RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: In a class of 20 students, 2 students did not borrow any books from the library, 8 students each borrowed 1 book, 3 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed?
A.8
B.9
C.10
D.11
Answer: A.8
Explanation: The total number of books the students borrowed is 20*2=40.
The students who borrowed zero, one, or two books borrowed 8*1+3*2=14 books.
The 7 students who borrowed at least three books borrowed 40-14=26 books.
If 6 of these students borrowed exactly 3 books, then the maximum that one student could have borrowed is 26-18= 8 books.
The answer is A.
Question: In a group of ducks and cows, the total number of legs are 24 more than twice the no. of heads. Find the total no.of buffaloes.
A.10
B.12
C.14
D.16
Answer: B.12
Explanation: Let the number of buffaloes be x and the number of ducks be y
=> 4x + 2y = 2 (x + y) + 24
=> 2x = 24 => x = 12
B
Question: Which one of the following numbers is exactly divisible by 11?
A.11
B.13
C.14
D.15
Answer: A.11
Explanation: (4 + 5 + 2) - (1 + 6 + 3) = 1, not divisible by 11.
(2 + 6 + 4) - (4 + 5 + 2) = 1, not divisible by 11.
(4 + 6 + 1) - (2 + 5 + 3) = 1, not divisible by 11.
(4 + 6 + 1) - (2 + 5 + 4) = 0, So, 415624 is divisible by 11.
A
Question: P and Q started a business investing Rs. 54,000 and Rs. 36,000 respectively. Out of a total profit of Rs. 18,000, Q's share is :
A.5980
B.5990
C.6000
D.6010
Answer: C.6000
Explanation: Ratio of their shares = 54000 : 27000 = 6 : 3.
Q’s share = Rs. 18000 * 3/9
= Rs. 6000
ANSWER:C
Question: A train 250 m long running at 72 kmph crosses a platform in 50 sec. What is the length of the platform?
A.150m
B.200m
C.250m
D.750m
Answer: D.750m
Explanation: D = 72 * 5/18 = 50 = 1000 â€“ 250 = 750m
ANSWER:D
Question: The average salary/head of all the workers in a workshop is Rs.1100, if the average salary/head of 9 technician is Rs.1300 and the average salary/head of the rest is Rs.880, the total no. of workers in the work-shop is ?
A.18
B.20
C.22
D.17
Answer: D.17
Explanation: Let the total number of workers be y.So sum of salary for all workers = sum of salary of 9 technician + sum of salary for other y -9 workers.9 x 1300 + 880(y -9) = 1100 y⇒ 11700 + 880y - 7920 = 1100y⇒ 220y = 3780∴ y = 17 So total number of workers = 17 D
Question: The perimeter of a square is equal to the perimeter of a rectangle of length 15 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)
A.22.78
B.23.54
C.24.5
D.25.55
Answer: A.22.78
Explanation: Let the side of the square be a cm.
Perimeter of the rectangle = 2(15 + 14) = 58 cm
Perimeter of the square = 58 cm
i.e. 4a = 58
A = 14.5
Diameter of the semicircle = 14.5 cm
Circumference of the semicircle
= 1/2(∏)(14.5)
= 1/2(22/7)(14.5) = 22.78 cm to two decimal places
Answer: A
Question: In a consumer survey, 75% of those surveyed liked at least one of three products: 1, 2, and 3. 50% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 5% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products?
A.5
B.10
C.15
D.20
Answer: D.20
Explanation: pick 100 and x= all set with exactly two items
75=30+50+20 -(X)-10
X=15
Answer D
Question: Jill invests $10000 in an account that pays an annual rate of 3.96%, compounding semi-annually. Approximately how much W does she have in her account after two years?
A.$10079.44
B.W=$10815.83
C.$12652.61
D.$14232.14
Answer: B.W=$10815.83
Explanation: PS. I guess one can use simple interest to solve cause the answer choices are quite spread between you can easily arrive at something near 8%
Hence B the answer
Question: A man can row upstream at 15 kmph and down strem 30 kmph. He takes 9 hours to row from lower point A to upper point B and back to A. What is the total distance traveled by him in 9 hours? He must return back to base point A in remaining time.
A.80
B.120
C.140
D.180
Answer: D.180
Explanation: Upward distance traveled per hour - 15 km,
distance traveled after 6 hours = 90 km.
He remained with 3 hours travel downward, i.e. distance traveled in remaining 3 hours downward = 90 km
so total distance traveled from A to B and Back to point A = 90 km upward + 90 km downhill = 180 km
(Answer : D)
Question: The calender for the year 2007 will be the same for the year :
A.2014
B.2016
C.2017
D.2018
Answer: D.2018
Explanation: Answer D
Question: Calculate the circumference of a circular field whose radius is 6 centimeters.
A.12
B.4
C.6
D.8
Answer: A.12
Explanation: Circumference C is given by
C = 2Ï€r = 2Ï€*6 = 12 Ï€ cm
correct answer A
Question: How many real roots does the equation x^4y+16xy+64y=0 have if y < 0?
A.0
B.1
C.2
D.3
Answer: D.3
Explanation: x^4y+16xy+64y=0
=> y ( x^2 + 16x + 64) = 0
=> y (x+8)^2 = 0
if y<0 , then x=-6
So although there are 2 factors , they are the same x=-6 .
The equations has 3 distinct real root .
Answer D
Question: The area of sector of a circle whose radius is 12 metro and whose angle at the center is 42° is?
A.52.7 m2
B.57.8 m2
C.52.8 metre sq
D.72.8 m2
Answer: C.52.8 metre sq
Explanation: 42/360 * 22/7 * 12 * 12
= 52.8 m2
Answer: C
Question: Solution A is made up of alcohol and water mixed in the ratio of 21:4 by volume; Solution B is made up of alcohol and water mixed in the ratio of 2:3 by volume. If Solution A and Solution B are mixed in the ratio of 5:6 by volume, what percent of the resultant mixture is alcohol?
A.32.5%
B.40%
C.60%
D.65%
Answer: C.60%
Explanation: let mixture after mixing A and B is 110 ml (number assumed for calculation because of 5:6)
now solution A is 50 ml and solu B is 60 ml
further in A 100 ml A contains 84 ml alch
so 50 ml contain 42 ml
in mix B 100 ml solution contain 40 ml alc , 60 ml of B , it will be 24 ml alcohol.
so 42+24 = 66 in 110 ml solution which is 60%
ANSWER:C
Question: How long will it take a sum of money invested at 5% p.a. S.I. to increase its value by 40%?
A.6 years
B.7 years
C.8 years
D.9 years
Answer: C.8 years
Explanation: Sol.
Let the sum be x. Then, S.I. = 40% of x = 2x/5; Rate = 5%.
∴ Time = [100 * 2x/5 * 1/x*5] = 8 yea
Answer C
Question: Aman started a business investing Rs. 70,000. Rakhi joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business?
A.12:17:16
B.12:15:16
C.13:15:16
D.12:35:16
Answer: B.12:15:16
Explanation: Aman : Rakhi : Sagar = (70000 * 36) : (105000 * 30) : (140000 * 24)
= 12:15:16
Answer:B
Question: In the first 20 overs of a cricket game, the run rate was only 4.2. What should be the rate in the remaining 30 overs to reach the target of 250 runs?
A.6.25
B.6.28
C.6.11
D.5.53
Answer: D.5.53
Explanation: Required run rate
= [250 - (4.2 * 20)]/30
= 166/30
= 5.53
Answer:D
Question: Today is Sunday. After 65 days, it will be:
A.Tuesday
B.Saturday
C.Friday
D.Thursday
Answer: A.Tuesday
Explanation: Each day of the week is repeated after 7 days.
So, after 63 days, it will be Sunday.
After 65 days, it will be Tuesday.
Answer :A
Question: Calculate the distance covered by 150 revolutions of a wheel of radius 20.5 cm.
A.293.3 m
B.197.3 m
C.193.3 m
D.143.3 m
Answer: C.193.3 m
Explanation: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.
= 150 * 2 * 22/7 * 20.5 = 19328.57 cm = 193.3 m
ANSWER:C
Question: Given f(x) = 3x – 5, for what value of x does 2*[f(x)] + 8 = f(3x – 6)
A.0
B.4
C.6
D.7
Answer: D.7
Explanation: Answer = D = 7
f(x) = 3x – 5
2*[f(x)] + 8 = f(3x – 6)
2(3x-5) + 8 = 3 (3x-6) - 5
6x - 2 = 9x - 23
x = 7
Question: A dishonest dealer professes to sell goods at the cost price but uses a weight of 950 grams per kg, what is his percent?
A.2%
B.25%
C.5.26%
D.29%
Answer: C.5.26%
Explanation: 950 --- 50
100 --- ? => 5.26%
Answer:C
Question: By selling an article at Rs.800, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%?
A.338
B.480
C.888
D.266
Answer: B.480
Explanation: SP = 800
Profit = 25%
CP = (SP)*[100/(100+P)]
= 800 * [100/125]
= 640
Loss = 25% = 25% of 640 = Rs.160
SP = CP - Loss = 640 - 160 = Rs.480
Answer: B
Question: What is the least possible value of expression E = (x-1)(x-3)(x-4)(x-6)+10 for real values of x?
A.1
B.10
C.9
D.0
Answer: A.1
Explanation: Explanation :
E = (x-1)(x-6)(x-3)(x-4)+10
E = (x2-7x+6)(X2-7x+12)+10
Let x2-7x+6 = y
E = y2+6y+10
E = (y+3)2 + 1
Minimum value = 1 , when y = -3
Answer : A
Question: The average age of a group of 10 persons was decreased by 3 years when one person, whose age was 42 years, was replaced by a new person. Find the age of the new person?
A.22
B.99
C.12
D.88
Answer: C.12
Explanation: Initial average age of the 10 persons be P.
Age of the new person Q.
Sum of the ages of the initial 10 persons = 10P
New average = (P-3) 10(P-3) = 10P - 42 + Q => Q = 12.Answer:C
Question: A can run a kilometer race in 4 1/2 min while B can run same race in 5 min. How many meters start can A give B in a kilometer race, so that the race mat end in a dead heat?
A.177 m
B.786 m
C.272 m
D.100 m
Answer: D.100 m
Explanation: A can give B (5 min - 4 1/2 min) = 30 sec start.
The distance covered by B in 5 min = 1000 m.
Distance covered in 30 sec = (1000 * 30)/300
= 100 m.
A can give B 100m start.
Answer:D
Question: A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales in 1997 were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996 ?
A.1:2
B.4:5
C.1:1
D.3:2
Answer: A.1:2
Explanation: Let c = revenue from car sales in 1996
Let t = revenue from truck sales in 1996
Equating the total revenue in 1997 with the individual revenue from selling cars and trucks in 1997,
c(0.89) + t(1.07) = (c+t) (1.01)
Dividing throughout by t,
(c/t) (0.89) + 1.07 = (c/t + 1) (1.01)
=> (c/t) (0.12) = 0.06
=> (c/t) = 1/2
Option (A).
Question: Find the area of a parallelogram with base 36 cm and height 24 cm?
A.760
B.284
C.288
D.864
Answer: D.864
Explanation: Area of a parallelogram = base * height
= 36 * 24
= 864 cm2
Answer: D
Question: Shreehari has 500 chocolates in his self. He eats 10% of the chocolates per month. How many chocolates will he have after 2 months?
A.450
B.400
C.405
D.410
Answer: C.405
Explanation: Formula :
( After =100 denominator
Ago = 100 numerator)
500 Ã— 90/100 Ã— 90/100 = 405
C
Question: A, B and C started a business with capitals of Rs.6000, Rs.8000, and Rs.10000 respectively. At the end of the year, the profit share of B is Rs1000. The difference between the profit shares of A and C is
A.Rs. 400
B.Rs. 450
C.Rs. 500
D.Rs. 550
Answer: C.Rs. 500
Explanation: Ratio of investments of A,B and C is 6000 : 8000 : 10000 = 3 : 4 : 5.
And also given that, Profit share of ‘B’ is Rs.1000.
Now required difference is 5 – 3 = 2 parts.
Therefore, Required difference = 2/4 (1000) = Rs.500.
ANSWER:C
Question: A shopkeeper labeled the price of his articles so as to earn a profit of 20% on the cost price. He then sold the articles by offering a discount of 5% on the labeled price. What is the actual percent profit earned in the deal?
A.24%
B.20%
C.17%
D.18%
Answer: A.24%
Explanation: Explanation:
Let the CP of the article = Rs.100.
Then labeled price = Rs.120.
SP = Rs.120- 5% of 120 = Rs.120-6 = Rs.124.
Gain = Rs.124 â€“ Rs.100 = Rs.24
Therefore, gain/profit percent = 24%.
Answer: Option A
Question: A set consist of 2l-1 element. What is the number of subsets of this set which contain at most l-1 elements?
A.2^(2l-2)
B.2^(2l) - 2
C.2^(2l) -1
D.2^(2l)
Answer: A.2^(2l-2)
Explanation: I used l=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 (l-1) and may be risky since 1 is a number with certain unique properties
Question: During the months May through October, Teddy the bear quintuples his weight, and during the months November through April, Teddy loses 100 pounds. If at the beginning of November 1973, Teddy's weight was m pounds, what was Teddy's weight in pounds by the end of April 1976?
A.25m - 1300
B.25m - 1200
C.5m - 1300
D.5m - 1200
Answer: A.25m - 1300
Explanation: Nov ' 73 = m
April ' 74 = m - 100
Oct ' 74 = 5m - 300
April' 75 = 5m - 400
Oct' 75 = 25m - 1200
April'76 = 25m - 1300
Hence answer will be (A) 25m - 1300
Question: If X and Y are positive integers, X - 5 is divisible by 4 and Y - 1 is divisible by 4, all of the following could be the value of X - Y Except?
A.0
B.8
C.4
D.7
Answer: D.7
Explanation: X-5 = 4Y
=> P = 4Y + 5 = 5,9,13,17,21,25,29,33,37,41,45
Y-1 = 4X
=> Y = 4X + 1 = 1,5,9,13,17,21,25,29,33,37,41
0=5-5
8=13-5
4=5-1
24=45-21
So , we can see that all the answer choices are possible here except D
Question: The average price of an antique car increases over the years. If from 1990 to 1996, the price of the car increased by 13% and from 1996 to 2001 it increased by 20%, what is the price of the car in 2001 if the price in 1990 was $11,500?
A.$15,594.
B.$15,322.
C.$14,786.
D.$14,543.
Answer: A.$15,594.
Explanation: Whenever you have a question in which a value is increased by x% and then increased by y% then the overall effective increase = (x + y + xy/100 ) %
The effective increase = 13 + 20 + (13×20/100) = 35.6%
This is a little more 33% or 1/3 the original value.
THE QUICKEST WAY TO SOLVE THIS QUESTION IS TO USE APPROXIMATION.
11500 + 1/ 3 (12000) = 15500
Therefore option A is the answer.
I selected 12000 because it's value is a little more 11500 and it's easier to divide by 3 ( ie to calculate 1/3 or 33%).
Question: Each of seven different locks has a matching key. The keys are randomly reassigned to the locks. What is the probability that exactly two of the keys fit the locks to which they are reassigned?
A.1/8
B.1/6
C.1/49
D.3/8
Answer: C.1/49
Explanation: I was just going over probability questions.
can some one explain me what's wrong in my approach here.
Probability of choosing one right key out of 7 is 1/7.
Probability of choosing another right key is 1/7.
since the question is asking for 2 right keys , probability is multiplication of both = 1/7 * 1/7 = 1/49.
Ans C
Question: Which of the following options represents an approximate value for the question mark (?) in the following equation?
87.542 + 62.511 × 3.2 + ? = 805.925
A.913.4
B.918.4
C.911.4
D.988.4
Answer: B.918.4
Explanation: 87.542 + 62.511 × 3.2 + ? = 805.925
or, ? = 805.925 – 87.542 + 62.511 × 3.2
? = 805.925 – 87.542 + 200.0352
≈ 918.4
Answer B
Question: Which of these must the factor Q of the product of four consecutive even integers:-
1) 48
2) 64
3) 96
4) 192
5) 80
A.1,2 only
B.Q=2,3 only
C.Q=1,2,3 only
D.Q=1,2,3,4 only
Answer: D.Q=1,2,3,4 only
Explanation: Let the four variables be a< b< c< d.
Assume a worst case scenario where the a equal to a prime number (hence odd).
therefore
a = divisible by 1
b = a + 1 (divisible by 2)
c = a + 3 (divisible by 3)
d = a + 4 (divisible by 4)
therefore
each answer choice must be divisible Q by 2 x 3 x 4 = 24
only 80 is not divisible. Therefore answer = D
Question: A five-year promissory note with a face value of $3500, bearing interest at 11% compounded semiannually, was sold 21 months after its issue date to yield the buyer 10% compounded quarterly.What amount was paid for the note
A.$4336.93
B.4336.99
C.4336.96
D.4336.92
Answer: A.$4336.93
Explanation: Explanation:
i=j/m
Maturity value = PV (1 + i)^n
Term = 5 years - 21 months= 3.25 years
Price paid = FV(1+ i )^-n
Answer: A) 4336.93
Question: What is the height of a circular cone?
I. The area of that cone is equal to the area of a rectangle whose length is 33 cm.
II. The area of the base of that cone is 154 sq. cm.
A.I alone sufficient while II alone not sufficient to answer
B.II alone sufficient while I alone not sufficient to answer
C.Either I or II alone sufficient to answer
D.Both I and II are not sufficient to answer
Answer: D.Both I and II are not sufficient to answer
Explanation: EXPLANATION
II gives the value of r.
But, in I, the breadth of rectangle is not given.
So, we cannot find the surface area of the cone.
Hence, the height of the cone cannot be determined.
Correct answer is (D).
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good.
A.20/69
B.20/63
C.20/61
D.20/66
Answer: B.20/63
Explanation: Explanation:
Required probability =
= (10 * 4)/126 = 20/63
Answer: B
Question: In a class of 50 students, 20 play Golf, 15 play Cricket and 11 play Football. 7 play both Golf and Cricket, 4 play Cricket and Football and 5 play Golf and football. If 18 students do not play any of these given sports, how many students play exactly two of these sports?
A.45
B.12
C.35
D.10
Answer: D.10
Explanation: Notice that7 play both Golf and Cricket does not mean that out of those 7, some does not play Football too. The same for Cricket/Football and Golf/Football.
[color=#ffff00]{Total}={Golf}+{Cricket}+{Football}-{HC+CH+HF}+{All three}+{Neither}For more checkADVANCED OVERLAPPING SETS PROBLEMS
[/color]
50=20+15+11-(7+4+5)+{All three}+18 --> {All three}=2;
Those who play ONLY Golf and Cricket are 7-2=5;
Those who play ONLY Cricket and Football are 4-2=2;
Those who play ONLY Golf and Football are 5-2=3;
Hence, 5+2+3=10 students play exactly two of these sports.
Answer: D.
Question: A family made a down payment of $75 and borrowed the balance on a set of encyclopedias that cost $500. The balance with interest was paid in 23 monthly payments of $20 each and a final payment of $9. The amount of interest paid was what percent of the amount borrowed?
A.10.3%
B. 12.5%
C. 13%
D. 11%
Answer: A.10.3%
Explanation: borrowings = 500-75 = 425
total pmt = 23x20 + 9 = 469
so int = 469 - 425 = 44
interest in terms of borrowing = 44/425 = 10.3%
Answer is A
Question: There were two candidates in an election. Winner candidate received 62% of votes and won the election by 324 votes. Find the number of votes casted to the winning candidate?
A.456
B.837
C.912
D.1200
Answer: B.837
Explanation: W = 62% L = 38%
62% - 38% = 24%
24% -------- 324
62% -------- ? => 837
ANSWER:B
Question: A family pays $800 per year for an insurance plan that pays 70 percent of the first $1,000 in expenses and 100 percent of all medical expenses thereafter. In any given year, the total amount paid by the family will equal the amount paid by the plan when the family's medical expenses total how much?
A.$1,000
B.$1,200
C.$1,400
D.$1,800
Answer: C.$1,400
Explanation: Assuming the medical expenses are $1000 or more, the family pays $800 + $300 = $1100.
The total amount paid by insurance plan for the first $1000 of expenses is $700.
The insurance will pay another $400 when the medical expenses are $1400.
The answer is C.
Question: When positive integer N is divided by positive integer J, the remainder is 10. If N/J = 134.08, what is value of J?
A.125
B.56
C.78
D.112
Answer: A.125
Explanation: When a number is divided by another number, we can represent it as : Dividend = Quotient * Divisor + Remainder
So, Dividend/Divisor = Quotient + Remainder/Divisor
Given that N/J = 134.08
Here 134 is the quotient.
Given that Remainder = 10
So, 134.08 = 134 + 10/J
So, J = 125 ANS A
Question: A young girl counted in the following way on the fingers of her left hand. She started collang the thumb 1, the index finger 2, the middle finger 3, the ring finger 4, the little finger 5, then reversed direction calling the ring finger 6, the the middle finger 7, the index finger 8, the thumb 9 then back to the index finger for 10, the middel finger for 11, and so on. She counted up to 1995. She ended on her
A.a) thumb
B.b) the index finger
C.c) the middle finger
D.d) the ring finger
Answer: C.c) the middle finger
Explanation: Notice the pattern. The thumb lansd up at numbers 1,9,17,25,33,... so every 8th number
By this patter the thumb is also at number 1993 (multiple of 8 + 1)
Hence 1995 has to be the middle finger
Answer is (C)
Question: if samaira wallet have 10rs. note,50 rs. note,2000 rs.note.if 10rs. is 3/5 part of his money and 50rs. is 1/5 part of his money.if he has 8000 money consist of 2000 rs.calculate total money in samaira wallet?
A.18000
B.32000
C.30000
D.40000
Answer: D.40000
Explanation: if samaira have total money is x.
part of money in 2000 rs.=(1-(3/5+1/5))=1-4/5=1/5
x*1/5=8000,x=40,000rs.
answer D
Question: A vessel contains 20 liters of a mixture of milk and water in the ratio 3:2. 10 liters of the mixture are removed and replaced with an equal quantity of pure milk. If the process is repeated once more, find the ratio of milk and water in the final mixture obtained?
A.9:1
B.9:6
C.9:2
D.9:9
Answer: A.9:1
Explanation: Milk = 3/5 * 20 = 12 liters, water = 8 liters
If 10 liters of mixture are removed, amount of milk removed = 6 liters and amount of water removed = 4 liters.
Remaining milk = 12 - 6 = 6 liters
Remaining water = 8 - 4 = 4 liters
10 liters of pure milk are added, therefore total milk = (6 + 10) = 16 liters.
The ratio of milk and water in the new mixture = 16:4 = 4:1
If the process is repeated one more time and 10 liters of the mixture are removed, then amount of milk removed = 4/5 * 10 = 8 liters.
Amount of water removed = 2 liters.
Remaining milk = (16 - 8) = 8 liters.
Remaining water = (4 -2) = 2 liters.
The required ratio of milk and water in the final mixture obtained
= (8 + 10):2 = 18:2 = 9:1.
Answer: A
Question: A five-digit number divisible by 3 is to be formed using numerical 0, 1, 2, 3, 4 and 5 without repetition. The total number Q of ways this can be done is:
A.122
B.210
C.216
D.217
Answer: C.216
Explanation: We should determine which 5 digits from given 6, would form the 5 digit number divisible by 3.
We have six digits: 0, 1, 2, 3, 4, 5. Their sum=15.
For a number to be divisible by 3 the sum of the digits must be divisible by 3. As the sum of the six given numbers is 15 (divisible by 3) only 5 digits good to form our 5 digit number would be 15-0={1, 2, 3, 4, 5} and 15-3={0, 1, 2, 4, 5}. Meaning that no other 5 from given six will total the number divisible by 3.
Second step:
We have two set of numbers:
1, 2, 3, 4, 5 and 0, 1, 2, 4, 5. How many 5 digit numbers can be formed using these two sets:
1, 2, 3, 4, 5 --> 5! as any combination of these digits would give us 5 digit number divisible by 3. 5!=120.
0, 1, 2, 4, 5 --> here we can not use 0 as the first digit, otherwise number won't be any more 5 digit and become 4 digit. So, desired # would be total combinations 5!, minus combinations with 0 as the first digit (combination of 4) 4! --> 5!-4!=4!(5-1)=4!*4=96
120+96=216=Q
Answer: C.
Question: Two airplanes, one from Atlanta to New York and the other from New York to Atlanta, start simultaneously. After they meet, the airplanes reach their destinations after 16 hours and 4 hours respectively The ratio of their speeds is
A.2 : 3
B.4 : 3
C.4 : 2
D.1 : 2
Answer: C.4 : 2
Explanation: Solution
Let us name the planes
as A and B.	= (A'S speed) : (B's speed)
=âˆšb : âˆša
= âˆš16 : âˆš4
= 4 : 2
Answer C
Question: If the roots of a quadratic equation are 20 and -7, then find the equation?
A.x2 - x - 15 = 0
B.x2 - 12x - 50 = 0
C.x2 - 13x - 140 = 0
D.x2 - 4x - 40 = 0
Answer: C.x2 - 13x - 140 = 0
Explanation: Explanation:
Any quadratic equation is of the form
x2 - (sum of the roots)x + (product of the roots) = 0 ---- (1)
where x is a real variable. As sum of the roots is 13 and product of the roots is -140, the quadratic equation with roots as 20 and -7 is: x2 - 13x - 140 = 0.
Answer C