RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
A.217
B.444
C.728
D.278
Answer: B.444
Explanation: 1h ----- 5
? ------ 60
12 h
RS = 16 + 21 = 37
T = 12
D = 37 * 12 = 444
Answer: B
Question: A, B and C have Rs.700 between them, A and C together have Rs.300 and B and C Rs.600. How much does C have?
A.200
B.250
C.300
D.350
Answer: A.200
Explanation: A+B+C = 700
A+C = 300
B+C =600
--------------
A+B+2C = 900
A+B+C = 700
----------------
C = 200
ANSWER:A
Question: If the average of e, b, c, 14 and 15 is 12. What is the average value of e, b, c and 29
A.12
B.13
C.14
D.15
Answer: D.15
Explanation: e+b+c+14+15 = 12*5 = 60
=>e+b+c = 60-29 = 31
e+b+c+29 = 31+29= 60
Average = 60/4 = 15
Answer D
Question: The diagonals of a rhombus are 30 cm and 12 cm. Find its area?
A.176
B.190
C.180
D.278
Answer: C.180
Explanation: 1/2 * 30 * 12
= 180
Answer:C
Question: Three years ago the average age of a class of six members was 22 years. A boy have been added, the average age of the class is the same today. What is the age of the boy?
A.A)1
B.B)2
C.C)3
D.D)4
Answer: D.D)4
Explanation: 6 * 25 = 150
7 * 22 = 154
`4
D
Question: Consider a lady took a loan from a bank at the rate of 12% p.a. simple interest. After 3 years she had to pay Rs. 5400 interest only for the period. The principal amount borrowed by her was
A.Rs. 2000
B.Rs. 10000
C.Rs. 15000
D.Rs. 20000
Answer: C.Rs. 15000
Explanation: Explanation :
Principal = Rs. (100×5400 / 12×3)
=> Rs. 15,000.
Answer : C
Question: A, B and C enter into a partnership. They invest Rs. 1,20,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. In what ratio will the profit be shared at the end of 3 years ?
A.9 : 4 : 8
B.9 : 4 : 7
C.3 : 4 : 2
D.3 : 4 : 1
Answer: B.9 : 4 : 7
Explanation: A : B : C = (120000 x 36) : (80000 x 12 + 40000 x 24) : (120000 x 24 + 40000 x 12)
= 432 : 192 : 336
= 9 : 4 : 7.
Answer: B
Question: If w is the square of a positive integer, which of the following must be equal to the square of the next positive integer?
A.√n + 1
B.n + 1
C.n^2 + 1
D.w + 2√w + 1
Answer: D.w + 2√w + 1
Explanation: If w is the square of a positive integer, which of the following must be equal to the square of the next positive integer?
w = (x)^2 where x is a positive integer
To calculate -
(x+1)^2 = x^2 + 2x + 1
root(w) = x
Ans - w + 2 root(w) + 1
This should beD
Question: Apple costs X rupees per kilogram for first 30 kgs and Y rupees per kilogram for each additional kilogram. If the price of 40 kilograms is 420 and for 50 kgs of Apples is 540 then the cost of first 10 kgs of Apples is
A.100
B.3.66
C.3.6
D.3.62
Answer: A.100
Explanation: Ans: By framing equations we get
30X+10Y=420
30X+20Y=540
Eliminate Q by multiplying the first equation by 2 and subtracting second equation from the first
60x+20y = 840 -
30x+20y = 540
=> 30x = 300 => x = 10
Then we get X = 10
Cost of 10 kgs of apples = 10x 10 = 100
Answer:A
Question: A cricket player whose bowling average was 24.85 runs per wicket, takes 5 wicket for 52 runs in a match. Due to this his average decreases by 0.85. What will be the number of wickets taken by him till the last match?
A.64
B.72
C.85
D.96
Answer: C.85
Explanation: Average = Total Runs / Total wickets
Total runs after last match = 24.85w + 52
Total wickets after last match = w + 5
(24.85w + 52) / (w + 5) = 24.85 - 0.85 = 24
w = 80
so total wickets aftr last match = w+5 = 85
ANSWER:C
Question: A box contains ten bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that at least one bulb is good?
A.1/6
B.16/625
C.609/625
D.5/6
Answer: C.609/625
Explanation: Required probability
= 1 - 16/625
= 609/625
Answer: C
Question: A bag contains 10 balls numbered from 0 to 9. the balls are such that the person picking a ball out of the bag is equally likely to pick anyone of them. A person picked a ball and replaced it in the bag after noting its number. He repeated this process 2 more times. What is the probability that the ball picked first is numbered higher than the ball picked second and the ball picked second is numbered higher than the ball picked third?
A.72/100
B.3/25
C.4/5
D.1/6
Answer: B.3/25
Explanation: Explanation :
Let, the number of the ball picked first =a, second =b and third =c and these three numbers a, b and c are distinct.
Three distinct ball can be picked in (10×9×8) ways.
The order of a, b and c can be as follows:-
(i) a>b>c.
(ii) a>c>b.
(iii) b>c>a.
(iv) b>a>c.
(v) c>a>b.
(vi) c>b>a.
They will occur equal number of times. So, the number of ways in which (a>b>c) are :-
=>1/6 x 10 x 9 x 8.
=>120.
Hence, the required probability is :-
=>120 / (10x10x10).
=>3/25.
Answer : B
Question: In a certain pond, 100 fish were caught, tagged, and returned to the pond. A few days later, 100 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond?
A. 400
B. 625
C. 1,250
D. 2,500
Answer: D. 2,500
Explanation: total fish = x
percentage of second catch = (2/100)*100 = 2%
so, x * 2% = 50
x = 2500 ans. D
Question: P has $21 more than what Q and R together would have had if both B and C had 1/5 of what P has. How much does P have?
A.$35
B.$36
C.$37
D.$38
Answer: A.$35
Explanation: P = (2/5)*P+21
(3/5)*P=21
P=35
The answer is A.
Question: A circle graph shows how the MegaTech corporation allocates its Research and Development budget: 14% microphotonics; 24% home electronics; 10% food additives; 29% genetically modified microorganisms; 8% industrial lubricants; and the remainder for basic astrophysics. If the arc of each sector of the graph is proportional to the percentage of the budget it represents, how many degrees of the circle are used to represent basic astrophysics research?
A.8°
B.10°
C.18°
D.54°
Answer: D.54°
Explanation: 14% microphotonics;
24% home electronics;
10% food additives;
29% genetically modified microorganisms;
8% industrial lubricants;
100-(14+24+10+29+8)=15% basic astrophysics.
15% of 360° is 54°.
Answer: D.
Question: If x = 147, which of the following numbers could be subtracted from x to create a sum that is divisible by 6?
A.1
B.2
C.3
D.4
Answer: C.3
Explanation: Divisibility rule of 6: A number is divisible by 6 if it is divisible by both 2 and 3
Divisibility rule of 3: A number is divisible by 3 if the sum of the digits is divisible by 3
x = 147. We need to make this number even in order for it to be divisible by 2.
Hence we need to subtract an odd number from it.
Hence left over options are A, C, and E
147 - 1 = 146. Sum of digits = 11.
This is not divisible by 3.
147 - 3 = 144. Sum of digits = 9
This is divisible by 3.
Hence 3 should be subtracted from 147 to make the resultant a multiple of 6.
Correct Option: C
Question: If log 27 = 1.467, then the value of log 9 is:
A.0.978
B.0.945
C.0.954
D.0.958
Answer: A.0.978
Explanation: log 27 = 1.467
log (3cube ) = 1.467
3 log 3 = 1.467
log 3 = 0.489
log 9 = log(3square ) = 2 log 3 = (2 x 0.489) = 0.978.
Answer: Option A
Question: If the integer x is rounded to the nearest hundred, the result represents a 66 2/3 % increase over the value obtained when x is rounded to the nearest ten. which of the following is a possible value of x?
A.64
B.67
C.99
D.133
Answer: A.64
Explanation: 100= (x-y) + 2/3(x-y)
300=5(x-y)
x-y =60
64 rounded to nearest tenth will result in 60.
Answer A
Question: How many numbers between 1 and 100 are divisible by 7 ?
A.9
B.11
C.17
D.14
Answer: D.14
Explanation: No. of divisible by 7 7, 14 --------- 98, n = a + (N - 1)d
98 = 7 + (N - 1) 7, 98 = 7 + 7N - 7
98/7= N = 14
Answer:D
Question: A sum of money is to be divided among Ann, Bob and Chloe. First, Ann receives $4 plus one-half of what remains. Next, Bob receives $4 plus one-third of what remains. Finally, Chloe receives the remaining $32. How much money N did Bob receive?
A.20
B.22
C.24
D.26
Answer: B.22
Explanation: Notice that we need not consider Ann's portion in the solution. We can just let K = the money REMAINING after Ann has received her portion and go from there.
Our equation will use the fact that, once we remove Bob's portion, we have $32 for Chloe.
So, we getK - Bob's $ = 32
Bob received 4 dollars plus one-third of what remained
Once Bob receives $4, the amount remaining is K-4 dollars. So, Bob gets a 1/3 of that as well.
1/3 of K-4 is (K-4)/3
So ALTOGETHER, Bob receives4 + (K-4)/3
So, our equation becomes:K -[4 + (K-4)/3 ]= 32
Simplify to get: K - 4 - (K-4)/3 = 32
Multiply both sides by 3 to get: 3K - 12 - K + 4 = 96
Simplify: 2K - 8 = 96
Solve: K = 52
Plug this K-value intoK - Bob's $ = 32to get: 52 - Bob's $ = 32
So, Bob's $ N= 20
Answer:
B
Question: If d is a positive even integer, and n and m are consecutive integers, then (n - m)^d/(m - n)d =
A.-2
B.-1
C.0
D.1
Answer: D.1
Explanation: d= +ve even integer
Since,n and m are consecutive integers , their difference will be 1
((n-m)^d)/((m-n)d)= ((n-m)/(m-n))^d = (-1)^d
Since we are raising the difference of n and m to power d , which is even , the answer will be 1 .
Answer D
Question: A sum of $800 amounts to $920 in 3 years at simple interest. If the interest rate is increased by 3% it would amount to how much ?
A.$506
B.$774
C.$992
D.$854
Answer: C.$992
Explanation: S.I = 920-800 = 120
P = $800
T = 3 years
R = 100*120 / 800*3 = 5%
New rate = 5+3 = 8%
New S.I. = 800*8*3/100 = $192
New amount = 800+192 = $992
Answer is C
Question: Expenditures of a Company (in Lakh Rupees) per Annum Over the given Years.
Year	Item of Expenditure
Salary	Fuel and Transport	Bonus	Interest on Loans	Taxes
1998	288	98	3.00	23.4	83
1999	342	112	2.52	32.5	108
2000	324	101	3.84	41.6	74
2001	336	133	3.68	36.4	88
2002	420	142	3.96	49.4	98
Total expenditure on all these items in 1998 was approximately what percent of the total expenditure in 2002?
A.62%
B.69.45%
C.70%
D.71%
Answer: B.69.45%
Explanation: Required percentage
=	[	(288 + 98 + 3.00 + 23.4 + 83)	x 100	]	%
(420 + 142 + 3.96 + 49.4 + 98)
=	[	495.4	x 100	]	%
713.36
~= 69.45%.
B)
Question: The area of sector of a circle whose radius is 12 metro and whose angle at the center is 54Â° is?
A.52.6
B.52.9
C.67.9
D.52.1
Answer: C.67.9
Explanation: 54/360 * 22/7 * 12 * 12 = 67.9 m2
Answer: C
Question: What is 1! + 2! + ... + 10! ?
A.4,037,910
B.4,037,913
C.4,037,915
D.4,037,916
Answer: B.4,037,913
Explanation: All options have different Unit digit so calculating unit digit of the sum above will suffice
Unit digit of (1! + 2! + 3! + 4! + 5! + 6!+... + 10!) = 1 + 2+ 6 + 4 + 0 + 0 + 0 + 0+ 0 + 0 = Unit digit 3, Hence
every Factorial of an integer greater than 4 will have Unit digit 0 as it will be a multiple of 10
Answer: option B
Question: There are two groups of students in the sixth grade. There are 20 students in group A, and 80 students in group B. If, on a particular day, 20% of the students in group A forget their homework, and 15% of the students in group B forget their homework, then what percentage of the sixth graders forgot their homework?
A.13%
B.14%
C.15%
D.16%
Answer: D.16%
Explanation: Number of students in group A = 20
students who forget homework in group A = 20 % of 20 = 4 students
Number of students in group B = 80
students who forget homework in group B = 15 % of 80 = 12 students
Total number of students = 20 + 80 = 100
students who forgot homework = 4 + 12 = 16 students
percentage of students who forget homework = 16/100 * 100 = 16%
Answer: D
Question: What is the value of (44444445*88888885*44444442+44444438)/44444444^2
A.88888883
B.88888827
C.16992677
D.88888237
Answer: A.88888883
Explanation: Ans: A
Let x = 44444444
(x+1)×(2x−3)×(x−2)+(x−6)x2(x+1)×(2x−3)×(x−2)+(x−6)x2
(x2−x−2)×(2x−3)+(x−6)x2(x2−x−2)×(2x−3)+(x−6)x2
2x3−2x2−4x−3x2+3x+6+x−6x22x3−2x2−4x−3x2+3x+6+x−6x2
2x3−5x2x2=2x−52x3−5x2x2=2x−5
Substituting the value of x in 2x - 5, we get 88888883
Answer:A
Question: Find average speed if a man travels at speed of 20km/hr up and 26km/hr dawn at an altitude of 240m.
A.25.8
B.26.8
C.22.6
D.28.8
Answer: C.22.6
Explanation: avg speed=2*x*y/(x+y)
=2*20*26/(20+26)=22.6
ANSWER:C
Question: Find the remainder Y when 12^190 is divided by 1729 ?
A.12
B.1
C.1728
D.1717
Answer: D.1717
Explanation: 12^(190) can be written as. ((12^3)^63)* 12. 12^3 when divided by 1729 gives a remainder Y -1. so in the numerator we have -12. Now acccording to remainder theorm the answer will be 1729-12=1717.D
Question: What is the perimeter of a square with area 9p^2/36 ?
A.3p/4
B.3p^2/4
C.2p
D.3p^2
Answer: C.2p
Explanation: Area of square, (side)^2 = (3p/6)^2
Therefore side of the square = 3p/6
Perimeter of square = 4*side = 4* (3p/6) = 2p
Answer is C.
Question: Find the simple interest on Rs.500 for 9 months at 6 paisa per month?
A.238
B.270
C.987
D.167
Answer: B.270
Explanation: I = (500*9*6)/100 = 270
Answer:B
Question: A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 20%?
A.600
B.267
C.132
D.277
Answer: A.600
Explanation: Cost price = Rs.500
profit = 20% of 500 = Rs.100
Selling price = Cost price + Profit
= 500 + 100 = 600
Answer:A
Question: Two vessels A and B contain spirit and water in the ratio 5 : 2 and 7 : 6 respectively. Find the ratio in which these mixture be mixed to obtain a new mixture in vessel C containing spirit and water in the ration 8 : 5?
A.4 : 3
B.3 : 4
C.5 : 6
D.7 : 9
Answer: D.7 : 9
Explanation: Let the C.P. of spirit be Re. 1 litre.
Spirit in 1 litre mix. of A = 5/7 litre, C.P. of 1 litre mix. in A = Re. 5/7
Spirit in 1 litre mix. of B = 7/13 litre, C.P. of 1 litre mix. in B = Re. 7/13
Spirit in 1 litre mix. of C = 8/13 litre, Mean price = Re. 8/13.
By the rule of alligation, we have:
Required ratio = 1/13 : 9/91 = 7 : 9.
Answer D
Question: Three numbers are in the ratio of 2 : 3 : 4 and their L.C.M. is 240. Their H.C.F. is:
A.30
B.20
C.40
D.60
Answer: B.20
Explanation: Explanation:
Let the number be 2x, 3x and 4x
LCM of 2x, 3x and 4x = 12x
12x = 240
=> x = 240/12 = 20
HCF of 2x, 3x and 4x = x = 20
Answer: Option B
Question: A box contains 40 balls, numbered from 1 to 40. If three balls are selected at random and with replacement from the box, what is the probability that the sum of the three numbers on the balls selected from the box will be odd?
A.1/4
B.3/8
C.1/2
D.5/8
Answer: A.1/4
Explanation: I don't think order matters in this case, because 2 + 2 + 1 = 2 + 1 + 2
My answer is: 1/4
A
Question: How many even prime numbers are there less than 50?
A.15
B.1
C.2
D.16
Answer: B.1
Explanation: 2 is the only even prime number
Answer is B
Question: The total number of plums that grow during each year on a certain plum tree is equal to the number of plums that grew during the previous year, less the age of the tree in years (rounded down to the nearest integer). During its 4th year, the plum tree grew 50 plums. If this trend continues, how many plums will it grow during its 6th year?
A.36
B.41
C.38
D.40
Answer: B.41
Explanation: 1st year : 0-1 (age), we take age = 0 (as the question says that we have to(rounded down to the nearest integer))
2ndyear : 1-2 (age), we take age = 1
3rd year : 2-3 (age), we take age = 2
4th year : 3-4 (age), we take age = 3
5th year : 4-5 (age), we take age = 4
6th year : 5-6 (age), we take age = 5
Thus for the 4th year = 50,
5th year = 50 -4 = 46
6th year = 46-5 = 41
The correct answer is B.
Question: Jill, who lives in City C, plans to visit 3 different cities, M, L, and S. She plans to visit each city exactly once and return to City C after the 3 visits. She can visit the cities in any order. In how many different orders can she visit the 3 cities?
A.3
B.6
C.8
D.9
Answer: B.6
Explanation: 3! = 6
M	L	S	C
M	S	L	C
L	M	S	C
L	S	M	C
S	M	L	C
S	L	M	C
She can visit the cities in any order. Number of ways of arranging the three cities is 3! = 6 ways. Hence B.
Question: If 4 (A's capital) = 6 (B's capital) = 10 (C's capital), then out of a profit of Rs. 372, C will receive
A.60
B.51
C.900
D.72
Answer: D.72
Explanation: Explanation:
Let 4A = 6B = 1OC = k. Then, A = k/4, B = k/6, and C =k/10 .
A : B :C = k/4 : k/6 : k/10 = 15 : 10 : 6.
Hence, C's share (372 * 6/31) = Rs, 72.
Answer: D) Rs.72
Question: If y exceeds x by 25%, then x is less than y by?
A.22%
B.67%
C.20%
D.16%
Answer: C.20%
Explanation: X=100	y=125
125--------25
100--------? => 20%
Answer: C
Question: In a 500 member association consisting of men and women, exactly 20% of men and exactly 50 % women are homeowners. What is the least number of members who are homeowners?
A.149
B.147
C.101
D.143
Answer: C.101
Explanation: Solution simple
Out of 500 20% are male i.e 100 and 50% are female i.e 250 , so total homeowner is 350.
Now min number homeowner is 100 and max is 250 so question ask us to find least and 101 has least value among all option.
So ans is 101.
Ans: C
Question: 7/9 of 3/5 of a number is greater than 2/9 of 5/6 of the same number by 152. What is half of that number?
A.165
B.195
C.240
D.270
Answer: D.270
Explanation: Let no. be x
7/9*3/5*x - 2/9*5/6*x =152
by further solving
21x/45- 10x/54=152
114x/405=152
x=540
we have to find x/2
=540/2=270
ANSWER:D
Question: In a class of 120 students, 25 did not opt for math. 10 did not opt for science and 2 did not opt for either. How many students of the class opted for both math and science?
A.63
B.95
C.77
D.87
Answer: D.87
Explanation: 120 students total
25 did not opt for math
10 did not opt for science
2 did not opt for either
Total of 95 students in math and 8 did not opt for sci but did for math
95-8=87
87 students of the class opted for both math and science
Answer:
D. 87
Question: A man invested Rs. 1552 in a stock at 97 to obtain an income of Rs. 128. The dividend from the stock is:
A.8%
B.6%
C.9%
D.10%
Answer: A.8%
Explanation: Rs 1552 income = Rs 128
By investing Rs 97 income = 128/1552*97 = Rs 8
Divdend = 8%
ANSWER A
Question: A Scooter is sold for Rs. 65000, a shop keeper gains 25%. During a clearance sale, the shopkeeper allows a discount of 10% on the marked price. His gain percent during the sale is?
A.25%
B.12.5%
C.22.5%
D.15%
Answer: B.12.5%
Explanation: Explanation:
Marked price = Rs. 65000
C.P. = 100/125 * 65000 = Rs. 52000
Sale price = 90% of Rs. 65000 = Rs. 58500
Required gain % = 650/52000 * 100 = 12.5%.
Answer: B
Question: How many 6 digit number can be formed from the digits 1, 2, 3, 4, 5, 6 which are divisible by 4 and digits are not repeated?
A.192
B.122
C.140
D.242
Answer: A.192
Explanation: Solution
For the number to be divisible by 4, the last two digits must be any of 12, 24, 16, 64, 32, 36, 56 and 52. The last two digit places can be filled in 8 ways. Remaining 3 places in 4P3 ways.
Hence no. of 5 digit nos. which are divisible by 4 are 24 × 8 = 192
Answer A
Question: The current birth rate per thousand is 50, where as corresponding death rate is 10 per thousand. The net growth rate in terms of population increase in percent is given by?
A.2%
B.3%
C.4%
D.6%
Answer: C.4%
Explanation: Net growth on 1000 = 50-10 = 40
Net growth on 100 = 40*100/1000 = 4%
Answer is C
Question: A machine puts c caps on bottles in m hours. How many hours will it take to put caps on b bottles?
A.60bm/c
B.bm/60c
C.bc/60m
D.bm/c
Answer: D.bm/c
Explanation: A machine puts c caps on bottles in m minutes.
So, the machine puts 1 cap in m/c minutes
To put caps on b bottles, the machine will take bm/c hours
Answer : D
Question: A certain cube floating in a bucket of water has between 80 and 90 percent of its volume below the surface of the water. If between 6 and 13 cubic centimeters of the cube's volume is above the surface of the water, then the length of a side of the cube is approximately
A.4
B.5
C.7
D.8
Answer: A.4
Explanation: If sides are 7, vol=7^3=343
80%= 274.4, 90%=308.7
so vol above water, between 68.6 and 34.3 -->too big
If side are 4, vol = 64
80%=51.2, 90%=57.6
vol above water between 12.8 and 6.4
So 4 should be the answer.
Check option C,
If sides are 5, vol = 125
80%= 100, .90%=112.5
vol above water between 12.5-25
(Sides are 4 cubic centimeters)
A
Question: the radius of the circle is reduced from 5cm to 4cm then the % change of area .
A.36%
B.37%
C.35%
D.38%
Answer: A.36%
Explanation: for 5cm -> pi*r^2 --> 3.14 * 5 ^ 2 -> 78.539
for 4cm -> pi*r^2 --> 3.14 * 4 ^ 2 -> 50.265
%change -> (1- 50.265/78.539)*100= 36
ie 36%
ANSWER:A
Question: Sum of the squares of three numbers is 138 and the sum of their products taken two at a time is 131. Find the sum?
A.20
B.22
C.25
D.27
Answer: A.20
Explanation: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 138 + 2* 131
a + b + c = √400 = 20
A
Question: Balls of equal size are arranged in rows to form an equilateral triangle. the top most row consists of one ball, the 2nd row of two balls and so on. If 1104 balls are added, then all the balls can be arranged in the shape of square and each of the sides of the square contain 8 balls less than the each side of the triangle did. How many balls made up the triangle?
A.2145
B.2209
C.2878
D.1210
Answer: A.2145
Explanation: As expected, this question boils down to 2 equation,
Consider total number of Balls in Triangle = T and number of balls in last row = x.
1+2+3+...+x = T
x(x+1)/2 = T ----(a)
As mentioned in the question, side of a square will be (x-8) and total number of Balls in square will be (T+1104)
(x-8)^2 = T+1104 -----(b)
Now the hardest part of the question will be to solve these 2 equations and this looks like time consuming BUT the easy way will be plug and play. Also, we've to find a value of T (from 5 optiosn given below) which can make a square of a a number. One we know this, it will be a cake walk.
We can see that option A fits this criteria in eq (b). Add - 2145+1104 = 3249 = 57^2 = (x-8)^2 Hence, x = 65.
Cross check by putting in eq (a) = x(x+1)/2 = T = > 65*66/2=2145
Hence, answer is A.
Question: Find the probability that a number selected from numbers 1, 2, 3,..., 30 is a prime number, when each of the given numbers is equally likely to be selected?
A.10/30
B.1/30
C.8/30
D.3/30
Answer: C.8/30
Explanation: Let X be the event of selecting a prime number.
X = {2, 3, 5, 7, 11, 13, 17, 19, 23,29}
n(X) = 10,
n(S) = 30
Hence, the required probability is 10/30.
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 75 km/hr?
A.25
B.30
C.99
D.88
Answer: A.25
Explanation: Speed of train relative to man = 75 - 3 = 72 km/hr.
= 72 * 5/18 = 20 m/sec.
Time taken to pass the man = 500 * 1/20 = 25 sec.
Answer: A
Question: John was thrice as old as Tom 6 yrs back. He will be 5/3 times as old as Tom 6 years hence. How old is Tom today?
A.8
B.10
C.12
D.16
Answer: C.12
Explanation: Sol. RMBflSk -6 = 3 (Ravi - 6) ...(j)
and Rupesh + 6 = | (Ravi + 6) ...(ii)
Solving both the equations we get,
John= 12 years.
C
Question: A dishonest dealer professes to sell goods at the cost price but uses a weight of 840 grams per kg, what is his percent?
A.19
B.25
C.77
D.88
Answer: A.19
Explanation: 840 --- 160
100 --- ? => 19%
Answer:A
Question: A person started from point A to point B and returned back to A with a speed of 60 kmh. If the distance between A and B is 120km, calculate the time he travelled
A.4 hours
B.2 hours
C.3 hours
D.6 hours
Answer: A.4 hours
Explanation: Time = Distance/Speed
Total distance = (from A->B and from B->A) = 120+120=240 km
Speed = 60 kmh
240/60 = 4
Answer: A
Question: If the sum of three consecutive even numbers is 44 more than the average of these numbers, then the largest of these numbers is?
A.24
B.66
C.9
D.7
Answer: A.24
Explanation: ANSWER: 24
Explanation:
Let the smallest of these number be x. The other two numbers are (x + 2) and (x + 4).
x + (x + 2) + (x + 4) = (X + (X+2) + (x+4)) / 3 + 44
3x + 3*(x + 2) + 3*(x + 4) = x + (x + 2) + (x + 4) + 132
9x + 18 = 3x + 138
6x = 120
x = 20
Therefore, the largest number is 24.
ANSWER: A
Question: If a: b :: 3 : 7, then what is (5a+6b): (a-2b)?
A.57:11
B.-57:11
C.11 : 10
D.-11 : 10
Answer: B.-57:11
Explanation: a/b= 3/7
Dividing numerator & denominator of ' (5a+6b)/(a-2b) 'by b,
[5(a/b)+6]/[(a/b)-2]= [5*(3/7)+6]/[(3/7)-2]= -57/11
ANSWER:B