RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: a student reached his school late by 20mins by travelling at a speed of 9kmph.if he had travelled at a speed of 12kmph,he would have reached his school 20mins early.what is the distance between house and school?
A.24
B.25
C.26
D.27
Answer: A.24
Explanation: distance = distance either student reaches school before time or after time
9(t+20/60) = 12(t-20/60)
i.e
9(t+1/3) = 12(t-1/3)
9(3t+1) = 12(3t-1)
t=7/3
put t value in any of distance equation
put t= 7/3 in 9(t+1/3)
we get 24 km
ANSWER:A
Question: Rajesh can finish 1/3 of his home work in one hour. Seema can finish 3/7 of
her homework in 70 minutes and Ramya can finish 3/4 of her homework in
three and a quarter hours. If all of them start their home work at 12.00 PM and can
go to play as soon as they all finish their homework. When can they start to
play, if they take a break at 3.00 PM for 30 minutes?
A.4:30pm
B.5:30pm
C.6:30pm
D.4:50pm
Answer: D.4:50pm
Explanation: ajesh can finish his work in 3 hr,
ramya can finish her work in 2.7 hr
seema can finish in 4.3 hr
so 4:50pm they can go to play
ANSWER:D
Question: Which of the following is a even number ?
A.9
B.11
C.4
D.3
Answer: C.4
Explanation: Explanation :
4 is a even number
Hence the even numbers are 2,4,6,8,10,12,14,... Answer : Option C
Question: in a certain tournament certain rules are followed: any player is eliminated the moment he losses for the third time (irrespective of how many wins he has), any player can play another player any number of times. If 512 contestants enter the tournament what is the largest number of games that could be played?
A.1535
B.1533
C.1536
D.1534
Answer: A.1535
Explanation: Explanation :
As there are 512 contestants , 511 contestants must be eliminated so that there can be only 1 winner.
In a single match there is only 1 loss and for elimination of a contestant he must lose 3 matches;
therefore for eliminating 511 contestants , the nos of matches required is : 511 x 3 = 1533
The last contestant i.e the winner can also lose a maximum of 2 matches.
So the maximum nos of games that could be played is 1533+2 = 1535
Answer : A
Question: The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:
A.9000
B.9400
C.9600
D.9670
Answer: C.9600
Explanation: Greatest number of 4-digits is 9999.
L.C.M. of 15, 25, 40 and 75 is 600.
On dividing 9999 by 600, the remainder is 399.
Required number (9999 - 399) = 9600. Answer: Option C
Question: Amul's Ice Cream Shop sells ice cream at a cents a scoop. For an additional b cents, a customer can add 7 toppings to his or her sundae. How much would a sundae with 7 scoops and 7 toppings cost, in terms of a and b?
A.7a+2b
B.7a+b
C.6a+b
D.5a+b
Answer: B.7a+b
Explanation: Answer B 7a+b
Question: At 1:00 pm, a truck left city P and headed toward City Q at a constant speed of 50 km/h. One hour later, a car left City Q and headed toward City P along the same road at a constant speed of 40 km/h. If the distance between City P and City Q is 230 km, at what time will the truck and the car meet each other?
A.4:00
B.4:30
C.5:00
D.5:30
Answer: A.4:00
Explanation: At 2:00 pm, the truck and the car are 180 km apart.
The truck and the car complete a distance of 90 km each hour.
The time it takes to meet is 180/90 = 2 hours.
They will meet at 4:00 pm.
The answer is A.
Question: A set consist of 2m-1 element. What is the number of subsets of this set which contain at most m-1 elements?
A.2^(2m-2)
B.2^(2m) - 2
C.2^(2m) -1
D.2^(2m)
Answer: A.2^(2m-2)
Explanation: I used m=3, so then we have
5!/2!3! + 5!/4!1! + 5!/0!5!
10 + 5 + 1 = 16
So our target is 16
Now replace in answer choices
A gives us 2^4 = 16
Hence A is the correct option
Read carefully it says at most so keep in mind that picking a small number such as 3 will help you save time since you have to list fewer outcomes
Avoid 2 since you will get 1 arrangement (m-1) and may be risky since 1 is a number with certain unique properties
Question: A boatman can row 3 km against the stream in 20 minutes and return in 18 minutes. Find the rate of current ?
A.7/2 kmph
B.8/2 kmph
C.5/2 kmph
D.1/2 kmph
Answer: D.1/2 kmph
Explanation: Explanation:
Speed in upstream = Distance / Time = 3 x 60/20 = 9 km/hr.
Speed in downstream = 3 x 60/18 = 10 km/hr
Rate of current = (10-9)/2 = 1/2 km/hr.
Answer: D
Question: Ron walks to a viewpoint and returns to the starting point by his car and thus takes a total time of 6 hours 45 minutes. He would have gained 2 hours by driving both ways. How long K would it have taken for him to walk both ways.
A.8 h 45 min
B.7 h 45 min
C.6 h 45 min
D.5 h 30 min
Answer: A.8 h 45 min
Explanation: 1.Walking to to a viewpoint+Driving back=6 hours 45 minutes
2.Driving to a viewpoint+Driving back=6 hours 45 minutes - 2 hours=4 hours 45 minutes, thereforeone way driving=4 hours 45 minutes/2 =2 hours 22.5 minutes.
3. From 1.one way driving=6 hours 45 minutes-2 hours 22.5 minutes=4 hours 22.5 minutes.
4.Walking to to a viewpoint+Walking back K=4 hours 22.5 minutes+4 hours 22.5 minutes=8 hours 45 minutes.
Answer: A.
Question: Set W includes elements {8, 2, 11, x, 3, y} and has a mean of 7 and a median of 5.5. If x < y, then which of the following is the maximum possible value of x?
A.0
B.1
C.2
D.3
Answer: D.3
Explanation: First, reach to the point of getting the equation W: x + y = 18
It should take about 20 seconds.
Then Substitute the answer choices into the equation.
I don't know what the answer choices in this case are.
But I'm sure, you would be able to eliminate at least 2 or 3 answer choices. (about 10 seconds).
Say you are left with 2 answer choices. (If you are short on time, guess One of the two and you'll have a 50% probability of getting it right.)
The Median (of 6 numbers) = 5.5. See if the AVERAGE of any two numbers among (2,3,8,11) results in the median. In this case, it does for 3 and 8. (15 seconds).
Once you know that the numbers that contribute towards Median are 3 and 8, and not x or y, then given x < y, x≤3. (about 10 seconds)=D
Question: A person lent a certain sum of money at 5% per annum at simple interest and in 8 years the interest amounted to $420 less than the sum lent. What was the sum lent?
A.500
B.600
C.700
D.800
Answer: C.700
Explanation: P - 420 = (P*5*8)/100
P = 700
The answer is C.
Question: Departments A, B, and C have 6 employees each, and department D has 20 employees. Departments A, B, C, and D have no employees in common. A task force is to be formed by selecting 1 employee from each of departments A, B, and C and 2 employees from department D. How many different task forces are possible?
A.19,000
B.41,040
C.100,000
D.190,000
Answer: B.41,040
Explanation: 6c1 * 6c1* 6c1*20c2 = 6*6*6*190=41,040. Hence B is the correct answer.
Question: An investor invests in a new fund. The fund averages 10% growth annually for the first three years, but it loses 20% of its value in the fourth year. At the end of four years, the value of the fund is approximately what percent of the original amount?
A.97.64%
B.100.98%
C.103.45%
D.106.48%
Answer: D.106.48%
Explanation: 0.8*1.1^3 = 1.0648
The answer is D.
Question: Which of the following is closest to (-2/3)^199？
A.-1
B.-1/2
C.0
D.1
Answer: C.0
Explanation: (-2/3)^4 = 16/81 which is already less than 1/2.
For larger exponents, the expression will get closer and closer to zero.
The answer is C.
Question: If a, b, c are consecutive positive integers and a<b<c, which of the following must be true?
I. a-c=-2
II. abc is an even integer
III. (a+b+c)/3 is an integer
A.All are correct
B.II
C.I and II
D.II and III
Answer: A.All are correct
Explanation: 1. a-c=-2 --> a, b, c are consequitive positive integers and a<b<c then c=a+2 --> a-c=2. So this statement is always true;
2. abc is an even integer --> out of any 3 consecutive integers at least one must be even thus abc=even. So this statement is also always true;
3. (a+b+c)/3 is an integer --> the sum of odd number of consecutive integers is ALWAYS divisible by that odd number. So this statement is also always true. Or: (a+b+c)/3=(a+a+1+a+2)/3=(3a+3)/3=a+1=integer.
Answer: A.
Question: E is the midpoint of AC in right triangle ABC shown above. If the area of ΔABC is 24, what is the area of ΔBED?
A.
B.
C.
D.
E.
A.9√3
B.9√2
C.12
D.9
Answer: D.9
Explanation: Since BE is the median, Area of triangle ABE = Area of triangle EBC = 1/2 * Area of triangle ABC = 12.
Also, since Angle C = 45, AB = AC.
But, 1/2 * AB*AC = 24 => AC = \sqrt{48} = 4\sqrt{3}
AE = AC/2 = 2\sqrt{3}
Now, triangle EDC is again right angled. so area of triangle EDC = 1/2 * ED * DC .
But ED = DC and ED^2 + DC^2 = 12 => ED = \sqrt{6}
So area of triangle EDC = 1/2 *\sqrt{6} *\sqrt{6} = 3
Now area of triangle BCD = Area of triangle EBC - Area of triangle EDC => 12 -3 = 9.
ANSWER:D
Question: The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square?
A.768
B.268
C.260
D.480
Answer: D.480
Explanation: Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively.
4a = 2(l + b)
2a = l + b
l . b = 480
We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found .
Area of the square cannot be found.
Answer: D
Question: The length of a rectangular hall is 5m more than its breadth. The area of the hall is 750 m. The length of the hall is
A.20
B.25
C.30
D.35
Answer: B.25
Explanation: Let breadth = x m
Then, length = (x+5)m
x(x+5) = 750
x² + 5x - 750= 0
(x+30)(x-25)= 0
x = 25 Answer: B
Question: The area of a square is equal to five times the area of a rectangle of dimensions 125 cm * 64 cm. What is the perimeter of the square?
A.600 cm
B.800 cm
C.400 cm
D.1000 cm
Answer: B.800 cm
Explanation: Area of the square = s * s = 5(125 * 64)
=> s = 25 * 8 = 200 cm
Perimeter of the square = 4 * 200 = 800 cm.
ANSWER:B
Question: Two cars, A and B, travel along interstate 20 from Atlanta to Dallas. Car A left Atlanta at 10 PM traveling at a constant speed of 60 mph. Car B left the same point in Atlanta 30 minutes later traveling at a constant speed of 80 mph. In how many minutes will Car B overtake Car A if neither car stops at any exit or experiences traffic (and thus both cars maintain their constant speeds)?
A.90
B.95
C.100
D.110
Answer: A.90
Explanation: We need to use a form of D=RT [distance=rate*time]
Car A will have travelled 30 minutes longer than car B when they meet, so
Car A travel time: T+.5 (use 1/2 hour since the rates are in hours)
Car B travel time: T
Car A rate: 60 mph
Car B rate: 80 mph
Car A distance = Car B distance
so
(R car A)*(T car A) = (R car B)*(T car B)
60*(T+.5) = 80*T
60T + 30 = 80T
30 = 20T
1.5 = T
1.5 hours = 90 minutes
A
Question: Two numbers are in the ratio of 5:7. If 25 is subtracted from each number, they are in the ratio of 5:9. What are the two numbers?
A.45, 63
B.50, 70
C.55, 77
D.60, 84
Answer: B.50, 70
Explanation: (5x-25):(7x-25) = 5y:9y
5x - 25 = 5y
7x - 25 = 9y
175-125 = 45y - 35y
50 = 10y
y = 5
5x-25 = 25
x = 10
The two numbers are 5x and 7x which are 50 and 70.
The answer is B.
Question: The percentage increase in the area of rectangle , if each of its side is increased by 20% is?
A.30%
B.44%
C.50%
D.55%
Answer: B.44%
Explanation: Let original length = x meters
original breadth = y meters
original area = xy m^2
New length = 120x/100
New breadth = 120y/100 = 6y/5
New area = 6x/5 * 6y/5 = 36xy/25 m^2
Increase percent = 11xy/25 * 1/xy *100 = 44%
Answer is B
Question: In how many different number of ways 3 men and 2 women can sit on a shopa which can accommodate persons?
A.A)60
B.B)70
C.C)1
D.D)5
Answer: D.D)5
Explanation: 5p1 = 5
Option 'D'
Question: If 75 percent of a class answered the first question on a certain test correctly, 25 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percent answered both correctly?
A. 10%
B. 20%
C. 30%
D. 50%
Answer: B. 20%
Explanation: {Total} = {First} + {Second} - {Both} + {Neither}
100% = 75% + 25% - {Both} + 20% --> {Both} = 20%.
Answer: B.
Question: A man buys an article for $10. and sells it for $25. Find the gain percent?
A.25%
B.50%
C.20%
D.150%
Answer: D.150%
Explanation: C.P. = $10
S.P. = $25
Gain = $15
Gain% = 15/10 *100 = 150%
Answer is D
Question: A train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 80 seconds. What is the length of the train in meters?
A.400 meters
B.1111 meters
C.800 meters
D.1822 meters
Answer: C.800 meters
Explanation: Train overtakes a bike means that we are talking about total length of the train. (train's head is close to bike when it started and its tail crosses the bike when it overtakes the bike)
Relative speed= 100-64= 36Km/h = 36000 m/h
time= 80 seconds
Distance= speed*time
36000* 80/3600= 800 meters.
C is the answer.
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 60 kg. What is the correct weight?
A.58.6kgs
B.58.85kgs
C.58.95kgs
D.59kgs
Answer: A.58.6kgs
Explanation: Actual total weight is (20X 58.4 - 56 + 60) = 1172 Kgs
Actual average weight is 1172/20 = 58.6kgs
A
Question: A necklace is made by stringing N individual beads together in the repeating pattern white bead, green bead, red bead, yellow bead, and blue bead. If the necklace design begins with a white bead and ends with a red bead, then N could equal
A.65
B.68
C.55
D.45
Answer: B.68
Explanation: Recognize that we are going to have to look for an answer thats a multiple of 5, plus 3.
Mutliple of 5 because there are 5 beads in the pattern, and plus 3 because the bead ends on red, which is 3 into the pattern.
I just went through all the answer choices, and only E fits. 5x13 = 65, and 65+3=68
Answer : B
Question: Three boys are ages 4, 6 and 7 respectively. Three girls are ages 5, 8 and 9, respectively. If two of the boys and two of the girls are randomly selected and the sum of the selected children's ages is w, what is the difference between the probability that w is even and the probability that w is odd?
A. 1/9
B. 1/6
C. 2/9
D. 1/4
Answer: A. 1/9
Explanation: Age of Boys w:4, 6, 7
Sum of ages taken 2 at a time: 10,13,11
Ages of Girls:5, 8, 9
Sum of ages taken 2 at a time: 13,17,14
9 Combinations of sum between sets(10,12,11)(13,17,14)
=23,27,24- 16,30,17- 24,28,25
Prob(Even)= 5/9
Prob(Odd) =4/9
Answer=5/9 - 4/9 = 1/9
Question: What is the place value of 4 in the numeral 4259
A.A)2700
B.B)4000
C.C)2900
D.D)2980
Answer: B.B)4000
Explanation: 4 * 1000 = 4000
B
Question: From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?
A.756
B.700
C.650
D.654
Answer: A.756
Explanation: We may have (3 men and 2 women) or (4 men and 1 woman) or (5 men only).
Required number of ways	= (7C3 x 6C2) + (7C4 x 6C1) + (7C5)
= (525 + 210 + 21)
= 756.
ANSWER A 756
Question: A cave is going to explode. A family is trapped inside that cave. The only way to get outside is a narrow tunnel. But the tunnel is weak and thus only two people can go at one time. Also, everybody is afraid of going alone.
The father takes one minute to go through till the end, the mother takes two, the son takes four and the daughter takes five. The cave and tunnel will explode in twelve minutes. Can they make it to the other end in that time frame?
PS: Keep in mind that when two people are moving, the total time taken will be as per the slower one.
A.10 minutes.
B.12 minutes.
C.11 minutes.
D.13 minutes.
Answer: B.12 minutes.
Explanation: Solution:
12 minutes
Explanation:
Yes, surely they can all make it out of the cave.
First, father and mother will go. Time taken = 2 minutes.
Father comes back. Time taken = 2 + 1 = 3 minutes.
Both children go. Time taken = 3 + 5 = 8 minutes.
Mother comes back. Time taken = 8 + 2 = 10 minutes.
Mother and Father go. Time taken = 10 + 2 = 12 minutes.
Thus in 12 minutes, all of them will be out of the cave through the tunnel.
Answer B
Question: Find the value of (√1.1)/(√0.81) + (√1.44)/(√0.49) is
A.195/63
B.2.879
C.155/63
D.125/63
Answer: B.2.879
Explanation: (√1.1)/(√0.81) + (√1.44)/(√0.49)
=> 2.879
Answer is B
Question: Find the sum of prime numbers lying between 58 and 75?
A.198
B.331
C.252
D.272
Answer: B.331
Explanation: Solution
Required sum	=59 + 61 + 67 + 71 + 73)
= 331.
Answer B
Question: For any integer n greater than 1, #n denotes the product of all the integers from 1 to n, inclusive. How many prime numbers R are there between #6 +2 and #6 +6 , inclusive?
A.None
B.One
C.Two
D.Three
Answer: A.None
Explanation: None is the answer. A.
Because for every k 6! + k :: k, because 6! :: k, since k is between 2 and 6.A
Question: A box measuring 24 inches long by 40 inches wide by 16 inches deep is to be filled entirely with identical cubes. No space is to be left unfilled. What is the smallest number of cubes that can accomplish this objective?
A.28
B.30
C.32
D.35
Answer: B.30
Explanation: least number of cubes will be required when the cubes that could fit in are biggest.
8 is the biggest number that could divide all three, 24, 40 and 16.
Thus side of cube must be 8, and total number of cubes = 24/8 * 40/8*16/8 = 30
Ans B
Question: Ram, Raj started a business in partnership, which Ram invested Rs.8000/- for 1 year, Raj invested Rs.16000/- for 2 years.
At the end of the profit received by them is Rs.4000/-. What is Ram’s share?
A.Rs. 1200
B.Rs. 900
C.Rs. 1000
D.Rs. 800
Answer: D.Rs. 800
Explanation: Answer:	Solution: Ram : Raj = (8,000 * 1) : (16,000 * 2) = 1 : 4.
So Ram's share = Rs. (4000 * 1/5) = Rs. 800.
Answer: Option D
Question: If N = 2^0.15 and N^b = 1, b must equal
A.3/80
B.20/3
C.4
D.5/3
Answer: B.20/3
Explanation: 15/100 = 3/20
N = 2 ^ 3/20
N^b = 2^1
(2^3/20)^b = 2^1
b = 20/3
Answer: B
Question: The distance light travels in one year is approximately 5,870,000,000,000 miles. The distance light travels in 100 years is:
A.587 × 10^8 miles
B.587 × 10^10 miles
C.587 × 10^-10 miles
D.587 × 10^12 miles
Answer: D.587 × 10^12 miles
Explanation: Solution:
The distance of the light travels in 100 years is:
5,870,000,000,000 × 100 miles.
= 587,000,000,000,000 miles.
= 587 × 10^12 miles.
Answer: (D)
Question: What is the tens digit of 7^1033?
A.0
B.1
C.0
D.3
Answer: C.0
Explanation: 7^1 = 7
7^2 = 49
7^3 = 343
7^4 = 2401
7^5 = 16807
7^6 = 117649
We should see this as pattern recognition . We have a cycle of 4 . (We can multiply the last 2 digits only as we care about ten's digit )
0 , 4 , 4 , 0 .
1033= 4*258 + 1
The ten's digit will be 0 .
Answer C
Question: A bag contains 10 red jellybeans and 10 blue jellybeans. If 3 jellybeans are removed one at a time, at random and are not replaced, what is the probability Q that all 3 jellybeans removed from the bag are blue?
A.9/100
B.2/19
C.1/8
D.3/20
Answer: B.2/19
Explanation: Method-1
10 red jellybeans and 10 blue jellybeans
Total Outcomes = No. of ways to choose 3 Jelly bean at random out of a total 20 jellybeans = 20C3 = 1140
Favourable Outcomes = No. of ways to choose 3 Jelly bean such that they are all Blue out of 10 Blue = 10C3 = 120
Probability = Favourable Outcomes / Total Outcomes = 10C3 / 20C3
Probability Q= 120 / 1140 = 2/19
Answer: option B
Method-2
Probability of First jelly bean to be Blue = 10/20 [Total 10 Blue out of total 20 jellybeans]
Probability of Second jelly bean to be Blue = 9/19 [Total 9 Blue remaining out of total 19 jellybeans remaining]
Probability of Third jelly bean to be Blue = 8/18 [Total 8 Blue remaining out of total 18 jellybeans remaining]
Required Probability = (10/20)*(9/19)*(8/18) = 2/19
Answer: option B
Question: If (x + 1) times (2x + 3) is an odd integer, then x must be:
A.an odd integer
B.an even integer
C.a prime number
D.a composite number
Answer: B.an even integer
Explanation: Solution:
(x + 1) times (2x + 3) means (x + 1)(2x + 3)
(x + 1)(2x + 3) = 2x^2+5x+3
For 2x^2+5x+3 to be odd, 5x+3 must be odd since 2x^2 is always even.
So 5x must be even, hence x must be even.
Therefore x is an even integer.
Answer: B
Question: Water boils at 212°F or 100°C and ice melts at 32°F or 0°C . If the temperature of a pot of water is 55°C, what is the temperature of the pot of water in °F?
A.116°F
B.125°F
C.131°F
D.138°F
Answer: C.131°F
Explanation: Let F and C denote the temperature in Fahrenheit and Celsius respectively.
(F - 32) /(212 - 32) = (C - 0)/(100 - 0)
F = 9C/5 + 32
F = 9(55)/5 + 32 = 131°F
The answer is C.
Question: A, B and C rent a pasture. If A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing and the rent of the pasture is Rs. 175, then how much amount should C pay as his share of rent?
A.35
B.45
C.25
D.15
Answer: B.45
Explanation: A : B : C
=10×7:12×5:15×3
=2×7:12×1:3×3
=14:12:9
Amount that C should pay
=175×9/35=5×9=45
Answer is B.
Question: The sum of five numbers is 200. The average of the first two numbers is 20 and the third number is 50. Find the average of the two numbers?
A.50
B.55
C.60
D.65
Answer: B.55
Explanation: Let the five numbers be P, Q, R, S and T.
=> P + Q + R + S + T = 200
(P + Q)/2 = 20 and R = 50
P + Q = 40 and R = 50
P + Q + R = 90
S + T = 200 - (P + Q + R) = 110
Average of the last two numbers
= (S + T)/2 = 55
Answer:B
Question: What approximate value should come in place of the question mark (?) in the following equation?
159% of 6531.8 + 5.5 × 1015.2 = ? + 5964.9
A.10,000
B.10,900
C.11,000
D.10,600
Answer: A.10,000
Explanation: ? ≈ 160% of 6530 + 5.5 × 1010 – 5965
≈ 10448 + 5555 – 5965 ≈ 10,000
Answer A
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
A.120 m
B.240 m
C.300 m
D.400 m
Answer: B.240 m
Explanation: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m.
ANSWER:B
Question: One boys picked up 30 mangoes .In how many ways can they divide them if all mangoes be identical?
A.A)4^30
B.B)2^30
C.C)1^30
D.D)3^30
Answer: C.C)1^30
Explanation: Each Mango can be given to any one of the four people or in other words..1 mango can be divided into 1 ways...so all 30 can be divided in 1^30 ways
ANS:C
Question: 1370 , 1320 , 1070 , -180, -6430, X
A.-37680
B.6530
C.6630
D.6730
Answer: A.-37680
Explanation: 1370-50*(5^0)=1320
1320-50*(5^1)=1070
1070-50*(5^2)=-180
-180-50*(5^3)=-6430
-6430-50*(5^4)=-37680
ANSWER:A.
Question: A square is drawn inside a right-angled triangle with the two perpendicular sides as 12 cm and 8 cm. what is the side of the largest possible square that can be drawn?
A.4.8 cm
B.4.4 cm
C.4.9 cm
D.5.0 cm
Answer: A.4.8 cm
Explanation: Explanation :
Area of triangle is 1/2 * 12 * 8 = 48
Side of square = x
The entire triangle split into two right angled triangle and one square with dimensions as follows
i) square with side x
ii) Right angled triangle with perpendicular sides x and 12-x
iii) Right angled triangle with perpendicular sides 8-x and x
Sum of area of all three = 48
=> x2 + 1/2*x*(12-x) + 1/2*x*(8-x) = 48
=> x = 4.8 cm
Hence (A) is the correct answer.
Answer : A
Question: 7, 10.5, 15.75, 23.63, 35.43, (...)
A.52.112
B.53.156
C.54
D.89
Answer: B.53.156
Explanation: 7
(7Ã—3)Ã· 2 = 10.5
(10.5Ã—3)Ã· 2 = 15.75
(15.75Ã—3)Ã· 2 = 23.63
(23.63Ã—3)Ã· 2 = 35.43
(35.43Ã—3)Ã· 2 = 53.156
Answer is B
Question: If E is the product of all positive integers less than 31, than what is the greatest integer k for which E/18^k is an integer?
A.3
B.6
C.7
D.14
Answer: C.7
Explanation: 30!E must be divisible by (3*3*2)^k.
As I will find a lot of 2's among 30!'s factors I will focus on the 3's (that also occurs twice instead of only once as a factor in 18).
Every multiple of 3 will provide me with atleast one factor of 3. There aren't that many so I list them quickly.
3 6 9*
12 15 18*
21 24 27**
30
The stars are marked as they are multiples of 9* or 27** and thus provides two or three 3's respectively.
3=3 (occurs 10 times) +10
3*3=9 (occurs 3 times) +3(adding just one additional three each as they were not counted for in the multiples of 3)
3*3*3=27 (occurs 1 time) +1 (again, adding just one as they were previously not counted)
Total: 14.
For every k we add two 3's. So we must divide 14 by 2 to get the highest integer K before we receive a non-integer result.
Answer: 7 -> Answer choice: C.