RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Each month a retailer sells 100 identical items. On each item he makes a profit of $30 that constitutes 16% of the item's price to the retailer. If the retailer contemplates giving a 5% discount on the items he sells, what is the least number of items he will have to sell each month to justify the policy of the discount?
A.157
B.213
C.221
D.223
Answer: A.157
Explanation: For this question, we'll need the following formula:
Sell Price = Cost + Profit
We're told that the profit on 1 item is $20 and that this represents 16% of the cost:
Sell Price = Cost + $20
Sell Price = $125 + $20
Thus, the Sell Price is $145 for each item. Selling all 100 items gives the retailer...
100($20) = $2,000 of profit
If the retailer offers a 5% discount on the sell price, then the equation changes...
5%(145) = $7.25 discount
$137.75 = $125 + $12.75
Now, the retailer makes a profit of just $12.75 per item sold.
To earn $2,000 in profit, the retailer must sell....
$12.75(X) = $2,000
X = 2,000/12.75
X = 156.8627 =157 items
A
Question: A bag has 1, 3, 5, 7, 9,11 and 13 cm sticks. Find the probability that they they will form a triangle if 3
sticks are drawn?
A.13 / 35
B.14 / 35
C.1 / 2
D.5 / 6
Answer: A.13 / 35
Explanation: Explanation :
Total Cases: =7C3=35
Favourable Cases: (3,5,7),(3,7,9),(3,9,11),(3,11,13),(5,7,9),(5,7,11),(5,9,11),(5,9,13),(5,11,13),
(7,9,11),(7,9,13),(7,11,13),(9,11,13)=total 13.
[Others are rejected because to form a triangle it is necessary that the sum of 2 small
sides must be greater than the third greatest side.]
Hence (A) is correct answer.
Answer : A
Question: If the probability that the NY Giants win the Super Bowl is 1/12 and the probability that the NY Mets win the World Series is 1/15, what is the probability that either the NY Giants win the Super Bowl or the NY Mets win the World Series (but not both)?
A.1/18
B.5/36
C.7/48
D.11/72
Answer: B.5/36
Explanation: 11/12*1/15 + 1/12*14/15 = 25/180 = 5/36
The answer is B.
Question: If n is a positive integer and n^3 is a multiple of 550, what is the least possible value of n?
A.8
B.27
C.81
D.110
Answer: D.110
Explanation: cube of a number entails having 3 copies of the original prime factors. Since 550 is a factor of n^3 the least possible value of n is 5(11)2 = 110
the answer is D.
Question: Two containers of milk contain mixtures of water and milk in ratio 5:4 and 7:9. In what ratio they should be mixed so that mixture is of 6:6 ratio?
A.6:5
B.7:5
C.9:8
D.8:9
Answer: C.9:8
Explanation: 6/6-5/4==>-1/4
7/9-6/6==>-2/9
now, -1/4=-2/9==>1/4=2/9==>9:8
ANSWER:C
Question: If a motorist had driven 1 hour longer on a certain day and at an average rate of 5 miles per hour faster, he would have covered 50 more miles than he actually did. How many more miles would he have covered than he actually did if he had driven 2 hours longer and at an average rate of 10 miles per hour faster on that day?
A. 100
B. 120
C. 140
D. 150
Answer: A. 100
Explanation: Case 1:
let rate = R, Time = T, and Distance =D
so D=RT
Case 2:
(D+50)=(R+5)(T+1)
Case 3:
(D+X)=(R+10)(T+2)
X=100
Ans A
Question: Angela’s grade was in the 90th percentile out of 80 grades in her class. In another class of 100 students there were 19 grades higher than Angela’s. If nobody had Angela’s grade, then Angela was what percentile of the two classes combined?
A.72
B.80
C.81
D.85
Answer: D.85
Explanation: If someone's grade is in xth percentile of the nn grades, this means that xx of people out of nn has the grades less than this person.
Being in 90th percentile out of 80 grades means Angela outscored 80∗0.9=7280∗0.9=72 classmates.
In another class she would outscored 100−19=8 students (note: Angela herself is not in this class).
So, in combined classes she outscored 72+81=153. As there are total of 80+100=180 students, so Angela is in 153/180=0.85=85, or in 85th percentile.
Answer: D.
Question: Jeremy needs to choose three flowers for his mother from a group of 10 roses, six of which are red and four of which are white. What is the ratio of the number of ways in which he can select only red roses to the number of ways in which he can select only white roses?
A.30:1
B.10:1
C.5:1
D.3:2
Answer: C.5:1
Explanation: you are given 10 roses out of which 6 are red and 4 are white.
Ways of selecting 3 red roses only out of 6 available = 6C3 = 6!/(3!*3!)
Similarly, Ways of selecting 3 white roses only out of 4 available = 4C3 = 4!/(3!*1!)
Thus the ratio = 6C3/4C3 = 5:1
C is the correct answer.
Question: Yane and Thomas are among the 8 people from which a committee of 4 people is to be selected. How many different possible committees of 4 people can be selected from these 8 people if at least one of either Yane or Thomas is to be selected?
A.28
B.46
C.55
D.63
Answer: C.55
Explanation: Ans:C
Solution:
Y+T+6 = total 8 ,
we need to select at least one of the Y and T or both= total 4 out of 8 - 4 out of 6
8C4 - 6C4
=55
Question: The length of a rectangulat plot is 20 metres more than its breadth. If the cost of fencing the plot @ Rs. 26.50 per metre is Rs. 5300, what is the length of the plot in metres?
A.40
B.50
C.200
D.120
Answer: C.200
Explanation: Solution
Let breadth = x metres
Then, length = (x + 20)metres.
Perimeter	= (5300 / 26.50) m
= 200m
Answer C
Question: If two positive numbers are in the ratio 1/8 : 1/5, then by what percent is the second number more than the first?
A.67%
B.70%
C.60%
D.62%
Answer: C.60%
Explanation: Given ratio
= 1/8 : 1/5 = 5 : 8
Let first number be 5x and the second number be 8x.
The second number is more than first number by 3x.
Required percentage
= 3x/5x * 100 = 60%.
Answer:C
Question: A shopkeeper sold an article offering a discount of 5% and earned a profit of 20.65%. What would have been the percentage of profit earned if no discount was offered?
A.60%
B.27%
C.30%
D.56%
Answer: B.27%
Explanation: Let C.P. be Rs. 100.
Then, S.P. = Rs. 120.65
Let marked price be Rs. x. Then, 95/100 x = 120.65
x = 12065/95 = Rs. 127
Now, S.P. = Rs. 127, C.P. = Rs. 100
Profit % =27%.
Answer: B
Question: At a dinner party 4 people are to be seated around a circular table. Two sitting arrangements are considered different only when the positions of the people are different relative to each other.What is the total number of possible sitting arrangements or the group?
A.6
B.10
C.24
D.32
Answer: A.6
Explanation: Hi there,
You can treat this as an ordering question except thatfor a circular arrangement you need to divide by the number of spaces.So in this case:
4!/4=6
If you spin the circle to right, that doesn't count as a new arrangement. Dividing by the number of spaces takes that into consideration.
Happy Studies,
HG.
A
Question: A dress on sale in a shop is marked at $X. During the discount sale its price is reduced by 15%. Staff are allowed a further 10% reduction on thediscounted price. If a staff member buysthe dress what will she have to pay in terms of X?
A.0.560X
B.0.560X
C.0.765X
D.0.608X
Answer: C.0.765X
Explanation: If the price is reduced by 15 %, then the new price will be 0.85D
If this new price is further reduced by 10%, the discounted price will be 0.9 x 0.85X = 0.765X
C
Question: A password consists of two letters of the alphabet followed by three digits chosen from 0 to 9. Repeats are allowed. How many different possible passwords are there?
A.492,804
B.650,000
C.676,000
D.1,757,600
Answer: C.676,000
Explanation: 26*26*10*10*10=676000
ANSWER:C
Question: If n is a positive integer and n^2 is divisible by 72, then the largest positive integer Q that must divide n is?
A.6
B.12
C.24
D.36
Answer: B.12
Explanation: Q: If n is a positive integer and n^2 is divisible by 72, then the largest positive integer Q that must divide n is:
A 6, B 12, C 24, D 36, E 48
n^2 is divisible by 72, but it must also be greater than 72. If n is an integer, then n^2 must be a perfect square. The factorization of 72 is (8)(9), so if it is multiplied by 2, it will be (2)(8)(9) = (16)(9) = 144, a perfect square. So n^2 must be at least 144 or a multiple of 144, which means that n must be 12 or a multiple of 12.B
Question: If 0 < x ≤ 6, then which one of the following is the maximum value of (x – 1)^2 + x ?
A.–2
B.–1
C.0
D.31
Answer: D.31
Explanation: the maximum value of (x – 1)^2 + x for 0 < x ≤ 6 is when x=6 --> (x – 1)^2 + x = 31
Answer: D.
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
A.16 sec
B.15 sec
C.48 sec
D.44 sec
Answer: C.48 sec
Explanation: Relative speed = 45 + 30
= 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 500 + 500
= 1000 m.
Required time = 1000 * 6/125
= 48 sec.
Answer:C
Question: Machines P and Q are two different machines that make items in a factory. When Machine P works alone, it covers 15 items in m hours. When Machines P and Q work simultaneously at their respective rates, they cover 15 items in n hours. In terms of m and n, how many hours does it take Machine Q, working alone at its constant rate, to cover 15item?
A.m
B.n
C.15n/225-mn
D.m+n
Answer: C.15n/225-mn
Explanation: working rate p = 15/m ; working rate pq =( 1/p +1/q)* n =15 or mn/15 +n/q =15 0r n/q = 15-mn/15 = 225-mn/15
q = 15n/225-mn
C
Question: Four-ninths of a drink mix is dye and the rest is sugar. When the mix is added to water a gallon of drink is made that is 9% sugar. What percentage of the gallon is dye?
A. 6
B. 6.5
C. 7.2
D. 8
Answer: C. 7.2
Explanation: The proportion of Dye and sugar will remain constant.
Dye/Sugar = (4/9)/(5/9) = x/9
=> 4/5 = x/9 => x = 4*9/5 = 7.2.
Answer is C.
Question: City A to city B, Michael drove for 1 hour at 80 mph and for 3 hours at 60 mph. What was the average speed for the whole trip?
A.57
B.57.5
C.58.2
D.60
Answer: D.60
Explanation: The total distance is 1×80+3×60=240
And the total time is 4 hours. Hence,
Average Speed=(Total Distance/Total Time)=240/4=60
Answer : D
Question: If in a race of 80m, A covers the distance in 20 seconds and B in 25 seconds, then A beats B by:
A.20m
B.16m
C.11m
D.10m
Answer: B.16m
Explanation: Explanation:
The difference in the timing of A and B is 5 seconds. Hence, A beats B by 5 seconds.
The distance covered by B in 5 seconds = (80 * 5) / 25 = 16m
Hence, A beats B by 16m.
ANSWER B
Question: Kelsey travelled for 10 hours. He covered the first half of the distance at 25 kmph and remaining half of the distance at 40 kmph. Find the distance travelled by Kelsey?
A.583 km
B.400 km
C.670 km
D.360 km
Answer: B.400 km
Explanation: Let the distance travelled be x km.
Total time = (x/2)/25 + (x/2)/40 = 10 => x/50 + x/80
= 10 => (8x + 5x)/400 = 10 => x
= 400 km
Answer: B
Question: In how many ways can 6 boys and 3 girls sit around a table in such a way that no two girls sit together?
A.10000
B.14000
C.14400
D.18000
Answer: C.14400
Explanation: The 6 boys can be seated around a table in 5! Ways. In between them there are 6 places.
The 3 girls can be placed in the 6 places in 6P3 ways.
Therefore, Required number of ways= 5!* 6P3
=120*120
=14400
ANSWER:C
Question: John and Ingrid pay 30% and 40% tax annually, respectively. If John makes $56000 and Ingrid makes $74000, what is their combined tax rate?
A.32%
B.34.4%
C.35%
D.35.6%
Answer: D.35.6%
Explanation: (1) When 30 and 40 has equal weight or weight = 1/2, the answer would be 35.
(2) When 40 has larger weight than 30, the answer would be in between 35 and 40. Unfortunately, we have 2 answer choices D and E that fit that condition so we need to narrow down our range.
(3) Get 74000/128000 = 74/128 = 37/65 is a little above 1/2. Thus, our answer is just a little above 35.
Answer: D
Question: A ball is bought for Rs.400 and sold at a gain of 20% find its selling price
A.Rs.400/-
B.Rs.420/-
C.Rs.480/-
D.Rs.500/-
Answer: C.Rs.480/-
Explanation: 100 % ------> 400 (100 * 4 = 400)
120 % ------> 480 (120 * 4 = 480)
Selling price = Rs.480/-
C)
Question: Fresh grapes contain 90% water by weight while dried grapes contain 20% water by weight. What is the weight of dry grapes available from 20 kg of fresh grapes?
A.2 kg
B.2.5 kg
C.2.4 kg
D.None of these
Answer: B.2.5 kg
Explanation: Explanation :
Fresh grapes contains 10% pulp.
So, 20 kg fresh grapes contains 2kg pulp.
Dry grapes contain 80% pulp.
2kg pulp would contain 2/0.8 = 20/8 = 2.5 kg dry grapes.
Answer : B
Question: If "WATER" is given a code of 67, then what is the difference between "RIVER" and "LAKE"?
A.101
B.29
C.43
D.42
Answer: C.43
Explanation: Case – Codes : A - 1, B - 2, C - 3, D - 4, E - 5, F - 6, G - 7, H - 8, I - 9, J - 10, K - 11, L - 12, M - 13, N - 14, O - 15, P - 16, Q - 17, R - 18, S - 19, T - 20, U - 21, V - 22, W - 23, X - 24, Y - 25, Z - 26
RIVER: 72
LAKE: 29
Answer: C
Question: If x is an odd negative integer and y is an even integer, which of the following statements must be true?
I. (3x - 2y) is odd
II. xy^2 is an even negative integer
III. (y^2 ) is an odd negative integer
A.I only
B.II only
C.I
D.I and III
Answer: C.I
Explanation: If x is an odd negative integer and y is an even integer, which of the following statements must be true?
I. (3x - 2y) is odd
3x - is always negative and odd
2y - can be 0, when y=0, or always even integer (positivie or negative)
odd integer +/- even integer = always odd
I statement is always true
II. xy^2 is an even negative integer
y can be 0 => xy^2 = 0 (non-negative even) => II statement is not true
III. (y^2 ) is an odd negative integer
y can be 0 => III statement is not true
basing on above, only I statement will always be true
C
Question: Find 62976 ÷ ? = 123
A.412
B.502
C.512
D.522
Answer: C.512
Explanation: Answer
Let 62976/N = 123
Then N = 62976 / 123 = 512.
Option: C
Question: An investor bought 200 shares of stock in ABCD company in 1990. By 1992, the investment was worth only 2/3 of its original value. By 1995, the 200 shares were worth only 1/3 of their value in 1990. By what percent did the value of the investment drop from 1992 to 1995?
A.16 2/3%
B.25%
C.33 1/3%
D.50%
Answer: D.50%
Explanation: Let price of each share in 1990 = X.
Total cost in 1990 = 200X
Now Price in 1992 = 2/3 * 200X = 400/3 * X
Now price in 1995 = 1/3 *200X= 200/3X
%Change in 1995 from 1992 = [(400/3* X -200/3X) / (400/3 *X) ] *100 = 50%
Answer D
Question: The numerator of a fraction is 1 less than twice the denominator. If the numerator and denominator are both increased by 1, the fraction becomes 4/5. Find the fraction?
A.A)2/3
B.B)3/5
C.C)7/4
D.D)5/9
Answer: C.C)7/4
Explanation: Let the numerator and denominator of the fraction be 'n' and 'd' respectively.
n = 2d - 1
(n + 1)/(d + 1) = 4/5
5n + 5 = 4d + 4
5(2d-1) + 5 = 4d + 4 => d = 4
n = 2d - 1 => n = 7
Hence the fraction is : 7/4
ANSWER:C
Question: A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 42, the how old is B?
A.16
B.9
C.8
D.11
Answer: A.16
Explanation: Explanation:
Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.
(2x + 2) + 2x + x = 42
⇒ 5x = 40
⇒ x = 8.
Hence, B's age = 2x = 16 years.
Answer: A
Question: The two trains of lengths 400 m, 600 m respectively, running at same directions. The faster train can cross the slower train in 180 sec, the speed of the slower train is 48 km. then find the speed of the faster train?
A.87 Kmph
B.68 Kmph
C.54 Kmph
D.15 Kmph
Answer: B.68 Kmph
Explanation: Length of the two trains = 600m + 400m
Speed of the first train = X
Speed of the second train= 48 Kmph
1000/X - 48 = 180
1000/x - 48 * 5/18 = 180
50 = 9X - 120
X = 68 Kmph
Answer: B
Question: Andrew has a certain number of coins in his pocket. He has three times as many dimes as quarters and five times as many nickels as dimes. A nickel is worth $0.05, a dime is worth $0.10 and a quarter is worth $0.25. If he has a total of $10.15, then which of the following represents the number of dimes in Andrew’s pocket?
A.9
B.10
C.18
D.24
Answer: D.24
Explanation: E.
Let number of quarters be q. Therefore , dimes are 3q and nickels are 18q.
Total value = 15q(.05) + 3q(0.1) + .25q =1.3q
Given total value = 10.15
therefore, 1.3q=10.15 or q=8
Number of dimes = 3q or 24
Answer : D
Question: To reach her destination, Jeanette must drive 90 miles. If she drives 5 miles every 9 minutes, how much time will it take her to reach her destination?
A.2 hours and 2 minutes
B.2 hours and 42 minutes
C.2 hours and 10 minutes
D.2 hours and 12 minutes
Answer: B.2 hours and 42 minutes
Explanation: 9 minute for 5 miles how much for 90? minutes for 1(9/5) mile multiplied by 90 miles.
9*90/5= 162> 2 hours 42 min answer is B
Question: For the positive integers x, x + 2, x + 4, x + 7, and x + 37, the mean is how much greater than the median?
A.6
B.1
C.2
D.4
Answer: A.6
Explanation: Mean = (x + x+2 + x+4 + x+7 + x+37)/5
=(5x+50)/5
=x+10
Median = x+4
Thus Mean - Median = x+10 - (x+4)
=6
Answer = A
Question: In how many different ways can the letters of the word ‘PROBE’ be arranged ?
A.120
B.130
C.150
D.110
Answer: A.120
Explanation: A
120
Required number of arrangements = 5! = 120
Question: Statement : Company X has marketed the product. Go ahead, purchase it if price and quality are your considerations.
Conclusions :
I. The product must be good in quality.
II. The price of product must be reasonable.
A. I only
B. II only
C. I and II only
D. I and III only
Answer: C. I and II only
Explanation: Explanation:
Both conclusions follow as per statement.
Option C
Question: A dealer purchased an article at 3/4 of its list price and sold 50% more than the list price. Find his gain percent?
A.233
B.877
C.100
D.286
Answer: C.100
Explanation: Explanation:
MP = 100
CP = 75
SP = 150
------
75 ---- 75
100 ---- ? => 100%
Answer:C
Question: A, B and C invest in the ratio of 3 : 4: 5. The percentage of return on their investments are in the ratio of 6 : 5 : 4. Find the total earnings, If B earns Rs. 250 more than A :
A.2348
B.7250
C.2767
D.1998
Answer: B.7250
Explanation: Explanation:
A B C
investment 3x 4x 5x
Rate of return 6y% 5y% 4y%
Return \inline \frac{18xy}{100} \inline \frac{20xy}{100} \inline \frac{20xy}{100}
Total = (18+20+20) = \inline \frac{58xy}{100}
B's earnings - A's earnings = \inline \frac{2xy}{100} = 250
Total earning = \inline \frac{58xy}{100} = 7250
Answer: B) Rs.7250
Question: How many liters of pure alcohol must be added to a 100-liter solution that is 20 percent alcohol in order to produce a solution that is 24 percent alcohol?
A. 7/2
B. 5
C. 20/3
D. 100/19
Answer: D. 100/19
Explanation: 20% Alcohol solution means; in the 100 liter solution, 20 liters of solution is alcohol and 80 liters other solvents.
If we addxliters of alcohol to the solution, the solution becomes100+xliters and alcohol, which was 20 liters, becomes 20+x liters.
According to the statement;
20+x = 24% of (100+x)
OR
20+x=(100+x)6/25
500+25x=600+6x
19x=100
x=100/19
Ans:D
Question: Area of four walls of a room is 99 m2. The length and breadth of the room are 7.5 m and 3.5m respectively. The height of the room is:
A.2.5m
B.3.5m
C.1.5m
D.4.5m
Answer: D.4.5m
Explanation: 2(7.5+3.5)×h = 99
2(11)h = 99
22h = 99
h = 99/22 = 9/2 = 4.5 m
Answer is D.
Question: 3 OUT OF 2500 PARTS OF EARTH IS SULPHUR. WHAT IS THE PERCENTAGE OF SULPHUR IN EARTH
A.11/50
B.1/8
C.1/45
D.2/45
Answer: B.1/8
Explanation: REQUIRED PERCENTAGE=(3/2500*100)%=1/8%
CORRECT OPTIONS: B
Question: How many multiples of 5 are there between 1 and 100 (both are inclusive)?
A.1.2
B.20.8
C.2.3
D.6.7
Answer: B.20.8
Explanation: the answer is (100-1)/5+1=20.8
Answer is B
Question: A truck covers the distance of 550 meters in 1 minute where as a bus covers a distance of 33kms in 45 minutes.Find the ratio of their speed?
A.3:1
B.4:3
C.5:2
D.3:4
Answer: D.3:4
Explanation: Formula: d=s*t
Ratio of speed=[(550/50)*(18/5)]:[33*(45*60)](1 minute=60 sec)
=(11*3):(11*4)
=33:44
=3:4
Ratio of speed in car and bus is 3:4
Answer: option D
Question: The area of a circular place is 17.56 hectares. Find the cost of fencing it at the rate of Rs. 3/meter approximately.
A.Rs. 4233
B.Rs. 4350
C.Rs. 4457
D.Rs. 4670
Answer: C.Rs. 4457
Explanation: Area = (17.56 x 10000) m2= 175600 m2.
ΠR2 = 175600 ⇔ (R)2 = (175600 x (7/22)) ⇔ R = 236.37 m.
Circumference = 2ΠR = (2 x (22/7) x 236.37) m =1485.78 m.
Cost of fencing = Rs. (1485.78 x 3) = Rs. 4457.
C
Question: A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of A?
A.9179
B.3000
C.2997
D.2678
Answer: B.3000
Explanation: 60*5:36*6:75*3
100: 72: 75
100/247 * 7410 = 3000
Answer: B
Question: As x increases from 111 to 112, which of the following increases? I) x−1/x II) 17−1/x III) (17+x)/x
A.II only
B.I,II only
C.III only
D.I only
Answer: B.I,II only
Explanation: On Increasing the value of x from 111 to 112
I) x−1/x will increase as 1/x will be very small and x will increase by 1 unit
II) 17−1/x Will Increase as the value of 1/x will decrease thereby increasing the value of 17-(1/x)
III) (17+x)/x = (17/x)+1 will Decrease as 1/x will decrease thereby decreasing the value of (17/x)
Answer: B
Question: If the probability T of rain on any given day in city x is 50% what is the probability it with rain on exactly 3 days in a five day period?
A.8/125
B.2/25
C.5/16
D.8/25
Answer: C.5/16
Explanation: 5C3 (1/2)^3(1/2)^2
= (5 * 4 * 3!)/2!3! * 1/32
T= 5/16
Answer - C
Question: a father said to his son ,i was as old as your are at the 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.14
B.19
C.33
D.38
Answer: A.14
Explanation: son's age x years, then (38-x) = x
2x=38, x=19, therefore = son's age 5 years back (19-5)=14 years
correct answer(A)
Question: On his drive to work, Leo listens to one of three radio stations A, B or C. He first turns to A. If A is playing a song he likes, he listens to it; if not, he turns it to B. If B is playing a song he likes, he listens to it; if not, he turns it to C. If C is playing a song he likes, he listens to it; if not, he turns off the radio. For each station, the probability is 0.15 that at any given moment the station is playing a song Leo likes. On his drive to work, what is the probability that Leo will hear a song he likes?
A.0.027
B.0.386
C.0.417
D.0.657
Answer: B.0.386
Explanation: Probability he hears a song is like:
Tune to A and likes what he is hearing = 0.15
Tune to A, don't find he like what they are airing, then tune to B and likes what he finds there = 0.85 * 0.15 = 0.1275
Tune to A, finds crap there, Tune to B, hears a similar crap, Tune to C and finally falls in love with the program = 0.85^2 * 0.15 = 0.1084
Total = 0.386
Ans B
Question: Three students appear at an examination of Mathematics. The probability of their success are 2/3, 1/4, 1/5 respectively. Find the probability of success of at least two.
A.17/60
B.2/50
C.3/40
D.13/50
Answer: A.17/60
Explanation: The probability of success of at least two students will involve the following possibilities.
The first two students are successful, the last two students are successful, the first and third students are successful and all the three students are successful.
Therefore, the required probability = 2/3 x 1/4 x 4/5 + 1/4 x 1/5 x 1/3 + 2/3 x 1/5 x 3/4 + 2/3 x 1/4 x 1/5 = 17/60
ANSWER:A
Question: A train crosses a platform of 130 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
A.150
B.230
C.77
D.62
Answer: B.230
Explanation: Length of the train be â€˜Xâ€™
X + 130/15 = X + 250/20
4X + 520 = 3X + 750
X = 230m
Answer: B
Question: The ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle?
A.1:96
B.2:96
C.1:86
D.1:94
Answer: A.1:96
Explanation: Let the length and the breadth of the rectangle be 4x cm and 3x respectively.
(4x)(3x) = 6912
12x2 = 6912
x2 = 576 = 4 * 144 = 22 * 122 (x > 0)
=> x = 2 * 12 = 24
Ratio of the breadth and the areas = 3x : 12x2 = 1 : 4x = 1: 96.
Answer:A
Question: Two persons starting from the same place walk at a rate of 4kmph and 5.5kmph respectively. What time will they take to be 9km apart, if they walk in the same direction?
A.6 hrs
B.22 hrs
C.25 hrs
D.12 hrs
Answer: A.6 hrs
Explanation: The relative speed of the boys = 5.5kmph â€“ 4kmph
= 1.5 kmph
Distance between them is 9 km
Time= 9km / 1.5 kmph = 6 hrs
Answer : A.