RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Mike's age is 57 years. If he is 5 more than twice the age of his son, find the age of his son.
A.20 years
B.26 years
C.16 years
D.18 years
Answer: B.26 years
Explanation: Let Mike's son age be x.
5 + 2 x = 57
x = 26
Hence Mike's son age is 26years
Answer : B
Question: Subtracting 2% of A from A is equivalent to multiplying A by how much ?
A.0.98
B.9.4
C.0.094
D.94
Answer: A.0.98
Explanation: Answer
Let A - 2% of A = AB.
⇒ (98 x A) / 100 = AB
∴ B = 0.98
Correct Option: A
Question: P, Q, R, S and T are five speakers who have to speak on a particular day, not necessarily in the same order. R is neither the first nor the last speaker. There are three speakers after S and three speakers ahead of T. If P speaks after Q, then who is the last speaker to speak?
A.S
B.T
C.P
D.Q
Answer: C.P
Explanation: Explanation:
There are three speakers after S. So, S is the 2nd speaker.
There are three speakers before T. So, T is the 4th speaker.
R is neither the 1st nor the 5th. So, R is the 3rd speaker.
P speaks after Q, So P is the 5th and Q is the 1st speaker. So, P is the last speaker.
ANSWER IS C
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.81.7
C.81.2
D.81.3
Answer: A.81.6
Explanation: SI = 40 + 40
CI = 40 + 40 + 1.6 = 81.6
Answer: A
Question: A charity collected $4,199 from donors during the last month. If each donor gave at least $20, what is the greatest possible number of donors the charity could have?
A.209
B.205
C.200
D.250
Answer: A.209
Explanation: Min fund = 20
Total = 4199
The closest multiple of 20 to 4199 is : 208
Which implies 208 people gave 20 and 1 person gave 39
Ans. A
Question: Tanaka and Sam worked all summer mowing lawns to earn money for college. They combined what they made everyday and at the end of summer they split all of their earnings evenly (50/50) between themselves. If Sam earned an even number of dollars, and the product of Tanaka and Sam's earnings is an even number, then which of the following is true?
A.Tanaka made $522.
B.Tanaka made $306.
C.Tanaka made $333.
D.Tanaka made $666.
Answer: C.Tanaka made $333.
Explanation: From Parity Mathematics Rule: If the sum of two numbers is odd, then the product is even. x + y = odd; then, xy = even.
And, the sum of an even and odd number are odd, but the sum of two even numbers is even.
Sam's earning are even, so Tanakas must be odd.
Answer: C
Question: x men working x hours per day can do x units of a work in xx days. How much work can be completed by y men working y hours per day in y days?
A.x2/y2 units
B.y3/x2 units
C.x3/y2 units
D.y2/x2 units
Answer: B.y3/x2 units
Explanation: Explanation:
Let amount of work completed by y men working y hours per in y days = w units
More men, more work(direct proportion)
More hours, more work(direct proportion)
More days, more work(direct proportion)
Hence we can write as
(men)x:y
(hours)x:y
(days)x:y }::x:w
⇒x^3w=y^3x
⇒w=y^3x/x^3
=y^3/x^2
Answer: Option B
Question: Max planned to buy bike, sales man advised him to buy within this month, If he purchase next month means State Tax will be increasing 10% than its cost and it would be 82500. What is the bike's Selling price in this month
A.70000
B.73000
C.75000
D.77000
Answer: C.75000
Explanation: SP* (110/100) = 82500
SP= 750 * 100 => SP = 75000
Answer:C
Question: Which one of the following numbers is exactly divisible by 11?
A.A)11
B.B)13
C.C)14
D.D)15
Answer: A.A)11
Explanation: (4 + 5 + 2) - (1 + 6 + 3) = 1, not divisible by 11.
(2 + 6 + 4) - (4 + 5 + 2) = 1, not divisible by 11.
(4 + 6 + 1) - (2 + 5 + 3) = 1, not divisible by 11.
(4 + 6 + 1) - (2 + 5 + 4) = 0, So, 415624 is divisible by 11.
A
Question: If two of the four expressions x + y , x + 3y , x - y , and 3x - y are chosen at random, what is the probability that their product will be of the form of x^2-(by)^2, where b is an integer?
A.1/2
B.1/6
C.1/5
D.1/3
Answer: B.1/6
Explanation: Total number of expressions if 2 are multiplied = 4C2 = 4!/2!*2! = 6
now we have to find the expressions that are in form of x^2 - (by)^2
one is (x+y)(x-y) = x^2 - (1y)^2
If you see any other combination we are always going to have one term of xy since 3x and 3y are there, so there can be only one type of combination like this.
therefore, probablity is 1/6
Answer : B
Question: Which is the smallest no which divides 2880 and gives a perfect square?
A.4
B.9
C.3
D.5
Answer: D.5
Explanation: 2880=20*144(because w.k.t 144 is perfect square)
=2*10*144
=2*2*5*144
=4*5*144(here 4 and 144 are perfect square)
so the smallest number is 5
ANSWER:D
Question: A and B together can complete a piece of work in 6 days. B and C can complete the same work in 8 days.A and C can finish it in 12 days. If they all work together, how long it will take to finish the work
A.48/9 days
B.58/9 days
C.68/9 days
D.78/9 days
Answer: A.48/9 days
Explanation: Solution: Work done by A,B & C together in one day= ½(1/6 +1/8 + 1/12)=9/48
=> days taken to complete the work by A,B & C together =48/9 days
Answer A
Question: If k, m, and n are consecutive integers such that k > m > n and the sum of k, m, and n is a multiple of 10, which of the following could be the value of k?
A.0
B.1
C.9
D.10
Answer: B.1
Explanation: We're given a very specific set of restrictions in this prompt:
1) K, M and N are CONSECUTIVE INTEGERS
2) K > M > N
3) K+M+N = a multiple of 10
We're asked which of the 5 answer COULD be the value of K given these restrictions. Rather than staring at the screen or doing layered math, we canbrute forcethe answers until we find one that fits these restrictions..
Answer A: K = 0
In this case, the numbers would be 0, -1, and -2. The sum = -3 which is NOT a multiple of 10. Eliminate A.
Answer B: K = 1
In this case, the numbers would be 1, 0, and -1. The sum = 0 which IS a multiple of 10. B IS the answer.
Final Answer:
B
Question: If the cost price is 90% of sp then what is the profit %
A.1.10%
B.1.11%
C.1.15%
D.1.17%
Answer: B.1.11%
Explanation: Sol. sp=Rs100 : then cp=Rs 90:profit =Rs 10.
Profit={(10/90)*100}%=1.11%
Answer is B.
Question: The sum of ages of 5 girls born at the intervals of 3 years each is 70 years. What is the age of the youngest girl?
A.years
B.years
C.years
D.years
Answer: A.years
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) = 70
5x = 40
x = 8.
Age of the youngest child = x = 8years.
A)
Question: There is a five digit code consist of letters and digit. the code can have one digit from 1,2,3 and any four letters from A,b,c,d,e. first and last code must be a letter and all letters can be repeated. How many combinations can be possible?
A.625
B.3840
C.5625
D.11,520
Answer: C.5625
Explanation: 5c1*(5c1*5c1*3c1)*3!/2!*5c1=5625
First fix the 1st and last digit, that can be filled with any of the 5 letters in 5c1 ways
Remaining 3 digits includes a no which can be filled in 3c1 ways
Remaining 2 digits are again letters and can be filled in 5c1 ways
these 3 digits can be arranged among themselves in 3!/2! ways
5625 is the answer!
ANSWER:C
Question: If apples cost x dollars per m dozen, how many dollars will it cost to buy n apples?
A.xn/(12m) dollars
B.xn/m
C.m/(xn)
D.12m/(xn)
Answer: A.xn/(12m) dollars
Explanation: let it 2 dollars for 2 dozens(24) and we are asked to find the value n apples...let n be 4...
In order to buy 24 apples it took 2 dollars...then for 4 apples it'll take 4*2/12*2 = 1/3.. i.e. n*x/12*m.
Answer: option A is correct answer...
Question: What is the next number of the following sequence
1,2,3,5,8,13,?
A.25
B.21
C.20
D.24
Answer: B.21
Explanation: 1+2=3
2+3=5
3+5=8
5+8=13
8+13=21
therefore next no. is 21
ANSWER:B
Question: A child must place 3 different toys in 4 different bins. If any of the toys can go in any of the bins, in how many ways can the child place the toys into the bins?
A.6^6
B.6^4
C.4^6
D.4^3
Answer: D.4^3
Explanation: there are 4 different bins and each of the toy can go to any of these bins..
so answer 4âˆ—4âˆ—4=4^3
ANSWER:D
Question: The ratio of two numbers is 3:4 and their sum is 28. The greater of the two numbers is?
A.12
B.14
C.16
D.18
Answer: C.16
Explanation: 3:4
Total parts = 7
= 7 parts --> 28 (7 × 4 = 28)
= 1 part ---->4 (1 × 4 = 4)
= The greater of the two number is = 4
= 4 parts ----> 16 (4 × 4 = 16)
C
Question: A boat goes 8 km upstream in 24 minutes. The speed of stream is 4 km/hr. The speed of boat in still water is:
A.24 km/hr
B.29 km/hr
C.27 km/hr
D.25 km/hr
Answer: A.24 km/hr
Explanation: Speed upstream =8(24/60) = 20 km/hr
Speed of the stream = 4 km/hr
speed of boat in still water = (20+4) = 24 km/hr
Answer: A
Question: The sale price sarees listed for Rs.500 after successive discount is 10% and 5% is?
A.427.5
B.277
C.342
D.882
Answer: A.427.5
Explanation: 500*(90/100)*(95/100) = 427.5
Answer: A
Question: A merchant has 1000kg of sugar, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity sold at 18% profit is
A.348
B.600
C.277
D.188
Answer: B.600
Explanation: Rule of Allegation
Answer with Explanation: Profit on I kind (%) (c) Profit of II kind (d) 8 18
Mean Price (m) d-m (18-14) = 4 14 m-c (14-8) = 6
Ratio of Profits on I and II kind = 4:6 = 2:3
Step (ii) Quantity sold at 18% profit = (3/5 x 1000) kg = 600 kg.
Answer:B
Question: Larry, Michael, and Doug have five donuts to share. If any one of the men can be given any whole number of donuts from 0 to 5, in how many different ways can the donuts be distributed?
A.21
B.42
C.120
D.504
Answer: A.21
Explanation: If you get confused about combinations, there's a simple way to count these combinations as well, by counting the number of ways 5 can be summed with 3 numbers.
{5,0,0} = 3 possibilities.
{4,1,0} = 6 possibilities.
{3,2,0} = 6 possibilities.
{3,1,1} = 3 possibilities.
{2,2,1} = 3 possibilities.
Total = 21 possibilitieS
ANSWER:A
Question: A class has three girls and three boys. These students line up at random, one after another.
What is the probability that no boy is right next to another boy, and no girl is right next to
another girl?
A.1 /20
B.1 /12
C.1 /10
D.3 /10
Answer: C.1 /10
Explanation: We pick the students in order. The first choice is always okay. There is a probability
3/5 that the second choice is okay; for example, if you picked a boy first then there are two boys
and three girls left. Similarly the probabilities that the remaining choices are okay is 1/2 , 2/3 , 1/2,1. The answer is 1/10 , the product of all these probabilities.
correct answer C
Question: In an examination 35% of the students passed and 260 failed. How many students appeared for the examination?
A.A)540
B.B)400
C.C)700
D.D)650
Answer: B.B)400
Explanation: Let the number of students appeared be x
then, 65% of x = 260
65x/100 = 260
x = 260*100/65 = 400
Answer is B
Question: Ram sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles?
A.2000
B.2772
C.8122
D.2888
Answer: A.2000
Explanation: (10*10)/100 = 1%loss
100 --- 99
? --- 1980 => Rs.2000
Answer: A
Question: In a fuel station the service costs $2.20 per vehicle and every liter of fuel costs $0.70. Assuming that you fill up 3 mini-vans and 2 trucks, what will be the total cost, if a mini-van's tank is 65 liters and a truck's tank is 120% bigger and they are all empty?
A.$341.50
B.$344.60
C.$347.70
D.$350.80
Answer: C.$347.70
Explanation: The service cost of 3 vans and 2 trucks is 5*2.20 $11.00
The fuel in 3 vans is 3*65 = 195 liters
The fuel in 2 trucks is 2*65*2.2 = 286 liters
The total fuel (vans + trucks) = 481 liters
The total fuel cost is 481*0.7 = $336.70
The total cost is $336.70 + $11.00 = $347.70
The answer is C.
Question: GOOD is coded as 164 then BAD coded as 21.if ugly coded as 260 then DAB?
A.20
B.21
C.22
D.23
Answer: B.21
Explanation: GOOD=(7+15+15+4)*4=164
BAD= (2+1+4)*3=21
UGLY= (21+7+12+25)*4=260
coding follows
(sum of position of alphabets)*(no. of letters in the given word)
so,
DAB=(4+1+2)*3= 21
ANSWER:B
Question: A family has a man, his wife, their four sons and their wives and one daughter. The family of every son also has 3 sons and one daughter. Find out the total number of female members in the family ?
A.15
B.10
C.12
D.16
Answer: B.10
Explanation: Explanation:
1) Man's wife. = 1
2) Man's 4 son's wives. = 4
3) Man's daughter. = 1
4) 4 son's has each one daughter. = 4
Therefore, total number of female members in the family = 1+4+1+4 = 10.
Answer B
Question: In five football games thus far this season, Barry has run for 98, 107, 85, 89, and 91 yards. At a minimum, how many yards M will he need to gain this Sunday if he wants to keep his season average above 100 yards?
A.101
B.116
C.M=130
D.M=131
Answer: D.M=131
Explanation: Sorry the answer M=141 is D.
Question: At a local beach, the ratio of little dogs to average dogs to enormous dogs is 3:4:8. Late in the afternoon, the ratio of little dogs to average dogs doubles and the ratio of little dogs to enormous dogs increases. If the new percentage of little dogs and the new percentage of average dogs are both integers and there are fewer than 30 total dogs at the beach, which of the following represents a possible new percentage of enormous dogs?
A.25%
B.40%
C.55%
D.50%
Answer: D.50%
Explanation: Little Dogs(L), Average Dogs(A) and Enormous Dogs (E)
The initial ratio for L:A:E :: 3:4:8
Initial Total dogs = 15X ( x assumed; 2+5+8= 15), Since the total dogs are less than 30 therefore initial total value has to be 15
L = 3, A = 4 E = 8
L:A= 3:4
This ratio doubles
Hence New Dog count is
L= 6 , A = 4 E= X: Also 6+4+x<30
We need to Find X*100/(4+6+X)
Now it says that new percentage of little dogs and Average dogs is an integer
%L = 6*100/(10+x) %A = 4*100/(10+x); Only Value for X is 10 ; 9+x<30 and % integer
Therefore, Enormus Dogs % is = 10*100/(20) = 50%
D
Question: Two trains 121 meters and 153 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?
A.7.19
B.6.8
C.7.2
D.7.15
Answer: B.6.8
Explanation: T = (121 + 153)/ (80 + 65) * 18/5
T = 6.8
Answer:B
Question: A profit of Rs. 500 is divided between X and Y in the ratio of 1/2:1/3 . What is the difference between their profit shares ?
A.Rs. 200
B.Rs. 100
C.Rs. 300
D.Rs. 50
Answer: B.Rs. 100
Explanation: A profit of Rs. 500 is divided between X and Y in the ratio of 1/2 : 1/3 or 3:2.
so profits are 300 and 200.
difference in profit share = 300-200=100
ANSWER:B
Question: 33 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be :
A.84 m
B.88 m
C.42 m
D.137 m
Answer: C.42 m
Explanation: Sol.
Let the length of the wire b h.
Radius = 1/2 mm = 1/20 cm. Then,
22/7 * 1/20 * 1/20 * h = 33 ⇔ = [33 * 20 * 20 * 7 / 22] = 4200cm = 42 m.
Answer C
Question: If the President and Vice President must sit next to each other in a row with 3 other members of the Board, how many different seating arrangements are possible?
A.48
B.240
C.300
D.360
Answer: A.48
Explanation: We need to take President and VP as one unit. Therefore we have 3 people to arrange=4! ways
Also, we both President and VP can be arranged in 2 ! ways.
Reqd no of ways=4!*2!=48ways
Answer A
Question: Tickets numbered from 1 to 24 are mixed and then a ticket is selected randomly. What is the probability that the selected ticket bears a number which is a multiple of 3?
A.1/3
B.2/5
C.3/10
D.3/7
Answer: A.1/3
Explanation: Here, S = [1, 2, 3, 4, …., 19, 20, 21, 22, 23, 24]
Let E = event of getting a multiple of 3 = [3, 6, 9, 12, 15, 18, 21, 24]
P (E) = n (E) / n (S) = 8 / 24 = 1/3
The answer is A.
Question: 25 is a perfect square and x is also a perfect square. when x is added to 25 and 1 is substrate from it will give an answer which is also a perfect square. then what is the square root of x?
A.6
B.2
C.3
D.5
Answer: D.5
Explanation: here
6*6=36, 25+36-1=60
2*2=4, 25+4-1=28
3*3=9, 25+9-1=33
5*5=25, 25+25-1=49
4*4=16, 25+16-1=40
So 49 is the perfect square of 7
so the answer is D
Question: The average height of the four Torres towers is 800 feet. If the four Torres towers have a median height of 900 feet, what is the greatest possible height of the shortest building of the four?
A.100 feet
B.300 feet
C.500 feet
D.600 feet
Answer: C.500 feet
Explanation: a1≤a2≤a3≤a4;
The average height of the four Torres towers is 800 feet: a1+a2+a3+a4=4∗800
The median height of 900 feet: a2+a32=900 --> a2+a3=1800
Substitute a2+a3=1800 into a1+a2+a3+a4=4∗80: a1+1800+a4=4∗800 --> a1+a4=1400
To maximize a1a1 we should minimize a4a4. Minimum value of a4a4 is 900 (the median value), thus the maximum value of a1a1 is 1400 - 900 = 500.
Answer: C
Question: The L.C.M of 2/3, 3/ 5, 4/7, 9/13 is :
A.45
B.28
C.36
D.42
Answer: C.36
Explanation: Required L.C.M =L.C.M. of 2,3,4,9/H.C.F. of 3,5,7,13 =36/1=36
Answer is C
Question: 49, 98, 686, 1372....
A.9052
B.8711
C.9279
D.9604
Answer: D.9604
Explanation: 49 x 2 = 98
98 x 7 = 684
684 x 2 =1372
1372 x 7 = 9604
Answer = D
Question: A salesman’s terms were changed from a flat commission of 5% on all his sales to a fixed salary of Rs.1000 plus 2.5% commission on all sales exceeding Rs. 4,000. If his remuneration as per new scheme was Rs. 600 more than that by the previous schema, his sales were worth?
A.Rs. 14,000
B.Rs. 12,000
C.Rs. 30,000
D.Rs. 40,000
Answer: B.Rs. 12,000
Explanation: [1000 + (X-4000) * (2.5/100)] - X * (5/100) = 600
X = 12000
ANSWER:B
Question: The average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 24 years. Find the average age of the women?
A.87
B.98
C.30
D.28
Answer: C.30
Explanation: 20 + 24 + 8 * 2
= 60/2
= 30
Answer:C
Question: If an article is bought at a profit of 15% and sold at a loss of 15% what is my total profit percent or loss percent?
A.1.25
B.2.25
C.3.25
D.4.25
Answer: B.2.25
Explanation: in the case if profit and loss is given same then in that case we can put the direct formula given as
(15*15)/100=2.25%
ANSWER:B
Question: A, B, C subscribe Rs. 50,000 for a business, A Subscribes Rs. 4000 more than B and B Rs. 5000 more thanC. Out of a total profit of Rs. 35,000, A receives?
A.14700
B.14298
C.23877
D.27297
Answer: A.14700
Explanation: Let C = x. Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.
So, x + x + 5000 + x + 9000 = 50000 <=> 3x = 36000 <=>
x = 12000.
A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.
A's share = Rs. (35000 * 21/50 ) = Rs. 14,700.
Answer: A
Question: Joke is faster than Paul, Joke and Paul each walk 24 KM. The sum of their speed is 7 Km per hour. And the sum of times taken by them is 14 hours. Then, Joke speed is
A.2
B.8
C.7
D.3
Answer: D.3
Explanation: Speed=DistanceTimeSpeed=DistanceTime
let the speed of joke x then speed of paul will be 7-x
24x+247−x=1424x+247−x=14
Try to plugin the values from the options. If Joke speed is 4 the paul is 3.
Answer:D
Question: Line J has a y-intercept of 10 and passes through point (a,b). What is the slope of Line J in terms of a and b?
A.(a−6)/b
B.(a−b)/6
C.(6−a)/b
D.(b-10)/a
Answer: D.(b-10)/a
Explanation: You know that the line goes through point (a,b) and the y-intercept of 10 tells you that the line also goes through point (0,10).
slope m = (y-y1)/(x-x1) = (b-10)/(a-0)= (b-10)/a
D
Question: The product of n-1 consecutive positive integers is always divisible by
A.n^2 -1
B.(n-1)!
C.2n +1
D.n^2 + 1
Answer: B.(n-1)!
Explanation: Plug in some vlues and check -
Product of first 2 number is 2*1
Product of first 3 number is 3*2*1
Product of first 4 number is 4*3*2*1
Product of first 5 number is 5*4*3*2*1
So, The product of first n natural numbers is always divisible by n! , answer will be (B)
Question: If A and B are two events such that P (A) = 3/4, P (B) = 1/4 and P (A n B) = 3/8,
find P (not A and not B).
A.A)3/7
B.B)3/8
C.C)3/9
D.D)3/10
Answer: B.B)3/8
Explanation: P(not A and not B) = 1 - (P(A) + P(B) - P(AB))
which you might find somewhere in your text.
Substituting in our probabilities we get:
P(not A and not B) = 1 - (3/4 + 1/4 - 3/8)
P(not A and not B) = 1 - (5/8)
P(not A and not B) = 3/8.
B
Question: How many arrangements of the letters of the word BEGIN can be made, without changing the place of the vowels in the word?
A.5 ways
B.6 ways
C.7 ways
D.9 ways
Answer: B.6 ways
Explanation: E,I fixed. Consonants can be arrangements in 3P3 = 3! = 6 ways
B)
Question: The sum of the numbers is 264. If the first number be twice the second and third number be one-third of the first, then the second number is:
A.48
B.54
C.72
D.84
Answer: C.72
Explanation: Explanation:
Let the second number be x. Then, first number = 2x and third number = 2x/3.
2x + x + 2x/3 = 264
11x/3 = 264
x = 72
ANSWER IS C
Question: A train is 360 meter long is running at a speed of 54 km/hour. In what time will it pass a bridge of 140 meter length?
A.33.33 seconds
B.38 seconds
C.40 seconds
D.88 seconds
Answer: A.33.33 seconds
Explanation: Speed = 54 Km/hr = 54*(5/18) m/sec = 15 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (1/15) = 33.33 seconds
Answer: A
Question: A reduction of 24% in the price of salt enables a lady to obtain 10kgs more for Rs.100, find the original price per kg?
A.2.8
B.3.2
C.2.5
D.2.1
Answer: B.3.2
Explanation: 100*(24/100) = 24 --- 10
? --- 1 => Rs.2.4
100 --- 76
? --- 2.4 => Rs.3.2
Answer: B
Question: In a BCCI meeting there are 15 people. All shake hands with each other once. How many handshakes will be there altogether?
A.28
B.14
C.15
D.19
Answer: B.14
Explanation: There will be n-1 handshakes as A person will shake hands with all the other members.
=15-1=14
Answer:B
Question: P and Q can complete a work in 80 days and 48 days respectively. P alone started the work and Q joined him after 8 days till the completion of the work. How long did the work last?
A.35 days
B.10 days
C.14 days
D.22 days
Answer: A.35 days
Explanation: Explanation :
Work done by P in 1 day = 1/80
Work done by Q in 1 day = 1/48
Work done by P in 8 days =8 Ã— (1/80) = 1/10
Remaining work = 1 â€“ 1/10 = 9/10
Work done by P and Q in 1 day = 1/80 + 1/48 = 1/30
Number of days P and Q take to complete the remaining work = (9/10) / (1/30) = 27
Total days = 8 + 27 = 35
Answer : Option A
Question: How many pairs (e, e+1) have one or more prime factors common, where e is an integer and 2 ≤ e ≤9 ?
A.0
B.1
C.2
D.3
Answer: A.0
Explanation: e and e+1 are consecutive integers.
Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1. For example 20 and 21 are consecutive integers, thus only common factor they share is 1.
Answer: A.
Question: A bundle of flowers consists of 5 focal flowers and 7 foliage fillers. If a bouquet is created with 3 focal flowers and 5 foliage fillers, in how many ways can an original bouquet be formed?
A.29
B.30
C.45
D.204
Answer: D.204
Explanation: Choose 3 focal flowers from 5 focal flowers and choose 3 foliage fillers from 5 foliage fillers:
3C5 * 5C7 = 10*21 = 210
Ans: D
Question: In ten years, David will be four times as old as Aaron. Twenty years ago, David was twice as old as Ellen. If David is eleven years older than Ellen, how old is Aaron?
A.3–5
B.6–10
C.11–15
D.16–20
Answer: A.3–5
Explanation: Let David's present age be 'd', Aaron's present age be 'a' and Ellen's present age be 'e'
In ten years, David will be four times as old as Aaron --> d+10 = 4(a+10)
Twenty years ago, David was twice as old as Ellen --> d-20 = 2(e-20)
David is seven years older than Ellen --> d = e + 11
e+11-20 = 2e-40
e-9 = 2e-40
e = 31
d = 42
52 = 4a + 40
a = 3
Answer: A
Question: Trapezoid JKLM in the x-y plane has coordinates J = (–3, –4), K = (–3, 1), L = (5, 7), and M = (5, –4). What is its perimeter?
A. 34
B. 36
C. 38
D. 40
Answer: A. 34
Explanation: JK = 5
LM = 11
KL =using distance formula 10
JM = using distance formula 8
Sum of all is 34
A
Question: Two men starting from the same place walk at the rate of 5 kmph and 5.5 kmph respectively. What time will they take to be 8.5 km apart, if they walk in the same direction?
A.12 hrs
B.14 hrs
C.15 hrs
D.17 hrs
Answer: D.17 hrs
Explanation: Sol.
to be 0.5 km apart, they take 1 hour.
To be 8.5 km apart, they take [1/0.5 * 8.5] hrs = 17 hrs.
Answer D