RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: At present, the ratio between the ages of Arun and Deepak is 4 : 3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present ?
A.12 years
B.15 years
C.19 and half
D.21 years
Answer: B.15 years
Explanation: Let the present ages of Arun and Deepak be 4x years and 3x years respectively. Then,
4x + 6 = 26
4x = 20
x = 5.
Deepak's age = 3x = 15 years.
Answer: Option B
Question: The sum of digits of a two digit number is 12,The difference between the digits is 4. Find the number
A.84
B.94
C.83
D.72
Answer: A.84
Explanation: Description :
=> x+y=12, x-y=4
Adding these 2x =16
=> x=8, y=4.
Thus the number is 84
Answer A
Question: X starts a business with Rs.45000. Y joins in the business after 6 months with Rs.30000. What will be the ratio in which they should share the profit at the end of the year?
A.1:2
B.2:1
C.3:1
D.2:3
Answer: C.3:1
Explanation: Ratio in which they should share the profit
= Ratio of the investments multiplied by the time period
=45000×12:30000×6
=45×12:30×6
=3×12:2×6
=3:1
Answer is C
Question: A rectangular window is twice as long as it is wide. If its perimeter is 16 feet, then what are its dimensions in feet?
A.3/2 by 7/2
B.8/3 by 16/3
C.2 by 4
D.3 by 6
Answer: B.8/3 by 16/3
Explanation: Let x be the width of the window. Then the length is 2x.
x+2x+x+2x = 16
6x = 16
x = 16/6 = 8/3
The width is 8/3 and the length is 16/3.
The answer is B.
Question: A cistern is filled by a tap in 3 1/2 hours. Due to leak in the bottom of the cistern, it takes half an hour longer to fill the cistern. If the cistern is full how long will it take the leak to empty it?
A.11
B.12
C.29
D.28
Answer: D.28
Explanation: 2/7 - 1/x = 1/4
x = 28
Answer:D
Question: If the annual increase in the population of a town is 4% and the present number of people is 15625, what will the population be in 3 years?
A.15265
B.16458
C.25600
D.17576
Answer: D.17576
Explanation: The required population is = 15625 (1 + 4/100)^3
= 15625 * 26/25 * 26/25 * 26/25
= 17576
Answer is D
Question: The ratio of three numbers is 1:2:5 and the sum of their squares is 4320. The sum of the numbers is?
A.A)10
B.B)12
C.C)15
D.D)14
Answer: B.B)12
Explanation: Let the numbers be x,2x,5x
then, x^2+4x^2+25x^2 = 4320
30x^2 = 4320
x^2 = 144
x=12
Answer is B
Question: A and B can do a piece of work in 10 days. With the help of C they finish the work in 5 days. C alone can do that piece of work in?
A.40 days
B.20 days
C.10 days
D.60 days
Answer: C.10 days
Explanation: C
10 days
C = 1/5 – 1/10 = 1/10 => 10 days
Question: If a store adds 60 chairs to its current inventory, the total number of chairs will be the same as three-halves the current inventory of chairs. If the manager wants to increase the current inventory by 30%, what will the new inventory of chairs be?
A.40
B.60
C.100
D.156
Answer: D.156
Explanation: Explanation:
Letâ€™s say t = total current inventory of chairs. The first sentence states that 60 + t = (3/2)t. First solve for the current inventory:
60 + t = (3/2)t
60 = (3/2)t âˆ’ t
60 = (1/2)t
120 = t
The manager wants to increase this by 30%.
30% of 120 is 36, so the new inventory will be 120+36=156
Answer: (D).
Question: Sushil got thrice as many marks in English as in Science. His total marks in English, Science and Maths are 162. If the ratio of his marks in English and Maths is 3:5, find his marks in Science?
A.18
B.66
C.77
D.55
Answer: A.18
Explanation: S:E = 1:3
E:M = 3:5
------------
S:E:M = 3:9:15
3/27 * 162 = 18
Answer: A
Question: A motorist covers a distance of 39km in 45min by moving at a speed of x kmph for the first 15min, then moving at double the speed for the next 20 min, and then again moving at his original speed for the rest of the journey. Find x.
A.29 kmph
B.27 kmph
C.55 kmph
D.36 kmph
Answer: D.36 kmph
Explanation: D
36 kmph
Total distance = 39 km
Total time = 45 min
D = S*T
x * 15/60 + 2x * 20/60 + x * 10/60 = 39 km
x = 36 kmph
Question: A sum of money on compound interest amounts to Rs. 8240 in 2 years and Rs. 9888 in 3 years. The rate of interest is
A.10%
B.25%
C.20%
D.12%
Answer: C.20%
Explanation: Explanation: Let the sum be P and rate of interest be R% per annum.
Amount after 2 year = 8240
P(1+R/100)T = 8240
P(1+R/100)2 = 8240 --- ( 1)
Amount after 3 year = 9888
P(1+R/100)T = 9888
P(1+R/100)3 = 9888 --- (2)
(2) ÷ (1) => [P(1 + R/100)3]/[P(1+R/100)2 = 9888/8240
1+R100 = 9888/8240
R/100 = (9888/8240 − 1 )= 1648/8240 = 15
R = 100/5 = 20%
Solution 2
---------------------------------------------------------------------------------------
If a certain sum of money at compound interest amounts to Rs.x in t1 years and Rs.y in t2 years, then the rate of interest per annum can be given by
R = [(y/x)<sup>1/(t2−t1)</sup> − 1] × 100%
R = [(y/x)<sup>1/(t2−t1)</sup> − 1] × 100 = [(9888/8240)<sup>1/(3−2)</sup> − 1] × 100 = [(9888/8240) − 1] × 100
= (1648/8240) × 100 = (15) × 100 = 20%
Answer: Option C
Question: A, B and C invested Rs. 27000/-, Rs. 35000/- and Rs. 14000/- respectively in a business. At theend of year, they earn a profit of Rs 5320/-. B’s share of profit is:
A.Rs. 2540/-
B.Rs. 2450/-
C.Rs. 2045/-
D.Rs. 2504/-
Answer: B.Rs. 2450/-
Explanation: Explanation:
A : B : C = 27000 : 35000 : 14000 = 27 : 35 : 14
B’s Share = Rs. (5320 * 35/76)
= Rs. (140 * 35/2)
= Rs. (70 * 35) = Rs 2450/-
Answer: Option B
Question: Rajeev purchased six calculators at the cost of Rs.690. How many calculators can he purchase for Rs.920?
A.8
B.9
C.11
D.12
Answer: A.8
Explanation: Explanation:
Price of one calculator = Rs.690/6 = Rs.115
1. The No. of calculators which can be bought for Rs.920 = 920/115 = 8 Nos.
Answer: Option A
Question: Working alone, Mary can pave a driveway in 5 hours and Hillary can pave the same driveway in 2 hours. When they work together, Mary thrives on teamwork so her rate increases by 33.33%, but Hillary becomes distracted and her rate decreases by 50%. If they both work together, how many hours will it take to pave the driveway?
A.2 hours
B.4 hours
C.5 hours
D.6 hours
Answer: A.2 hours
Explanation: Initial working rates:
Mary = 1/5 per hour
Hillary = 1/2 per hour
Rate when working together:
Mary = 1/5 + (1/3*1/5) = 1/4 per hour
Hillary = 1/2 - (1/2*1/2) = 1/4 per hour
Together they work 1/4 + 1/4 = 1/2 per hour
So they will need 2 hours to complete the driveway. The correct answer is A.
Question: Which of the following equations describes a line that is perpendicular to y=x+5?
A.y = x − 5
B.y = −1 − x
C.y = 5x
D.y = 5x+1
Answer: B.y = −1 − x
Explanation: Two perpendicular lines have slopes that are inverse reciprocals of each other.
The slope of y=x+5 is 1 so the slope of a perpendicular line will be -1.
The answer is B.
Question: If c= (a-1)(a+2), then what is the least possible value of c?
A.1/2
B.2
C.-9/4
D.1
Answer: C.-9/4
Explanation: Answer : C
Question: A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 31150. What percentage of profit did he make?
A.80%
B.80%
C.40%
D.48%
Answer: C.40%
Explanation: The total CP = Rs. 16000 + Rs. 6250
= Rs. 22250 and SP = Rs. 31150
Profit(%) = (31150 - 22250)/22250 * 100
= 40%
Answer: C
Question: (100 x 60) + (138 x 400) = ? x 60
A.880
B.550
C.1100
D.1020
Answer: D.1020
Explanation: Explanation :
? = (100 x 60) + (138 x 400)/60
= 6000 + 55200/60 = 1020
Answer : Option D
Question: Yearly subscription to professional magazines cost a company $940.00. To Make a 25% cut in the magazine budget, how much less must be spent?
A.705
B.655
C.656
D.657
Answer: A.705
Explanation: total cost 940
940*25/100=235
so the cut in amount is 235
the less amount to be spend is 940-235=705
ANSWER:A
Question: The population of a city increases by 9% per year but due to migration it decrease by 1% per years. What will be the percentage increase in population in 3 years?
A.9%
B.9.27%
C.25.97%
D.12%
Answer: C.25.97%
Explanation: Actual increase in population=8%
Let, earlier population=100 then the population after 3 years
=100(1+8/100)^3=125.97
∴Required percentage=25.97%
ANSWER:C
Question: A wizard named Nepo says "I am only three times my son's age. My father is 40 years more than twice my age. Together the three of us are a mere 1240 years old." How old is Nepo?
A.340 yr
B.330 yr
C.350 yr
D.360 yr
Answer: D.360 yr
Explanation: nepo's age=x yr
nepo's son's age=x/3 yr
nepo's father's age=2x+40 yr
total age=1240
x+x/3+2x+40=1240
3x+x+6x+120=1240*3
10x=3720-120
x=360
Hence nepo's age is 360 yr
ANSWER:D
Question: 4,6,10,14,22,34,38,46 ? what is next term in the series.
A.50
B.52
C.56
D.58
Answer: D.58
Explanation: 4,6,10,14,22,26,34,38,46,?
this is right question .
It satisfy prime number like(2,3,5,7,11,13,17,19,23,29,31.....)
2*2=4
2*3=6
2*5=10
2*7=14
2*11=22
2*13=26
2*17=34
2*19=38
2*23=46
2*29=58
ANSWER:D
Question: In one hour, a boat goes 11km along the stream and 5 km against it. Find the speed of the boat in still
water
A.6
B.7
C.8
D.9
Answer: C.8
Explanation: Explanation:
We know we can calculate it by 1/2(a+b)
=> 1/2(11+5) = 1/2(16) = 8 km/hr
Answer: C
Question: A batsman makes a score of 87 runs in the 17th match and thus increases his average by 3. Find his average after 17th match
A.36
B.37
C.38
D.39
Answer: D.39
Explanation: Explanation:
Let the average after 17th match is x
then the average before 17th match is x-3
so 16(x-3) + 87 = 17x
=> x = 87 - 48 = 39
Option D
Question: Together, Andrea and Brian weigh p pounds; Brian weighs 8 pounds more than Andrea. Brian and Andrea's dog, Cubby, weighs p/4 pounds more than Andrea. In terms of p, what is Cubby's weight in pounds?
A. p/2 - 10
B. 3p/4 - 4
C. 3p/2 - 5
D. 5p/4 - 10
Answer: B. 3p/4 - 4
Explanation: Together, Andrea and Brian weigh p pounds --> A + B = p.
Brian weighs 10 pounds more than Andrea --> B = A + 8 --> A + (A + 8) = p --> A = (p - 8)/2 = p/2 - 4.
Brian and Andrea's dog, Cubby, weighs p/4 pounds more than Andrea --> C = A + p/4 = (p/2 - 4) + p/4 = 3p/4 -4.
Answer: B.
Question: Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm.
A.280
B.234
C.285
D.236
Answer: C.285
Explanation: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them) = 1/2 (20 + 18) * (15) = 285 cm2
Answer: Option C
Question: The average age of applicants for a new job is 30, with a standard deviation of 8. The hiring manager is only willing to accept applicants whose age is within one standard deviation of the average age. Assuming that all applicants' ages are integers and that the endpoints of the range are included, what is the maximum number of different ages of the applicants?
A.8
B.16
C.17
D.18
Answer: C.17
Explanation: Minimum age = Average - 1 Standard deviation = 30 - 8 = 22
Maximum age = average + 1 Standard deviation = 30+ 8 = 38
Maximum number of different ages of the applicants = 38 - 22 + 1 = 17
Answer C
Question: If m and n are the roots of the quadratic equation x^2−(2√5)x−2=0, the value of m2+n2 is:
A.18
B.20
C.22
D.24
Answer: D.24
Explanation: Product of root, MN = C/A = -2/1 = -2
Sum of root, M+N = -B/A = -(-2\sqrt{5}/1 )= 2\sqrt{5}
(M+N)^2 = M^2 + N^2 + 2MN = 4*5 = 20
2MN = -2(2) = -4
M^2 + N^2 = 20 + 4 = 24
ANSWER:D
Question: If x^2 + y^2 = 16 and xy = 3, then (x − y)^2 =
A.8
B.11
C.10
D.17
Answer: C.10
Explanation: but you cannot take xy+ 3 to mean xy=-3..
only if xy+3=0, it will mean xy=-3..
rest your solution is perfect and you will get your correct answer as 16-2*3=10..
Answer C
Question: At Veridux Corporation, there are 250 employees. Of these, 90 are female, and the rest are males. There are a total of 40 managers, and the rest of the employees are associates. If there are a total of 150 male associates, how many female managers are there?
A.15
B.20
C.25
D.30
Answer: D.30
Explanation: 250 Employees:
90 Male, 160 Female
40 Managers, 210 Associates
150 Male Associates implies 60 Female Associates which means the remaining 30 females must be Managers
D. 30
Question: A man takes 3 hours 45 minutes to row a boat 30 km downstream of a river and 2 hours 30 minutes to cover a distance of 5 km upstream. Find the speed of the current.
A.1 km/hr
B.2 km/hr
C.3 km/hr
D.4 km/hr
Answer: C.3 km/hr
Explanation: Explanation:
First of all, we know that
speed of current = 1/2(speed downstream - speed upstream) [important]
So we need to calculate speed downstream and speed upstream first.
Speed = Distance / Time [important]
Speed upstream =(30/3 3/4)km/hr
=8 km/hr
Speed Downstream = (5/2 1/2)km/hr
=2km/hr
So speed of current = 1/2(8−2)
=3 km/hr
Option C
Question: There are 7 man and 5 women sitting in a circle, find the all possible way so that two women wont sit together?
A.6!*7P5
B.6!*7P4
C.6!*7P3
D.5!*7P5
Answer: A.6!*7P5
Explanation: 7 men can sit in a circle in (7-1)!= 6! ways
no two women sit together,so woman have to sit alternate to men
there will be 7 places,in which 5 women have to sit
so women can sit in 7 places as 7P5 ways
reqd ways= 6!*7P5
ANSWER:A
Question: In a stockpile of products produced by three machines M1, M2 and M3, 40% and 30% were manufactured by M1 and M2 respectively. 3% of the products of M1 are defective, 1% of products of M2 defective, while 90% of the products of M3 III are not defective. What is the percentage of defective in the stockpile?
A.3%
B.5%
C.4.5%
D.4%
Answer: C.4.5%
Explanation: Explanation :
Let there be 100 products in the stockpile. 40% and 30% were manufactured by M1 and M2 respectively. So, 30% are manufactured by M3.
Products from M1 = 40, from M2 = 30 and from M3 = 30.
Number of defective products from M1 = 0.03 x 40 = 1.2, from M2 = 0.01 x 30 = 0.3 and from M3 = 0.1 x 30 = 3
Therefore, total number of defective products = 4.5.
Answer : C
Question: Convert the 8/36 m/s into kilometers per hour?
A.0.8 kmph
B.9.9 kmph
C.1.3 kmph
D.1.2 kmph
Answer: A.0.8 kmph
Explanation: 8/36 m/s = 8/36 * 18/5 = 8/10
= 0.8 kmph.
Answer: A
Question: Bill made a profit of 10% by selling a product. If he had purchased that product for 10% less and sold it at a profit of 30%, he would have received $42 more. What was his original selling price?
A.$480
B.$570
C.$660
D.$720
Answer: C.$660
Explanation: Let P be the original purchase price of the product.
Bill originally sold the product for 1.1*P.
In the second scenario, the purchase price is 0.9*P.
A 30% profit means the selling price would be 1.3*0.9*P = 1.17*P
Thus, according to the information in the question, 1.17P - 1.1P = 42
0.07 = 42
P = 600
The original selling price was 600*1.1 = 660.
The correct answer is C.
Question: If X is the set of prime single-digit numbers and Y is a set containing each of the numbers in set X raised to the power of 2, how much greater is the median of set Y than the median of set X?
A.2
B.4
C.9
D.13
Answer: D.13
Explanation: set X={2,3,5,7} set of prime single digit numbers
set Y={4,9.25.49} each of the numbers in set X raised to the power of 2
Median set X= (3+5)/2= 4
Median set Y= (9+25)/2= 17
Required set Y - set X= 13
ANSWER:D
Question: A merchant marks his goods up by 20% and then offers a discount of 10% on the marked price. What % profit does the merchant make after the discount?
A.8%
B.10%
C.21%
D.15%
Answer: A.8%
Explanation: Let the price be 100.
The price becomes 120 after a 20% markup.
Now a discount of 10% on 120.
Profit=108-100
8%
answer A
Question: A started a business with an investment of Rs. 70000 and after 3 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 43000, then the share of B is?
A.33888
B.36000
C.27778
D.27772
Answer: B.36000
Explanation: Ratio of investments of A and B is (70000 * 12) : (120000 * 9) = 7 : 36
Total profit = Rs. 43000
Share of B = 36/43 (43000) = Rs. 36000
Answer: B
Question: If 3x+y=40, 2x-y=20, for integers of x and y, 3y^2=?
A.2
B.48
C.0
D.10
Answer: B.48
Explanation: 3x+y = 40
2x-y = 20
5x = 60
x = 12
y = 4
3y^2 = 3*16=48
Answer is B
Question: At a certain fast food restaurant, Brian can buy 3 burgers, 7 shakes and 1 order of fries for exactly Rs 120. At the same place it would cost Rs 164.5 for 4 burgers, 10 shakes and 1 order of fries. How much would it cost for an ordinary meal of 1burgers, 1 shakes and 1 order of fries ?
A.Rs. 31
B.Rs 41
C.Rs 21
D.Cannot be determined
Answer: A.Rs. 31
Explanation: Explanation :
Let the cost of 1 burger, 1 shake and 1 fries be x, y
and z.
Then
3x + 7y + z = 120 ... (i)
4x + 10y + z = 164.5 ... (ii)
x + 3y = 44.5 ... (iii) [ After subtracting (i) from (ii) ]
Multiplying (iii) by 4 and subtracting (ii) from it, we find
2y – z = 13.5 ...(iv)
Subtracting (iv) from (iii), we get x + y + z = 31.
Answer : A
Question: If 0.764 B = 1.236 A, then what is the value of (B - A)/(B + A) ?
A.0.764
B.0.236
C.2
D.0.472
Answer: B.0.236
Explanation: Answer
Given, 0.764 B = 1.236 A
⇒ B/A = 1.236 / 0.764
Now, (B - A)/(B + A) = (B/A - 1) / (B/A + 1)
= (1.236/0.764 - 1) / (1.236/0.764 + 1)
= (1.236 - 0.764)/(1.236 + 0.764)
= 0.472/2.000
= 0.236
Correct Option: B
Question: A certain car dealership offers its newest model in ten exterior and ten interior colors. If the ten interior colors are identical to the ten exterior colors, and the dealership sells every pair of colors except those that would result in a car with an identically colored interior and exterior, how many different color combinations are possible?
A.45
B.81
C.90
D.10!/2!
Answer: C.90
Explanation: The question says there are 10 different colors.
Since interior and exterior are to be painted with different colors, the order is important while counting the color combination.
Therefore, the number of possible ways can be found out by permutation of 2 colors out of 10 colors.
10P2 = 10!/(10-2)! = 10!/8! = 90 [10P2 = 10C2*2!]
Answer: (C
Question: A and B rent a pasture for 10 months. A put in 80 cows for 7 months. How many can B put in for the remaining 3 months, if he pays half as much again as A?
A.2: 7
B.2: 0
C.2: 4
D.2: 3
Answer: D.2: 3
Explanation: 80* 7: x* 3 = 1:1 1/2
560: 3x = 2: 3
x = 280.Answer:D
Question: On a certain day, Tim invested $500 at 10 percent annual interest, compounded annually, and Lana invested 900 at 5 percent annual interest, compounded annually.The total amount of interest earned by Tim’s investment in the first 2 years was how much greater than the total amount of interest earned by Lana’s investment in the first 2 years?
A.$5
B.$12.75
C.$51.75
D.$100.75
Answer: B.$12.75
Explanation: Compounded annually means that the interest is applied once per year. One can have 10% annual interest compounded monthly - in this case 10%/12 would be applied each month, or 10% annual interest compounded daily etc.
With respect to the problem at hand, at the end of two years, Tim would have
500(1.10)^2 = 500(1.21) = 605
and Lana would have
900(1.05)^2 = 900(1.1025) = 992.25
Thus, Tim earned 105 dollars, while Lana earned 92.25 dollars
The difference is $12.75 and the answer is B.
Question: If the sum of a set of 5 different positive prime numbers is 94, what is the difference between smaller 2 prime numbers between them?
A.6
B.4
C.5
D.9
Answer: C.5
Explanation: All prime numbers apart from 2 are odd.
Even + Even = Even
Odd + Even = Odd
Odd + Odd = Even
We are given 5 different prime numbers, whose sum is 94 i.e even
If we include 2, we will have 4 odd prime numbers and one even.
This sum would be odd
If we exclude 2, we will have 5 odd numbers.
This sum would be even
Hence 2 is included.
The possible 5 no. are = 11+7+2+43+31 = 94
difference between smaller 2 prime numbers between them = 7 - 2 = 5
Ans - C
Question: If 6 (A's capital) = 8 (B's capital) = 12 (C's capital). Then the ratio of their capitals is?
A.20:15:16
B.4:3:1
C.4:3:2
D.20:15:11
Answer: C.4:3:2
Explanation: 6A = 8B = 12 C
A:B:C = 1/6:1/8:1/12
= 4:3:2
Answer: C
Question: How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
A.22
B.30
C.88
D.26
Answer: B.30
Explanation: Speed of train relative to man = 63 - 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 500 * 3/50
= 30 sec.
Answer: B
Question: The ratio of two numbers is 3:4 and their sum is 35. The greater of the two numbers is?
A.12
B.20
C.16
D.17
Answer: B.20
Explanation: 3:4
Total parts = 7
= 7 parts --> 35 (7 Ã— 5 = 35)
= 1 part ---->5 (1 Ã— 5 = 5)
= The greater of the two number is = 4
= 4 parts ----> 20 (4 Ã— 5 = 20)
B)
Question: Tough and Tricky questions: Exponents.
If a and b are positive integers and x = 26^a and y = 9^b, which of the following is a possible units digit of xy?
A.1
B.6
C.5
D.7
Answer: B.6
Explanation: Only Units digit of X and Y contribute to the Units digit of XY.
Finding all values ofXfor positive values ofa
When,
a=1; X=26
a=2; X=676
a=3; X=17576........ Units digit repeat in a cycle of 6,6,6,6......
Similarly, Finding all values of Y for positive values of b
When,
b=1; Y=9
b=2; Y= 81
b=3; Y= 729....... Units digit repeat in cycle of 9,1,9,1....
So, possible value of Units digit of XY can be found by considering all possibilities of Units digit of X and Y
When X=6 and Y=9: Units digit of XY = 4
When X=6 and Y=1: Units digit of XY = 6
When X=6 and Y=9: Units digit of XY = 4
When X=6 and Y=1: Units digit of XY = 6
Only two possibilities for Units digit of XY i.e. 4 and 6.
Only 6 is given in answer choices, therefore answer is B
Question: A coin is tossed live times. What is the probability that there is at the least one tail?
A.31/32
B.31/37
C.31/67
D.31/17
Answer: A.31/32
Explanation: Let P(T) be the probability of getting least one tail when the coin is tossed five times.
= There is not even a single tail.
i.e. all the outcomes are heads.
= 1/32 ; P(T) = 1 - 1/32
= 31/32
Answer: A
Question: A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from opposite direction in 6 seconds. What is the speed of the second train ?
A.48 km/hr
B.54 km/hr
C.66 km/hr
D.82 km/hr
Answer: D.82 km/hr
Explanation: Let speed of d second train= xkm/hr
Distance covered=(108+112)=220m=0.22km
Time=6sec= 6/3600hr =1/600hr
So
1/600hr= 0.22km/(50+x)
x=82km/hr
answer :D
Question: The length of the bridge, which a train 140 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
A.328
B.279
C.235
D.288
Answer: C.235
Explanation: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (140 + X)/30 = 25/2 ==> 2(140 + X) = 750 ==> X = 235 m.Answer: C
Question: If 2^x + 2^y = x^2 + y^2, where x and y are non negative and non zero integers, what is the greatest possible value of x + y possible from options below?
A.4
B.5
C.2
D.3
Answer: A.4
Explanation: x + y for x and y 2^x + 2^y = x^2 + y^2
A. x= y x=y=2 4 + 4 = 4 + 4 right
B. x=2, y=3 4 + 8 = 4 + 9 wrong
C. x=1, y=1 2 + 2 = 1 + 1 wrong
D. x=2, y =1 4 + 2 = 4 + 1 wrong
E. as option A is correct E is wrong
My answer is A.
Question: A jar contains only red, yellow, and orange marbles. If there are 1 red, 5 yellow, and 4 orange marbles, and 3 marbles are chosen from the jar at random without replacing any of them, what is the probability that 2 yellow, 1 red, and no orange marbles will be chosen?
A.1/60
B.1/45
C.2/45
D.3/22
Answer: B.1/45
Explanation: I started by finding the 2 probabilities, without calculation, like this:
P(YYR)
P(YRY)
P(RYY)
I calculated the first one and ended in 1/22. I looked at the answer choices at this point and saw answer D: 1/45.
This helped me realise that for the 3 possible orderings the probabbility is the same. So, it should be (1/45)*(1), which indeed is 1/45.
B
Question: The average age of husband, wife and their child 3 years ago was 25 years and that of wife and the child 5 years ago was 18 years. The present age of the husband is:
A.34 Years
B.36 Years
C.38 Years
D.39 Years
Answer: C.38 Years
Explanation: Sum of the present ages of husband, wife and child = (25 x 3 + 3 x 3) years = 84 years.
Sum of the present ages of wife and child = (18 x 2 + 5 x 2) years = 46years.
Husband's present age = (84 - 46) years = 38 years.
answer : C