RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A five digit number is to be formed using each of the digits 1, 2, 3, 4 and 5 ONLY ONCE. How many numbers can be formed when 2 and 3 are not together ?
A. 48
B. 72
C. 36
D. 60
Answer: B. 72
Explanation: Reqd ways = (Total No. of ways - cases when both 2 and 3 are together)
5 numbers can be arranged in 5 places in 5! ways. Now tie 2 and 3 together so effectively there are 4 nos. they can be arranged in 4! ways. 1 and 2 can be arranged within themselves in 2!ways.
Reqd. Answer = 5! - 4!2! = 120 - (24*2) = 72
Answer: B
Question: A water tank is two-fifth full.Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes.If both the pipes are open,how long will it take to empty or fill the tank completely?
A.6 min.to empty
B.9 min.to empty
C.5 min.to empty
D.4 min.to empty
Answer: A.6 min.to empty
Explanation: Explanation:
Clearly,pipe B is faster than pipe A and so,the tank will be emptied.
part to be emptied = 2/5
part emptied by (A+B) in 1 minute=
so, the tank will be emptied in 6 min
Answer: A
Question: 3 men and 8 women complete a task in same time as 6 men and 2 women do. How much fraction of work will be finished in same time if 4 men and 2 women will do that task.
A.5/7
B.3/10
C.5/18
D.5/16
Answer: A.5/7
Explanation: 3 m + 8 w = 6 m + 2 w
3 m = 6 w
1 m = 2 w
Therefore 3 m + 8 w = 14 w
4 m + 2 w =10 w
Answer is 10/14 =5/7
Answer: A
Question: Jessica can text 85 words per minute, while Maurice can text 55 words per minute. An abridged English translation of Tolstoy’s War and Peace contains 410,400 words. Working together, how many days will it take Jessica and Maurice to text the entire abridged translation of War and Peace?
A.0.3
B.1.9
C.3
D.9
Answer: B.1.9
Explanation: Since the answer choices are reasonably spaced out, we can approximate and save time
Combined words per day = 150*60*24 which should be 216000
410400/216000 will be 1.9,
So, Answer should be B
Question: A case of 12 rolls of paper towels sells for $9. The cost of one roll sold individually is $1.What is the percent W of savings per roll for the 12-roll package over the cost of 12 rolls purchased individually?
A.9%
B.11%
C.15%
D.25%
Answer: D.25%
Explanation: Cost of 12 paper towels individually = 1*12=12
Cost of a set of 12 paper towels = 9
Cost of one roll = 9/12 = 3/4 = 0.75
Savings per roll = 1-.75 = 0.25
% of savings is W= .25/ 1 *100 = 25% D is the answer.
Question: In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?
A.5/7
B.2/7
C.3/7
D.7/9
Answer: B.2/7
Explanation: =10/10+25
=10/35=2/7
ANSWER B
Question: The speed of a train is 70 kmph. What is the distance covered by it in 10 minutes?
A.10.66 kmph
B.11.66 kmph
C.21.66 kmph
D.12.66 kmph
Answer: B.11.66 kmph
Explanation: 70 * 10/60 = 11.66 kmph
ANSWER:B
Question: pipes P and Q would fill a cistern 18 and 24 minutes respectively. Both pipes being opened, find when the first pipe must be turned off so that the cistern may be just filled in 12 minutes?
A.after 12 mins
B.after 9 mins
C.after 8 1/2 mins
D.after 10 mins
Answer: B.after 9 mins
Explanation: Explanation:
x/18 + 12/24 = 1
x = 9
ANSWER IS B
Question: For a performance, a few dancers are arranged in a row. Nancy is standing in the middle of the row at the 6th position.
Can you find out the total number of girls in that row?
A.8
B.9
C.10
D.11
Answer: D.11
Explanation: Since Nancy is the middle at 6th position, there should be 5 girls on both her sides.
5 + 5 = 10
Counting Nancy as well, the total number of girls in that row = 10 + 1 = 11
correct answer is D)11
Question: A train 250 m long passed a pole in 25 sec. How long will it take to pass a platform 700 m long?
A.28 sec
B.89 sec
C.95 sec
D.16 sec
Answer: C.95 sec
Explanation: Speed = 250/25 = 10 m/sec.
Required time = (250 + 700)/10
= 95 sec.
Answer:C
Question: A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price?
A.17%
B.62%
C.12%
D.8%
Answer: C.12%
Explanation: Original price = 100
CP = 80
S = 80*(140/100) = 112
100 - 112 = 12%
Answer:C
Question: In a classroom teacher has 20 boxes, they issues 8 boxes gifted to their students. Then how many boxes they had?
A.9
B.28
C.12
D.15
Answer: C.12
Explanation: 20-8=12. Answer is C
Question: Two quarts containing 5⁄6 water and 1/6 formula are mixed with three quarts containing 7⁄10 water and 2⁄10 formula. Approximately what percent of the combined five-quart mixture is water?
A.70.4%
B.72.4%
C.75%
D.73.4%
Answer: C.75%
Explanation: 5/6 of 2 quarts = 10/6 quarts of water
7/10of 3 quarts = 21/10 quarts of water
10/6 = 1.67
21/10 = 2.1
Total water = 1.67 + 2.1= 3.77
Total quarts = 5
3.77/5 = 75.4% approx. 75%
Answer : C
Question: What is the least value of x. So that 23x57 is divisible by 3.
A.2
B.0
C.1
D.3
Answer: C.1
Explanation: Explanation:
The sum of the digits of the number is divisible by 3, then the number is divisible by3.
2 + 3 + x + 5 + 7 = 17 + x
Least value of x may be 1
Therefore 17 + 1 = 18 is divisible by 3.
Answer: Option C
Question: Ana climbs up stairs 20 floors building and back. She takes the exact same route both ways. On the trip up she climbs an average speed of 2 steps per second. On the trip back she climbs down at an average speed of 4 steps per second. What is her approximate average speed for the round trip in miles per hour?
A.1
B.1.25
C.1.33
D.1.5
Answer: C.1.33
Explanation: Average speed = total distance/total time
Here number of steps to 20th floor and back is same as she takes the same route.
D = 2T1 and D=4T2
Therefore, T1 = D/2 and T2 = D/4
T1+T2 = 3D/4
Therefore, average speed = 2d/3d/4 =2d * 4/3d
Answer is 1.3 Since, the options are far away we need not solve till the decimal points
So correct answer is option C
Question: A drawer holds 5 red hats and 5 blue hats. What is the probability of getting exactly three red hats or exactly three blue hats when taking out 6 hats randomly out of the drawer and returning each hat before taking out the next one?
A.3/8
B.1/4
C.5/8
D.5/16
Answer: D.5/16
Explanation: Let's find the probability of getting exactly 3 red hats.
One possible case is red-red-red-blue-blue-blue.
The probability of this is 1/2*1/2*1/2*1/2*1/2*1/2 = 1/64
There are 6C3 = 20 such cases so we need to multiply this by 20.
P(exactly 3 red hats) = 20*1/64 = 5/16
Note that when we get exactly 3 red hats, then we also get exactly 3 blue hats.
So we don't need to consider the case of exactly 3 blue hats separately.
The answer is D.
Question: The population of a town is 176400. If it increase at the rate of 5% per annum. What was its population 1 year ago?
A.152460
B.214560
C.168000
D.210000
Answer: C.168000
Explanation: population 2 years ago = 176400/(1 + 5/100)
Answer is C
Question: For any non-zero a and b that satisfy |ab| = -ab and |a| = -a, |b-4| + |ab-b| =
A.ab-4
B.2b-ab-4
C.ab+4
D.ab-2b+4
Answer: A.ab-4
Explanation: Given: |ab| = -ab and |a| = -a
Question: |b-4| + |ab-b| = ?
**** Looking at |ab| = -ab tells us that either one of a or b is negative.
**** Looking at |a| = -a tells us that a must be negative
**** Combine two observations: b is positive
Let a=-1 and b=1
|b-4| + |ab-b| = |1-4| + |-1-1| = 5
Test a) |ab-4| = |(1)(-1)-4| = |-5|=5
Test b) 2b-ab-4 = (2)(1) - (-1) - 4 = -1
Test c) ab+4 = -1 + 4 = 3
Test d) ab-2b+4 = -1-2(1)+4=1
test e) 4-1=3
ANSWER=A
Question: A train passes a 50 metres long platform in 14 seconds and a man standing on the platform in 10 seconds. The speed of the train is:
A.24 km/hr
B.36 km/hr
C.40 km/hr
D.45 km/hr
Answer: D.45 km/hr
Explanation: Explanation:
Let the length of train be L m.
L/10 = (L+50)/14
14L= 10L+500
L= 125 m .
Speed = (25/2) m/s = (25/2) x 18/5= 45 Km/hr
Answer D
Question: A multiple choice test consists of 4 questions, and each question has 5 answer choices. In how many F ways can the test be completed if every question is unanswered?
A.24
B.120
C.625
D.720
Answer: C.625
Explanation: 5 choices for each of the 4 questions, thus total F of 5*5*5*5 = 5^4 = 625 ways to answer all of them.
Answer: C.
Question: In a room there are 11 people. Each person shook hands with every other person. How many hand shakes were there?
A.52
B.53
C.54
D.55
Answer: D.55
Explanation: 11C2 = 55
The answer is D.
Question: How many total number of ways in which y distinct objects can be put into two different boxes is
A.n2
B.2y
C.2n
D.3n
Answer: B.2y
Explanation: Let the two boxes be B1 and B2. There are two choices for each of the y objects. So, the total number of ways is
2 × 2 ×.....× 2 (y times ) = 2y
Answer B
Question: Find the number of ways in which 7 different beads can be arranged to form a necklace.
A.30
B.20
C.420
D.60
Answer: C.420
Explanation: Since in forming a necklace clockwise and anticlockwise arrangements are not different, therefore,7 beads can be arranged to form a necklace in(7-1)! /2ways
= 6*5*4*3*2/2 = 420 ways
Answer is C
Question: Five pieces of wood have an average length of 126cm and a median length of 140cm. What is the maximum possible length, in cm, of the shortest piece of wood?
A.a) 90
B.b) 105
C.c) 110
D.d) 130
Answer: B.b) 105
Explanation: B. 105
sum of all lengths of all 5 pieces of wood = 126 * 5 = 630
3rd piece (sorted in increasing length) length = 140 (median)
for sum of first 2 wood length to become max, last two should be least.
let 4th, 5th wood also have length 140 each.
total of last 3 = 140 * 3 = 420
sum of first 2 = 630 - 420 = 210
each of these 2 will have length 210/2 = 105
Aswer B
Question: A Vendor sells 10 clips for a rupee gaining thereby 40%. How many clips did he buy for a rupee?
A.10
B.12
C.14
D.15
Answer: C.14
Explanation: S.P of 10 Clips=Re 1
Gain= 40%.
C.P of 10 Clips=Rs(100/140)*1=Re 5/7
For Rs 5/7, Clips bought=10.
For Re 1,Clips bought=10*(7/5)=14
Question: If c is an even integer and c/18 is an odd integer, which of the following is NOT an even integer?
A.(c^2)/54
B.(c^2)/16
C.(c^2)/9
D.(c^2)/6
Answer: B.(c^2)/16
Explanation: since c is an even integer and c/18 is an odd integer. thus maximum power of 2 in a is one. why ?? because if the power of 2 in the expression has been 2 or greater, then the c/18 must have been an even integer. (18=2*3^2. as 18 contain only one 2 in the expression)
now, any expression in which we have 4 at the denominator will be odd. out of the given options only 16 is a multiple of 4. hence answer should be B
Question: Out of nine consonants and three vowels, how many words can be made so that each word contains two consonants and three vowels?
A.3180
B.3510
C.3920
D.4320
Answer: D.4320
Explanation: 9C2 x 3C3 x 5! = 4320
The answer is D.
Question: 7 baseball players each stand at different corners of a baseball diamond. The sides of the diamond are all of equal length. Two arrangements of baseball players are considered different only when the relative positions of the players differ. How many different ways can the baseball players arrange themselves around the diamond?
A.445
B.632
C.720
D.240
Answer: C.720
Explanation: it is like a circular arrangement.
total ways for n people to arrange in a circle is = factorial (n-1)
in this case n= 7
hence ans = 7 factorial = 720
hence C
Question: Eighteen years ago, a father was three times as old as his son. Now the father is only twice as old his son. Then the sum of the present ages of the son and the father is?
A.176 years
B.168 years
C.186 years
D.108 years
Answer: D.108 years
Explanation: Let the present ages of the father and son be 2x and x years respectively.
Then, (2x - 18) = 3(x - 18) => x = 36
Required sum = (2x + x)
= 108 years.
Answer:D
Question: The length of a rectangle is halved, while its breadth is tripled. What is the % change in area?
A.30%
B.40%
C.50%
D.60%
Answer: C.50%
Explanation: Let original length = x and original breadth = y.
Original area = xy.
New length =	x	.
2
New breadth = 3y.
New area = x	x 3y =	3	xy.
2	2
Increase % = 1	xy x	1	x 100	%	= 50%.
2	xy
C
Question: The largest 5 digit number exactly divisible by 91 is?
A.99918
B.99919
C.99921
D.99923
Answer: A.99918
Explanation: Largest 5-digit number = 99999
91) 99999 (1098
91
---
899
819
----
809
728
---
81
---
Required number = (99999 - 81)
= 99918.
Option A
Question: 5^100 is divided by 18 then what is the remainder?
A.10
B.11
C.13
D.15
Answer: C.13
Explanation: Here N = 18=2×32
ϕ(18)=18(1−12)(1−13) = 6
So 56 when divided by 18, remainder is 1.
So we can write the given expression 5100=(56)16×54 = (1)16×54 = 52×52=7×7=49
Now 49 when divided by 18, remainder is 13.
C
Question: In Smithtown, the ratio of right-handed people to left-handed people is 3 to 1 and the ratio of men to women is 3 to 2. If the number of right-handed men is maximized, then what S percent of all the people in Smithtown are left-handed women?
A. 50%
B. 40%
C. 25%
D. 20%
Answer: C. 25%
Explanation: looking at the ratio we can take total number of people=20..
ans 5/20 or 25% C
Question: 60kg of an alloy A is mixed with 100 kg of alloy B. If alloy A has lead and tin in the ratio 3:2 and alloy B has tin and copper in the ratio 1:4, then the amount of tin in the new alloy is?
A.24kg
B.44kg
C.20kg
D.30kg
Answer: B.44kg
Explanation: Quantity of tin in 60kg of A = 60*2/5 = 24kg
Quantity of tin in 100kg of B = 100*1/5 = 20kg
Quantity of tin in the new alloy = 24+20 = 44kg
Answer is B
Question: In an election between two candidates A and B, the number of valid votes received by A exceeds those received by B by 15% of the total number of votes polled. If 20% of the votes polled were invalid and a total of 5720 votes were polled, then how many valid votes did B get?
A.1859
B.2999
C.2834
D.2777
Answer: A.1859
Explanation: Let the total number of votes polled in the election be 100k.
Number of valid votes = 100k - 20% (100k) = 80k
Let the number of votes polled in favour of A and B be a and b respectively.
a - b = 15% (100k) => a = b + 15k
=> a + b = b + 15k + b
Now, 2b + 15k = 80k and hence b = 32.5k
It is given that 100k = 5720
32.5k = 32.5k/100k * 85720 = 1859
The number of valid votes polled in favour of B is 1859.
Answer: A
Question: People are allowed to add an apple or take an apple from a large barrel. If people are only adding apples, the barrel can be filled in 5 hours. If people only take apples, the barrel can be emptied in 15 hours. If it is desired that the barrel should be filled, from empty, exactly 6 hours after people begin adding apples at 9:30am, then at what time should people begin taking apples?
A.10:00am
B.10:45am
C.12:00pm
D.12:30pm
Answer: D.12:30pm
Explanation: In 6 hours the amount of apples added equals to 6*1/5 = 6/5 of the barrel. So, 1/5 more than necessary, which should be compensated by people taking apples. To rid 1/5 of the apples people take, it will require 15/5 = 3 hours.
Therefore, people should begin taking apples at 9:30am + 6 hours - 3 hours = 12:30pm.
Answer: D.
Question: A women walking at 4 Kmph reaches her office 8 minutes late. If she walks at 6 Kmph, she reaches there 8 minutes earlier. How far is the office from her house?
A.2 1/5 Km
B.3 1/5 Km
C.4 1/3 Km
D.5 Km
Answer: B.3 1/5 Km
Explanation: Formula = S1*S2/S2-S1 * T1+T2/60
= 4*6/2 * 16/6
= 24/2 * 16/60
= 8 * 2/5
= 16/5 = 3 1/5 Km
B)
Question: A began business with 12500 and is joined afterwards by B with 25000. When did B join, if the profits at the end of the year are divided equally?
A.8 months
B.9 months
C.10 months
D.6 months
Answer: D.6 months
Explanation: Let B join after x months of the start of the business so that B’s money is invested for (12 – x) months.
∴ Profit ratio is 12 × 12500 : (12 – x) × 25000
or 12 : 2(12 – x)
Since profit is equally divided so
12 = 2(12 – x) or x = 6. Thus B joined after 8 months.
Answer D
Question: At a circular table for ten will sit eight adults and two small children. The two children will sit next to each other, and the two parents of the children will sit next to the children so that there is one parent on each side of the two children. If rotating their positions around the table is not considered changing the arrangement, in how many different ways can the ten people be arranged around the table.
A.1220
B.1660
C.2440
D.2880
Answer: D.2880
Explanation: Consider the two parents and two children as one unit.
Then there are six adults and one family unit.
The number of ways 7 can form a line is 7!
Around a circular table, there would be 7 rotations so we divide this number by 7.
There are 6! ways for 7 to sit around the circular table.
Then the two children have two options and the two parents have two options.
Then the total number of ways is 6!*2*2= 2880
The answer is D.
Question: The perimeters of two squares are 60 cm and 40 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares?
A.76 cm
B.24 cm
C.88 cm
D.44.8 cm
Answer: D.44.8 cm
Explanation: We know perimeter of square = 4(side)
So Side of first square = 60/4 = 15 cm
Side of second square = 40/4 = 10 cm
Area of third Square = 15*15 - 10*10
= 125 cm
So side of third square = 11.2 [because area of square = side*side]
Perimeter = 4*Side = 4*11.2 = 44.8 cm
Answer:D
Question: Of the diplomats who attended a summit conference: 20 spoke Latin, 32 did not speak Russian and 20% of the diplomats spoke neither Latin nor Russian. If 10% of the diplomats spoke both Latin and Russian, then how many diplomats attended the conference?
A.70
B.96
C.108
D.120
Answer: D.120
Explanation: 2X2 matrix will be the easiest way to calculate this.
Text in black: given statements
Text in red: calculated values
Thus D=120 is the correct answer
Question: A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
A.37
B.25
C.36
D.08
Answer: C.36
Explanation: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 240 + 120 = 360 m.
Time taken = 360/10 = 36 sec.
Answer: C
Question: If 0.75: x :: 5:7, then x is equal to:
A.1.05
B.1.16
C.1.2
D.1.3
Answer: A.1.05
Explanation: Explanation:
(x * 5) = (0.75 *7)
X=5.25/5 = 1.05
Answer: A
Question: If a man crosses a 650 m long street in 5 minutes. What is his speed?
A.7 km/hr
B.7.1 km/hr
C.7.8 km/hr
D.8 km/hr
Answer: C.7.8 km/hr
Explanation: distance = 650 meter
time = 5 minutes = 5 x 60 seconds = 300 seconds
Speed = distance/time=650/300=2.17m/s
=2.17×18/5=7.8 km/hr
C
Question: The salary of a typist was at first raised by 10% and then the same was reduced by 5%. If he presently draws Rs.1045.What was his original salary?
A.1000
B.970
C.765
D.654
Answer: A.1000
Explanation: X * (110/100) * (95/100) = 1045
X * (11/10) * (1/100) = 11
X = 1000
ANSWER A
Question: Two dogsled teams raced across a 300 mile course in Wyoming. Team A finished the course in 3 fewer hours than team E. If team A's average speed was 5 mph greater than team E's, what was team E's average mph?
A.12
B.15
C.18
D.20
Answer: D.20
Explanation: This is a very specific format that has appeared in a handful of real GMAT questions, and you may wish to learn to recognize it: here we have a *fixed* distance, and we are given the difference between the times and speeds of two things that have traveled that distance. This is one of the very small number of question formats where backsolving is typically easier than solving directly, since the direct approach normally produces a quadratic equation.
Say Team E's speed was s. Then Team E's time is 300/s.
Team A's speed was then s+5, and Team A's time was then 300/(s+5).
We need to find an answer choice for s so that the time of Team A is 3 less than the time of Team E. That is, we need an answer choice so that 300/(s+5) = (300/s) - 3. You can now immediately use number properties to zero in on promising answer choices: the times in these questions will always work out to be integers, and we need to divide 300 by s, and by s+5. So we want an answer choice s which is a factor of 300, and for which s+5 is also a factor of 300. So you can rule out answers A and C immediately, since s+5 won't be a divisor of 300 in those cases (sometimes using number properties you get to the correct answer without doing any other work, but unfortunately that's not the case here). Testing the other answer choices, if you try answer D, you find the time for Team E is 15 hours, and for Team A is 12 hours, and since these differ by 3, as desired, D is correct.
Question: Find the largest 6 digit number which is exactly divisible by 88?
A.998765
B.998907
C.999944
D.999954
Answer: C.999944
Explanation: Largest 6 digit number is 999999
After doing 999999 ÷ 88 we get remainder 55
Hence largest 6 digit number exactly divisible by 88 = 999999 - 55 = 999944
C
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
A.120 metres
B.180 metres
C.324 metres
D.150 metres
Answer: D.150 metres
Explanation: Explanation:
Speed= 60 x	5/18	m/sec	= 50/3	m/sec.
Length of the train = (Speed x Time).
Length of the train = 50/3	x 9	m = 150 m
ANSWER IS D
Question: How many of the positive divisors of 600 are also multiples of 4 not including 600?
A.6
B.8
C.9
D.11
Answer: D.11
Explanation: 600 = 2^6 * 3 * 5 = (4) * 2 * 3 * 5^2
Besides (4), the exponents of 2, 3, and 5 are 1, 1, and 2.
There are (1+1)(1+1)(2+1) = 12 ways to make multiples of 4.
We must subtract 1 because one of these multiples is 600.
The answer is D.
Question: A bookseller has two display windows. She plans to display 4 new fiction books in the left window, and 3 new non-fiction books in the right window. Assuming she can put the four fiction books in any order, and separately, the three non-fiction books in any order, how many total configurations will there be for the two display windows?
A.24
B.72
C.144
D.336
Answer: C.144
Explanation: Explanations
1) The left window will have permutations of the 4 fiction books, so the number of possibilities for that window is
permutations = 4! = (4)(3)(2)(1) = 24
The right window will have permutations of the 3 non-fiction books, so the number of possibilities for that window is
permutations = 3! = (3)(2)(1) = 6
Any of the 24 displays of the left window could be combined with any of the 6 displays of the right window, so the total number of configurations is 24*6 = 144
Answer: C.
Question: How many even 4-digit integers greater than 8000 are there such that all their digits are different?
A.240
B.369
C.469
D.520
Answer: C.469
Explanation: Case 1: Numbers starting with 8 followed by EVEN number
The hundreds digit can take 4 numbers (0,2,4,6) so 4 ways
The unit digit can take remaining 3 EVEN numbers left after using 2, to be EVEN so 3 ways.
The tens digit can take remaining 7 numbers left after using 3 numbers so 7 ways
Total=4*3*7=84
Case 2: Numbers starting with 8 followed by ODD number
The hundreds digit can take 5 numbers (1,3,5,7,9) so 5 ways
The unit digit can take remaining 4 EVEN numbers (0,2,4,6) to be EVEN so 4 ways.
The tens digit can take remaining 7 numbers left after using 3 numbers so 7 ways
Total=5*4*7=140
Case 3: Numbers starting with 9 followed by EVEN number
The hundreds digit can take 5 numbers (0,2,4,6,8) so 5 ways
The unit digit can take remaining 4 EVEN numbers left after using 1, to be EVEN so 3 ways.
The tens digit can take remaining 7 numbers left after using 3 numbers so 7 ways
Total=5*3*7=105
Case 4: Numbers starting with 9 followed by ODD number
The hundreds digit can take 4 numbers (1,3,5,7) so 4 ways
The unit digit can take 5 numbers (0,2,4,6,8) to be EVEN so 5 ways.
The tens digit can take remaining 7 numbers left after using 3 numbers so 7 ways
Total=4*5*7=140
Hence 84+140+105+140=469, correct answer is C
Question: A marketing firm determined that, of 200 households surveyed, 80 used neither Brand K nor Brand B soap, 60 used only Brand K soap, and for every household that used both brands of soap, 3 used only Brand B soap. How many of the 200 households surveyed used both brands of soap?
A. 15
B. 20
C. 30
D. 40
Answer: D. 40
Explanation: SOLUTION FOR SOAP K AND SOAP B
(D) 40