RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: In one hour, a boat goes 6 km along the stream and 2 km against the stream. the sped of the boat in still water (in km/hr) is :
A.4
B.5
C.8
D.9
Answer: A.4
Explanation: Solution
Speed in still water= 1/2(6+2) km/hr= 4kmph. Answer A
Question: If 13 persons meet at a reunion and each person shakes hands exactly once with each of the others, what is the total number of handshakes?
A. 10•9•8•7•6•5•4•3•2•1
B. 10•10
C. 78
D. 45
Answer: C. 78
Explanation: We got #13 people who shake each other's hands once ==> a pair of 2
13!/11!2! = 13*12 / 2*1 = 78.
Hence answer C.
Question: On a track for remote controlled racing cars, racing car A completes the track in 59 seconds, while racing car B completes it in 35 seconds. If they both start at the same time after how many seconds will they be side by side again.
A.275
B.325
C.2065
D.425
Answer: C.2065
Explanation: Time required in seconds will be LCM ( 35, 59 ) = 2065
Hence, answer will be (C) 2065
Question: The average salary/head of all the workers in a workshop is Rs.1000, if the average salary/head of 10 technician is Rs.1200 and the average salary/head of the rest is Rs.820, the total no. of workers in the work-shop is ?
A.120/9
B.140/9
C.150/9
D.190/9
Answer: D.190/9
Explanation: Let the total number of workers be y.So sum of salary for all workers = sum of salary of 10 technician + sum of salary for other y -10 workers.10 x 1200 + 820(y -10) = 1000 y⇒ 12000 + 820y - 8200 = 1000y⇒ 180y = 3800∴ y = 190/9 So total number of workers = 190/9 D
Question: A car travels at a speed of 65 miles per hour. How far will it travel in 8 hours?
A.125 miles
B.225 miles
C.520 miles
D.425 miles
Answer: C.520 miles
Explanation: During each hour, the car travels 65 miles. For 8 hours it will travel
65 + 65 + 65 + 65 + 65+ 65 + 65 + 65 = 8 × 65 = 520 miles
correct answer is C) 520 miles
Question: If it takes 6 identical printing presses exactly 4 hours W to print 5,000 newspapers, how long would it take 3 of these presses to print 3,000 newspapers?
A.3 hours, 20 minutes
B.4 hours, 20 minutes
C.4 hours, 48 minutes
D.5 hours, 48 minutes
Answer: C.4 hours, 48 minutes
Explanation: 6 presses - 5,000 newspapers - 4 hours ;
3 presses - 2,500 newspapers - 4 hours ;
3 presses - 3,000 newspapers - 4 hours + 1/5*4 hours = 4 hours, 48 minutes (since 2,500+1/5*2,500=3,000) = W.
Answer: C.
Question: Mangala completes a piece of work in 30 days, Raju completes the same work in 70 days. If both of them work together, then the number of days required to complete the work is
A.4 days
B.21 days
C.8 days
D.10 days
Answer: B.21 days
Explanation: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 30 × 70/100 = 21 days.
Answer : B
Question: Seats for Maths, Physics and Biology are in the ratio of 6 : 7 : 8 respectively. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the respective ratio of increased seats?
A.12 : 15 : 20
B.6 : 7 : 8
C.6 : 8 : 9
D.Cannot be determined
Answer: A.12 : 15 : 20
Explanation: Reqd ratio 6 Ã— 140â„100 : 7 Ã— 150â„100 : 8 Ã— 175â„100
= 6 Ã— 140 : 7 Ã— 150 : 8 Ã— 175 = 12 : 15 : 20
Answer A
Question: There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:
A.20
B.80
C.100
D.200
Answer: C.100
Explanation: EXPLANATION
Let the number of students in rooms A and B be x and y respectively.
Then, x – 10 = y + 10 x – y = 20 …. (i)
and x + 20 = 2(y – 20) x – 2y = -60 …. (ii)
Solving (i) and (ii) we get: x = 100 , y = 80.
The required answer A = 100.
Answer C
Question: If the probability that the Cleveland Browns win the Super Bowl is 1/100 and the probability that the Cleveland Indians win the World Series is 1/10, what is the probability that either the Browns win the Super Bowl or the Indians win the World Series (but not both)?
A.9/50
B.17/100
C.27/250
D.53/500
Answer: C.27/250
Explanation: 99/100*1/10 + 1/100*9/10 = 108/1000 = 27/250
The answer is C.
Question: In a group of ducks and cows, the total number of legs are 24 more than twice the no. of heads. Find the total no.of buffaloes.
A.10
B.12
C.16
D.17
Answer: B.12
Explanation: Let the number of buffaloes be x and the number of ducks be y
=> 4x + 2y = 2 (x + y) + 24
=> 2x = 24 => x = 12
B
Question: Calculate how much time could be saved if the train would run at its usual speed, given that it ran at 5/7 of its own speed and got to its destination in 15 hours?
A.1.29 hrs
B.2.29 hrs
C.4.29 hrs
D.5.29 hrs
Answer: C.4.29 hrs
Explanation: New speed = 5/7 of usual speed
New time = 5/7 of usual time
5/7 of usual time = 15 hrs
Usual time = 15*5/7 = 10.71 hrs
Time saved = 15-10.71 = 4.29 hrs
Answer is C
Question: Find the average of all the numbers between 6 and 34 which are divisible by 5
A.18
B.20
C.24
D.30
Answer: B.20
Explanation: Multiples of 5 between 6 and 34 are 10,15,20,25,30
Average = (10+15+20+25+30)/5
=5(10+30)/2*5
=40/2
=20
ANSWER:B
Question: What annual payment dischargea debit of Rs.12900, due in 4yrs.At 5% rate?
A.1000
B.2300
C.3000
D.4000
Answer: C.3000
Explanation: A.P.=(200X12900)/[4(200+5X3)]=3000 Ans
Alternative
100+105+110+115=12900
430=12900
100=12900/(430)X100=3000
C
Question: A gardener increased the length of a rectangle-shaped garden by 25 percent and decreased its width by 10 percent. The area of the new garden
A.has increased by 15 percent
B.has increased by 12.5 percent
C.has increased by 7.5 percent
D.is exactly the same as the old area
Answer: B.has increased by 12.5 percent
Explanation: Let L be the original length and let W be the original width.
The original area was L*W.
The new area is 0.9W*1.25L = (0.9)(1.25)L*W = 1.125*L*W
The answer is B.
Question: √289 - √625 ÷ √25 is equal to ?
A.17
B.15
C.12
D.-8/5
Answer: C.12
Explanation: Answer
√289 - √625 ÷ √25
= √17 x 17 - √25 x 25 ÷ √5 x 5
= 17 - 25 ÷ 5 = 17 - 5 = 12
Correct Option: C
Question: At what price must an article costing Rs.47.50 be marked in order that after deducting 8% from the list price. It may be sold at a profit of 25% on the cost price?
A.64.54
B.62.6
C.62.1
D.62.7
Answer: A.64.54
Explanation: CP = 47.50
SP = 47.50*(125/100) = 59.375
MP*(92/100) = 59.375
MP = 64.54
Answer: A
Question: Ten boys picked up 30 mangoes .In how many ways can they divide them if all mangoes be identical?
A.A)10^30
B.B)2^30
C.C)1^30
D.D)3^30
Answer: A.A)10^30
Explanation: Each Mango can be given to any one of the Ten people or in other words..1 mango can be divided into 10 ways...so all 30 can be divided in 10^30 ways
ANS:A
Question: Solve for x the equation log9(x3) = log2(8)
A.9
B.8
C.7
D.6
Answer: A.9
Explanation: log9(x3) = log2(8) : given
log2(23) = 3 : simplify right hand side of given equation.
log9(x3) = 3 : rewrite the above equation
log9(x3) = log9(93) : rewite 3 as a log base 9.
x3 = 93 : obtain algebraic equation from eqaution D.
x = 9 : solve above for x
correct answer A
Question: A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m3) is:
A.4830
B.5120
C.6420
D.8960
Answer: B.5120
Explanation: EXPLANATION
Clearly, l = (48 – 16)m = 32 m,
b = (36 -16)m = 20 m,
h = 8 m.
Volume of the box = (32 x 20 x 8) m3 = 5120 m3.
Answer B
Question: A sequence contains an alternation of positive and negative numbers. The sequence contains x numbers, and begins with a positive number. How many positive numbers are in it If x is an odd number?
A.(x+1)/2
B.x/3
C.x/(2-1)
D.x/(2+1)
Answer: A.(x+1)/2
Explanation: Lets put values for x, say x=7 since it's odd
and first number is neg so sequence will be {pos,neg,pos,neg,pos,neg,pos} we can see that it has 4 positive terms
so putting x=7 in the options,
option A = (x+1)/2 => (7+1)/2 = 4 , the number of positive integers
So, A is the answer
Question: The average length of 6 ropes is 80 cm. If the average length of one third of the ropes measure to 70 cm, what is the average of the other ropes?
A.75.
B.85.
C.90.
D.94.
Answer: B.85.
Explanation: Edit:
Given ( X1 + X2 ... + X6 ) / 6 = 80
( X1 + X2 ... + X6 ) = 480 --> Eq 1.
Now given avg length of one third ropes is 70. That means out 6 / 3 = 2 ropes.
let the avg length of two ropes be ( X1 + X2 ) / 2 = 70 .
( X1 + X2 ) = 140. --> eq 2.
Now we are asked to find the average of the remaining i.e. ( X3 + X4 + X5 + X6 )
Substitute eq 2 in eq 1 then we get
140 + X3 + X4 + X5 + X6 = 480
=> X3 + X4 + X5 + X6 = 340
Now divide 340 by 4 we get 85.
=> ( X3 + X4 + X5 + X6) / 4 = 85 = avg length of remaining ropes.
IMO correct option is B.
Question: Of the three numbers, the first is twice as second and three times the third. The average of the three numbers is 55, and the three numbers in order are?
A.116,58,36
B.90,45,30
C.126,63,36
D.108,54,36
Answer: B.90,45,30
Explanation: Explanation :
Solution: Let A =x,
B =x/2, C = x/3.
=x + x/2 + x/3 / 3 = 55
By solving we will get x = 90.
Hence A= 90
B= 90/2= 45
C= 90/3 = 30
Answer : B
Question: The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?
A.4
B.8
C.6
D.2
Answer: A.4
Explanation: Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
5x = 20
x = 4.
So Age of the youngest child = x = 4 years.
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.42, the number of 25 paisa coins is?
A.76
B.42
C.78
D.26
Answer: B.42
Explanation: 5x 6x 2x
50 25 100
250x + 150x + 200x = 4200
600x = 4200
x = 7 => 6x = 42
Answer: B
Question: A group of 8 employees book a full row at a movie theater. There are 2 best buddies and a couple and the 2 people in both those cases must always sit together. in how many arrangements can the students sit?
A.A.1296
B.B.2880
C.C.1850
D.D.3546
Answer: B.B.2880
Explanation: If we Glue the best buddy and couple together: {AB}, {CD}.
6 units {AB}, {CD}, {E}, {F}, {G}, {H} can be arranged in 6! ways. Each couple within their unit can be arranged in 2! ways.
Therefore the final answer is 6!*2!*2!=2,880.
Answer: B.
Question: In seventeen given numbers, the average of first 9 numbers is 4 and that of the last 9 numbers is also 4. If the average of these 17 numbers is 3, the 9th number is
A.23
B.4
C.17
D.21
Answer: D.21
Explanation: Explanation :
9th number = (9*4 + 9*4 - 17*3)
= 21.
Answer : D
Question: A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.200 when the rate to profit rises from 5 to 7 percent. Find the Capital of B?
A.2888
B.2778
C.2500
D.2818
Answer: C.2500
Explanation: A:B:C = 2/3:1/6:1/6 = 4:1:1
x * 2/100 * 2/3 = 200
B capital = 15000*1/6 = 2500.AnswerC
Question: The average of 6 no.'s is 3.95. The average of 2of them is 4.4, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's?
A.4.2
B.4.4
C.3.6
D.5.6
Answer: C.3.6
Explanation: Sum of the remaining two numbers = (3.95 * 6) - [(4.4 * 2) + (3.85 * 2)]
= 7.20.
Required average = (7.2 / 2) = 3.6.
C
Question: A and B started a business in partnership investing Rs.20,000 and Rs.15,000 respectively. After 6months, C joined them with Rs.20,000. Whatwill be B's share in total profit of Rs.20,000 earned at the end of 2years from the startingof the business?
A.s. 5,000
B.s. 5,500
C.s. 5,700
D.s. 6,000
Answer: D.s. 6,000
Explanation: A : B : C = (20,000 x 24) : (15,000 x 24) : (20,000 x 18) = 4 : 3 : 3.
B's share = Rs. 20000 x	3/10	= Rs. 6,000.
D
Question: Diesel costs Rs.4 per lit and petrol costs 7.23 per litre. If the price of diesel rise by 10% a month and the price of petrol is unchanged.How many months will it take until a litre of Diesel costs more than a litre of petrol.
A.9 months
B.5 months
C.7 months
D.3 months
Answer: C.7 months
Explanation: Explanation :
=>In the First Month the price of the diesel would be 4*110/100 = 4.4
=>In the Second Month the price of the diesel would be 4.4*110/100 = 4.84
=>In the Third Month the price of the diesel would be 4.84*110/100 = 5.324
=>In the fourth Month the price of the diesel would be 5.324*110/100 = 5.85
=>In the fifth Month the price of the diesel would be 5.85*110/100 = 6.44
=>In the sixth Month the price of the diesel would be 6.44*110/100 = 7.08
=>In the seventh Month the price of the diesel would be 7.08*110/100 = 7.79 which is higher than the price of petrol
Answer : C
Question: The ratio, by volume, of bleach to detergent to water in a certain solution is 2 : 25 : 100. The solution will be altered so that the ratio of bleach to detergent is tripled while the ratio of detergent to water is halved. If the altered solution will contain 300 liters of water, how many liters of detergent will it contain?
A.40
B.45
C.50
D.75/2
Answer: D.75/2
Explanation: B:D:W = 2:25:100
Bnew / Dnew = (1/3)*(2/25) = (2/75)
Dnew / Wnew = (1/2)*(25/100) = (1/8)
Wnew = 300
Dnew = Wnew/5 = 300/8 =75/2
So, answer will be D
Question: In digging a pond 20 m * 12 m * 5 m the volumes of the soil extracted will be?
A.3387
B.1000
C.1200
D.2787
Answer: C.1200
Explanation: 20 * 12 * 5 = 1200
Answer: C
Question: Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?
A.8 sec
B.12 sec
C.15 sec
D.10 sec
Answer: B.12 sec
Explanation: Speed of the first train = 120/10 m/sec = 12 m/sec.
Speed of the second train = 120/15 m/sec = 8 m/sec.
Relative speed = (12 + 8) = 20 m/sec.
Required time = (120 + 120)/20 sec = 12 sec.
Answer : B.
Question: The average of a couple was 23Yrs when they were married 5Yrs ago.The avg age of
the couple and a child, who was born during the interval, is 20Yrs now. How old is the
child now ?
A.2 Yrs
B.4 Yrs
C.3 Yrs
D.1 Yrs
Answer: B.4 Yrs
Explanation: (a+b-5-5)/2=23;
a+b=56;
a+b+c/3=20;
solving both c=4
ANSWER:B
Question: By selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 5 p.c?
A.38020
B.38000
C.38028
D.38019
Answer: B.38000
Explanation: CP + CP/8 = 45000
CP = 40000
SP = 40000*(95/100)
=38000
Answer: B
Question: A and B can do a work in 4 hours and 12 hours respectively. A starts the work at 6AM and they work alternately for one hour each. When will the work be completed?
A.7 days
B.9 days
C.4 days
D.6 days
Answer: D.6 days
Explanation: Work done by A and B in the first two hours, working alternately = First hour A + Second hour B = 1/4 + 1/12 = 1/3.
Total time required to complete the work = 2 * 3
= 6 days.
Answer: D
Question: What approximate value should come in place of the question mark (?) in the following equation?
95.245 + 25.912 × 7.2 + ? = 905.293
A.986.6
B.936.6
C.996.6
D.995.6
Answer: C.996.6
Explanation: 95.245 + 25.912 × 7.2 + ? = 905.293
or, ? = 905.293 – 95.245 + 25.912 × 7.2
? = 905.293 – 95.245 + 186.5664
≈ 996.6
Answer C
Question: If a number between 10 and 30 (inclusive) at random. What is the probability that the tens digit is greater than ones digit?
A.31/41
B.4/21
C.14/41
D.27/41
Answer: B.4/21
Explanation: If tens digi is 3 ---> ones digit : 0,
If tens digi is 2 ---> ones digit : 0, 1
If tens digi is 1 ---> ones digit : 0
So the number of numbers whose tens digit is greater than ones digit is 11.
The total number is 30-10+1=21.
So the probability is 4/21.
The answer is (B).
Question: Find the ones digit of 73^351
A.3
B.5
C.6
D.7
Answer: D.7
Explanation: The units digit of 73^351 will be the same as the units digit of 3^351
3^1=3 --> the units digit is 3;
3^2=9 --> the units digit is 9;
3^3=27 --> the units digit is 7;
3^4=81 --> the units digit is 1;
3^5=243 --> the units digit is 3 AGAIN;
...
So, as you can see the units digit repeats in blocks of 4: {3, 9, 7, 1}, {3, 9, 7, 1}, ... Now, since 351=348+3=(multiple of 4)+3, then the units digit of 3^351 will be the third number in the pattern thus 7.
Answer: D.
Question: A shopkeeper loses 15%,if an article is sold for Rs. 102. What should be the selling price of the article to gain 20%?
A.Rs.146
B.Rs.144
C.Rs.129
D.Rs.123
Answer: B.Rs.144
Explanation: Given that SP = Rs. 102 and loss = 15%
CP = [100(SP)]/(100 - l%) = (100 * 102)/85 = 20 * 6 = Rs. 120.
To get 20% profit, New SP = [(100 + p%)CP]/100 = (120 * 120)/100
= Rs.144
Answer:B
Question: A car travels at a speed of 10 miles per hour. How far will it travel in 5 hours?
A.50 miles
B.62 miles
C.325 miles
D.70 miles
Answer: A.50 miles
Explanation: During each hour, the car travels 65 miles. For 5 hours it will travel
10 + 10 + 10 + 10 + 10 = 5 *10 = 50 miles correct answer A
Question: Anup start a bike at 6am. and rides it at 60kmph. Raghu started at 7pm with his car at 90kmph. When will Raghu overtake Anup?
A.9:00am
B.9:40am
C.10:00am
D.12:00pm
Answer: A.9:00am
Explanation: Suppose bike is overtaken by car xhrs after 6am
Distance covered by the bike in x hrs = distance covered by the car in x-1 hr
60x = 90(x-1)
30x = 90
x = 3 hrs
Required time = 6+3 = 9:00am
Answer is A
Question: A shopkeeper buys mangoes at the rate of 7 a rupee and sells them at 3 a rupee. Find his net profit or loss percent?
A.33 4/3 %
B.33 1/7 %
C.400/7 %
D.32 1/3 %
Answer: C.400/7 %
Explanation: The total number of mangoes bought by the shopkeeper be 21.
If he buys 7 a rupee, his CP = 3
He selling at 3 a rupee, his SP = 7
Profit = SP - CP = 7 - 3 = 4
Profit Percent = 4/7 * 100 = 400/7 %
Answer:C
Question: An apple tree has 30 apples. 10 apples have fallen off of the tree. How many apples remain on the tree?
A.20
B.1
C.0
D.5
Answer: A.20
Explanation: A. 20
Question: In a fort, there are 1200 soldiers. If each soldier consumes 3 kg per day, the provisions available in the fort will last for 30 days. If some more soldiers join, the provisions available will last for 25 days given each soldier consumes 2.5 kg per day. Find the number of soldiers joining the fort in that case?
A.537
B.528
C.645
D.538
Answer: B.528
Explanation: Assume X soldiers join the fort. 1200 soldiers have provision for 1200(days for which provisions last them)(rate of consumption of each soldier)
= 1200(30)(3) kg
Also provisions available for (1200 + x) soldiers is (1200 + x)(25)(2.5) kg
As the same provisions are available
=> 1200(30)(3) = (1200 + x)(25)(2.5)
x = [1200(30)(3)]/[(25)(2.5)] - 1200
Answer:B
x = 528
Question: What approximate value should come in place of question mark (?) in the following equation?
33 1⁄3% of 768.9 + 25% of 161.2 – 67.12 = ?
A.230
B.231
C.235
D.220
Answer: B.231
Explanation: ? = 33 1⁄3% of 768.9 + 25% of 161.2 – 67.12
= 1⁄3 of 768.9 + 1⁄4 of 161.2 – 67.12
= 256.3 + 40.3 – 67.12 ≈ 231
Answer B
Question: Find the least number by which (59)(36)(17) has to be multiplied to obtain a perfect square?
A.5
B.17
C.85
D.221
Answer: C.85
Explanation: For any perfect square the index of the power of each of its prime factors is even. in the given number the power of 5 and 17 have odd indices, while 3 has an even index.
The least number = (5)(17) = 85.
ANSWER:C
Question: What is the least value of x. So that 43x87 is divisible by 3?
A.4
B.5
C.2
D.6
Answer: C.2
Explanation: The sum of the digits of the number is divisible by 3, then the number is divisible by3.
4 + 3 + x + 8 + 7 = 22 + x
Least value of x may be 2
Therefore 22+ 2 = 24 is divisible by 3.
C
Question: The average salary per head of the entire staff of an office including the officers and clerks is Rs.90. The average salary of officers is Rs.600 and that of the clerks is Rs.84. If the number of officers is 2, find the number of officers in the office?
A.1
B.8
C.7
D.6
Answer: A.1
Explanation: 6 * 22 = 132
7 * 19 = 133
--------------
1.Answer: A
Question: (1+0.0001)/(0.00004+1)
The value of the expression above is closet to which of the following?
A.0.0001
B.0.001
C.0.1
D.1
Answer: D.1
Explanation: Notice that we need approximate value of the fraction.
Now, the nominator is very close to 1 and the denominator is very close to 1, hence the value of the fraction is very close to 1/1=1.
Answer: D.
Question: 49 * 49 * 49 * 49 = 7?
A.4
B.5
C.7
D.9
Answer: D.9
Explanation: Sol.
49 * 49 * 49 * 49 = (72 * 72 * 72 * 72) = 7(2+2+2+2) = 78.
So, the correct answer is 8.
Answer D
Question: One fourth of a solution that was 10% salt by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight. The second solution was what percent salt by weight?
A.24%
B.34%
C.22%
D.18%
Answer: B.34%
Explanation: Say the second solution (which was 1/4 th of total) was x% salt , then 3/4*0.1+1/4*x=1*0.16 --> x=0.34. Alternately you can consider total solution to be 100 liters and in this case you'll have: 75*0.1+25*x=100*0.16 --> x=0.34.
Answer: B.
Question: If a, b, c are consecutive positive integers and b<a<c, which of the following must be true?
I. c-b=2
II. abc is an even integer
III. (a+b+c)/3 is an integer
A.I
B.II
C.I and II
D.II and III
Answer: C.I and II
Explanation: 1. c-b=2 --> b, a, c are consequitive positive integers and a<b<c then c=b+2 --> c-b=2. So this statement is always true;
2. abc is an even integer --> out of any 3 consecutive integers at least one must be even thus abc=even. So this statement is also always true;
3. (a+b+c)/4 is an integer --> the sum of odd number of consecutive integers is ALWAYS divisible by that odd number. Or: (a+b+c)/4=fraction.
Answer: C.
Question: A tank has both an inlet pipe and an outlet pipe. Working alone, the inlet pipe can fill up the tank in 5 hours. Working alone, the outlet pipe can empty out the tank in 15 hours. If it is desired that the tank should be filled, from empty, exactly 7 hours after the inlet pipe is turned on at 9:30am, then at what time should the outlet pipe be opened ?
A.9:30am
B.10:30am
C.11:30am
D.10:40am
Answer: B.10:30am
Explanation: In 7 hours the inlet pipe will pump in water equal to 7*1/5 = 7/5 of the pool. So, 2/5 more than necessary, which should be compensated by the outlet pipe. To pump out 2/5 of the water the outlet pipe needs 30/5 = 6 hours.
Therefore, the outlet pipe should be opened at 9:30am + 7 hours - 6 hours = 10:30am.
Answer: B
Question: An entrance exam question paper consists of five problems, each problem having three choices. In how many ways can a student attempt one or more problems?
A.500
B.1023
C.1024
D.1035
Answer: B.1023
Explanation: paper 5 problems and each 3 choices so no of ways = 4^5 -1
= 2^10 - 1 = 1024 - 1 = 1023
ANSWER B
Question: A man can hit a target once in 5 shots. If he fires 4 shots in succession, how many ways that he will hit his target?
A.71/234
B.81/133
C.81/343
D.34/83
Answer: D.34/83
Explanation: The man will hit the target if he hits it once or twice or thrice or all four times in the four shots that he takes.
So, the only possibility when the man will not hit the target is when he fails to hit the target in even one of the four shots that he takes.
The event of not hitting the target even once is the complement of the event of hitting the target at least once.
The probability that he will not hit the target in any given shot = 1 - 1/5 = 4/5
Therefore, the probability that he will not hit the target in any of the four shots = 4/5^4 = 34/83
D
Question: One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in
A.144 mins
B.140 mins
C.136 mins
D.132 mins
Answer: A.144 mins
Explanation: Explanation:
Let the slower pipe alone fill the tank in x minutes
then faster will fill in x/3 minutes.
Part filled by slower pipe in 1 minute = 1/x
Part filled by faster pipe in 1 minute = 3/x
Part filled by both in 1 minute =1/x+3/x=1/36
=>4/x=1/36
x=36âˆ—4=144mins
ANSWER IS A