RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: 12 + 13 + 14 + ... 61 + 62 + 63 = ?
A.1361
B.1362
C.1950
D.1364
Answer: C.1950
Explanation: Sum = 12 + 13 + 14 + ... 61 + 62 + 63
Sum of n consecutive positive integers starting from 1 is given as n(n+1)/2
Sum of first 63 positive integers = 63*64/2
Sum of first 11 positive integers = 11*12/2
Sum = 12 + 13 + 14 + ... 61 + 62 + 63 = 63*64/2 - 11*12/2 = 1950
Answer : C
Question: A 3-letters code consists of three different letters. If the code contains at least 2 vowels, how many such codes are possible?
A.480
B.510
C.520
D.430
Answer: A.480
Explanation: 5 Vowels
21 Consonants
Remember that the letters have to different.
At least 2 = 2-Vowels + 3-Vowels
2-Vowels: 5*4*21 = 420
3-Vowels: 5*4*3 = 60
Total = 480
ANS:A
Question: By selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 5 p.c?
A.28000
B.29000
C.37000
D.38000
Answer: D.38000
Explanation: Option B
Explanation:
CP + CP/8 = 45000
CP = 40000
SP = 40000*(95/100) = 38000
Option D
Question: A sum of 725 is lent in the beginning of a year at a certain rate of interest. After 8 months, a sum of 362.50 more is lent but at the rate twice the former. At the end of the year, 33.50 is earned as interest from both the loans. What was the original rate of interest?
A.3.6%
B.4.5%
C.5%
D.3.46%
Answer: D.3.46%
Explanation: Let the original rate be R%. Then, new rate = (2R)%
∴ (725×R×1/100)+(362.50×2R×1/100×3)=33.50
⇒ (2175 + 725)R = 33.50 × 100 × 3 = 10050
⇒ R = 10050⁄2900 = 3.46%
Answer D
Question: 2 no's are respectively 40% & 60% more than 3rdnumber. Find the ration of two numbers ?
A.3:4
B.4:5
C.7:8
D.9:7
Answer: C.7:8
Explanation: Step 1: Let the third number is A
Then first number is 140% of A = 140 x A / 100 = 7A / 5 and second number is 160% of B = 160 x B / 100 = 8B /5.
Step 2: now ratio of first and second number is 7A / 5 : 8B / 5 = 35A : 40B = 7:8.
C
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.29 Kmph
B.27 Kmph
C.68 Kmph
D.22 Kmph
Answer: C.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: C
Question: A three-character password consists of one letter of the alphabet and three different digits between 0 and 9, inclusive. The letter must appear as the second or third character of the password. How many different passwords are possible?
A.4,680
B.18,720
C.26,000
D.37,440
Answer: A.4,680
Explanation: 4 character password: DLDD
First digit can be chosen in 10 ways.
The letter can be chosen in 26 ways.
Next digit can be chosen in 9 ways.
This gives us 10*26*9ways
Now, the letter can also be DDLD so there will be another 10*9*26 ways
Total = 10*26*9*2 = 4680 ways A
Question: The diameter of a ball is 20 inches. If the surface area of the diameter is the same as the surface area of a cube, what does 1 side of the cube measure? Round to the nearest whole number.
A.10
B.5
C.8
D.4
Answer: B.5
Explanation: The surface area of a sphere is determined by squaring the radius, multiply by Pi and multiply by 4. The radius is half of the diameter of a circle. So the radius of the ball is 10 inches. Multiply 10 by Pi, then multiply the answer by 4 will calculate to 125.663 inches as the surface area of the ball. Since a cube has 6 evenly measured sides we can divide the surface are by 6. This comes to 20.943 inches as the surface area for each square side of the cube. To find out the measurement for each side of the cube you will need to find out the square root of 20.943 inches. This comes to 4.576 inches. Rounding to the nearest whole number, each side of the cube measures 5 inches. The correct answer is (B).
Question: A hiker walked for 3 days. She walked 18 miles on the first day, walking 3 miles per hour. On the second day she walked for one less hour but she walked one mile per hour, faster than on the first day. On the third day she walked at 4 miles per hour for 5 hours. How many miles in total did she walk?
A.24
B.44
C.58
D.60
Answer: C.58
Explanation: First day - 18 miles with 3 miles per hours then total - 6 hours for that day
Second day - 4 miles per hour and 5 hours - 20 miles
Third day - 4 miles per hour and 5 hours - 20 miles
Total 18+20+20 = 58
Answer: option C
Question: Jerry, an electrician, worked 8 months out of the year. What percent
of the year did he work? (round answer to the nearest hundredth)
What percent 12 is 8? 12 months = 1 year
A.58.33%
B.66.67%
C.78.33%
D.88.33%
Answer: B.66.67%
Explanation: 1. Multiply the opposites
8 x 100 = 800
100=8/12
Divide by the remaining number
66.67% (rounded to hundredth)
correct answer B
Question: A man in a train notices that he can count 41 telephone posts in one minute. If they are known to be 50 metres apart, then at what speed is the train travelling?
A.60 km/hr
B.100 km/hr
C.110 km/hr
D.120 km/hr
Answer: D.120 km/hr
Explanation: Explanation :
Number of gaps between 41 poles = 40So total distance between 41 poles = 40*50= 2000 meter = 2 kmIn 1 minute train is moving 2 km/minute.Speed in hour = 2*60 = 120 km/hour
Answer : D
Question: Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 8 : 4?
A.16
B.45
C.277
D.92
Answer: B.45
Explanation: Let the distances between city A to B and B to C be 8x km and 4x km respectively.
Total time taken to cover from A to C
= (8x)/40 + (4x)/60 = (4x + 8x)/120 = 32x/120 = 4x/15 Average speed = (8*x + 4x)/(4x/15) = 45 kmph.
Answer:B
Question: Rahul went to a shop and bought things worth Rs. 30, out of which 40 Paise went on sales tax on taxable purchases. If the tax rate was 8%, then what was the cost of the tax free items?
A.17.6
B.24.6
C.21.6
D.18.6
Answer: B.24.6
Explanation: Total cost of the items he purchased = Rs.30
Given that out of this Rs.30, 40 Paise is given as tax
=> Total tax incurred = 40 Paise = Rs.40/100
Let the cost of the tax free items = x
Given that tax rate = 8%
∴ (30−40/100−x)8/100 = 40/100
⇒ 8(30 −0.4−x) = 40
⇒ (30− 0.4 − x) = 5
⇒ x = 30 − 0.4 − 5 = 24.6.
B)
Question: If the quantity (p − 4) is 5 times the quantity (q − 5), then what is the relationship between p and q?
A.p = 5q + 30
B.p = 5q − 21
C.5p = q + 20
D.p = 5q
Answer: B.p = 5q − 21
Explanation: p-4=5(q-5)
p-4=5q-25
p=5q-21
option B
Question: Kyle, David, and Catherine each try independently to solve a problem. If their individual probabilities for success are 1/8, 1/4 and 3/5, respectively, what is the probability no one will solve the problem?
A.3/80
B.21/80
C.5/16
D.25/76
Answer: B.21/80
Explanation: P(Kyle will not solve)=1 - 1/8 = 7/8
P(David will not solve)= 1 - 1/4 = 3/4
P(Catherine will not solve) = 1- 3/5 = 2/5
P= (7/8)*(3/4)*(2/5) = 42/160 = 21/80
Answer:B
Question: What percent of a day is nine hours?
A.20.83%
B.16x1/2%
C.18x2/3%
D.37.5%
Answer: D.37.5%
Explanation: Explanation :
Required percentage = (9/24100)%
= 37.5%.
Answer : D
Question: If 10 ounces of a strong vinegar solution are diluted with 50 ounces of water to form a four-percent vinegar solution, what was the concentration of the original solution?
A.20%
B.24%
C.25%
D.28%
Answer: B.24%
Explanation: Let x be the concentration of the original solution.
10x = 0.04(60)
x = 0.24
The answer is B.
Question: 1/x+1/y=1/z where x=12 and y,z positive integer how many possible value of y and z ?
A.4
B.7
C.12
D.15
Answer: B.7
Explanation: 1/12 = 1/z - 1/y
y = 12 * z / ( 12 - z )
0 < z < 12
Only for z = 3 ,4 ,6 ,8 , 9 ,10 and 11 , y is intiger
Hence seven solutions
ANSWER:B
Question: For all positive integers m and v, the expression m Θ v represents the remainder when m is divided by v. What is the value of (( 94 Θ 33 ) Θ 17 ) - ( 96 Θ (33 Θ 17)) ?
A.-10
B.-2
C.8
D.13
Answer: D.13
Explanation: (( 94 Θ 33 ) Θ 17 )
The remainder of 98 divided by 33 is 28;
The remainder of 28 divided by 17 is 11;
( 96 Θ (33 Θ 17))
The remainder of 33 divided by 17 is 16;
The remainder of 96 divided by 16 is 0.
11 - 0 = 11.
Answer: D.
Question: Audrey 4 hours to complete a certain job. Ferris can do the same job in 3hours. Audrey and Ferris decided to collaborate on the job, working at their respective rates. While Audrey worked continuously, Ferris took 4 breaks of equal length. If the two completed the job together in 2 hours, how many minutes long was each of Ferris’ breaks ?
A.5
B.7
C.15
D.20
Answer: B.7
Explanation: Audery and Ferris collective Work rate:
1/4 + 1/3 = 7/12
Collective work Time = 12/7 = 1.7 Hrs
Job Was actually done in = 2 (Includes breaks)
Breaks = Actual time taken - Collective work time
= 2 - 1.7
= .3 Hrs = 1/2
so ferrais took 4 breaks
=.3/4=.07 hrs = 7 m
so Answer is B) 10 mins
Question: 1370 , 1320 , X, -180, -6430
A.1070
B.6530
C.6630
D.6730
Answer: A.1070
Explanation: 1370-50*(5^0)=1320
1320-50*(5^1)=1070
1070-50*(5^2)=-180
-180-50*(5^3)=-6430
ANSWER:A.
Question: The product of the digits of the four-digit number Q is 36. No two digits of are identical. How many different numbers are possible values of Q ?
A.6
B.12
C.24
D.36
Answer: C.24
Explanation: The main question here is how can you arrange 4 different digits Q. We don't even need to find the number. from the question itself we know that there are 4 different digits and none of them is 0 as the product is non-zero.
Therefore no of ways to arrange 4 diff. digits is 4! which is 24
hence C
Question: If x is a positive integer, which of the following must be odd?
A.x+1
B.x^2+x
C.x^2+x+11
D.x^2−1
Answer: C.x^2+x+11
Explanation: A. X+1 = can be odd or even. Since O + O =E or E + O = O
B. X^2 + X = X(X+1). Since from the above derivation we already know the term X+1 can be Odd or Even, directly substitute here. X(ODD) = Even (When X is Even) or X(EVEN) = EVEN [When X is ODD]
C. Here's the answer. Since we know the term x^2 + X can always take a EVEN number, EVEN + 11 = ODD
Hence C.
Question: A school committee consists of 2 teachers and 4 students. The number of different committees that can be formed from 5 teachers and 10 students is
A.3000
B.2520
C.2100
D.2510
Answer: C.2100
Explanation: There are C(5,2) ways to select 2 teachers from 5 and C(10,4) ways to select 4 students from 10 where C(n,r) is the combinations of n items taken r at the time. Using the multiplication counting principle,the number of different committees that can be formed is given by
C(5,2)*C(10,4) = 2100
Question: A garrison of 2000 men has provisions for 54 days. At the end of 18 days, a reinforcement arrives, and it is now found that the provisions will last only for 20 days more. What is the reinforcement?
A.1977
B.1600
C.1979
D.1900
Answer: B.1600
Explanation: 2000 ---- 54
2000 ---- 36
x ----- 20
x*20 = 2000*36
x = 3600
2000
-------
1600
Answer: B
Question: In a group of cows and hens, the number of legs are 12 more than twice the number of heads. The number of cows is :
A.5
B.6
C.7
D.10
Answer: B.6
Explanation: Let no of cows be x, no of hens be y.
So heads=x+y
Legs=4x+2y
Now, 4x+2y = 2(x+y)+ 12
2x = 12
x = 6.
ANSWER:B
Question: The average of 11 numbers is 10.9. If the average of first six is 10.5 and that of the last six is 11.7 the sixth number is?
A.11.4
B.11.3
C.13.3
D.11.5
Answer: C.13.3
Explanation: 1 to 11 = 11 * 10.9 = 119.9
1 to 6 = 6 * 10.5 = 63
6 to 11 = 6 * 11.7 = 70.2
63 + 70.2 = 133.2 – 119.9 = 13.3
6th number = 13.3
Answer: C
Question: A circle graph shows how the MegaTech corporation allocates its Research and Development budget: 17% microphotonics; 24% home electronics; 15% 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.26°
D.36°
Answer: C.26°
Explanation: Here all percentage when summed we need to get 100% . As per data 17+24+15+29+8 = 93%.
So remaining 7% is the balance for the astrophysics.
Since this is a circle all percentage must be equal to 360 degrees.
100% ---- 360 degrees
Then 7% will be 26 degrees..
IMO option C.
Question: A certain car's price decreased by 2.5% (from the original price) each year from 1996 to 2002, during that time the owner of the car invested in a new carburetor and a new audio system for the car, which increased car's price by $2,000. If the price of the car in 1996 was $22,000, what is the car's price in 2002?
A.$18,400
B.$19,500
C.$20,200
D.$20,700
Answer: D.$20,700
Explanation: Price in 96 = 22000
Price decrease each year = 2.5/100*22000 = 550
Price in 97 = 22000 - 550
Price in 98 = 22000 - 2*550
Price in 99 = 22000 - 3*550
Price in 00 = 22000 - 4*550
Price in 01 = 22000 - 5*550
Price in 02 = 22000 - 6*550 = 18700
Investment in the car = 1500
Net price of the car in 02 = 18700 + 2000 = $20700
Correct Option: D
Question: A reduction of 23% in the price of salt enables a lady to obtain 10kgs more for Rs.100, find the original price per kg?
A.s.2.99
B.s.2.4
C.s.2.5
D.s.2.2
Answer: A.s.2.99
Explanation: 100*(23/100) = 23 --- 10
? --- 1 => Rs.2.3
100 --- 77
? --- 2.3 => Rs.2.99
Answer:A
Question: 60% of a number is added to 120, the result is the same number. Find the number?
A.300
B.788
C.677
D.256
Answer: A.300
Explanation: (60/100) * X + 120 = X
2X = 600
X = 300
Answer: A
Question: If A lends Rs.3200 to B at 12% per annum and B lends the same sum to C at 14.5% per annum then the gain of B in a period of 5 years is?
A.157.78
B.157.98
C.400
D.420
Answer: C.400
Explanation: (3200*2.5*5)/100
=> 400
Answer: C
Question: A train covers a distance in 50 min, if it runs at a speed of 48kmph on an average. The speed at which the train must run to reduce the time of journey to 45min will be.
A.60 km/h
B.53 km/h
C.40 km/h
D.70 km/h
Answer: B.53 km/h
Explanation: Time=50/60 hr=5/6hr
Speed=48mph
distance=S*T=48*5/6=40km
time=45/60hr=3/4hr
New speed = 40* 4/3 kmph= 53kmph
Answer : B
Question: A specialized type of sand consists of 40% mineral X by volume and 60% mineral Y by volume. If mineral X weighs 2.5 grams per cubic centimeter and mineral Y weighs 3 grams per cubic centimeter, how many grams does a cubic meter of specialized sand combination weigh? (1 meter = 100 centimeters)
A.5,500,000
B.2,800,000
C.55,000
D.28,000
Answer: B.2,800,000
Explanation: Let the volume be 1 m^3 = 1m * 1m * 1m = 100cm * 100cm * 100cm = 1,000,000 cm^3
By volume
40% is X = 400,000 cm^3
60% is Y = 600,000 cm^3
By weight,
In 1 cm^3, X is 2.5 gms
In 400,000 cm^3 , X = 2.5 * 400,000 = 1,000,000 grams
In 1 cm^3, Y is 3 gms
In 600,000 cm^3, Y = 3 * 600,000 = 1,800,000 gms
Total gms in 1 m^3 = 1,000,000 + 1,800,000 = 2,800,000
ANSWER:B
Question: A, B and C have Rs.900 between them, A and C together have Rs.400 and B and C Rs.750. How much does C have?
A.100
B.150
C.200
D.250
Answer: D.250
Explanation: A+B+C = 900
A+C = 400
B+C = 750
--------------
A+B+2C = 1150
A+B+C = 900
----------------
C = 250
ANSWER:D
Question: Mohan purchased 14 kgs of rice at the rate of Rs.26 per kg and 8 kgs of pulses at the rate of Rs.26 per kg. Whaat is the total amount that he paid to the shopkeeper?
A.A)Rs.572
B.B)Rs.594
C.C)Rs.596
D.D)Rs.595
Answer: A.A)Rs.572
Explanation: Explanation:
Price of 14 kgs of rice at Rs.26/kg = 14x26 = Rs.364
Price of 8 kgs of pulses at Rs.26/kg = 8x26 = Rs.208
Therefore, Total amount = Rs.364+Rs.208 = Rs.572.
Answer: Option A
Question: If |20x-10| = 170, then find the product of the values of x?
A.-45
B.50
C.-72
D.35
Answer: C.-72
Explanation: |20x-10| = 170
20x-10 = 170 or 20x-10 = -170
20x = 180 or 20x = -160
x = 9 or x = -8
product = -8*9 = -72
Answer is C
Question: 0.35 represents what percent of 0.7?
A.0.05%
B.0.5%
C.50%
D.500%
Answer: C.50%
Explanation: One more method
0.35 represents what percent of 0.7?
Adjusting the decimal
3.5 represents what percent of 7?
Divide by 7
0.5 represents what percent of 1?
Answer = 0.5*100 = 50% = C
Question: A pipe can fill a tank in 15 minutes and another one in 10 minutes. A third pipe can empty the tank in 5 minutes. The first two pipes are kept open for 4 minutes in the beginning and then the third pipe is also opened. In what time will the tank be empited ?
A.35 min
B.15 min
C.20 min
D.Cannot be emptied
Answer: C.20 min
Explanation: Proportion of the volume of the tank filled by both the
pipes in 4 min = 4(1⁄15 + 1⁄10) = 2⁄3rd of the tank
Volume of the tank filled by all the pipes working together = 1⁄15 + 1⁄10 - 1⁄5 = -1⁄30
i.e. 1⁄30 tank is emptied in 1 min.
∴ 2⁄3 rd of the tank can be emptied in 2×30/3=20min
Answer C
Question: Two heavily loaded sixteen-wheeler transport trucks are 855 kilometers apart, sitting at two rest stops on opposite sides of the same highway. Driver A begins heading down the highway driving at an average speed of 90 kilometers per hour. Exactly one hour later, Driver B starts down the highway toward Driver A, maintaining an average speed of 80 kilometers per hour. How many kilometers farther than Driver B, will Driver A have driven when they meet and pass each other on the highway?
A.90
B.130
C.135
D.320
Answer: C.135
Explanation: I've been reading the website for a while and I'm always keen to see different approaches so I would like to share one that works for me:
Short version:
Truck A travels for an hour.
Distance remaining = 855-90 = 765k
Ratio of speeds 9:8 -> 765/17 = 45
Truck A = 90 + 45*9 = 495
Truck B = 45*8 = 360
Delta = 135km
Answer C
Question: For a certain set, the value range of its members is 96.8. A new set is created from the members of the old set as follows: 12 is subtracted from a member of the old set, and the result is divided by 4. The resulting value is a member of the new set. If this operation is done for each member of the old set, what is the range of values of the members of the new set?
A.21.2
B.24.2
C.36.3
D.48.4
Answer: B.24.2
Explanation: Let x and z be the smallest and largest of the original set, respectively.
z - x = 96.8
The smallest and largest members of the new set will be (x-12) / 4 and (z-12) / 4.
Then the range is (z-12) / 4 - (x-12) / 4 = (z-x) / 4 = 96.8 / 4 = 24.2
The answer is B.
Question: A regular hexagon is there. The mid points of the sides were joined and formed another hexagon.Then What is the percentage reduction in area.
A.25%
B.35%
C.45%
D.55%
Answer: A.25%
Explanation: Let ABCDEF be the regular hexagon with sides AB and ED parallel. P and Q are mid points of AF and EF resp.
AE=root(3) * s (s is side of hexagon)
then PQ =(root(3) * s)/2 mid point theorem
Now u know side of inner hexagon
use formula area of hexagon = (3 * root(3))2 * s^2
and find diff in area of two hexagon multiply by 100 and divide the product by area of bigger hexagon
Ans 25%
ANSWER:A
Question: The average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 68 kg. What is the correct weight?
A.58kgs
B.58.85kgs
C.58.95kgs
D.59kgs
Answer: D.59kgs
Explanation: Actual total weight is (20X 58.4 - 56 + 68) = 1180 Kgs
Actual average weight is 1180/20 = 59kgs
D
Question: A train covers a distance in 50 minutes, if it runs at a speed of 48kmph on an average. Find the speed at which the train must run to reduce the time of journey to 40 minutes.
A.50 km/hr
B.60 km/hr
C.65 km/hr
D.70 km/hr
Answer: B.60 km/hr
Explanation: Explanation:
We are having time and speed given, so first we will calculate the distance. Then we can get new speed for given time and distance.
Lets solve it.
Time = 50/60 hr = 5/6 hr
Speed = 48 mph
Distance = S × T = 48 × 5/6 = 40 km
New time will be 40 minutes so,
Time = 40/60 hr = 2/3 hr
Now we know,
Speed = Distance/Time
New speed = 40 × 3/2 kmph = 60kmph
Answer: B
Question: If all of the telephone extensions in a certain company must be even numbers, and if each of the extensions uses all four of the digits 1, 2, 6, and 7, what is the greatest number of four-digit extensions that the company can have?
A.4
B.6
C.11
D.12
Answer: D.12
Explanation: Since the phone number must be even, the unit's digit can be either 2 or 6.
When the unit's digit is 2 --> number of possibilities is 3! = 6
When the unit's digit is 6 --> number of possibilities is 3! = 6
Largest number of extensions = 6 + 6 =12
Answer:D
Question: Alice is now 10 years older than Bob. If in 6 years Alice will be twice as old as Bob, how old will Alice be in 5 years?
A.19
B.21
C.23
D.25
Answer: A.19
Explanation: A=B+10 so B=A-10.
A+6=2(B+6).
A+6=2(A-10+6).
A+6=2A-8.
A=14.
In 5 years, Alice will be 19 years old.
The answer is A.
Question: The sides of a square region, measured to the nearest centimeter, are 4 centimeters long. The least possible value of the actual area of the square region is
A.15.25 sq cm
B.18.25 sq cm
C.12.25 sq cm
D.21.25 sq cm
Answer: C.12.25 sq cm
Explanation: Though there might be some technicalities concerning the termnearest(as 3.5 is equidistant from both 3 and 4) the answer still should be : 3.5^2=12.25.
Answer: C
Question: A, B, C, D, E, F, G, and H are all integers, listed in order of increasing size. When these numbers are arranged on a number line, the distance between any two consecutive numbers is constant. If G and H are equal to 5^12 and 5^16, respectively, what is the value of A?
A.-24(5^12)
B.-27(5^12)
C.-24(5^6)
D.23(5^12)
Answer: B.-27(5^12)
Explanation: Ans : B
Assume that the numbers appear as shown below on the number line
A-----B-----C-----D-----E-----F-----G-----H
(5^12) (5^13)
As the values for G and H are given , we can calculate the difference between any two terms of the series .
Common Difference ,d = (5^13) - (5^12)
= (5^12) *[ 5-1 ]
= (5^12)*(4)
Also F + d = G as the terms are in equidistant and in increasing order.
So F + (5^12)*(4) = (5^12).
That is , F = (5^12) - (5^12)*(4)
= (5^12)[ 1-4]
= (5^12) (-3)
Similarly , E = F - d
= (5^12)[-3-4]
= (5^12)*(-7)
You can see a -4 getting added to the non-exponent part of the values . That is , according to the pattern , D SHOULD BE (5^12)*(-7-4)= (5^12)*(-11)
Following this pattern , A = (5^12)*(-27)
B
Question: The smallest number which when diminished by 7, is divisible by 12, 16, 18, 21 and 28 is
A.2333
B.1015
C.2683
D.2693
Answer: B.1015
Explanation: Explanation:
Required Number = (L.C.M of 12, 16, 18,21,28)+7
= 1008 + 7
= 1015
Answer: B) 1015
Question: If the probability of rain on any given day in City X is 40%, what is probability that it rains on exactly 3 days in a 4 day period?
A.16/25
B.48/125
C.96/625
D.108/625
Answer: C.96/625
Explanation: One possible way is rain-rain-rain-no rain.
The probability of this is 2/5*2/5*2/5*3/5 = 24/625
The number of possible ways is 4C3 = 4, so we multiply this by 4.
P(rain on exactly 3 days) = 4*24/625 = 96/625
The answer is C.
Question: What are the least number of square tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad ?
A.714
B.814
C.850
D.866
Answer: B.814
Explanation: Explanation:
In this type of questions, first we need to calculate the area of tiles. With we can get by obtaining the length of largest tile.
Length of largest tile can be obtained from HCF of length and breadth.
So lets solve this,
Length of largest tile = HCF of (1517 cm and 902 cm)
= 41 cm
Required number of tiles =
Area of floor/Area of tile=(1517×902/41×41)=814
Option B
Question: A father said to his son, "I was as old as you 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 years
B.10 years
C.8 years
D.17 years
Answer: A.14 years
Explanation: Explanation:
Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
⇒ 5x = 20
⇒ x = 4.
⇒ Age of the youngest child = x = 4 years.
Answer: A
Question: The probability that a number selected at random from the first 50 natural numbers is a composite number is
A.21/25
B.17/25
C.4/25
D.8/25
Answer: B.17/25
Explanation: The number of exhaustive events = ⁵⁰C₁ = 50.
We have 15 primes from 1 to 50.
Number of favourable cases are 34.
Required probability = 34/50 = 17/25.
ANSWER:B