RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Consider the following game, in which a referee picks a random integer between 1 and 100.
One after the other, each of three players tries to guess the number the referee picked. Each
player announces his or her guess before the next player guesses. Each guess has to be different
from the previous guesses. The winner is the player who comes closest to the referee’s
number without exceeding it. (It is possible for none of the players to win.)
Suppose that Player 1 guesses 24, and that Player 3 will guess a number that gives her/him the
best chance of winning. What number should Player 2 guess to maximize his/her chances of
winning?
A.1
B.25
C.62
D.63
Answer: D.63
Explanation: First of all, observe that it always gives the third player the best chances to win if
[s]he guesses the lowest number in some range which the other players left open. Thus, if you
choose 63, this narrows the third player’s choices down to 1, 25, and 64. Guessing 25 gives
a range of 38 numbers (25 through 62 inclusive) which win for the third player if the referee
picked one of them, while a choice of 64 would only give 37 favorable numbers, and a choice
of 1 only gives 23 favorable numbers.
Note that 63 gives you 38 favorable numbers also (63 through 100 inclusive) so this way you
and the third player both have a 38% chance of winning, while the first player only has a 24%
chance.
The other four given answers do not give you such a good result. Answer (e), 64, still makes
25 the best choice for the third player, but cuts your chances down to 37% while raising the
third player’s to 39%. Answer (a), 1, is even worse than (e) because it only gives 23 chances
for you. Answer (c), 62, would give the third player 63 as the best guess, (38% versus 37%
if 25 is guessed instead) drastically reducing your winning chances to 1%. You would get the
same baleful result if you guessed 25 [answer (b)], because then the obvious best guess for
the third player is 26.
correct answer D
Question: The average monthly salary of 20 employees in an organisation is Rs. 1700. If the manager's salary is added, then the average salary increases by Rs. 100. What is the manager's monthly salary ?
A.Rs.6003
B.Rs.3800
C.Rs.1288
D.Rs.6108
Answer: B.Rs.3800
Explanation: Explanation:
Manager's monthly salary Rs. (1800 * 21 - 1700 * 20) = Rs.3800.
Answer: B
Question: Out of 40 applicants to a law school, 15 majored in political science, 20 had a grade point average higher than 3.0, and 10 did not major in political science and had a GPA equal to or lower than 3.0. How many W applicants majored in political science and had a GPA higher than 3.0?
A.5
B.10
C.15
D.25
Answer: A.5
Explanation: Total applicants = 40
Political science = 15 and Non political science = 40 - 15 = 25
GPA > 3.0 = 20 and GPA <= 3.0 = 20
10 Non political science students had GPA <= 3.0 --> 15 Non political science students had GPA > 3.0
GPA > 3.0 in political science = Total - (GPA > 3.0 in non political science) W= 20 - 15 = 5
Answer: A
Question: A certain bridge is 4,424 feet long. Approximately how many minutes does it take to cross this bridge at a constant speed of 10 miles per hour? (1 mile = 5,280 feet)
A. 1
B. 2
C. 4
D. 5
Answer: D. 5
Explanation: Distance: 4424 feet. This is (4424/5280) miles = 0.84 miles
Speed: 10 miles per hour
Time: (Distance / Speed) (0.84/10) {This will come in Hours}. Multiply by 60 to get answer in minutes. It is 5.04 minutes.
Answer to be 5 minutes.
ANS D
Question: A train 900 m long passed a pole in 9 sec. How long will it take to pass a platform 800 m long?
A.17
B.18
C.19
D.20
Answer: A.17
Explanation: Speed = 900/9
= 100 m/sec.
Required time
= (900 + 800)/100
= 17 sec.
Answer:A
Question: Two pipes can fill a tank in 18 minutes and 60 minutes. An outlet pipe can empty the tank in 45 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank?
A.1/15
B.1/16
C.1/20
D.1/10
Answer: C.1/20
Explanation: Part of the filled by all the three pipes in one minute
= 1/18 + 1/60 - 1/45 = 1/20
So, the tank becomes full in 20 minutes.
Answer:C
Question: In a city, the streets are aligned in a grid, where the east-west roads are called 1st Rd, 2nd Rd, 3rd Rd, etc, increasing in number as one moves northward. The north-south roads are called 1st Ave, 2nd Ave, 3rd Ave, etc, increasing in number as one moves eastward. If Bill needs to walk from the corner of 2nd Rd and 3rd Ave to the corner of 9th Rd and 6th Ave in the shortest possible time, how many different routes could he take?
A.90
B.120
C.150
D.180
Answer: B.120
Explanation: Bills needs to walk 7 blocks north and 3 blocks east.
One possible solution is NNNNNNNEEE.
There are 10C7 = 120 possible solutions.
The answer is B.
Question: It takes printer A 4 more minutes more than printer B to print 40 pages. Working together, the two printers can print 50 pages in 6 minutes. How long will it take Printer A to print 60 pages?
A.12
B.18
C.20
D.24
Answer: B.18
Explanation: If it takes 4 more minutes for A to print 40 pages than it takes B,
it takes 5 more minutes for A to print 50 pages than it takes B.
Thus if b is the number of minutes than B takes to print 50 pages,
we can write:
1/b+1/(b+5)=1/6 (since in 1 minute, they print 1/6th of the 50 page job)
6(2b+5)=b(b+5)
b^2-7b-30=0
(b-10)(b+3)=0
b=10
Thus it takes A 15 minutes to print 50 pages and 15*60/50=18 minutes to print 60 pages (ANSWER B)
Question: In a 2000 m race, A beats B by 100 meters or 15 seconds. Find the speed of B?
A.10m/s
B.2m/s
C.5m/s
D.6.7m/s
Answer: D.6.7m/s
Explanation: Since A beats B by 100 m or 15 seconds,
it implies that B covers 100 m in 15 seconds.
Hence speed of B = 100/15 = 6.7 m/s.
Answer: D
Question: The probability that event A occurs is 0.4, and the probability that event B occurs is 0.45. If the probability that either event A or event B occurs is 0.6, what is the probability that event B and event B will occur?
A.0.25
B.0.15
C.0.45
D.0.5
Answer: A.0.25
Explanation: P(A or B) = P (A) + P(B) - p(a n b)
0.6= 0.4 + p(a n b) + 0.45
P(B) = 0.25
Ans : A
Question: A 480 m long train is running at a speed of 55 Km/hr. It crossed a platform of length 620 m in ?
A.41.1 sec
B.72 sec
C.31.8 sec
D.50.4 sec
Answer: B.72 sec
Explanation: Speed = 55 Km/hr
(to convert km/hr in to M/s)
= 55 x 5/18 M/s
Distance = 480 m + 620 m ( If questions is about train crossing a post you need to consider only the length of Train, )
= 1100 m
Time = Distance / Speed
= 1100 x 18 / (5 x 55)
= 72 sec
Ans is :B
Question: A train is 360 meter long is running at a speed of 54 km/hour. In what time will it pass a bridge of 140 meter length?
A.65 seconds
B.33.33 seconds
C.40 seconds
D.97 seconds
Answer: B.33.33 seconds
Explanation: Speed = 54 Km/hr = 54*(5/18) m/sec = 15 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (1/15)
= 33.33 seconds
Answer:B
Question: A and B together have $100. If 3/10 of A's amount is equal to 1/5 of B's amount, how much amount does B have?
A.$60
B.$55
C.$42
D.$31
Answer: A.$60
Explanation: 3/10 A = 1/5 B
A = 1/5 * 10/3 B
A = 2/3 B
A/B = 2/3
A:B = 2:3
B's share = 100*3/5 = $60
Answer is A
Question: Donovan took a math test and got 35 correct and 14 incorrect answers.
What was the percentage of correct answers? (Round to the nearest
hundredth)
A.57.78%
B.67.78%
C.71.43%
D.47.78%
Answer: C.71.43%
Explanation: 35 correct our of 49 total (35+14)
35/49
correct answer C
Question: In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?
A.610
B.720
C.825
D.920
Answer: B.720
Explanation: Explanation:
The word 'OPTICAL' has 7 letters. It has the vowels 'O','I','A' in it and these 3 vowels should always come together. Hence these three vowels can be grouped and considered as a single letter. That is, PTCL(OIA).
Hence we can assume total letters as 5 and all these letters are different.
Number of ways to arrange these letters
=5!=5Ã—4Ã—3Ã—2Ã—1=120=5!=5Ã—4Ã—3Ã—2Ã—1=120
All the 3 vowels (OIA) are different
Number of ways to arrange these vowels among themselves
=3!=3Ã—2Ã—1=6=3!=3Ã—2Ã—1=6
Hence, required number of ways
=120Ã—6=720
ANSWER IS B
Question: A deer runs k miles in n hours. How many miles will it run in x hours at the same rate?
A.knx
B.k⁄n
C.kx⁄2n
D.kx⁄n
Answer: D.kx⁄n
Explanation: Given Speed = k/n
To Find distance in x hours with same speed
Distance = speed * time
Distance = k/n*x = kx/n
Answer D
Question: The average weight of 10 men is increased by 1 ½ kg when one of the men who weighs 60 kg is replaced by a new man. What is the weight of the new man?
A. 80 kg
B. 83 kg
C. 70 kg
D. 75 kg
Answer: D. 75 kg
Explanation: Since the average has increased by 1.5 kg, the weight of the man who stepped in must be equal to 60+10x1.5
60+15=75 Kg
Ans: 'D'
Question: Charlene's annual bonus is calculated in the following manner: Charlene receives 20 percent of her first $11,000 in sales and 30 percent of her sales in excess of $11,000. If Charlene received a bonus of $8,500, what were her annual sales?
A.$ 20,000
B.$ 22,000
C.$ 24,666
D.$ 26,000
Answer: C.$ 24,666
Explanation: Let x be the total sales in $.
For the 1st 11,000 you get 20% ---> 0.2*11000 = 2200$
For the remaining (x-11000) $, you get 30% ---> 0.3*(x-11000)
Thus, 0.3*(x-11000) + 2200 = 8500 ----> x= 24,666 $
C is thus the correct answer.
Question: If four coins are tossed, the probability of getting two heads and two tails is?
A.3/8
B.3/6
C.3/9
D.3/1
Answer: A.3/8
Explanation: Since four coins are tossed, sample space = 24
Getting two heads and two tails can happen in six ways.
n(E) = six ways
p(E) = 6/24 = 3/8
Answer:A
Question: Three-fifth of a two digit number exceeds its one fifth by 6. What is the sum of the digits of the number?
A.6
B.9
C.11
D.12
Answer: A.6
Explanation: Explanation:
3x/5 – x/5 = 6 => x =15
1 + 5 = 6
A)
Question: In a restaurant, the profit is 160% of the cost. If the cost increases by 12% but the selling price remains constant, approximately what percentage of the selling price is the profit?
A.30%
B.57%
C.90%
D.100%
Answer: B.57%
Explanation: Explanation :
Let C.P.= Rs. 100. Then, Profit = Rs. 160, S.P. = Rs. 260.
New C.P. = 112% of Rs. 100 = Rs. 112
New S.P. = Rs. 260.
Profit = Rs. (260 - 112) = Rs. 148.
Required percentage = (148 /260 *100) % = 57 % appox
Answer : B
Question: An investor purchased 100 shares of stock X at 6 1/8 dollars per share and sold them all a year later at 30 dollars per share. If the investor paid a 2 percent brokerage fee on both the total purchase price and the total selling price, which of the following is closest to the investor's percent gain on this investment?
A.92%
B.240%
C.280%
D.395%
Answer: D.395%
Explanation: If the purchase price was 6$ per share then the investor would have made a profit of 400%.
Since the purchase price is slightly more than 6$ the profit would be slightly less than 400%.
Also a 2% brokerage is negligible and it brings down the profit percentage only by a small value. Approximation is very useful to solve these kind of problems as the answer choices are far apart.
Answer: D
Question: A dishonest dealer professes to sell his goods at Cost Price but still gets 20% profit by using a false weight. What weight does he substitute for a kilogram?
A.223 1/3 grams.
B.833 1/3 grams.
C.2873 1/3 grams.
D.273 1/3 grams.
Answer: B.833 1/3 grams.
Explanation: Explanation:
If the cost price is Rs.100, then to get a profit of 20%, the selling price should be Rs.120.
If 120kg are to be sold, and the dealer gives only 100kg, to get a profit of 20%.
How many grams he has to give instead of one kilogram(1000 gm).
120 gm ------ 100 gm
1000 gm ------ ?
(1000 * 100)/120 = 2500/3 = 833 1/3 grams.
Answer:B
Question: Of 100 apples in a tree, 30 percent are green. How many red apples must be picked in order to bring the number of green apples up to 50 percent of the apples in the tree?
A.40
B.50
C.30
D.70
Answer: A.40
Explanation: Now, there are 30 green apples (30% of 100) and 100-30=70 red apples in the tree. We need there to be 30 green apples and 30 red apples, in this case there will be 50% green apples and 50% red apples.
Therefore 70-30=40 red apples must be picked.
Answer: A.
Question: A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train?
A.33
B.77
C.72
D.55
Answer: C.72
Explanation: Length = Speed * time
Speed = L/T
S = 400/20
S = 20 M/Sec
Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 72 Kmph
Answer:C
Question: The time it took car P to travel 300 miles was 2 hours less than the time it took car R to travel the same distance. If car P’s average speed was 10 miles per hour greater than that of car R, what was car R’s average speed, in miles per hour?
A.34
B.50
C.60
D.70
Answer: A.34
Explanation: Let speed of car R be=x
Then speed of car P= x+10
A/Q,
(300/x)-(300/(x+10))=2
Solving for x=34 miles\hr.
A
Question: A flagstaff 17.5 m high casts a shadow of length 40.25 m. What will be the height of a building, which casts a shadow of length 28.75 m under similar conditions?
A.12.5 m
B.10.5 m
C.14
D.12
Answer: A.12.5 m
Explanation: Explanation:
Let the required height of the building be x meter
More shadow length, More height(direct proportion)
Hence we can write as
(shadow length) 40.25 : 28.75 :: 17.5 : x
⇒40.25×x=28.75×17.5
⇒x=28.75×17.5/40.25
=2875×175/40250
=2875×7/1610
=2875/230 =575/46 =12.5
Answer: Option A
Question: A student can select one of 8 different math book, one of 3 different chemistry book & one of 4 different science book.In how many different ways students can select book of math, chemistry & science.
A.22
B.72
C.96
D.37
Answer: C.96
Explanation: 8C1×3C1×4C1 = 8x3x4=96 ways
Answer:C
Question: In how many ways can the letters of the word APPEAR be rearranged such that the vowels always appear together?
A.6!/2!
B.3!*3!
C.4!/2!
D.4! *3!/(2!*2!)
Answer: D.4! *3!/(2!*2!)
Explanation: In the word ABACUS , there are 3 vowels - 2 A's and U
Number of ways the letters of word APPEAR be rearranged such that the vowels always appear together
= (4! * 3! )/2!*2!
We can consider the the 3 vowels as a single unit and there are 3 ways to arrange them . But since 2 elements of vowel group AND 2 elements of consonant group are identical we divide by 2! 2! .
The entire vowel group is considered as a single group .
Answer D
Question: A die is thrown twice and the sum of the numbers appearing is observed to be 6.
find the conditional probability that the number 4 has appeared at least once?
A.2/5
B.3/5
C.4
D.4/11
Answer: A.2/5
Explanation: Let E be the event that ‘number 4 appears at least once’ and F be
the event
that ‘the sum of the numbers appearing is 6’.
Then, E = {(4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (1,4), (2,4), (3,4),
(5,4), (6,4)}
and F = {(1,5), (2,4), (3,3), (4,2), (5,1)}
We have P(E) = 11/36
and P (F) = 5/36
Also EnF = {(2,4), (4,2)}
Therefore P(EnF) = 2/36
the required probability
P(E|F) = P(EnF)/P(F) = (2/36)/(5/36) = 2/5
Option is A
Question: How many numbers between 100 and 798 are divisible by 2, 3, and 7 together?
A.112
B.77
C.267
D.17
Answer: D.17
Explanation: Explanation:
As the division is by 2, 3, 7 together, the numbers are to be divisible by: 2*3*7 = 42
The limits are 100 and 798
The first number divisible is 42*3 = 126
To find out the last number divisible by 42 within 798:
798/42 = 19
Hence, 42*19 = 798 is the last number divisible by 42 within 798
Hence, total numbers divisible by 2, 3, 7 together are (19 â€“ 2) = 17
ANSWER: D
Question: A and B rent a pasture for 10 months. A put in 80 cows for 7 months. How many can B put in for the remaining 3 months, if he pays half as much again as A?
A.221
B.287
C.288
D.280
Answer: D.280
Explanation: 80* 7: x* 3 = 1:1 1/2
560: 3x = 2: 3
x = 280
Answer: D
Question: A sum is divided among C, D and E in such a way that for each rupee C gets, D gets 75 paisa and E gets 50 paisa. If the share of E is RS. 80, what is the total amount?
A.360
B.350
C.340
D.330
Answer: A.360
Explanation: c:d:e = 100:75:50
20:15:10
10 --- 80
45 --- ? => 360
Answer:A
Question: How many times will the hands of a clock coincide in a day?
A.24
B.22
C.23
D.44
Answer: B.22
Explanation: solution
The hands of a clock coincide 11 times in every 12 hours (Since between 11 and 1, they coincide only once, i.e., at 12 o'clock). The hands overlap about every 65 minutes, not every 60 minutes. Thus the minute hand and the hour hand coincide 22 times in a day
so Answer is B
Question: The sector of a circle has radius of 14 cm and central angle 144o. Find its perimeter?
A.60cm
B.63.2cm
C.70cm
D.80cm
Answer: B.63.2cm
Explanation: Perimeter of the sector = length of the arc + 2(radius)
= (144/360 * 2 * 22/7 * 14) + 2(14)
= 35.2 + 28 = 63.2 cm
Answer:B
Question: The area of a square is equal to 2 times the area of a rectangle of dimensions 8 cm * 64 cm. What is the perimeter of the square?
A.482
B.268
C.800
D.128
Answer: D.128
Explanation: Area of the square = s * s = 2(8 * 64)
=> s = 4 * 8 = 32 cm
Perimeter of the square = 4 * 32 = 128 cm.
Answer: D
Question: In how many ways can a committee consisting of 4 men and 5 women be formed from a group of 7 men and 8 women?
A.7C4 8C5
B.4C7 5C8
C.7C5 8C4
D.9C4 7C5
Answer: A.7C4 8C5
Explanation: Group consisting of 7 men and 8 women
4 men can be selected from 7 men in 7C4 ways
5 women can be selected from 8 women in 8C5 ways
Therefore, Total number of ways= 7C4 8C5
ANSWER:A
Question: If p and q are integers and p divided by q is 16.15, then which of the following integers is a possible value for the remainder when p is divided by q?
I. 15
II. 5
III. 3
A.I only
B.II only
C.III only
D.I,III only
Answer: D.I,III only
Explanation: p=16.15q from which p = 16q + 15q/100 or p = 16q + 3q/20.
Since p and q are integers, 3q/20 must also be an integer. 3 is not divisible by 20, then q must be divisible by 20, and therefore, q/20 is an integer and 3q/20 is an integer which is a multiple of 3. From the given answers, only 15 and 3 are divisible by 3.
Answer D
Question: If, 7 years ago, Jamie was half as old as he is now, how old will he be in x years?
A.x + 10
B.x + 14
C.x + 2
D.x – 5
Answer: B.x + 14
Explanation: let his age be a. a-7=a/2 hence a=14. 14 years hence, a =x+14
Answer B
Question: The number of even factors of 21600 is
A.32
B.42
C.60
D.25
Answer: C.60
Explanation: Make a prime factorization of the number: 21,600=25∗33∗52
According to the above the number of factors is (5+1)(3+1)(2+1)=72
Now, get rid of powers of 2 as they give even factors --> you'll have 33∗52 which has (3+1)(2+1)=12 factors. All the remaining factors will be odd, therefore 21,600 has 72-12=60 even factors.
Answer: C.
Question: C and D walk around a circular track. They start at 11 a.m from the same point in the opposite directions. C and D walk at a speed of 7 rounds per hour and 8 rounds per hour respectively. How many times shall they cross each other before 5 p.m
A.90
B.95
C.100
D.105
Answer: A.90
Explanation: Explanation:
Relative speed = (7+8) =15 rounds per hour
So, they cross each other 15 times in an hour hence, they cross 90 times before 5 p.m
Answer: Option A
Question: In how many ways can the letters {U, U, U, R} be arranged?
A.4
B.20
C.120
D.720
Answer: A.4
Explanation: My answer : A
There is 4! ways to arrange those letters in total, however letter U repeats 3! times and letter R repeats 1! times
=> the way to arrange without repeating = 4!/ [3!x1!] = 4
Question: Find the value of X, Y by solving the below equations
X + Y = 12
X - Y = 4
A.5, 7
B.8, 4
C.6, 6
D.7, 5
Answer: B.8, 4
Explanation: X + Y = 12 ---(I)
X - Y = 4 -----(II) by adding (I) and (II)
------------
2X = 16 ==> X = 16/2 = 8
By Replacing the value of X in (I) we get 8 + Y = 12 ==> Y = 12-8=4.
So, X = 8, Y = 4
Answer B) 8, 4
Question: One hour after Adrienne started walking the 60 miles from X to Y, William started walking from X to Y as well. Adrienne walks 3 miles per hour and William walks 1 mile per hour faster than Adrienne. How far from X will William be when he catches up to Adrienne?
A.8 miles
B.9 miles
C.10 miles
D.11 miles
Answer: D.11 miles
Explanation: First, determine how far Adrienne has walked in the one hour. She has walked three miles which means she is three miles ahead of William when he sets off. William walks at four miles/hour which means that every hour, William will get one mile closer to Adrienne. If he gets one mile closer every hour, it will take him three hours to catch up to her which means he travels 3hours * 4 miles/hour = 12 miles and she travels 4 hours * 3 miles/hour = 12 miles. He will be 12 miles from X when he catches up to her.
A slightly different way to solve...
We don't know how long they will walk before they catch up to one another but we do know that A walks for one hour more than J. J = T and A = T+1. We are looking for the distance at which they meet up which means the distance will be the same. D=r*t so,
r*t (William ) = r*t (adrienne)
r*(t) = r*(t+1)
4t = 3t+3
t=3
d=r*t
d=4*3
d=12
D) 12 miles
Question: If -12 < x < 14, Then which of the following must be true ?
A.x = -11
B.x <= 13
C.x > 12
D.x > -43
Answer: D.x > -43
Explanation: SOLUTION:
A. x = -11 --> Not always true. x can be any value between -12 and 14
B. x <= 13 --> Not always true. If x = 13.5 then x > 13.
C. x > 12 --> Not always true. x can be a value less than 12.
D. x > -43 --> Always true. x can take a minimum value of -12 (approx.). Hence x is always greater than -43.
E. x >= 11 -->Not always true. x can be a value less than 11.
Answer: D
Question: The R train leaves station A moving at a constant speed, and passes by stations B and C, in this order. It takes the R train 7 hours to reach station B, and 5 additional hours to reach station C. The distance between stations A and B is m kilometers longer than the distance between stations B and C. What is the distance between stations A and C in terms of m?
A.1.8m
B.6m
C.7m
D.9m
Answer: B.6m
Explanation: The reason it is failing for you is that you chose incorrect numbers. If the question says R it took 7 hrs to reach from A to B and 5 hrs to reach from B to C at a constant speed. It shows that distance AB and BC should be in ratio of 7/5.
If you take such numbers you can solve problem.
AB = 7, BC=5
Therefore
AB-BC = 2
But from question, AB-BC =m
=> m=2
Now total distance = AB+BC= 12
Substitute 12 to get answer in terms of m
Total distance =12 =6m
Ans B
Question: A towel, when bleached, lost 20% of its length and 20% of its breadth. What is the percentage decrease in area?
A.24%
B.36 %
C.32%
D.54%
Answer: B.36 %
Explanation: percentage change in area
=(−20−20+(20×20)/100)%=−36%
i.e., area is decreased by 36%
ANSWER:B
Question: A class has a ratio of 3:6:7 of children with red hair, blonde hair and black hair respectively. If the class has 9 kids with red hair, how many kids are there with black hair?
A.7
B.6
C.9
D.21
Answer: D.21
Explanation: Since there is a 3:7 ratio between red haired children and black-haired children, if there are 9 children with red hair, then there must be 3 times the amount of black-haired children. Therefore, are 21 children with black hair.
Answer: D)
Question: What is the probability that out of the combinations that can be made using all the letters of the word EXCESS, Jerome will randomly pick a combination in which the first letter is a vowel and the last letter is a consonant?
A.96/320
B.24/180
C.33/100
D.48/180
Answer: D.48/180
Explanation: lets see the possiblilties with the given restrictions..
lets put the starting letter as vowel E..
then remaining 5 places can be filled in 5!/2!= 60..
but this consists of second E as the last letter and we will have to subtract these ways from 60..
so when first and last places are occupied by E, the remaining 4 places can be filled by 4!/2!=12 ways..
so ways with the restrictions= 60-12= 48..
so prob= 48/180
ANSWER :D
Question: A, B and C are inner angles in a triangle. If A= B+ C, what can't be the size of B?
A.90 DEGREES
B.70 DEGREES
C.760 DEGREES
D.940 DEGREES
Answer: A.90 DEGREES
Explanation: Given A= B+ C, and A, Band Care inner angles in a triangle. Thus A+ B+ C= 180
B+ C+ B+ C= 180 => 2(B+ C) = 180 => B+ C= 90. Thus beta will be less than 90.
Hence the answer is A.