RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: What will come in place of the x in the following Number series? 6, 12, 24, x , 66
A.42
B.40
C.46
D.41
Answer: A.42
Explanation: (A)
The pattern is + 6, + 12, + 18, +24 â€¦â€¦â€¦..
So the missing term is = 24+ 18 = 42
Question: Find the no.of ways of arranging the boy and 7 guests at a circular table so that the boy always sits in a particular seat?
A.7!
B.8!
C.9!
D.10!
Answer: A.7!
Explanation: Ans.(A)
Sol. Total number of persons = 8 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 8 places in 7P7 = 7! Ways ... The number of required arrangements = 7! x 1= 7! = 7! ways
Question: m and n are the x and y coordinates, respectively, of a point in the coordinate plane. If the points (m, n) and (m + p, n + 4) both lie on the line defined by the equation x = (y/2) - (2/5), what is the value of p?
A.4/5
B.1
C.2
D.5
Answer: C.2
Explanation: (m,n)
m = x
n = y
m = n/2 - 2/5
10m = 5n - 4 (multiplied by 10 to simplify equation)
(m+p, n+4)
m + p = x
n + 4 = y
m+p = (n+4)/2 - 2/5
multiplied by 10 again
10m + 10P = 5n + 20 - 4
use both equations to solve for p and you get 10p = 20
p = 2
ANSWER:C
Question: In a race of 1000 m, A can beat by 100 m, in a race of 800m, B can beat C by 100m. By how many meters will A beat C in a race of 600 m?
A.128.5 m
B.127.5 m
C.127.7 m
D.127.9 m
Answer: B.127.5 m
Explanation: When A runs 1000 m, B runs 900 m and when B runs 800 m, C runs 700 m.
When B runs 900 m, distance that C runs
= (900 * 700)/800 = 6300/8 = 787.5 m.
In a race of 1000 m, A beats C by (1000 - 787.5)
= 212.5 m to C.
In a race of 600 m, the number of meters by which A beats C
= (600 * 212.5)/1000 = 127.5 m.
Answer:B
Question: In how many ways, a committee of 5 members can be selected from 6 men and 5 ladies, consisting of 3 men and 2 ladies?
A.150
B.320
C.200
D.140
Answer: C.200
Explanation: (3 men out 6) and (2 ladies out of 5) are to be chosen.
Required number of ways = (6c3x5c2)
= [6x5x4/3x2x1] x [5x4/2x1] = 200.
Ans: C
Question: List I: 1, 6, 8, 19
List II: x, 1, 6, 8, 19
A.5
B.6
C.7
D.9
Answer: C.7
Explanation: List I has even number of terms, thus its median is the average of two middle terms (when arranged in ascending/descending order), so median=(6+8)/2=7.
List II has odd number of terms, thus its median is the middle term (when arranged in ascending/descending order). As no other number in the list equal to 7, then x=7.
Answer: C.
Question: Two trains travelling in the same direction at 60 and 42 kmph completely pass off another in 1 minute. If the length of the first train is 120 m, what is the length of the second train?
A.228
B.266
C.175
D.180
Answer: D.180
Explanation: RS = 60 â€“ 42 = 18 * 5/18 = 5 mps
T = 60 sec
D = 5 * 60 = 300 m
120
--------
180 m
Answer: D
Question: A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 50%?
A.750
B.882
C.772
D.652
Answer: A.750
Explanation: Cost price = Rs.500
profit = 50% of 500 = Rs.250
Selling price = Cost price + Profit
= 500 + 250 = 750
Answer:A
Question: 225 metres long yard, 26 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between 2consecutive trees
A.10
B.12
C.14
D.15
Answer: A.10
Explanation: 26 trees have 25 gaps between them,
Required distance (225/25) = 10
A
Question: Solve the equation:
A) |2x – (3x + 2)| = 1,
B) |x|/3 – 2|x|/2 = - 1,
C) |3x – 1| = 2|3x – 1| - 2
A.-1, - 3/2, - 1/3
B.-2, - 3/2, - 1/3
C.-3, - 3/2, - 1/3
D.-1/2, - 3/2, - 1/3
Answer: A.-1, - 3/2, - 1/3
Explanation: Solution:
A) |2x – 3x – 2| = 1 <=> |-x – 2| = 1 <=>
-x - 2 = 1 or –x - 2 = -1
From the first equation we get -2 - 1 = x <=> x = -3,
and from the second -2 + 1 = x <=> x = -1
B) |x|/3 – 2 |x|/2 = -1 We reduce to a common denominator and we get
2|x| – 3.2.|x| = - 6 <=>
2|x| - 6|x| = - 6 <=>
- 4|x| = -6 <=> |x| = 3/2 <=>
x = 3/2 or x = - 3/2
C) |3x – 1| = 2|3x – 1| – 2 <=>
2 = 2|3x – 1| – |3x – 1| <=>
2 = |3x – 1| <=>
3x - 1 = 2 or 3x - 1 = - 2,
from where 3x = 3 <=> x = 1 or 3x = - 1 <=> x = - 1/3
Answer A
Question: From a container, 6 liters milk was drawn out and was replaced by water. Again 6 liters of mixture was drawn out and was replaced by the water. Thus the quantity of milk and water in the container after these two operations is 9:16. The quantity of mixture is:
A.15
B.26
C.22
D.27
Answer: A.15
Explanation: Explanation:
Let quantity of mixture be x liters.
Suppose a container contains x units of liquid from which y units are taken out and replaced by water. After operations , the quantity of pure liquid = units, Where n = no of operations .
So, Quantity of Milk =
Given that, Milk : Water = 9 : 16
Milk : (Milk + Water) = 9 : (9+16)
Milk : Mixture = 9 : 25
Answer: A) 15
Question: A, B and C can do a piece of work in 24 days, 30 days and 40 days respectively. They began the work together but C left 8 days before the completion of the work. In how many days was the work completed?
A.12 days
B.16 days
C.18 days
D.11 days
Answer: A.12 days
Explanation: One day work of A, B and C = 1/24 + 1/30 + 1/40 = 1/10 Work done by A and B together in the last 8 days = 8*(1/24 + 1/30) = 3/5
Remaining work = 2/5
The number of days required for this initial work = 4 days.
The total number of days required = 8 + 4 = 12 days.
Answer: A
Question: Find the odd man out 4, 5, 15, 49, 201, 1011, 6073
A.10
B.7
C.5
D.2
Answer: C.5
Explanation: 4 x 1 + 2 = 6
6 x 2 + 3 = 15
15 x 3 + 4 = 49
49 x 4 + 5 = 210
ANSWER:C
Question: How many possible ways can 3 girls (Rebecca, Kate, Ashley) go on a date with 3 boys (Peter, Kyle, Sam)?
A.3
B.4
C.5
D.6
Answer: D.6
Explanation: Any one girl can go with 3 boys.
2nd girl can go with remaining 2 boys
and 3rd girl can go with remaining 1 boy
3! i.e 6 (D) is the answer
Question: What will come in place of the x in the following Number series? 6, 12, 21, 33 , 48 , x
A.33
B.66
C.39
D.41
Answer: B.66
Explanation: The pattern is + 6, + 9, + 12, +15 +18 â€¦â€¦â€¦..
So the missing term is = 48 + 18 = 66
Answer : B
Question: Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 192 as interest at the end of the loan period, what was the rate of interest?
A.3.6
B.6
C.18
D.4
Answer: D.4
Explanation: Let rate = R% and time = R years.
Then, (1200 x R x R)/100 = 192
12R2 = 192
R2 = 16
R = 4.
Answer: Option D
Question: At the quarterly birthday party of Sherry, a baby boy, 40 persons chose to kiss him and 25 chose to shake hands with him. 10 persons chose to both kiss him and shake hands with him. How many persons turned out at the party?
A.35
B.75
C.55
D.25
Answer: C.55
Explanation: Let n(A) = No. of persons who kissed Sherry = 40
n(B) = No. of persons who shook hands with Sherry = 25
and n(A ∩ B) = No. of persons who both shook hands with Sherry and kissed him = 10
Then, using the formula, n(A U B) = n(A) + n(B) - n(A ∩ B)
n(A U B) = 40 + 25 - 10 = 55.
ANSWER:C
Question: A large box contains 16 small boxes and each small box contains 25 chocolate bars. How many chocolate bars are in the large box?
A.250
B.350
C.450
D.400
Answer: D.400
Explanation: The number of chocolate bars is equal to
16 * 25 = 400
correct answer D
Question: A student needs 30% of the marks on a test to pass the test. If the student gets 80 marks and fails the test by 40 marks, find the maximum marks set for the test.
A.400
B.500
C.600
D.700
Answer: A.400
Explanation: 30% = 120 marks
1% = 4 marks
100% = 400 marks
The answer is A.
Question: Gold is 10 times as heavy as water and copper is 5 times as heavy as water. In what ratio should these be mixed to get an alloy 8 times as heavy as water?
A.3:2
B.1:2
C.3:1
D.5:2
Answer: A.3:2
Explanation: G = 10W
C = 5W
Let 1gm of gold mixed with x gm of copper to get 1+x gm of the alloy
1gm gold + x gm copper = x+1 gm of alloy
10W+5Wx = x+1 * 8W
10+5x = 8(x+1)
x = 2/3
Ratio of gold with copper = 1:2/3 = 3:2
Answer is A
Question: A bullet train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the bullet train is 54 km/hr, what is the length of the platform?
A.210 cm
B.120 cm
C.340 cm
D.240 cm
Answer: D.240 cm
Explanation: D
240 cm
Question: What is the ratio between perimeters of two squares one having 3 times the diagonal then the other?
A.3: 6
B.3: 3
C.3: 8
D.3: 1
Answer: D.3: 1
Explanation: d = 3d d = d
a√2 = 3d a√2 = d
a = 3d/√2 a = d/√2 => 3: 1
Answer: D
Question: Anand and Deepak started a business investing Rs.22,500 and Rs.35,000 respectively. Out of a total profit of Rs. 13,800. Deepak's share is
A.Rs.5400
B.Rs.7200
C.Rs.8400
D.Rs.9600
Answer: C.Rs.8400
Explanation: Solution
Ratio of their shares	= 22500 : 35000
=9 : 14.
Deepak's share	= Rs.(13800×14/23)
= Rs. 8400.
Answer C
Question: There are two numbers. If 45% of the first number is added to the second number, then the second number increases to its five-fourth. Find the ratio of the first number to the second number?
A.A)3/7
B.B)5/9
C.C)6
D.D)6/7
Answer: B.B)5/9
Explanation: Let the two numbers be x and y.
45/100 * x + y = 5/4y
=> 9/20 x = 1/4 y => x/y = 5/9
B)
Question: Find the number that fits somewhere into the middle of the series. Some of the items involve both numbers and letters
Look at this series: VI, 10, V, 11, __, 12, III, ... What number should fill the blank?
A.IV
B.X
C.VI
D.V
Answer: A.IV
Explanation: A
IV
This is an alternating addition and subtraction series. Roman numbers alternate with Arabic numbers. In the Roman numeral pattern, each number decreases by 1. In the Arabic numeral pattern, each number increases by 1.
Question: Find compound interest on $ 6000 at 15% per annum for 2 years 4 months, compounded annually.
A.2331.75
B.2209.75
C.2108.75
D.2107.75
Answer: A.2331.75
Explanation: Time = 2 years 4 months = 2(4/12) years = 2(1/3) years.
Amount = $ [6000 X (1+­(15/100))2 X (1+((1/3)*15)/100)]
=$ [6000 * (23/20) * (23/20) * (21/20)]
= $ 8331.75	.
:. C.I. = Rs. (8331.75 - 6000) = $ 2331.75
Answer A.
Question: A double decked bus can accomodate 70 passengers,30 in the upper deck and 40 in the lower deck.In how many ways can the passengers be accomodated if 15 refuse to be in the upper deck while 10 others refuse to be in the lower deck?
A.1. 85!50!60!/40!45!
B.2. 85!/40!45!
C.3. 45!/20!25!
D.4. 110!50!60!/40!45!
Answer: C.3. 45!/20!25!
Explanation: 70 passengers,30 in the upper deck and 40 in the lower deck.
25 passengers have issues as 15 refuse to be in the upper deck while 10 others refuse to be in the lower deck
So those 15 will be put in lower deck and 10 will be in upper deck
So from the rest 45 passengers(70-25), we need to find 20 people to put into upper deck and the rest go to lower deck
So the ways are: C(45,20) = 45!/20!25! . Answer C
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.89
B.20
C.36
D.88
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: Option C
Question: A rectangular courtyard 3.78 meters long 5.25 meters wide is to be paved exactly with square tiles, all of the same size. what is the largest size of the tile which could be used for the purpose?
A.33
B.21
C.88
D.77
Answer: B.21
Explanation: 3.78 meters =378 cm = 2 × 3 × 3 × 3 × 7
5.25 meters=525 cm = 5 × 5 × 3 × 7
Hence common factors are 3 and 7
Hence LCM = 3 × 7 = 21
Hence largest size of square tiles that can be paved exactly with square tiles is 21 cm.
Answer: B
Question: The are 6 Black & 6 White socks in a tub, You need to take a pair of socks of same color, what is the max possibility?
A.5/11
B.6/11
C.7/11
D.8/11
Answer: A.5/11
Explanation: 2*6c2/12c2=5/11
ANSWER:A
Question: A woman invested $1,000, part at 5% and the rest at 6%. Her total investment with interest at the end of the year was $1,052. How much did she invest at 5%?
A.$500
B.$600
C.$700
D.$800
Answer: D.$800
Explanation: et x be the portion invested at 5% and
Let (1-x) be the rest which is invested at 6%
The question states that the return after 1 year is (1052/1000)-1 = 0.052 = 5.2%
We want to find the dollar amount invested in X
Using our defined variables, put together the equation and solve for x (the percentage of 1000 invested at 5%)
0.05x+0.06(1-x)= 0.052
(0.05)x +0.06 - (0.06)x = 0.052
-0.01x = -0.008
x= -0.008/-0.01 = 8/10 = 80%
So X = 80% of the 1000 which is 800
ANSWER:D
Question: If the sum of the interior angles of a regular polygon measures up to 1440 degrees, then how many sides does the polygon have?
A.10
B.16
C.12
D.11
Answer: A.10
Explanation: one of the interior angle = 180 - 360/n
sum of the interior angles is = n (180 - 360/n)
given
n(180 - 360/n)=1440
180n - 360 = 1440
180n = 1800
n = 1800/180 = 10
ANSWER:A
Question: Disha drives a car at an average speed of 48 km/h and reach her destination in 6 hours. Himanshu covers that distance in 4 hours. If Disha increases her average speed by 8 km/h and Himanshu increases his average speed by 4 km/h, then what will be the difference in time taken by them to reach their destination?
A.1 47/133 hr
B.1 41/133 hr
C.2 47/133 hr
D.1 40/133 hr
Answer: A.1 47/133 hr
Explanation: 48=d/6
therefore, distance(d)=288km
himanshu's speed=288/4=72kmph
then, disha's speed=48+8=56kmph
disha's time=288/56=5.143hr
then, himanshu's speed=72+4=76kmph
himanshu's time=288/76=3.789hr
difference in time=5.143-3.789=1.354hr=1 47/133hr
ANSWER:A
Question: 75 is what percent of 125?
A.60%
B.40%
C.45%
D.50%
Answer: A.60%
Explanation: 75/125×100=50% ANSWER : A
Question: A man takes 6 hours 15 minutes in walking a distance and riding back to the starting place. He could walk both ways in 7 hours 45 minutes. The time taken by him to ride both ways, is ?
A.6 hours 45 minutes
B.2 hours 45 minutes
C.4 hours 45 minutes
D.9 hours 45 minutes
Answer: C.4 hours 45 minutes
Explanation: Explanation:
Time taken in walking both ways = 7 hours 45 minutes --------(i)
Time taken in walking one way and riding back= 6 hours 15 minutes-------(ii)
By equation (ii)*2 -(i), we have
Time taken to man ride both ways, = 12 hours 30 minutes - 7 hours 45 minutes
= 4 hours 45 minutes
Answer: C
Question: he distance light travels in one year is approximately 5,870,000,000,000 miles. The distance light travels in 100 years is:
A.587 × 108 miles
B.587 × 1010 miles
C.587 × 10-10 miles
D.587 × 1012 miles
Answer: D.587 × 1012 miles
Explanation: The distance of the light travels in 100 years is:
5,870,000,000,000 × 100 miles.
= 587,000,000,000,000 miles.
= 587 × 1012 miles.
CORRECT ANSWER :D
Question: The difference between two positive numbers is 10 and the ratio between them is 5:3. Find the product of the two numbers.
A.375
B.175
C.275
D.125
Answer: A.375
Explanation: Solution: Let the two positive numbers be 5x and 3x respectively.
According to question,
5x-3x = 10;
Or, x = 5.
Then numbers are 25 and 15.
Thus, their product = 25*15 = 375.
Answer: Option A
Question: A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 38 years now, the son's age five years back was:
A.19 years
B.14 years
C.33 years
D.38 years
Answer: B.14 years
Explanation: Explanation:
Let the son's present age be x years.
Then, (38 - x) = x
2x = 38 => x = 19
Son's age 5 years back = (19 - 5) = 14 years.
ANSWER IS B
Question: Anirudh, Harish and Sahil invested a total of Rs.35,000 in the ratio 5:6:4 Anirudh invested has capital for 8 months. Harish invested for 6 months and Sahil invested for 4 months. If they earn a profit of Rs.75,900,then what is the share of Sahil in the profit?
A.Rs.12,400
B.Rs.14,700
C.Rs.15,800
D.Rs.13,200
Answer: D.Rs.13,200
Explanation: Total units={(5*8)+(6*6)+(4*4)}
=92.
sahil profit={16/92}75,900.
=13,200.
ANSWER:D
Question: If an investor puts $700 in a savings account that earns 10 percent annual interest compounded semiannually, how much money will be in the account after one year?
A.$769.75
B.$771.75
C.$773.75
D.$775.75
Answer: B.$771.75
Explanation: 1.05*1.05*700=$771.75
The answer is B.
Question: 50,48,44,?,20
A.14
B.15
C.13
D.36
Answer: D.36
Explanation: The Pattern is - 2, - 4, -8, ...
44-8=36
Answer :D
Question: 2 + 2 + 2 + 2 × 2^2 + 2 × 2^3 + 2 × 2^4 + 2 × 2^5 + 2 × 2^6 + 2 × 2^7 =
A.2^7
B.2^14
C.2^10
D.2^15
Answer: C.2^10
Explanation: We have the sum of 9 terms. Now, if all terms were equal to the largest term 2*2^7 we would have: sum=9*(2*2^7)=18*2^7=~2^11, so the actual sum is less than 2^11 and more than 2^7 (option A) as the last term is already more than that. So the answer is clearly C.
Answer: C
Question: If two times of the daughter’s age in years is included to the mother’s age, the total is 70 and if two times of the mother’s age is included to the daughter’s age, the total is 95. So the Mother’s age is,
A.30
B.38
C.40
D.41
Answer: C.40
Explanation: Explanation:
Let daughter’s age = A and mother’s age = B
Given: 2A+B = 70 and A+2B = 95
Solving B, we will get B = 40. Answer: C
Question: X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of work. How long did the work last?
A.8 days
B.10 days
C.12 days
D.13 days
Answer: B.10 days
Explanation: Let the total units of work to be completed be 60.
Units of work completed by X in a single day = 60/20 = 3 units.
Units of work completed by Y in a single day = 60/12 = 5 units.
Thus, 8 units of work can be done by them in a single day working together.
X works for 4 days alone = 12 units of work.
Remaining work = (60 - 12) = 48 units.
Now, X and Y works together to complete the remaining work = 48/8 = 6 days
Hence, total days taken to complete the work = (6 + 4)= 10 days.
ANSWER:B
Question: A batsman in his 17th innings makes a score of 85 and their by increasing his average by 3. What is his average after the 17th innings ?
A.22
B.27
C.19
D.37
Answer: D.37
Explanation: 16x + 85 = 17(x + 3)
x = 34 + 3 = 37
Answer: D
Question: The diameter of a wheel of cycle is 21 cm. It moves slowly along a road. How far will it go in 500 revolutions?
A.140
B.150
C.289
D.330
Answer: D.330
Explanation: In revolution, distance that wheel covers = circumference of wheel Diameter of wheel = 21 cm
Therefore, circumference of wheel = πd
= 22/7 × 21
= 66 cm
So, in 1 revolution distance covered = 66 cm
In 500 revolution distance covered = 66 × 500 cm
= 33000 cm
= 33000/100 m
= 330 m
ANSWER : D
Question: A committee of 3 men and 3 women must be formed from a group of 6 men and 8 women. How many such committees can we form if 1 man and 1 woman refuse to serve together?
A.610
B.710
C.810
D.910
Answer: D.910
Explanation: The number of committees with John but not Mary:(1∗C52)(C73)=10∗35=350;
The number of committees with Mary but not John: (C53)(1∗C72)=10∗21=210;
The number of committees without John and without Mary: (C53)(C73)=10∗35=350.
Total = 350 + 350 + 210 = 910.
ANSWER:D
Question: The difference between the simple interest received from two different sources on Rs.1800 for 3 years is Rs.13.50. The difference between their rates of interest is
A.0.15%
B.0.25%
C.0.35%
D.0.45%
Answer: B.0.25%
Explanation: (1800xR1x3)/100-(100xR2x3)/100 =13.50
5400(R1-R2)=1350
R1-R2 = 1350/5400=0.25%
answer : B
Question: A and B complete a work in 10 days. A alone can do it in 14 days. If both together can do the work in how many days?
A.5.8 days
B.4.78 days
C.6.25 days
D.3.15 days
Answer: A.5.8 days
Explanation: 1/10 + 1/14 = 6/35
35/6 = 5.8 days
Answer: A
Question: The sum of the mean, the median, and the range of the set {1, 2, 3,4,5} equals which one of the following values?
A.12
B.14
C.10
D.17
Answer: C.10
Explanation: set {1, 2, 3,4,5}
Mean = (1+2+3+4+5)/5 = 3
Meadian = Middle term = 3
Range = Highest - Lowest = 5-1 = 4
Mean+Median+Range = 3+3+4 = 10
Answer: Option C
Question: If population of certain city increases at the rate of 5%. If population in 1981 was 277830, then population in 1978 was?
A.120000
B.228788
C.266891
D.240000
Answer: D.240000
Explanation: X * (105/100) * (105/100) * (105/100) = 277830
X = 277830/1.157625
X = 240000
Answer:D
Question: Find the value of x which satisfies the relation
Log10 3+log10 (4x+1)=log10 (x+1)+1
A.2.5
B.3.5
C.3.2
D.6.8
Answer: B.3.5
Explanation: [log10a + log10b = log10 ab]
and also 1 can be written as log10 10,
so question can be rewritten as: log10 (3(4x+1))=log10(10(x+1)),
this can be solved to get 12x+3=10x+10,
that gives x=7/2=3.5
ANSWER:B
Question: The average of first six prime numbers which are between 20 and 60 is
A.34
B.42
C.45.7
D.57
Answer: A.34
Explanation: Explanation :
first six prime numbers which are between 20 and 60 = 23, 29, 31, 37, 41, 43
average = (23 + 29 + 31 + 37 + 41 + 43)/6
= 34
Answer : A
Question: 4 people are sitting in a 4 seat row watching a football game. At halftime they all get up. When they return, they each randomly sit down on one of the 4 chairs. What is the likelihood that none of the 3 end up sitting in the same chair that they sat in during the first half?
A.3/24
B.9/24
C.15/24
D.1/8
Answer: D.1/8
Explanation: Originally seated A B C D
now when after they get up and when they sit back again .
1st- A has option to sit on 3 seats ( apart from his previous seat . thus he now sits on B's seat.)
2nd- Similarly B has option to sit on 3 seats ( because A has already occupied B's previous seat, thus B sits on a's seat.)
3rd- Now C has only 1 option to sit on D's seat . and similarly D also has one option to sit on C's seat.)
hence total favourable outcomes 3*1*1=3
and total possible outcomes =4!=24
probability of the favourable outcome= 1/8. D
Question: Sreenivas sells a table to Shiva at 10% profit and Shiva sells it to Mahesh at 10% loss. At what price did Sreenivas purchase the table if Mahesh paid Rs. 2178?
A.Rs.2278
B.Rs.2189
C.Rs.2200
D.Rs.2208
Answer: C.Rs.2200
Explanation: Let the cost price of table for Sreenivas be Rs. x and given that, cost price of table for Mahesh = Rs. 2178.
=> (90%) of (110%) of x = Rs. 2178.
=> (90/100)(110/100)x = 2178
=> x = (2178 * 100)/(9 * 11)
=> x = Rs.2200
Answer: C
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are drawn at random, what is the probability that at least one is green?
A.23/35
B.29/35
C.47/70
D.43/70
Answer: A.23/35
Explanation: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
Probability that at least one green marble can be picked in the random draw of two marbles = Probability that one is green + Probability that both are green
= (⁶C₁ * ⁹C₁)/¹⁵C₂ + ⁶C₂/¹⁵C₂
= (6 * 9 * 2)/(15 * 14) + (6 * 5)/(15 * 14) = 36/70 + 1/7
= 46/70 = 23/35
ANSWER:A
Question: 3 men or 9 women can do a piece of work in 20 days. In how many days will 12 men and 8 women do the same work?
A.2 days
B.3 days
C.4 days
D.5 days
Answer: C.4 days
Explanation: 3M = 9W ---- 20 days
12M + 8W -----?
36W + 8 W = 44W ---?
9W ---- 20 44W -----?
9 * 20 = 44 * x => x = 4 days
ANSWER:C
Question: The wages earned by Robin is 30% more than that earned by Erica. The wages earned by Charles is 50% more than that earned by Erica. How much percent is the wages earned by Charles more than that earned by Robin?
A.18.75%
B.23%
C.15%
D.50%
Answer: C.15%
Explanation: Let wage of Erica = 10
Wage of Robin = 1.3*10 = 13
Wage of Charles = 1.5 *10 = 15
Percentage by which wage earned by Charles is more than that earned by Robin = (15-13)/13 * 100%
= 2/13 * 100%
=15%
Answer C
Question: As x increases from 155 to 166, which of the following must increase?
I. 2x - 5
II. 1 - 1/x
III. 1/(x^2 - x)
A. I only
B. III only
C. I and II
D. I and III
Answer: C. I and II
Explanation: I. 2x - 5 --> x increases from 155 to 166 --> 2x increases --> 2x - 5 increases. Correct.
II. 1 - 1/x --> x increases from 155 to 166 --> 1/x decreases --> 1 -1/x increases. Correct.
III. 1/(x^2 - x) --> x increases from 155 to 166 --> x^2-x increases --> 1/(x^2 - x) decreases.
Answer: C.