RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: The S.I. on a certain sum of money for 4 years at 12% per annum is half the C.I. on Rs. 6000 for 2 years at 15% per annum. The sum placed on S.I. is?
A.2019.625
B.2017.625
C.2013.625
D.2015.625
Answer: D.2015.625
Explanation: C.I. = [6000 * (1 + 15/100)2 - 6000]= (6000 * 23/20 * 23/20 - 6000) = Rs. 1935.Sum = (967.5 * 100)/(4 * 12)= Rs.2015.625Answer:D
Question: $300 is divided amongst A,B and C so that A may get 2/3 as much as B and C together, B may get 6/9 as much as A and C together, then the share of A is
A.$100
B.$150
C.$125
D.$120
Answer: D.$120
Explanation: A:(B+C) = 2:3
A's share = 300*2/5 = $120
Answer is D
Question: An equal number of desks and bookcases are to be placed along a library wall that is 15 meters long. Each desk is 2 meters long, and each bookshelf is 1.5 meters long. If the maximum possible number of desks and bookcases are to be placed along the wall, then the space along the wall that is left over will be how many meters W long?
A.0.5
B.1
C.1.5
D.2
Answer: B.1
Explanation: Let x be the number of desks and bookcases that are placed along the library wall.
2x + 1.5x < 15
3.5x < 15
Since x is a non negative integer, the largest number x can be is 4.
When x is 4, the desks and bookcases take up 3.5 * 4 = 14m, leaving 1m of empty space.
Thus, I believe the answer is B) 1
Question: Some persons can do a piece of work in 16 days. Two times the number of these people will do half of that work in?
A.3
B.4
C.5
D.6
Answer: B.4
Explanation: 16/ (2 * 2) = 4 days
Answer:B
Question: 35.62 + 408.926 + 48.2 = ?
A.622.441
B.492.243
C.492.746
D.622.443
Answer: C.492.746
Explanation: Explanation :
35.62 + 408.926 + 48.2 = 492.746. Answer : Option C
Question: The arithmetic mean and standard deviation of a certain normal distribution are 10.5 and 1, respectively. What value is exactly 2 standard deviations less than the mean?
A.6
B.8.5
C.11.5
D.12
Answer: B.8.5
Explanation: Mean = 10.5
Two standard deviations is 1 + 1 = 2
There could be two calues for this.
Mean + two standard deviations = 12.5
Mean - Two standard deviations = 8.5
Answer choice has 8.5 and so B is the answer.
Question: How many digits are in the number 50^8 × 8^3 × 11^2 x 10^2?
A.22
B.20
C.21
D.18
Answer: C.21
Explanation: Whenever you are asked to find the number of digits, try to bring the number in multiples of 10. This way, we can wasily calculate the umber of 0's through the powers of 10
50^8 × 8^3 × 11^2 x 10^2 = (5^2*2)^8*2^9*11^2x 10^2 = 5^16*2^17*11^2 x10^2 = 2*11^2*10^16x10^2 = 242*10^18
Hence we would have 16 trailing 0's and the three digits from 242
Total digits = 3 + 18 = 21
Correct Option: C
Question: McDonald's ran a campaign in which it gave game cards to its customers. These game cards made it possible for customers to win hamburgers, French fries, soft drinks, and other fast-food items, as well as cash prizes. Each card had 10 covered spots that could be uncovered by rubbing them with a coin. Beneath three of these spots were "No Prize" signs. Beneath the other seven spots were names of prizes, two of which were identical.
For example, one card might have two pictures of a hamburger, one picture of a Coke, one of French fires, one of a milk shake, one of 5 Dollar, one of 1000 Dollar and three "No Prize" signs. For this card the customer could win a hamburger.
To win on any card, the customers had to uncover the two matching spots (which showed the potential prize for that card) before uncovering a "No Prize"; any card with a "No Prize" uncovered was automatically void. Assuming that the two matches and the three "No Prize" signs were arranged randomly on the cards, what is the probability of a customer winning?
A.0.1
B.0.15
C.0.12
D.0.18
Answer: A.0.1
Explanation: Explanation :
As per the question there are 10 cover spots out of which
(i) Three spots are there with no prize (identical)
(ii) Two spots of the same sign (Prize)
(iii) Five other spots which are distinct
Let three spots of no prize are (x,x,x), two spots of same sign are b(P,P) and five other spots are (A,B,C,D,E).
Total number of cases without restriction:
=>10!/(3!x2!).
Total number of favourable cases happen in the following ways which shows sequence of can covering are as follows:-
CASE I: Second uncovering is P
=>P P _ _ _ _ _ _ _ _=8C3×5!×1.
CASE II:
=>_ _ P _ _ _ _ _ _ =7C3×5!×2.
CASE III:
=>6C3×5!×3.
CASE IV:
=>5C3×5!×4.
CASE V:
=>4C3×5!×5.
CASE VI:
=>3C3×5!×6.
Hence, the total number of favourable cases are :-
=>case (I+II+III+IV+V+VI)/(10!3!X2!).
=>0.10.
Answer : A
Question: A box contains 60 balls, numbered from 1 to 60. 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: Shanthi went to the stationers and bought things forh Rs. 25, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
A.19.7
B.20
C.25
D.24.5
Answer: A.19.7
Explanation: amt tax consider as x
6% of x = 30/100
x=30/100*100/6 = 5
cost of tax free items = (25-(5+0.30) = 19.70
ANSWER A
Question: A boy has Rs. 720 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
A.90
B.110
C.140
D.135
Answer: D.135
Explanation: Let number of notes of each denomination be x.
Then x + 5x + 10x = 720
16x = 720
x = 45
Hence, total number of notes = 3x = 135
D
Question: If ax = by
A.log a/b = x/y
B.log a/ log b = x/y
C.log a/ log b = y/x
D.None
Answer: C.log a/ log b = y/x
Explanation: Solution
ax = by	= log ax= log by
‹=› x log a = y log b
‹=› log a / log b= y/x.
Answer C
Question: Fox jeans regularly sell for $15 a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $4 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the two discounts rates is 18 percent, what is the discount rate on Pony jeans?
A.45%
B.13%
C.11%
D.12%
Answer: A.45%
Explanation: You know that Fox jeans costs $15, and Pony jeans costs $18, you also know that 3 pairs of Fox jeans and 2 pairs of Pony jeans were purchased. So
3(15) = 45 - Fox
2(18) = 36 - Pony
The total discount discount is $4 and you are asked to find the percent discount of pony jeans,
so 45(18 - X)/100 + 36(X)/100 = 4 or 45*18 -45*x + 36*x =400 or - 9x = 400-45*18
or x= 410/9 =45%
=45% A
Question: A batsman scored 1 runs in his 18th innings and that makes his average 18. Find his average upto
the 17th innings?
A.19
B.20
C.21
D.22
Answer: A.19
Explanation: Avg = sum of the value/No. of the value
18 = (Sum of the first 17 innings Score +1)/18
(18*18-1)= Sum of the first 17 innings Score
Sum of the first 17 innings Score = 323
Ave upto 17 innings = 323/17=19
ANSWER:A
Question: The perimeter of a semi circle is 140 cm then the radius is?
A.27
B.28
C.19
D.11
Answer: A.27
Explanation: 36/7 r = 140 => r
= 27
Answer: A
Question: According to the directions on the can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make orange juice. How many 12 ounces cans of the concentrate are required to prepare 280 6 ounces servings of orange juice?
A.a) 35
B.b) 34
C.c) 50
D.d) 67
Answer: A.a) 35
Explanation: Its A.
Total juice rquired = 280*6 = 1680 ounce
12 ounce concentate makes = 12 * 4 = 48 ounce juice
Total cans required = 1680/48 = 35.
Answer A
Question: Fill in the blank with the correct number in this number series: 20, 65, 27, 61, __, 57, 41, ?
A.34
B.35
C.38
D.25
Answer: A.34
Explanation: This is a simple alternating subtraction and addition series; The first series begins with 20 and adds 7; the second begins with 65 and subtracts 4, and so on.
Answer: A
Question: A loan has a variable interest rate that fluctuates between 4% and 9% of the base payment per month. If base payments remain at $500 each month and an additional monthly surcharge of 2% is added to the combined (base + interest), what would be the greatest possible payment due in any given month?
A.$555.45
B.$555.55
C.$555.90
D.$556.45
Answer: C.$555.90
Explanation: The maximum interest in one month is 9%*$500=$45.
The combined payment (base plus interest) is $500 + $45 = $545.
The greatest possible payment is: 1.02*$545=$555.90.
The answer is C.
Question: In the city of San Durango, 60 people own cats, dogs, or rabbits. If 30 people owned cats, 40 owned dogs, 16 owned rabbits, and 12 owned exactly two of the three types of pet, how many people owned all three?
A.2
B.4
C.8
D.7
Answer: D.7
Explanation: You are considering a case when cat dogs and rabbit are not exactly equal to 12 .
The solution shall be 60=30+40+16-12-2x
and hence x shall be 7.
Answer D
Question: A sum of Rs. 12500 amounts to Rs. 15500 in 4 years at the rate of simple interest. What is the rate of interest?
A.4%
B.5%
C.6%
D.8%
Answer: C.6%
Explanation: S.I. = (15500 - 12500) = Rs. 3000/-
Rate = (100 * 3000) / (12500 * 4) = 6%
ANSWER:C
Question: The population of a town increased from 1,75,000 to 2,62,500 in a decade. What is the average percent increase of population per year?
A.5%
B.4%
C.6%
D.7%
Answer: A.5%
Explanation: increase in the population in 10 yrs=
262500 - 175000 = 87500
percent increase in the population in 10 yrs
= 87500/175000*100 = 8750/175=50%
avg percent increase of population per yr
50%/10=5%
ANSWER A
Question: A tightrope approximately 320 m long is suspended between two poles. During a performance, a break occurs in the line. Assume that the line has an equal chance of breaking anywhere along its length. What is the probability that the break happened in the first 50 meters of the rope?
A.27/32
B.1/2
C.5/32
D.5/27
Answer: C.5/32
Explanation: Simly 50/320 = 5/32
Answer will be (C)
Question: 8.036 divided by 0.04 gives :
A.200.9
B.2.06
C.20.06
D.100.9
Answer: A.200.9
Explanation: = 8.036/0.04
= 803.6/4
= 200.9
Answer is A.
Question: If s,u, and v are positive integers and 2s=2u+2v, which of the following must be true?
i. s=u
ii. u is not equal to v
iii. s > v
A.None
B.I only
C.II only
D.III only
Answer: D.III only
Explanation: Given: 2s=2u+2v --> s=u+v. Now, since s, u, and v are positive integers then s is more than either u or v, so I is never true and III is always true. As for II: it's not necessarily true, for example 4=2+2. So, we have that only option III must be true.
Answer: D.
Question: The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling alongthe oundary of the park at the speed of 12 km/hr completes one round in 8 min, then the area of the park (in sq. m) is?
A.1345460 m
B.134500 m
C.153600 m
D.167360 m
Answer: C.153600 m
Explanation: Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m.
60
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
Length = 480 m and Breadth = 320 m.
Area = (480 x 320) m2 = 153600 m
C
Question: If a survey shows that 56 citizens out of a sample of 200 support a particular Senate bill, what percent of the sample does not support the bill?
A. 56%
B. 64%
C. 72%
D. 82%
Answer: C. 72%
Explanation: 56 out of 200 supports the bill and we are asked to find the percent who the does not support the bill.
56 out of 200 supports the bill = 28 out of 100 supports the bill ( taking in % terms )
28 out of 100 supports the bill = 72 (100-28) doesn't support the bill
So, answer is (C) 72%
Question: Gopal borrows Rs 1,00,000 from a bank at 10% p.a. simple interest and clears the debt in five years. If the installments paid at the end of the first, second, third and fourth years to clear the debt are Rs 10,000, Rs 20,000, Rs 30,000 and Rs 40,000 respectively, what amount should be paid at the end of the fifth year to clear the debt?
A.Rs 20,000
B.Rs 24,500
C.Rs 30,000
D.Rs 35,900
Answer: C.Rs 30,000
Explanation: Explanation:
Always remember, In the case of simple interest, installment amount will always be reduced from principal and the interest will be calculated on the remaining principal.
Simple interest for the first year = P×T×R/100=100000×1×10/100 = Rs.10000
Amount after first instalment is paid = 1,00,000 - 10,000 = Rs 90,000
Simple interest for the second year = P×T×R/100=90000×1×10/100= Rs.90,000
Amount after second instalment is paid = 90,000 - 20,000 = Rs 70,000
Simple interest for the third year = P×T×R/100=70000×1×10/100= Rs.7000
Amount after third instalment is paid = 70,000 - 30,000 = Rs 40,000
Simple interest for the fourth year = P×T×R/100=40000×1×10/100 = Rs.4000
Amount after fourth instalment is paid = 40,000 - 40,000 = 0.
Balance of debt for the fifth year = simple interest for four years = 10,000 + 9,000 + 7,000 + 4,000 = Rs 30,000.
Answer C
Question: The cross-section of a cannel is a trapezium in shape. If the cannel is 15 m wide at the top and 4 m wide at the bottom and the area of cross-section is 1900 sq m, the depth of cannel is?
A.150
B.200
C.140
D.240
Answer: B.200
Explanation: 1/2 * d (15 + 4) = 1900
d = 200
Answer: B
Question: 40% of Ram's marks is equal to 20% of Rahim's marks which percent is equal to 30% of Robert's marks. If Robert's marks is 80, then find the average marks of Ram and Rahim?
A.12
B.61
C.17
D.90
Answer: D.90
Explanation: Given, 40% of Ram's marks = 20% of Rahim's marks = 30% of Robert's marks.
Given, marks of Robert = 80
30% of 80 = 30/100 * 8 = 24
Given, 40% of Ram's marks = 24.
=> Ram's marks = (24 * 100)/40 = 60
Also, 20% of Rahim's marks = 24
=> Rahim's marks = (24 * 100)/20 = 120
Average marks of Ram and Rahim = (60 + 120)/2 = 90.
Answer: D
Question: A 250 m long train is running at a speed of 55 Km/hr. It crossed a platform of length 520 m in ? (Its a Previously asked on SSC 2012 exam) (*without a train question it is impossible to conduct an exam, I think you got, what I mean)
A.40.4 sec
B.50.4 sec
C.40.5 sec
D.50.5 sec
Answer: B.50.4 sec
Explanation: Speed = 55 Km/hr
(to convert km/hr in to M/s)
= 55 x 5/18 M/s
Distance = 250 m + 520 m ( If questions is about train crossing a post you need to consider only the length of Train, )
= 770 m
Time = Distance / Speed
= 770 x 18 / (5 x 55)
= 50.4 sec
Answer: OPTION B
Question: 3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?
A.9
B.10
C.11
D.12
Answer: D.12
Explanation: Let the required number of working hours per day be x.
More pumps, Less working hours per day (Indirect Proportion)
Less days, More working hours per day (Indirect Proportion)
Pumps	4	:	3 :: 8 : x
Days 1	:	2
Therefore, 4 x 1 x x = 3 x 2 x 8
=> x =(3 x 2 x 8) / (4)
x = 12.
Correct answer is D
Question: The sum of number of boys and girls in a school is 1150. If the number of boys is x, then the number of girls becomes x% of the total number of students. The number of boys is?
A.50
B.40
C.60
D.92
Answer: D.92
Explanation: We have x+x% of 1150 = 1150
x + x/100 * 1150 = 1150
25/2 * x = 1150
x = 1150*2/25 = 92
Answer is D
Question: If the sum of the 4th term and the 12th term of an arithmetic progression is 10, what is the sum of the first 15 terms of the progression?
A.65
B.75
C.60
D.55
Answer: B.75
Explanation: 4th term + 12th term = 10
i.e., (a+3d)+(a+11d) = 10
Now, Sum of first 15 terms = (15/2) * [2a + (15-1)d]
= (15/2) * [2a + 14d]
= (15/2) * 10 --------------- From (1)
=75
Answer : B
Question: The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 5 per square feet if there is one door of dimensions 6 feet * 3 feet and three WINDOWS of dimensions 4 feet * 3 feet each?
A.4000
B.345
C.5673
D.4530
Answer: D.4530
Explanation: Area of the four walls = 2h(l + b)
Since there are doors and WINDOWS, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.
Total cost = 906 * 5 = Rs. 4530
Answer: Option D
Question: The compound interest earned by Sunil on a certain amount at the end of two years at the rate of 8% p.a. was Rs.2828.80. Find the total amount that Sunil got back at the end of two years in the form of principal plus interest earned.
A.19828.83
B.19828.8
C.19828.82
D.19828.89
Answer: B.19828.8
Explanation: Let the sum be Rs.P
P{ [ 1 + 8/100]2 - 1 } = 2828.80
P(8/100)(2 + 8/100) = 2828.80 [a2 - b2 = (a - b) ( a + b)] P = 2828.80 / (0.08)(2.08) = 1360/0.08 = 17000 Principal + Interest = Rs. 19828.80.Answer:B
Question: What amount does an investor receive if the investor invests $5000 at 10% p.a. compound interest for two years, compounding done annually?
A.$5850
B.$5950
C.$6050
D.$6150
Answer: C.$6050
Explanation: A = (1 + R/100)^n * P
(1.1)^2 * 5000 = 1.21 * 5000 = 6050
The answer is C.
Question: If shares of two persons in profits are Rs.600 and Rs.1000 then ratio of their capitals is
A.3:5
B.2:3
C.4:3
D.1:3
Answer: A.3:5
Explanation: profit=time*capital
so 600:1000=3:5
ANSWER:A
Question: What is the median from the below series
32, 36, 34, 29, 28, 37, and 39
A.29
B.34
C.37
D.39
Answer: B.34
Explanation: Ordering the data from least to greatest, we get:
28, 29, 32, 34, 36, 37, 39
The median number was 34. (three numbers were higher than 34	and three were lower.)
B
Question: A cycle is bought for Rs.670 and sold for Rs.880, find the gain percent?
A.31%
B.35%
C.54%
D.38%
Answer: A.31%
Explanation: Explanation:
670 ---- 210
100 ---- ? => 31%
Answer: A
Question: How many days per calendar year is the month a factor of the day
A.0
B.1
C.59
D.90
Answer: B.1
Explanation: Solution: 1
All 31 days in January, because 1 is a factor of all integers
14 of the 28 days in February (because every other day is divisible by 2)
10 of the 31 days in March (the multiples of 3 between 3 and 30)
7 days in April (the multiples of 4 between 4 and 28)
6 days in May (the multiples of 5 between 5 and 30)
5 days in June (the multiples of 6 between 6 and 30)
4 days in July (the multiples of 7 between 7 and 28)
3 days in August (the multiples of 8 between 8 and 24… so, so close if only the month were 32 days long!)
3 days in September (9th, 18th, 27th)
3 days in October (10th, 20th,30th)
2 days in November (11th, 22nd)
2 days in December (12th, 24th)
And there you have it! As you can see, as you move through the months, your job starts to get easier as you pick up on the patterns and are able to reuse some of your previous insights… This is a very valuable skill to remember on test day!
B
Question: The sale price of an article including the sales tax is Rs. 616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 15%, then the cost price of the article is:
A.487
B.277
C.222
D.297
Answer: A.487
Explanation: Explanation:
120% of S.P. = 616
S.P. = (616 * 100)/120 = Rs. 560
C.P = (100 * 560)/115 = Rs. 487
Answer:A
Question: What number is that, which is to 12 increased by three times the number, as 2 to 9 ?
A.6
B.7
C.8
D.9
Answer: A.6
Explanation: Let x = the number sought.
Then x/12 + x + 12 = 64.
And x - 624/13 = 48.
Question: One hour after Yolanda started walking from X to Y, a distance of 52 miles, Bob started walking along the same road from Y to X. If Yolanda's walking rate was 3 miles per hour and Bobт's was 4 miles per hour, how many miles had Bob walked when they met?
A.28
B.23
C.22
D.21
Answer: A.28
Explanation: When B started walking Y already has covered 3 miles out of 52, hence the distance at that time between them was 52-3=49 miles.
Combined rate of B and Y was 3+4=7 miles per hour, hence they would meet each other in 49/7=7 hours. In 6 hours B walked 7*4=28 miles.
Answer: A.
Question: Amanda has had 3 pay cuts in her salary in the past 6 months. If the first pay cut was 10%, the second pay cut was 10% and the third was 10%. What will be the percentage decrease, if the salary is decreased in a single shot?
A.27.1%
B.29.1%
C.21.1%
D.23.1%
Answer: A.27.1%
Explanation: Let Rs.100 be initial salary.
Salary After 1st decrease, 10% = 90
Salary After 2nd decrease, 10% = 81 i.e. reduced by 19 percent of 90
Salary After 3rd decrease, 10% = 72.9 i.e. reduced by 10 percent of 81
So if its decreased in single shot =
i = ( ( b - a ) /b ) * 100
=27.1%
ANSWER:A
Question: The tax on a commodity is diminished by 10% and its consumption increased by 20%. The effect on revenue is?
A.2% decrease
B.8% increase
C.9% decrease
D.3% decrease
Answer: B.8% increase
Explanation: 100 * 100 = 10000
90 * 120 = 10800
-----------
10000-----------800
100-----------? => 8% increase
Answer: B
Question: Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Five years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?
A.A)24
B.B)89
C.C)40
D.D)56
Answer: C.C)40
Explanation: Let the present ages of Sameer and Anand be 5x years and 4x years respectively.
Then,	(5x + 5/4x + 5)=11/9
9(5x + 5) = 11(4x + 5)
45x + 45 = 44x + 55
45x - 44x = 55 - 45
x = 10.
Anand's present age = 4x = 40 years.
Answer:C
Question: Tom and Jerry are running on the same road towards each other. If Tom is running at a speed of 5 meters per second and Jerry is running 50% slower, how much time will it take them to meet if the initial distance between the two is 200 meters and Tom started running 40 seconds before Jerry did?
A.40 sec
B.35 sec
C.1 mnt
D.52 sec
Answer: A.40 sec
Explanation: Tom is running alone for 40 seconds.
So he will cover a distance of 40*5 = 200 m in 40 seconds.
Basically, Jerry has not started yet , and Tom has covered the distance alone and met Jerry on the other side
answer is A
Question: If x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year, the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $48. If $1500 is the total amount invested, how much is invested at 8 percent?
A.a. $280
B.b. $566.67
C.c. $892
D.d. $1108
Answer: B.b. $566.67
Explanation: 2 equations with 2 unknowns
10x / 100 - 8y / 100 = 48
and
x + y = 1500
Solving these 2 equations, x = 933.33 and y = 566.67
Answer B.
Question: Jack, Jill, and Sandy each have one try to make a basket from half court. If their individual probabilities of making the basket are 1/6, 1/7, and 1/8 respectively, what is the probability that Jack and Jill will make a basket but Sandy will miss?
A.1/8
B.1/16
C.1/48
D.1/96
Answer: C.1/48
Explanation: The probability that Jack and Jill will make a basket but Sandy will miss is 1/6*1/7*7/8=1/48.
The answer is C.
Question: If 16x = 64^y, which of the following expresses x in terms of y?
A.4^(3y-2)
B.4^(y-1)
C.4^(2y-1)
D.4^(2y-3)
Answer: A.4^(3y-2)
Explanation: By exponential simplification. 16 = 4^2 and 64=4^3 therefore (4^2)x=(4^3)^y gives x=(4^3y)/(4^2) further simplified to x=(4^3y)(4^-2) which gives x=4^(3y-2) Because exponential is additive in multiplication. i.e. a^b*a^c=a^(b+c). Answer: A
Question: A jar has 6 green 4 red and 2 blue marbles what is the probability of drawing 2 marbles randomly and they will be of different colors
A.1/4
B.1/2
C.2/3
D.7/9
Answer: C.2/3
Explanation: 1G and 1R
OR
1G and 1B
OR
1R and 1B
C61∗C41+C61∗C21+C41∗C21C122C16∗C14+C16∗C12+C14∗C12C212
24+12+866=4466=2324+12+866=4466=23
Ans: "C"
Question: If {p} denote the remainder when 3p is divided by 2 then which of the following is equal to 1 for all positive integers p?
I. {2p+1}
II. {2p}+1
III. 2{p+1}
A.I only
B.II only
C.I and II
D.III only
Answer: C.I and II
Explanation: C - I and II
3p/2 = 0 or 1
I just substituted 1 in the equations and solved.
Question: A 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train?
A.230
B.240
C.250
D.260
Answer: A.230
Explanation: Relative speed = 120 + 80 = 200 km/hr.
= 200 * 5/18 = 500/9 m/sec.
Let the length of the other train be x m.
Then, (x + 270)/9 = 500/9 => x = 230.
Answer: Option A
Question: 45 men working 8 hours per day dig 30 m deep. How many extra men should be put to dig to a depth of 50 m working 6 hours per day?
A.74
B.55
C.44
D.75
Answer: B.55
Explanation: B
55
(45 * 8)/30 = (x * 6)/50 => x =100
100 – 45 = 55