: Let the son's present age be x years.
Then, man's present age = (x + 28) years.
(x + 28) + 2 = 2(x + 2)
x + 30 = 2x + 4
=> x = 26.
Answer: D
Question: Tough and Tricky questions: Probability.
Medical analysts predict that a quarter of all people who are infected by a certain biological agent could be expected to be killed for each day that passes during which they have not received an antidote. What fraction of a group of 1,000 people could be expected to be killed if infected and not treated for three full days?
A.37/64
B.8/27
C.2/3
D.19/27
Answer: A.37/64
Explanation: At the end of each day we will have 3/4 alive. So after 3 days we will have (3/4)^3 people alive. Therefore, fraction of dead people will be 1-(3/4)^3=37/64.
The correct answer is A.
Question: you need to pick a card at random from pack of 52 cards.
what are the chances of that card to be a jack or a king ?
A.2/15
B.1/16
C.3/25
D.2/13
Answer: D.2/13
Explanation: D
2/13
There 4 kings & 4 jacks, which implies there are 8 cards that can satisfy the above problem.
=>8/52
=> 2/13
Question: Find the compound interest on $ 26,000 at 20% per annum for 9 months, compounded quarterly
A.2532.93
B.2552.26
C.2524.23
D.4098.25
Answer: D.4098.25
Explanation: Principal = $ 26000; Time = 9 months =3 quarters;
Rate = 20% per annum = 5% per quarter.
Amount = $ [26000 x (1+(5/100))^3] = $ 30098.25
CI. = $ (30098.25 - 26000) = $ 4098.25
Answer D.
Question: How many multiples of 8 are less than 1600, and also multiples of 64?
A.25
B.28
C.62
D.83
Answer: A.25
Explanation: The LCM of 8 and 64 is 64. Divide 1600/64 = 25.xxx. So A is your answer.
Question: If the area of a triangle with base 6 cm is equal to the area of a square with side 6 cm, then the altitude of the triangle is
A.12 cm
B.10 cm
C.11 cm
D.15 cm
Answer: A.12 cm
Explanation: area of square = 6^2 = 36
area of triangle = 36
1/2 bh = 36
h = 12 cm
ANSWER A
Question: x - y = 3
2x = 2y + 8
The system of equations above has how many solutions?
A. None
B. Exactly one
C. Exactly two
D. Exactly three
Answer: A. None
Explanation: x-y=3 ---------------1
2x=2y+8 ---------------2
Divide equation 2 by 2:
2x/2=(2y+8)/2
x=y+4
x-y=4----------------3
Equation 1 and 3 are equation has no solution
Ans:A
Question: A grocer has a sale of Rs. 2435, Rs. 2920, Rs. 2855, Rs. 3230 and Rs. 2560 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 2500?
A.5000
B.4000
C.1000
D.6000
Answer: C.1000
Explanation: Total sale for 5 months = Rs. (2435 + 2920 + 2855 + 3230 + 2560) = Rs. 14000.
Required sale = Rs. [ (2500 x 6) - 14000 ]
= Rs. (15000 - 14000)
= Rs. 1000
Answer: Option C
Question: A man can hit the target once in five shots. If he fires four shots in succession, what is the probability that he will hit the target?
A.1
B.1/625
C.181/256
D.369/625
Answer: D.369/625
Explanation: In four shots he can hit once,twice,thrice,all hit
the probability of hitting the target is p(1hit out of 4)+P(2hit out of 4)+p(3hit out of 4)+p(All hit)
it is total probability-probability of not hitting the target
=>1-(4/5*4/5*4/5*4/5)
=>369/625
ANSWER:D
Question: I bought two houses for Rs. 48 L. I sold one at a loss of 10% and other at a gain of 20% and then I found each house was sold at the same price. Find the cost of the house sold at a loss?
A.A)65
B.B)28
C.C)43
D.D)18
Answer: B.B)28
Explanation: x*(90/100)
= (48 - x)120/100
x = 27.4
Answer:B
Question: R and B are integers. The expression (R+1)(B+1) is even. What can be said about R and B?
A.They are both even numbers.
B.At least one of them is even.
C.At least one of them is odd.
D.They are both odd.
Answer: C.At least one of them is odd.
Explanation: Odd x Odd = Odd
Odd x Even = Even
Even x Even = Even
To fulfill condition Either (R+1) or (B+1) needs to be Even
So either R or B needs to be odd
Or Atleast one of them is odd.
Atleast one of them is odd=C
Question: In a mixture of 45 litres the ratio of milk to water is 4:1. Additional 23 litres of water is added to the mixture. Find the ratio of milk to water in the resulting mixture.
A.9/8
B.4/1
C.2/3
D.3/4
Answer: A.9/8
Explanation: Given that Milk/Water=4x/x and 4x+x=45 --> x=9.
Thus Milk=4x=36 liters and Water=x=9 liters.
New ratio = 36/(9+23) = 36/32 = 9/8.
Answer: A.
Question: A women walking at 4 Kmph reaches her office 8 minutes late. If she walks at 8 Kmph, she reaches there 8 minutes earlier. How far is the office from her house?
A.2 2/15 Km
B.3 1/5 Km
C.4 1/3 Km
D.5 Km
Answer: A.2 2/15 Km
Explanation: Formula = S1*S2/S2-S1 * T1+T2/60
= 4*8/4 * 16/6
= 8* 16/60
= 8 * 4/15
= 2 2/15 Km
A
Question: A special municipal payroll tax charges not tax on a payroll less than $300,000 and only 1% on a company’s payroll above $300,000. If Belfried Industries paid $200 in this special municipal payroll tax, then they must have had a payroll of?
A.$180,000
B.$202,000
C.$230,000
D.$400,000
Answer: C.$230,000
Explanation: ANSWER : C , ( with different approach) :
The 300 paid is 1% of the additional amount above 200,000. Let it be X
Now 1% of X = 300
Therefore X= 30,000
Total = 200,000 + X= 230,000
Question: Working together at their respective constant rates, Machine A and Machine B can produce 1,500 units in 8 hours. Working alone, Machine B would complete that same output in 50% more time. If Machine A were to work on its own for an 8-hour shift, what percent of the 1,500 unit total would it produce?
A.25
B.36
C.30
D.67
Answer: C.30
Explanation: 1/A+1/B= 1/T
1/A +1/14= 1/8 (50% more of 8 is 14)
1/A= 1/24
Machine A can produce 1500 units in 24 hrs, so it can produce 1500*8/24= 500 units is 8 hrs.
500 is 30% of 1500.
C is the answer
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is?
A.48
B.77
C.55
D.27
Answer: C.55
Explanation: Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 1.10 + 0.9 = 2 km = 2000 m.
Required time = 2000 * 3/125 = 48 sec.
Answer: C
Question: A certain car can travel 56 kilometers on a liter of fuel. If the fuel tank’s contents decrease by 3.9 gallons over a period of 5.7 hours as the car moves at a constant speed, how fast is the car moving, in miles per hour? (1 gallon = 3.8 liters; 1 mile = 1.6 kilometers)
A.52
B.65
C.78
D.91
Answer: D.91
Explanation: Fuel used 3.9 gallons ;convert to liters--> 3.9 x 3.8 liters
Time = 5.7 hours
1 mile = 1.6 kilometers ;convert to miles--> 1km = 1/1.6 mile
Speed (km/hour)= D/T = 56(km*) x 3.9 x 3.8 / 5.7
replace (km*) to miles ; multiply by 1/1.6 mile
Speed (miles/hour)= 56 x 3.9 x 3.8 / 5.7 x 1.6 = 78 miles/hour
Ans :D
PS :i felt the factors were easy to cancel out ,so didn't require much rounding off
= 56 x 3.9 x 3.8 / 5.7 x 1.6
= 91
D
Question: Which of the following integers has the most number of divisors?
A.176
B.180
C.190
D.200
Answer: A.176
Explanation: 99 = 1*3*3*11
=> divisors of 99 are 1,3,11,9,33 and 99
101 = 1*101
divisors 182 are 1,2,7,13,14,26,91 and 182
176=is most no of divisors
ANSWER A
Question: A cube of side one meter length is cut into small cubes of side 5 cm each. How many such small cubes can be obtained?
A.2878
B.8000
C.1000
D.2997
Answer: B.8000
Explanation: Along one edge, the number of small cubes that can be cut
= 100/5 = 20
Along each edge 5 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut
= 20 * 20 * 20 = 8000
Answer: B
Question: Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?
A.5/5
B.5/9
C.5/1
D.5/6
Answer: D.5/6
Explanation: P(at least one graduate) = 1 - P(no graduates)
= 1 - 6C1/10C3
= 1 - (6 * 5 * 4)/(10 * 9 * 8)
= 5/6
Answer:D
Question: A security guard at a certain store is instructed to check the receipt of one out of every five customers as they are leaving the store. If, on the guard's shift, 13 customers leave the store, how many different samples of customers could have been selected to have their receipts checked?
A.20
B.78
C.59
D.90
Answer: B.78
Explanation: to choose the sample of 2 customers from 13. it can be done 13C2 possible ways.
So the answer is B. 78
Question: a = 5^15 - 625^3 and a/x is an integer, where x is a positive integer greater than 1, such that it does NOT have a factor p such that 1 < p < x, then how many different values for x are possible?
A.None
B.One
C.Two
D.Three
Answer: C.Two
Explanation: a= 5^15 - 625^3 => 5^15 - (5^4)^3 => 5^15 - 5^12 = 5^12(5^3 - 1) = 5^12*124
124 = 31*4
a/x is integer
For condition of 2<p<x only 5 and 31 satisfies this
Hence answer is C
Question: A positive integer n is called a “good” number if n3 + 7n − 133 = m3 for
some positive integer m. What is the sum of all “good” numbers?
A.24
B.25
C.29
D.30
Answer: D.30
Explanation: We consider the size of m relative to n. If m = n, then n is a good number if and only if
7n = 133. In this case, we get 19 is a good number. Now, suppose that m n + 1. Then
n3 + 7n − 133 = m3 (n + 1)3 = n3 + 3n2 + 3n + 1
so that 3n2 − 4n + 134 0. For positive integers n, it is easy to see that this is impossible. It
remains to consider m n − 1. For such m, we have
n3 + 7n − 133 = m3 (n − 1)3 = n3 − 3n2 + 3n − 1
which implies 3n2 + 4n − 132 0. It follows here that n 6. One checks that
63 + 7 · 6 − 133 = 53 and 53 + 7 · 5 − 133 = 33,
so 6 and 5 are good numbers. For n 4, we see that n3 +7n−133 < 0 and, hence, n3 +7n−133
cannot equalm3 for a positive integerm. Therefore, the sum of all good numbers is 19+6+5 = 30.
correct answer D
Question: Mac has £ 3 more than Ken, but then Ken wins on the horses and trebles his money, so that he now has £ 2 more than the original amount of money that the two boys had between them. How much money did Mac and Ken have between them before Ken's win ?
A.£ 9
B.£ 11
C.£ 13
D.£ 15
Answer: C.£ 13
Explanation: Explanation:
Let money with Ken = x. Then, money with Mac = x + £ 3.
Now, 3x = (x + x + £ 3) + £ 2 x = £ 5.
Therefore Total money with Mac and Ken = 2x + £ 3 = £ 13.
Answer: C
Question: What is the number of integers from 1 to 1000 (inclusive) that are divisible by neither 15 nor by 20?
A.887
B.678
C.765
D.345
Answer: A.887
Explanation: In 1000 consecutive numbers, number of multiples of 15 = 1000/15 = 66 (Ignore decimals)
In 1000 consecutive numbers, number of multiples of 20 = 1000/20 = 50
Number of multiples of 15*20 i.e. 300 = 1000/300 = 3
Number of integers from 1 to 1000 that are divisible by neither 15 nor by 20 = 1000 - (66 + 50 - 3) {Using the concept of sets here) = 887
Answer is A
Question: Four-ninths of a drink mix is dye and the rest is sugar. When the mix is added to water a gallon of drink is made that is 8% sugar. What percentage of the gallon is dye?
A. 6
B. 6.4
C. 7.5
D. 8
Answer: B. 6.4
Explanation: The proportion of Dye and sugar will remain constant.
Dye/Sugar = (4/9)/(5/9) = x/8
=> 4/5 = x/8 => x = 4*8/5 = 6.4
Answer is B
Question: Little John had $10.10. He spent $3.25 on sweets and gave to his two friends $2.20 each. How much money was left?
A.$2.45
B.$2.54
C.$2.35
D.$2.48
Answer: A.$2.45
Explanation: John spent and gave to his two friends a total of
3.25 + 2.20 + 2.20 = $7.65
Money left
10.10 - 7.65 = $2.45
Answer :A
Question: What is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular 9-sided polygon)?
A.1/2
B.1/3
C.1/4
D.1/6
Answer: B.1/3
Explanation: From any vertex, there are two vertices on sides, which do not make a diagonal but a side.
So the remaining n-3 vertices make diagonals.
There are 2 of these diagonals which are the shortest.
The probability of choosing one of the shortest diagonals is 2/6 = 1/3.
The answer is B.
Question: A man invests some money partly in 12% stock at 105 and partly in 8% stock at 88. To obtain equal dividends from both, he must invest the money in the ratio.
A.35:44
B.34:44
C.22:44
D.20:40
Answer: A.35:44
Explanation: In case of stock1, if he invest Rs.105, he will get a dividend of Rs.12 (assume face value = 100)
In case of stock2, if he invest Rs.88, he will get a dividend of Rs.8 (assume face value = 100)
ie, if he invest Rs.(88*12)/8, he will get a dividend of Rs.12
Required ratio = 105 : (88 × 12)/8 = 105 : (11 × 12) = 35 : (11 × 4) = 35 : 44
Answer is A.
Question: A car dealership has 40 cars on the lot, 15% of which are silver. If the dealership receives a new shipment of 80 cars, 45% of which are not silver, what percentage of total number of cars are silver?
A.30%
B.35%
C.40%
D.45%
Answer: B.35%
Explanation: The number of silver cars is 0.15*40 + 0.45*80 = 42
The percentage of cars which are silver is 42/120 = 35%
The answer is B.
Question: In an exam, Amar scored 64 percent, Bhavan scored 36 percent and Chetan 44 percent. The maximum score awarded in the exam is 800. Find the average mark scored by all the three boys?
A.384
B.288
C.277
D.299
Answer: A.384
Explanation: Average mark scored by all the three boys
= [64/100 (800) + 36/100 (800) + 44/100 (800)] / 3
= 384
Answer: A
Question: A set of numbers has the property that for any number t in the set, t + 5 is in the set. If -1 is in the set, which of the following must also be in the set?
I. -3
II. 4
III. 5
A. I only
B. II only
C. I and II only
D. II and III only
Answer: B. II only
Explanation: The question is which of the followingmustbe in the set, notcouldbe in the set.
If -1 is in the set so must be -1+5=4, as 4 is in the set so must be 4+5=9, as 9 is in the set so must be 9+5=14 and so on.
Answer: B.
Question: When 2 is added to half of one-third of one-fifth of a number, the result is one-fifteenth of the number. Find the number?
A.40
B.65
C.73
D.60
Answer: D.60
Explanation: D
60
Let the number be
2 + 1/2[1/3(a/5)] = a/15
=> 2 = a/30 => a = 60
Question: Martin buys a pencil and a notebook for 80 cents. At the same store, Gloria buys a notebook and an eraser for 95 cents, and Zachary buys a pencil and an eraser for 55 cents. How many cents would it cost to buy three pencils, three notebooks, and three erasers? (Assume that there is no volume discount.)
A.305
B.325
C.345
D.365
Answer: C.345
Explanation: pencil + notebook = 80
notebook + eraser = 95
pencil + eraser = 55
Let's add all three equations.
2 pencils + 2 notebooks + 2 erasers = 230 cents
The cost to buy 3 of each would be (3/2)(230) = 345
The answer is C.
Question: Bon-Bean, a coffee shop, served a total of 460 cups of coffee and tea yesterday. 270 of these cups contained caffeine, and the number of decaffeinated tea cups was twice the total number of tea cups that contained caffeine. If Bon-Bean served 250 coffee cups yesterday, how many of them were decaffeinated?
A.50
B.70
C.140
D.190
Answer: A.50
Explanation: Tc : Tea caffeine
Td : Tea No caffeine
Cc : Coffee Caffeine
Cd : Coffee No Caffeine
As per question, Tc + Td + Cc + Cd = 460 -- (1)
Also, Tc + Cc = 270 -- (2)
Td = 2 * Tc -- (3)
Cc + Cd = 250 -- (4)
Now, substituting (4) in (1), we will have Tc + Td + 250 = 460
or Tc + Td = 210. -- (5)
Substitute (3) in (5), we will get Tc = 70. Substitute Tc in (2), we will get Cc = 200
Now substitute Cc in (4), we will get Cd = 50. hence, A
Question: In an election contested by two parties, Party D secured 12% of the total votes more than Party R. If party R got 132,000 votes, by how many votes did it lose the election?
A.240,000
B.300,000
C.168,000
D.36,000
Answer: D.36,000
Explanation: Explanatory Answer
Let the percentage of the total votes secured by Party D be x%
Then the percentage of total votes secured by Party R = (x - 12)%
As there are only two parties contesting in the election, the sum total of the votes secured by the two parties should total up to 100%
i.e., x + x - 12 = 100
2x - 12 = 100
or 2x = 112 or x = 56%.
If Party D got 56% of the votes, then Party got (56 - 12) = 44% of the total votes.
44% of the total votes = 132,000
i.e., 44/100*T = 132,000
=> T = 132000*100/44 = 300,000 votes.
The margin by which Party R lost the election = 12% of the total votes
= 12% of 300,000 = 36,000.
The correct choice is (D)
Question: Each of the following numbers has a remainder of 4 when divided by 6 except:
A.4
B.16
C.64
D.26
Answer: D.26
Explanation: It's D
26 = 6*4+2
Question: A man spends 10% of his income in house rent, 20% of the rest on his childrenâ€™s education, 25% of the rest miscellaneous causes. If he now posses Rs. 1944 then his income is?
A.3600
B.4500
C.5000
D.2000
Answer: A.3600
Explanation: X * (90/100) * (80/100) * (75/100) = 1944
X * 0.9 * 0.8 * 0.75
X = 1944/0.54
X = 3600
ANSWER A
Question: In a party every person shakes hands with every other person. If there are 105 hands shakes, find the number of person in the party.
A.13
B.15
C.12
D.7
Answer: B.15
Explanation: Let n be the number of persons in the party. Number of hands shake = 105; Total number of hands shake is given by nC2.
Now, according to the question,
nC2 = 105;
Or, n!/[2!*(n-2)!] = 105;
Or, n*(n-1)/2 = 105;
Or, n^2-n = 210;
Or, n^2-n-210 = 0;
Or, n = 15, -14;
But, we cannot take negative value of n.
So, n = 15 i.e. number of persons in the party = 15.
Ans: B
Question: A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:
A.12 years
B.15 years
C.11years
D.22years
Answer: D.22years
Explanation: Let the son's present age be x years. Then, man's present age = (x + 24) years.
(x + 24) + 2 = 2(x + 2)
x + 26 = 2x + 4
x = 22.
Ans- D
Question: If Sand is coded as Brick, Brick as House, House as Temple, Temple as Palace then where do you worship?
A.Palace
B.Temple
C.Brick
D.House
Answer: A.Palace
Explanation: palace because temple is coded as palace
ANSWER:A
Question: Today X is twice as old as Y and Y is 3 years younger than Z. If X, Y, and Z are all alive 4 years from today, which of the following must be true on that day. I. X is twice as old as Y II. Y is 3 years younger than Z III. X is older than Z
A.I
B.II
C.I,II & III
D.III
Answer: C.I,II & III
Explanation: Say Z age is 10
Y age is 7
X age is 14
After 4 years
Z age is 14
Y age is 11
X age is 28
i.e ) after 4 years
Y is 3 years younger than Z
X is twice as old as Y
X is older than Z
Answer : C
Question: If a farmer wants to plough a farm field on time, he must plough 260 hectares a day. For technical reasons he ploughed only 85 hectares a day, hence he had to plough 2 more days than he planned and he still has 40 hectares left. What is the area of the farm field and how many days the farmer planned to work initially?
A.312
B.490
C.720
D.435
Answer: A.312
Explanation: Let x be the number of days in the initial plan. Therefore, the whole field is 260â‹…x hectares. The farmer had to work for x+2 days, and he ploughed 85(x+2) hectares, leaving 40 hectares unploughed. Then we have the equation:
260x=85(x+2)+40
175x=210
x=1.2
So the farmer planned to have the work done in 6 days, and the area of the farm field is 260(1.2)=312 hectares
correct answer A
Question: Find the last digit of (1021^3921)+(3081^3921)
A.0
B.1
C.2
D.3
Answer: C.2
Explanation: last digit of 1st expression is 1 and second expression is also 1
as, 1 raised to any power will be 1 itself
so, 1+1 = 2
so the last digit will be 2
ANSWER:C
Question: Three pipes A, B and C can fill a tank in 4 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 5 hours. How many hours will take C alone to fill the tank?
A.10/3
B.15/4
C.20/3
D.25/4
Answer: C.20/3
Explanation: The rate of A+B+C is 1/4 of the tank per hour.
After 2 hours, the tank is half full.
The rate of A+B is 1/2 * 1/5 = 1/10 of a tank per hour.
The rate of C is 1/4 - 1/10 = 3/20
C can fill the tank in 20/3 hours.
The answer is C.
Question: A man invested Rs. 4455 in Rs. 10 shares quoted at Rs. 8.25. If the rate of dividend be 12%, his annual income is:
A.207
B.530
C.648
D.600
Answer: C.648
Explanation: No of shares = 4455/8.25 = 540
face value = 540*10 = 5400
annual income = 12/100*5400 = 648
ANSWER C
Question: Given that 0 < a < b < c < d, which of the following the largest ?
A.(c+d) / (a+b)
B.(a+d) / (b+c)
C.(b+c) / (a+d)
D.(b+d) / (a+c)
Answer: A.(c+d) / (a+b)
Explanation: Explanation :
For the fraction to be largest, denominator should be minimum and numerator should be maximium.
Here a and b is minimum which is in denominator of option 1. and c and d is maximum which is also in the numerator of option 1.
Hence 1.) (c+d) / (a+b)
Answer : A
Question: The price of 2 sarees and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ?
A.Rs. 2000
B.Rs. 2200
C.Rs. 2300
D.Rs. 2400
Answer: D.Rs. 2400
Explanation: Let the price of a saree and a shirt be Rs. x and Rs. y respectively.
Then, 2x + 4y = 1600 .... (i)
and x + 6y = 1600 .... (ii)
Divide equation (i) by 2, we get the below equation.
=> x + 2y = 800. --- (iii)
Now subtract (iii) from (ii)
x + 6y = 1600 (-)
x + 2y = 800
----------------
4y = 800
----------------
Therefore, y = 200.
Now apply value of y in (iii)
=> x + 2 x 200 = 800
=> x + 400 = 800
Therefore x = 400
Solving (i) and (ii) we get x = 400, y = 200.
Cost of 12 shirts = Rs. (12 x 200) = Rs. 2400.
D
Question: In a Fish tank there are 8 fishes are there. In how many possibilities to choose 6 fishes from the tank?
A.20
B.21
C.28
D.8
Answer: C.28
Explanation: The possible way to select 6 fishes out of 10 fishes in the tank is 8C6.
8C6=8!/2!*6!=8*7*6!/6!*2*1
8C6=28
There are 28 ways to select a 6 fishes from the tank.
Question: John and Peter are among the nine players a volleyball coach can choose from to field a six-player team. If all six players are chosen at random, what is the probability of choosing a team that includes John and Peter?
A.3/10
B.4/11
C.5/12
D.6/13
Answer: C.5/12
Explanation: The total possible ways of selecting a 6-member team is 9C6 = 84
The possible ways which include John and Peter is 7C4 = 35
The probability of choosing both John and Peter is 35/84 = 5/12
The answer is C.
Question: A no.when divided by 220 gives a remainder 43, what remainder will beobtained by dividingthe same no.17?
A.2
B.8
C.9
D.11
Answer: B.8
Explanation: 220 + 43 = 263/17 = 8 (Remainder)
B
Question: The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is:
A.2520
B.2376
C.3235
D.3569
Answer: A.2520
Explanation: We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103.
Solving the two equations, we get: l = 63 and b = 40.
Area = (l x b) = (63 x 40) m2 = 2520 m2
Answer:A
Question: A boat can travel with a speed of 42 km/hr in still water. If the speed of the stream is 10 km/hr, find the time taken by the boat to go 84 km downstream
A.1 hour 40 min
B.2 hour 40 min
C.1 hour 20 min
D.1 hour 30 min
Answer: A.1 hour 40 min
Explanation: Speed of the boat in still water = 42 km/hr
speed of the stream = 10 km/hr
Speed downstream = (42+10) = 52 km/hr
Distance travelled downstream = 84 km
Time taken =distance/speed
=84/52
= 1.66 hours
= 1 hour 40 min.
ANSWER:A