RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: In a certain province in France there are 11 cities. If a single road segment connects only two cities, how many road segments are required in order to connect the cities so that each city is connected to all other cities with a single road segment?
A.55
B.105
C.330
D.143
Answer: A.55
Explanation: 1 city needs 10 roads to connect directly to the rest => 11 city needs 11*10 roads.
One road is counted twice => the number of road needed is 11*10/2 = 55
Answer A
Question: In the number 10,0AB, A and B represent the tens and units digits, respectively. If 11,0AB is divisible by 55, what is the greatest possible value of B × A?
A.0
B.5
C.10
D.15
Answer: D.15
Explanation: You should notice that 55*2=110 so 11,000 is divisible by 55: 55*200=11,000 (or you can notice that 11,000 is obviously divisible by both 5 and 11 so by 55) --> B*A=0*0=0. Next number divisible by 55 is 11,000+55=11,055: B*A=5*5=15 (next number won't have 110 as the first 3 digits so we have only two options 0 and 25).
Answer: E.
!
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D
Question: In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is
A.75 cu. m
B.750 cu. m
C.7500 cu. m
D.75000 cu. m
Answer: B.750 cu. m
Explanation: Solution
Area = (1.5 × 10000) m2 = 45000 m2.
Depth = m = m.
∴ Volume = (area × depth) = m3 = 750 m3.
Answer B
Question: If a point (x,y) is randomly selected within the square shown in the figure above, (the vertices are on 1,1 1,-1, -1,1 -1,-1) what are
the Q odds that x^2+y^2>1?
A.1. pi/4
B.2. pi/16
C.3. Q=1-pi/4
D.4. Q=1-pi/16
Answer: C.3. Q=1-pi/4
Explanation: area of the square will be 4, and the area of circle with center (0,0) and radius 1 will be pi.
then succesful outcomes = 4 - pi (the area where x2+y2 will be greater than 1)
total outcomes = 4
therefore probability = (4-pi)/4
C
Question: Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. If the faster train passes the slower train in 36 seconds,what is the length of each train?
A.50 m
B.80 m
C.76 m
D.58 m
Answer: A.50 m
Explanation: let length of each train = x m
total distance while passing the slower train = (x+x) = 2x m
relative speed = (46-36) = 10 km/hr
=10*5/18 = 50/18 m/s
time = 36 sec
2x/36 = 50/18 => x=50
ANSWER A
Question: The probability that A speaks truth is 23/35 and that of B speaking truth is 35/47. What is the probability that they agree in stating the same fact?
A.1553/1645
B.1262/2535
C.1257/1835
D.1903/1735
Answer: A.1553/1645
Explanation: If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 23/35 * 35/47 + 22/35 * 34/47
= 805/1645 + 748/1645 = 1553/1645
ANSWER:A
Question: Car Z travels 51 miles per gallon of gasoline when driven at a constant rate of 45 miles per hour, but travels 20 percent fewer miles per gallon of gasoline when driven at a constant rate of 60 miles per hour. How many miles does car Z travel on 10 gallons of gasoline when driven at a constant rate of 60 miles per hour?
A.320
B.375.2
C.400
D.408
Answer: D.408
Explanation: The question stem asks us for the distance possible with 10 gallons of fuel at a constant speed of 60 miles per hour. We therefore first calculate the fuel efficiency at that speed.
The stem tells us that at 45 miles/hour, the car will run 51 miles/gallon and at 60 miles/hour, that distance decreases by 20%. We can therefore conclude that the car will travel 40.8 miles/gallon at a constant speed of 60 miles/gallon. With 10 gallons of fuel, the car can therefore travel 40.8 miles/gallon * 10 gallons = 408 miles.
Answer D.
Question: The proportion of water to alcohol in Solution A is 4:1 and the proportion of water to alcohol in Solution B is 2:3. If an equal amount of each solution is mixed together, what is the concentration of alcohol in the new solution?
A.39%
B.40%
C.41%
D.42%
Answer: B.40%
Explanation: Let V be the total volume of the new solution.
Then a volume of V/2 was added from each solution A and B.
The amount of alcohol added to the new solution was:
(1/5)(V/2)+(3/5)(V/2)=V/10+3V/10=4V/10=2V/5.
The concentration of alcohol is 2/5=40%
The answer is B.
Question: The average marks scored by Ganesh in English, Science, Mathematics and History is less than 17 from that scored by him in English, History, Geography and Mathematics. What is the difference of marks in Science and Geography scored by him?
A.40
B.50
C.60
D.68
Answer: D.68
Explanation: E+H+G+M/4âˆ’E+S+M+H/4=17
â‡’ G - S = 68
Answer D
Question: Tea worth Rs.126 per kg are mixed with a third variety in the ratio 1: 1 : 2. If the mixture is worth Rs.133 per kg, the price of the third variety per kg will be
A.Rs.169.50
B.Rs.1700
C.Rs. 175.50
D.Rs. 155.50
Answer: D.Rs. 155.50
Explanation: Solution
Since first second varieties are mixed in equal proportions, so their average price = Rs.(126+135/2) = Rs.130.50
So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.
x-133/22.50 = 1 =â€º x - 133 = 22.50 =â€º x=155.50.
Hence, price of the third variety = Rs.155.50 per kg.
Answer D
Question: In an election, candidate A got 80% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favor of candidate.
A.330000
B.340000
C.380800
D.356000
Answer: C.380800
Explanation: Total number of invalid votes = 15 % of 560000
= 15/100 × 560000
= 8400000/100
= 84000
Total number of valid votes 560000 – 84000 = 476000
Percentage of votes polled in favour of candidate A = 80 %
Therefore, the number of valid votes polled in favour of candidate A = 80 % of 476000
= 80/100 × 476000
= 38080000/100
= 380800
C)
Question: Monica and Miya's age are in 2:5. Find teh age of Monica if the sum of their age is 28.
A.10 years
B.14 years
C.20 years
D.8 years
Answer: D.8 years
Explanation: Let the age of Monica be 2x and Miya be 5x.
2x + 5x = 28
x = 4
Monica's age is 8 years
Answer : D
Question: A boy has twelve trousers and 14 shirts. In how many different ways can he select a trouser and a shirt?
A.238 ways
B.287 ways
C.266 ways
D.168 ways
Answer: D.168 ways
Explanation: Explanation:
The boy can select one trouser in 12 ways.
The boy can select one shirt in 14 ways.
The number of ways in which he can select one trouser and one shirt is 12 * 14 = 168 ways.
Answer: D
Question: A bag contains 12 white and 18 black balls. 2balls are drawn in succession. What is the probability that first is white and second is black?
A.21/145
B.36/145
C.3/145
D.2/119
Answer: B.36/145
Explanation: The probability that first ball is white:
=12C130C1=12C130C1
=1230=1230
=25=25
Since, the ball is not replaced; hence the number of balls left in bag is 29.
Hence, the probability the second ball is black:
=18C129C1=18C129C1
=1829=1829
Required probability,
=(25)×(1829)=(25)×(1829)
=36/145
B
Question: When all the students in a school are made to stand in rows of 45, 40 such rows are formed. If the students are made to stand in rows of 40, how many such rows will be formed ?
A.31
B.36
C.45
D.40
Answer: C.45
Explanation: Explanation:
Total number of students = 45 x 40
When arranged in rows of 40, number of rows formed are,
= 45.
Answer: C
Question: Joe needs to paint all the airplane hangars at the airport, so he buys 360 gallons of paint to do the job. During the first week, he uses 1/4 of all the paint. During the second week, he uses 1/4 of the remaining paint. How many gallons of paint has Joe used?
A.18
B.157
C.175
D.216
Answer: B.157
Explanation: Total paint initially = 360 gallons
Paint used in the first week = (1/4)*360 = 90 gallons.
Remaning paint = 270 gallons
Paint used in the second week = (1/4)*270 = 67 gallons
Total paint used = 157 gallons.
Option B
Question: If Peter reads at a constant rate of 1 pages every 5 minutes, how many seconds will it take him to read N pages?
A.300
B.2N
C.5/2*N
D.24N
Answer: A.300
Explanation: Peter would read 1 page in 5/1 minutes
Peter would read N page in (5/1)*N min i.e. (5/2)*N*60 Seconds = 300N Seconds.
Option A is the correct Answer.
Question: If y is 60 percent greater than x, then x is what percent less than y?
A.30%
B.37.5%
C.45.5%
D.50%
Answer: B.37.5%
Explanation: y = 1.6x
x = y/1.6 = 10y/16 = y - (3/8)*y
3/8 is 37.5%.
The answer is B.
Question: A reduction of 40% in the price of apples would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen?
A.1
B.3
C.6
D.7
Answer: B.3
Explanation: B
40*(40/100) = 16 --- 64
? --- 12 => Rs.3
Question: When the positive integer x is divided by 9,the remainder is 5.What is the remainder when 6x is divided by 9?
A.0
B.1
C.3
D.4
Answer: C.3
Explanation: i tried plugging in numbers
x = 9q+5
x = 14
6x = 84
6x/9= 9*9 + 3
remainder is 3.
Answer is C.
Question: Find the one which does not belong to that group?
A.16
B.36
C.22
D.64
Answer: C.22
Explanation: Explanation:
16, 36, 64 and 4 are perfect squares but not 22.
Answer:C
Question: In a certain province in France there are 17 cities. If a single road segment connects only two cities, how many road segments are required in order to connect the cities so that each city is connected to all other cities with a single road segment?
A.30
B.105
C.330
D.136
Answer: D.136
Explanation: 1 city needs 16 roads to connect directly to the rest => 17 city needs 17*14 roads.
One road is counted twice => the number of road needed is 17*16/2 = 136
Answer D
Question: A woman has $252,125 in her savings account. What is the least amount of money (in whole number of dollars) that she must add to her account if she wants to split this money evenly among her nine children?
A.$1
B.$2
C.$3
D.$4
Answer: A.$1
Explanation: To find the least amount the woman should add to her saving account to split the money evenly among her 9 children,
she needs to make the total divisible by 9
Simply add the individual digits of the total = 2+5+2+1+2+5=17
If you add 1 , the number is divisible by 9 (17+ 1)
Correct Option : A
Question: If the numerator of a fraction is increased by 20% and its denominator is diminished by 25% value of the fraction is 2/15. Find the original fraction?
A.1/12
B.1/18
C.1/42
D.1/15
Answer: A.1/12
Explanation: X * (120/100)
---------------- = 2/15
Y * (75/100)
X/Y = 1/12
Answer: A
Question: x+(1/x) = 3.5 find x^2 + (1/x^2)
A.2.25
B.3.25
C.10.25
D.5.25
Answer: C.10.25
Explanation: squaring on both sides (x+1/x)^2=3.5^2
x^2+1/X^2=12.25-2
x^2+1/X^2=10.25
ANSWER:C
Question: What will be the compound interest on a sum of Rs. 35,000 after 3 years at the rate of 12% p.a.?
A.s:10123.19
B.s:14172.48
C.s:10123.20
D.s:10123.28
Answer: B.s:14172.48
Explanation: Amount
= [35000 * (1 + 12/100)3]
= 35000 * 28/25 * 28/25 * 28/25
= Rs. 49172.48
C.I. = (49172.48 - 35000)
= Rs:14172.48
Answer: B
Question: Tom drives his car at a speed of 40kmph and reaches his destination in 5hrs and John covers the same distance in 8 hours. If speed of Tomis increased by 10kmph and speed of Ram is increased by 15kmph, what would be the difference between the times taken by them to cover the distance?
A.2 hour
B.1 hour
C.3 hour
D.4 hour
Answer: B.1 hour
Explanation: Distance covered by Ravi at a speed of 40 kmph in 5 hours
ð Distance= Speed x Time = 40 x 5= 200 km
Ram covers same distance in 8 hours => Speed of Rama =
Distance
Time
= 200/8
= 25 kmph.
Ravi speed is increased by 10 kmph => New speed of Ravi = 40+10 = 50 kmph
Ram speed is increased by 15 kmph =>New speed of Ram = 25+15 = 40 kmph.
Therefore, time taken by Ravi to cover 200 km at 50 kmph = 200/50
= 4 hours
Time taken by Ram to cover 200 km at 40 kmph = 200/40
= 5 hours B)
Required time difference = 5 hours – 4 hours = 1 hour
B
Question: In how many ways the word ENGINEERING can be arranged so that no vowel come together???
A.273000
B.283000
C.293000
D.263000
Answer: A.273000
Explanation: Total no. of ways ENGINEERING can be arranged is
E=3, N=3, G=2, I=2, R=1
=> 11!/(3!*3!*2!*2!) => 277200
No. of ways vowels come together
Vowels ==> (eieei)ngnrng =>
eieei can be considered as 1 letter ... so 1!
ngnrng = 6!
eieei can be arranged as 5!/(3!*2!)
ngnrng can be arranged as 6!/(3!*2!)
So (1!+6 !)*5!/(3!*2!*3!*2!)
=> 4200
So no. of ways vowels not come together
=> 277200 - 4200 = 273000
ANSWER:A
Question: Car A takes 10 min lesser than Car B which is travelling at an average speed of 40mph to cover a distance of 60 miles. What is the average speed of car A?
A.30
B.35
C.45
D.50
Answer: C.45
Explanation: Time taken by Car B to cover 60 miles=60/40=1.5 hrs=90 min
Time taken by Car A to cover 60 miles=80min
Average speed of Car A=60/80= 0.75 miles per min= 45 miles per hour.
Answer: C
Question: In what ratio should water and wine be mixed so that after selling the mixture at the cost price a profit of 33.33% is made?
A.9:3
B.2:1
C.1:3
D.2:3
Answer: C.1:3
Explanation: 33.33% profit means there is one part water and 3 part is pure wine. so the required ratio of water and wine in the mixture is 1:3
Answer: Option C
Question: In a throw of dice what is the probability of geÆ«ng number greater than 2
A.1/2
B.2/3
C.1/5
D.1/6
Answer: B.2/3
Explanation: Explanation:
Number greater than 2 is 3, 4, 5 & 6, so only 4 number
Total cases of dice = [1,2,3,4,5,6]
So probability = 4/6 = 2/3
Answer: B
Question: A man is riding a bike downhill at 18 Km/hr, and uphill at 4 Km/hr, what is his rate?
A.1 Km/Hr
B.3 Km/Hr
C.5 Km/Hr
D.7 Km/Hr
Answer: D.7 Km/Hr
Explanation: Dh = 18
Uh = 4
s=?
s=(18-4)/2 = 14/2 = 7
Answer = D
Question: In an examination 40% failed in Hindi, 45% failed in English. If 25% students failed in both the subjects. Then the percentage of failed students is?
A.59%
B.50%
C.90%
D.60%
Answer: B.50%
Explanation: Male = 45,000* 5/9 = 25,000
Female = 45,000* 4/9 = 20,000
Married Male = 25,000* 40/100 = 10,000
Married Female = 10,000
20,000 ------------ 10,000
100 ------------- ? => 50%
Answer: B
Question: If Jan 1, 2006 was a Sunday, What was the day of the week Jan 1, 2010?
A.Friday
B.Thursday
C.Tuesday
D.Saturday
Answer: A.Friday
Explanation: Explanation :
Given that Jan 1 2006 was a Sunday
Number of odd days in the period 2006-2009
= 3 normal years + 1 leap year
= 3 x 1 + 1 x 2 = 5 (note that we have taken the complete year 2006 because the period in 2006 is from 01-Jan-2006 to 31-Dec-2006, which is the whole year 2006. Then the complete years 2007, 2008 and 2009 are also involved)
Hence Jan 1 2010 = (Sunday + 5 odd days) = Friday.. Answer : Option A
Question: The daytime telephone rate between two cities is 60 cents for the first 3 minutes and c cents for each additional minute. The total charge is reduced 50 percent on calls made after 10:00 P.M. The cost, in dollars, of a 35-minute call made at 10:30 P.M. between these two cities is:
A. 0.4(0.60) + 35c
B. 0.5(0.60 + 32c)
C. 0.4(0.60 + 9c)
D. 0.5(0.60 + 0.32c)
Answer: D. 0.5(0.60 + 0.32c)
Explanation: For first three minutes = 60 cents
Remaining minutes = 35 -3 = 32
charge for 32 minutes = 32c
total cost (if the call was made in daytime) = 0.60 + 32c
50% chargereducedon night calls => 50% charge
=>0.5(0.60 + 32c)
Hence, Answer is D
Question: A is faster than B. A and B each walk 24 km. The sum of their speeds is 7 km/hr and the sum of times taken by them is 14 hours. Then, A's speed is equal to?
A.5 km/hr
B.3 km/hr
C.6 km/hr
D.9 km/hr
Answer: B.3 km/hr
Explanation: Let A's speed = x km/hr. Then, B's speed = (7 - x) km/ hr.
So, 24/x + 24/(7 - x) = 14
x2 - 98x + 168 = 0
(x - 3)(x - 4) = 0 => x = 3 or 4.
Since, A is faster than B, so A's speed = 4 km/hr and B's speed
= 3 km/hr.
Answer: B
Question: A committee of 3 people is to be chosen from the president and vice president of four different companies. What is the number of different committees that can be chosen if two people who work for the same company cannot both serve on the committee?
A.16
B.24
C.28
D.32
Answer: D.32
Explanation: i just did the total number of possibilities first:
ab cd ef gh are the 4 companies for example
8c3. this will include the problem counts of a pres/vp of the same company
how many ways did we over count = How many ways can a president and VP of the same company be part of this group?
choose the group, 4c1, then take both the president and vp, 2c2, then a remaining member from one of the other 3, 6c1
4c1 * 2c2 * 6c1
4 * 1 * 6 = 24
8c3 - 24 = 56 - 24 = 32 answer is D
Question: A, B and C rents a pasture for Rs.841. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should B pay?
A.270
B.279
C.348
D.371
Answer: C.348
Explanation: 12*8 :16*9 = 18*6
8: 12: 9
12/29 * 841 = 348
Answer: C
Question: 2/5 of the fish in an aquarium is red and 1/4 of the fish is brown. 1/4of the red fish and 1/5 of the brown fish is male. If the rest of the fish in the aquarium is female, what is the probability that a fish randomly picked from the aquarium is male?
A.3/20
B.7/30
C.5/16
D.1/3
Answer: A.3/20
Explanation: Straight method....
1/4 of 2/5 + 1/5 of 1/4 = 2/20 +1/20 =3/20
ANSWER:A
Question: If a^2+b^2=177and ab=54 then find the value of a+b/a-b?
A.1
B.3
C.5
D.7
Answer: C.5
Explanation: (a+b)^2=a^2+b^2+2ab=117+2*24=225
a+b=15
(a-b)^2=a^2+b^2-2ab=117-2*54
a-b=3
a+b/a-b=15/3=5
Answer is C.
Question: The bankerâ€™s discount of a certain sum of money is Rs. 60 and the true discount on the same sum for the same time is Rs.54. The sum due is
A.210
B.280
C.360
D.720
Answer: D.720
Explanation: Sol.
Sum = B.D. * T.D. / B.D. - T.D. = Rs.[60 *54 / 60 - 54] = Rs. [72 * 60 / 6] = Rs. 720
Answer D
Question: Among all sales staff at Listco Corporation, college graduates and those without college degrees are equally represented . Each sales staff member is either a level-1 or level-2 employee. Level-1 college graduates account for 15% of Listco's sales staff. Listco employs 60 level-1 employees, 30 of whom are college graduates. How many sales staff members without college degrees are level-2 employees ?
A.46
B.42
C.56
D.70
Answer: D.70
Explanation: I'm going in on this one.
So let's say that we have the following
So we know that L1 = 60 and that C and L1 = 0.15X , we should set up a double set matrix btw but anyways, I'm just explaining the point with this problem. Now we are told that 0.15x = 30, therefore the grand total is 200. Now we know that L2 is 200 - 60 = 140. We also learn that C and No C are equally represented thus 100 each. Therefore No C and No L2 will be 100 - 30 = 70.
Thus D is the correct answer choice
Question: M, N and O can do a piece of work in 60, 30 and 20 days respectively. Inhow many days can M do the work if he is assisted by N and O on every third day?
A.10 days
B.12 days
C.15 days
D.25 days
Answer: C.15 days
Explanation: M's 2 day's work = 1	x 2 =	1	.
20	10
(M + N + O)'s 1 day's work = 1	+	1	+	1 =	6	=	1	.
20	30	60	60	10
Work done in 3 days = 1	+	1 =	1	.
10	10	5
Now,	1	work is done in 3 days.
5
Whole work will be done in (3 x 5) = 15 days.
C
Question: If f(a)=a^2, what is the value of (f(a+b)−f(a))/a ?
A.a
B.b
C.2b+b^2
D.2a + b
Answer: C.2b+b^2
Explanation: start with f(a+b) before start calculations: f(a+b)=(a+b)^2= a^2+2ab+b^2
a^2+2ab+b^2 - a^2/a = (simplify a^2)
2ab+b^2/b = (cancel b's)
= 2b+b^2
Ans : C
Question: Aishwarya was first to board to her flight to delhi.
She forgot her seat number and picks a random seat for herself.
After this, every single person who get to the flight sits on his seat if its available else chooses any available seat at random.
Abhishek is last to enter the flight and at that moment 99/100 seats were occupied.
Whats the probability what Abhishek gets to sit in his own seat ?
A.2
B.1/2
C.2/2
D.3
Answer: B.1/2
Explanation: Solution:
1/2
one of two is the possibility
1. If any of the first 99 people sit in Abhishek seat, Abhishek will not get to sit in his own seat.
2. If any of the first 99 people sit in Aishwarya's seat, Abhishek will get to sit in his seat.
Answer B
Question: A person with some money spends1/3 for cloths, 1/5 of the remaining for food and 1/4 of the remaining for travel.He is left with Rs 100/- How much did he have with him in the beginning ?
A.150
B.200
C.250
D.270
Answer: C.250
Explanation: x/3+ 2x/15 + 8x/60 + 100 = x
x/3 + 4x/15 = x-100
3x= 5x - 500
x = 250
ANSWER:C
Question: Ajay can walk 6km in 1 hour. In how many hours he can walk 45km?
A.5hrs
B.10hrs
C.7.5hrs
D.20hrs
Answer: C.7.5hrs
Explanation: 1 hour he walk 6km
he walk 45km in = 45/6 * 1 = 7.5hours
Answer is C
Question: The ratio of two numbers is 3:4 and their sum is 28. The greater of the two numbers is?
A.15
B.16
C.18
D.21
Answer: B.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)
B
Question: In a business, A and C invested amounts in the ratio 2:1, whereas the ratio between amounts invested by A and B was 3:2. If Rs. 1,57,300 was their profit, how much amount did B receive ?
A.48400
B.23777
C.12387
D.48213
Answer: A.48400
Explanation: A : B = 3 : 2 => B : A = 2 : 3 = 4 : 6 and A : C = 2 : 1 = 6 : 3.
So, B : A : C = 4 : 6 : 3 or A : B : C = 6 : 4 : 3.
B's share = Rs. (157300 x 4/13 ) = Rs. 48400
Answer: A
Question: A division of a company consists of five men and five women. If two of these employees are randomly selected as representatives of the division, what is the probability that both representatives will be female?
A.2/5
B.2/7
C.2/9
D.2/11
Answer: C.2/9
Explanation: Total number of ways to select 2 members = 10C2 = 45
Total number of ways to select 2 females = 5C2 = 10
P(two females) = 10/45 = 2/9
The answer is C.
Question: Simplify: 839478 x 625
A.524673750
B.546273750
C.562473750
D.564273750
Answer: A.524673750
Explanation: 839478 x 625 = 839478 x 5^4 = 8394780000/16 = 524673750.
Answer is A
Question: The probability of pulling a black ball out of a glass jar is 1/R. The probability of pulling a black ball out of a glass jar and breaking the jar is 1/Y. What is the probability of breaking the jar?
A.1/(XY)
B.R/Y
C.Y/X
D.1/(X+Y)
Answer: B.R/Y
Explanation: P of pulling a black ball out of a glass jar AND breaking the jar = 1/Y
P of pulling a black ball out of a glass jar is 1/R
Lets say P of breaking the jar = n
That means 1/R*n=1/Y
n= R/Y
B is the answer
Question: The average age of the mother and her six children is 13 years which is reduced by 5 years if the age of the mother is excluded. How old is the mother?
A.40
B.41
C.42
D.43
Answer: D.43
Explanation: Total age of mother and 6 children = avg x n = 13 x (6+1)= 91
If mother is excluded new average is (13 - 5) = 8
so for 6 children = 6 x 8=48
so mother's age is 91 - 48 =43
Answer: Option D
Question: A+B+C = 500
A+C = 200
B+C = 350
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A+B+2C = 550
A+B+C = 500
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C = 50
Answer: A
A.50
B.27
C.26
D.28
Answer: C.26
Explanation: S = 4
M = x
DS = x + 4
US = x - 4
6/(x + 4) + 6/(x - 4) = 2
x = 8
Answer: C
Question: An intelligence agency decides on a code of 2 digits selected from 0, 1, 2, …, 9. But on the slip on which the code is hand written allows confusion between top and bottom, because there are indistinguishable. Thus, for example, the code 91 could be confused with 16. How many codes are there such that there is no possibility of any confusion?
A.90
B.Required numbers = 80
C.40
D.50
Answer: B.Required numbers = 80
Explanation: Total digits that can be formed = 10C1 * 10C1 = 100.
The digits that still remain digits when turned upside down are 0, 1, 6, 8 and 9.
So codes that can create confusion are:
01, 06, 08, 09
10, 16, 18, 19
60, 61, 66, 68 (69 would still be 69 when inverted)
80, 81, 86, 89
90, 91, 98, 99 (96 would still be 96 when inverted)
There are 20 such numbers.
Required numbers = 100 - 20 = 80
ANSWER:B