RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A train of 25 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.0 km long?
A.2.5
B.3
C.5
D.7
Answer: A.2.5
Explanation: D = 25 * 60 + 1000 = 2500 m
T = 2500/60 * 18/5 = 150 sec = 2.5 mins
Answer: A
Question: Find the amount on Rs.8000 in 9 months at 20% per annum, if the interest being compounded quarterly?
A.9287
B.9261
C.9229
D.9285
Answer: B.9261
Explanation: A = 8000(21/20)3
= 9261
Answer: B
Question: If 0 < A < Y, A is an odd number and Y is a prime number, which of the following can be the value of A + Y ?
A.11.
B.13.
C.17.
D.10.
Answer: D.10.
Explanation: If A is odd ,implies a(odd)+y(odd/even prime)=(Even/Odd)
If Y is even, the 2 is the even prime , therefore y=2A=1 since 0<A<Y therefore A+Y =3. But 3 is not an option
which implies y is odd,
Now A(odd)+Y(odd)=Even
10 is the only option that is even=D
Question: One vessel contains a mixture of 5 parts pure wine and 3 parts soda, whereas the other vessel contains a mixture of 7 parts pure wine and 5 parts soda. Compare the strength of the wine.
A.35;36
B.7 : 8
C.15 : 14
D.14 : 5
Answer: C.15 : 14
Explanation: 5/8 : 7/12
LCM of 8,12 = 24
(5/8)*24 : (7/12)*24
15:14
Answer is C.
Question: Employees at a company will vote for an executive team of five people from eight qualified candidates. The executive team consists of a president, a treasurer, and three warrant officers. If an executive team is considered different if any of the same people hold different offices, then how many possible executive teams S could be selected from the eight candidates?
A.56
B.120
C.210
D.1120
Answer: D.1120
Explanation: If an executive team is considered different if any of the same people hold different offices,....
so you will not have answer as 6720..
president could be by any of 8 person..
treasurer could be any out of remaining 7 person..
remaining three order does not matter, so we have to choose 3 out of 6=6c3=20..
total ways S= 8*7*20=1120..
ans D...
Question: Find the least number of five digits which is exactly divisible by 12, 15 and 18?
A.1080
B.10080
C.10025
D.11080
Answer: B.10080
Explanation: LCM = 180
180) 10000 (55
9900
---------
100
10000 + 180 - 100 = 10080
ANSWER:B
Question: A waiter's salary consists of his salary and tips. During one week his tips were 5/2 of his salary. What fraction of his income came from tips ?
A.4/9
B.5/4
C.5/8
D.5/7
Answer: D.5/7
Explanation: Income = salary (s) +tips = s + s*5/2 = s*7/2
Tips = s*7/2
fraction of his income came from tips = (s*5/2)/(s*7/2)= 5/7
ANSWER:D
Question: A can do a work in 40days, B in 60days. A alone start the work after 10days he left work. In how many days B can finish the work?
A.20days
B.15days
C.30days
D.45days
Answer: D.45days
Explanation: 10days work of A = 10/40 = 1/4
remaining work = 1-1/4 = 3/4
B can finish 3/4 work = 60*3/4 = 45days
Answer is D
Question: When N is divided by 10 the remainder is 1 and when N is divided by 3 the remainder is 2. What is the remainder K when N is divided by 30?
A.(a) 4
B.(b) 7
C.(c) 11
D.(d) 13
Answer: C.(c) 11
Explanation: N ends in the digit 1 because when N is divided by 10, the remainder is 1. Since N ends in 1, the remainder K when N is divided by 30 also ends in a 1. 11 is the only choice which ends in a 1.C
Question: For every positive integer n, the nth term of a sequence is the total sum of three consecutive integers starting at n. What is the total sum of terms 1 through 60 of this series?
A.5330
B.5670
C.5990
D.6240
Answer: B.5670
Explanation: Each term of the series has the form (n+n+1+n+2) = 3n+3
Since the series goes from 1 to 60, the sum of the series is:
3(1+2+...+60) + 60(3) =
3(60)(61)/2 + 60(3) =
90*61 + 180 = 5670
The answer is B.
Question: Which of the following is closer to (6!+4!)*(6!-4!)?
A.587945
B.647280
C.587920
D.658230
Answer: B.647280
Explanation: Notice that 6! = (6*5)(4!)
(6!+4!)*(6!-4!)=[6!(30+1)]*[6!(30-1)]
= 21/19
≈ 647280
Answer: B
Question: |5 - 2| - |6 - 9| = ?
A.3
B.2
C.1
D.0
Answer: D.0
Explanation: |5 - 2| - |6 - 9| = | 3 | - | -3 | = 3 - 3 = 0
correct answer D
Question: In business, A and C invested amounts in the ratio 3:2, whereas the ratio between amounts invested by A and B was 3:4, If Rs 30,000 was their profit, how much amount did B receive.
A.1235
B.62896
C.6666
D.8974
Answer: C.6666
Explanation: Explanation:
A:B = 3:4 = 3:4
=> A:C = 3:2 = 3:2
=> A:B:C = 3:4:2
C share = (2/9)*30000
= 6666
Option C
Question: A wheel rotates 10 times every minute and moves 20 cm during each rotation. How many ems does the wheel move in 1 hour?
A.20000
B.14000
C.23000
D.120000
Answer: D.120000
Explanation: Explanation :
Number of wheel moves in 1 hour = 10 * 60 = 600distance moved = 600 * 200 = 12000
Answer : D
Question: There are 100 freshmen at a particular college, all of whom must take at least one of the three core classes: Art, Biology, and Calculus. Of these freshmen, 13 take only Biology, 10 take only Calculus, 5 take all three classes, and 20 take Art and exactly one of the other two core classes. If the number of freshmen who take only Art is 3 times the number of freshmen who take every core class except Art, how many freshmen take Art?
A.25
B.64
C.36
D.48
Answer: B.64
Explanation: Make a venn diagram to get a clear picture. Look at the diagram:
Each letter represents only one color. b represents the people who take only Art. d represents people who take only Art and Bio etc.
d + f = 20 (People who take Art and one other class)
b = 3e (people who take only Art is 3 times the people who take Bio and Calculus)
13 + 10 + 5 + b + d + e + f = 100 (Total people)
b + b/3 = 52
b = 39
Number of freshmen who take Art = 39 + 20 + 5 = 64
Answer B
Question: Find the value of x from logx 100 = 2
A.10
B.12
C.13
D.14
Answer: A.10
Explanation: solution:
logb 1000 = 3
We can write it as,
b3 = 1000
b3 = 103
So from the above equation
b = 10
ANSWER IS A
Question: The bankerâ€™s discount of a certain sum of money is Rs. 90 and the true discount on the same sum for the same time is Rs. 60. The sum due is
A.210
B.180
C.360
D.450
Answer: B.180
Explanation: Sol.
Sum = B.D. * T.D. / B.D. - T.D. = Rs.[90 * 60 / 90 - 60] = Rs. [90 * 60 / 30] = Rs. 180
Answer B
Question: A boat ma goes 2km against the current of the stream in 1 hr and goes 1 km along the current in 10 min. how long will it take to go 4 km in stationary water
A.40 min
B.1hr
C.1hr 15 min
D.1hr 30 min
Answer: B.1hr
Explanation: rate down stream=(1/10*60)km/hr=6km/hr
rate up stream=2km/hr
speed still water =1/2(6+2)=4km/hr
required time =(4/4)=1 hr
Answer(B)
Question: A shopkeeper increases the price of an article by X% and then decreases it by X%. As a result the price of the article is reduced by $180. After one more such change the price is further reduced by $153 Find the original price of the article.
A.$1200
B.$1100
C.$1400
D.$1000
Answer: A.$1200
Explanation: Given:
After a% decrease the price of the article is reduced by $180 --> pa=180;
After one more such change the price is further reduced by $153. After the first decrease the price became $(p−180), thus (p−180)a=153--> pa−180a=153a=15--->a=15 --> p∗0.15=180--> p=1,200
Answer: A.
Question: If x = 3 and y = −2, what is the value of (x − 2y)^y?
A.−100
B.0.02
C.0.25
D.4
Answer: B.0.02
Explanation: Quickly we can spot that answer is neither integer nor negative. Eliminate A, DE
Answer: B
Question: How many different positive integers are factors of 324 ?
A. 9
B. 16
C. 25
D. 36
Answer: D. 36
Explanation: 18×18=6^2 × 3^2
So total factors = (5+1)(5+1) = 36
Answer: D
Question: The average monthly salary of the employees of a firm is Rs.60 out of the employees 12 officers get an average of Rs.400 per month and the rest an average of Rs. 56 per month , Find the number of emp
A.1032
B.2766
C.2882
D.2788
Answer: A.1032
Explanation: Actual average salary of 12 officers = 400
\inline \fn_jvn \therefore Total salary of 12 officers = 400 x 12 = 4800
Average of these 12 officers as a whole =60
Total salary of 12 officers as a whole = 60 x 12 = 720
The total salary of rest = 4800 - 720 = 4080
Difference in average of the rest of officers = 60 - 56 = 4
Rest of the officers = \inline \fn_jvn \frac{4080}{4}=1020
Total number of employees = 1020 + 12 = 1032
ANSWER:A
Question: The average weight of a group of persons increased from 48 kg to 51 kg, when two persons weighing 78 kg and 93 kg join the group. Find the initial number of members in the group?
A.21
B.22
C.23
D.24
Answer: C.23
Explanation: Let the initial number of members in the group be n.
Initial total weight of all the members in the group = n(48)
From the data,
48n + 78 + 93 = 51(n + 2) => 51n - 48n = 69 => n = 23
Therefore there were 23 members in the group initially.
ANSWER:C
Question: Club X has more than 30 but fewer than 60 members. Sometimes the members sit at tables with 3 members at one table and 4 members at each of the other tables, and sometimes they sit at tables with 3 members at one table and 5 members at each of the other tables. If they sit at tables with 6 members at each table except one and fewer than 6 members at that one table, how many members will be at the table that has fewer than 6 members?
A.1
B.2
C.3
D.4
Answer: A.1
Explanation: The number of members is 4j+3 = 5k+3.
Let's start at 4(7)+3 = 31 and keep adding 4 until we find a number in the form 5k+3.
31, 35, 39, 43 = 5(8) + 3
The club has 43 members.
43/6 = 6(7) + 1
The answer is A.
Question: An old priest fell on a bottom of the well of a church.
The well is 19 inches deep.
At day time, the old priest climbs 5-inches but when at dark he slip back 4 inches.
In how many days priest will come out of the well ?
A.15-days
B.14-days
C.11-days
D.19-days
Answer: A.15-days
Explanation: A
15-days
In 14-days, he will climb 14-inch and when he climbs 5 inch more, he will be out of the well :-)
Question: Two trains, one from P to Q and the other from Q to P, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is
A.4:3
B.3:4
C.2:4
D.4:2
Answer: A.4:3
Explanation: Req ratio = root(16):root of(9)=4:3
ANSWER A
Question: If C is the temperature in degrees Celsins and F is the temperature in degrees Fahrenheit, then the relationship between temperatures on the two scales is expressed by the equation 9C=5(F-32). The temperature required to boil liquid A and liquid B differed by 35 degrees on the Fahrenheit scale, by how many degrees did the temperature extremes differ on the Celsius scale?
A.a) 17
B.b) 13
C.c) 25
D.d) 45
Answer: A.a) 17
Explanation: The relationship is 9/5 - 32, so approximately half of difference in Celsius (the -32 part won't be used in this case). Just looking at the answer choices you can pick A which is the only number near half of 35. The other answer choices are too far apart so no need to calculate.
Question: Ronald and Elan are working on an assignment. Ronald takes 6 hours to type 32 pages on a computer, while Elan takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?
A.3 hours
B.6 hours
C.4 hours
D.8 hours
Answer: D.8 hours
Explanation: Number of pages typed by Ronald in one hour = 32/6 = 16/3
Number of pages typed by Elan in one hour = 40/5 = 8
Number of pages typed by both in one hour = ((16/3) + 8) = 40/3
Therefore, time taken by both to type 110 pages = 110 x 3/40 = 8 hours.
ANSWER:D
Question: A copy machine, working at a constant rate, makes 30 copies per minute. A second copy machine, working at a constant rate, makes 55 copies per minute. Working together at their respective rates, how many copies do the two machines make in half an hour ?
A.90
B.2,700
C.4,500
D.2,550
Answer: D.2,550
Explanation: Together the two machines make 30+55=85 copies per minute. So, in half an hour they will make 85*30=2,550 copies.
Answer: D.
Question: Find the value of x. (47% of 1442 - 36% of 1412) + 63 = x?
A.1
B.2
C.3
D.5
Answer: C.3
Explanation: C) 3
Question: How much 60% of 50 is greater than 40% of 30?
A.18
B.99
C.66
D.55
Answer: A.18
Explanation: (60/100) * 50 – (40/100) * 30
30 - 12 = 18
Answer: A
Question: A 80 gallon solution of salt and water is 10% salt. How many gallons of water must be added to the solution in order to decrease the salt to 8% of the volume?
A.20
B.12
C.13
D.14
Answer: A.20
Explanation: Amount of salt = 8.0
Assume x gallons of water are added.
8.0 / 80 + x = 8/100
800 = 8x + 640
8x = 160
x = 20
Correct Option: A
Question: Find the amount on Rs.5000 in 2 years, the rate of interest being 4% per first year and 5% for the second year?
A.5418
B.5498
C.5460
D.5179
Answer: C.5460
Explanation: 5000 * 104/100 * 105/100
=> 5460
Answer:C
Question: The sum of four consecutive even numbers is 84. What would be the largest number?
A.33
B.88
C.24
D.123
Answer: C.24
Explanation: Let the four consecutive even numbers be 2(x - 2), 2(x - 1), 2x, 2(x + 1)
Their sum = 8x - 4 = 84 => x = 11
Smallest number is: 2(x +1) = 24.
Answer: C
Question: If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number?
A.5:9
B.5:5
C.5:3
D.5:2
Answer: C.5:3
Explanation: Let 40% of A = 2/3 B. Then,
40A/100 = 2B/3 => 2A/5 = 2B/3
A/B = (2/3 * 5/2) = 5/3
A:B = 5:3.
Answer:C
Question: Out of seven numbers, average of first six number is 40 and average of last six number is 35. the first number is 55. What is the difference between first and last number?
A.30
B.37
C.41
D.59
Answer: A.30
Explanation: Let the seven numbers be represented by
{a,b,c,d,e,f,g}
let sum(b-f) be the sum of numbers b through f.
For the average of the first six we have
(a + sum(b-f))/6 = 40
(a + sum(b-f)) = 240
We are given that the first number, a, is 55, so we have
sum(b-f) = 240 - a
sum(b-f) = 240 - 55
sum(b-f) = 185
Now for the average of the last six numbers we have
(sum(b-f) + g)/6 = 35
(sum(b-f) + g) = 210
185 + g = 210
g = 210 - 185
g = 25
The first number is 55 and the last number is 25 so, their difference is 30.
Answer A
Question: The lunch menu at a certain restaurant contains 4 different entrees and 5 different side dishes. If a meal consists of 1 entree and 2 different side dishes, how many different meal combinations W could be chosen from this menu?
A.10
B.20
C.40
D.80
Answer: C.40
Explanation: W=4C1 * 5C2
= 4 * (5*4*3!)/(3!2!)
= 4 * 10
= 40
Answer - C
Question: When we multiply a certain two digit number by the
sum of its digits 405 is achieved. If we multiply the
number written in reverse order of the same digits
by the sum of the digits,we get 486.Find the number?
A.40
B.45
C.50
D.55
Answer: B.45
Explanation: Let the number be x y.
When we multiply the number by the sum of its digit
405 is achieved.
(10x+y)(x+y)=405....................1
If we multiply the number written in reverse order by its
sum of digits we get 486.
(10y+x)(x+y)=486......................2
dividing 1 and 2
(10x+y)(x+y)/(10y+x)(x+y) = 405/486.
10x+y / 10y+x = 5/6.
60x+6y = 50y+5x
55x=44y
5x = 4y.
From the above condition we conclude that the above
condition is satisfied by the second option i e b. 45.
ANSWER : B 45
Question: For an agricultural experiment, 500 seeds were planted in one plot and 200 were planted in a second plot. If exactly 30 percent of the seeds in the first plot germinated and exactly 50 percent of the seeds in the second plot germinated, what percent of the total number of seeds germinated?
A.35.7%
B.25%
C.32%
D.30.8%
Answer: A.35.7%
Explanation: From the first plot 0.30*500=150;
From the second plot 0.50*200=100;
Total percent = (150+100)/(500+200) = 0.357.
Answer: A.
Question: If x - 5 > 2 and x + 3 < 7, the value of x must be between which of the following pairs of numbers?
A. -3 and 10
B. -3 and 4
C. 2 and 7
D. 3 and 4
Answer: D. 3 and 4
Explanation: Let’s isolate x in each inequality.
x - 5 > 2
x > 3
Next we simplify x +3 < 7.
x +3 < 7
x < 4
We know that x is greater than 3 and less than 4.
The answer is D.
Question: The average weight of a group of persons increased from 48 kg to 51 kg, when two persons weighing 88 kg and 93 kg join the group. Find the initial number of members in the group?
A.23
B.24
C.25
D.26
Answer: D.26
Explanation: Let the initial number of members in the group be n.
Initial total weight of all the members in the group = n(48)
From the data,
48n + 88 + 93 = 51(n + 2) => 51n - 48n = 79 => n = 26
Therefore there were 26 members in the group initially.
ANSWER:D
Question: If 20 toys cost Rs, 234, what do 35 toys cost?
A.409.5
B.564.5
C.546.5
D.654.5
Answer: A.409.5
Explanation: Let the required cost be Rs. x. Then,
More toys, More cost	(Direct Proportion)
. = x=(35 X 234)/20=409.50
Answer is A
Question: Nicole cycles at a constant rate of 15 kilometers per hour, and is passed by Jessica, who cycles at a constant rate of 30 kilometers per hour. If Jessica cycles at her constant rate for x minutes after passing Nicole, then stops to wait for her, how many minutes will Jessica have to wait for Nicole to catch up to her?
A.x/3
B.x/2
C.x
D.3x/2
Answer: C.x
Explanation: In x minutes, Jessica travels (x/60)*30 = x/2 miles
The time it takes Nicole to travel x/2 miles is (x/2) / 15 = x/30 hours = 2x minutes
Jessica needs to wait 2x - x = x minutes.
The answer is C.
Question: A bakery currently has 7 pies and 4 cakes in its inventory. The bakery’s owner has decided to display 5 of these items in the bakery’s front window. If the items are randomly selected, what is the probability that the display will have exactly 3 pies?
A.3/11
B.5/11
C.14/33
D.29/77
Answer: B.5/11
Explanation: The total number of ways to choose 5 from 11 is 11C5 = 462.
The number of ways that include 3 pies is 7C3*4C2 = 35*6 = 210
P(exactly 3 pies) = 210/462 = 5/11
The answer is B.
Question: In the rectangular coordinate system, if the line x = 6y + 5 passes through points (m,n) and (m + 2,n + p), what is the value of p?
A.1/2
B.1/3
C.1/4
D.1/5
Answer: B.1/3
Explanation: x = 6y+5, and thus y = x/6 - 5/6
The slope is 1/6.
The slope of a line through points (m,n) and (m + 2,n + p) is (n+p-n)/(m+2-m) = p/2
p/2 = 1/6 and thus p = 1/3
The answer is B.
Question: I remember during the school days , the teacher asked the class "can you tell me the sum of the first 50 odd numbers ?".
I ran quickly to the teacher and told her "the answer is 2500". The teacher replied "lucky guess".
She then asked me "can you tell me the sum of first 70 odd numbers ?".
I wait for approx 10 seconds and replied with the correct answer.
How can i answer so quickly and whats the correct answer ?
A.8715
B.0152
C.3581
D.4900
Answer: D.4900
Explanation: D
5625
n^1
70 * 70 = 4900(sum of first 70 odd numbers).
50 * 50 = 2500 (sum of first 50 odd numbers).
Question: Mary, Peter, and Lucy were picking chestnuts. Mary picked three times as much as much chestnuts than Peter. Lucy picked 5 kg more than Peter. Together the three of them picked 30 kg of chestnuts. How many kilograms of chestnuts did Mary, Peter, and Lucy pick respectively?
A.10, 15, and 5
B.15, 10, and 5
C.15, 5, and 10
D.10, 5, and 15
Answer: C.15, 5, and 10
Explanation: M = 3P
L = P+5
M + P + L = 30
3P + P + (P+5) = 30
P = 5, M = 15, L = 10
Therefore, Mary, Peter, and Lucy picked 15, 5, and 10 kg, respectively.
The answer is C.
Question: If there are 20 apples and the apples have to be shared equally among 3 babies. What number of apples are to be added?
A.1
B.2
C.3
D.4
Answer: A.1
Explanation: Given there are 20 apples.If 1 extra apple is added, then it becomes 21 which can be divided equally that is 7 apples to each baby.
Option A is correct.
Question: The Natural Woman, a women's health food store, offers its own blends of trail mix. If the store uses 3 different ingredients, how many bins will it need to hold every possible blend, assuming that each blend must have at least three ingredients? (Also assume that each bin can hold one and only one blend.)
A. 1
B. 4
C. 7
D. 11
Answer: B. 4
Explanation: We're told that there are 3 ingredients (we'll call them A, B, C ); we're told that each 'mix' must include AT LEAST 3 ingredients...
3 ingredient blends:
ABC
ABD
ACD
BCD
Total blends = 4
B
Question: A family consists of grandparents, parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?
A.31 5/8 years
B.31 5/7 years
C.31 9/7 years
D.38 5/7 years
Answer: B.31 5/7 years
Explanation: Required Average = [(67 * 2) + (35 * 2 ) + (6 * 3)]/(2 + 2 + 3)
= (134 + 70 + 18)/7
= 31 5/7 years.
Answer:B
Question: H.C.F of 3240, 3600 and a third number is 36 and their L.C.M is 24 * 35 * 52 * 72. The third number is?
A.22 * 35 * 72
B.22 * 35 * 78
C.22 * 35 * 72
D.22 * 35 * 71
Answer: A.22 * 35 * 72
Explanation: 3240 = 23 * 34 * 5; 3600 = 24 * 32 * 52
H.C.F = 36 = 22 * 32
Since H.C.F is the product of lowest powers of common factors, so the third number must have (22 * 32 ) as its factor.
Since L.C.M is the product of highest powers of common prime factors, so the third number must have 35 and 72 as its factors.
Third number = 22 * 35 * 72
Answer:A
Question: For any numbers a and b, a#b = ab(3 − b). If a and a#b both represent positive numbers, which of the following could be a value of b?
A.−5
B.−2
C.2
D.4
Answer: C.2
Explanation: if a#b is positive then there are 2 cases
either ab &(3-b) both are negatives or both positives
let both are positives then for (3-b) to be positive b has to less than 3 (3-b>0--->3>b)
from options b can be -5,-2,or 2
but if we take negative value of b then ab will negative & hence a#b which is not possible.
also if we do both negative then (3-b) to be negative b has to be greater than 3 which from options are only 4&7
if we take any value then the term ab will positive leaving a#b negative.which is not possible
Hence b=2
ANSWER:C
Question: A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
A.150
B.887
C.167
D.197
Answer: A.150
Explanation: Length of the train be ‘X’
X + 150/15 = X + 250/20
4X + 600 = 3X + 750
X = 150m
Answer: A
Question: Select a card from pack of 52 playing cards, 2cards are drawn together at random. Find the probability of both the cards being king ?
A.1/111
B.2/121
C.1/221
D.2/213
Answer: C.1/221
Explanation: Two cards can be drawn from a pack of 52 playing cards in 52C2 ways. i,e., 52 x 51 / 2 = 1326 ways. The event that two kings appear in a single drawn of cards is 4C2 ways, i.e 6 ways.
∴ The probability that the two cards drawn from a pack of 52 cards are kings = 6/1326 = 1/221
C
Question: Twelve coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?
A.2^9
B.2^11
C.3 * 2^8
D.3 * 2^9
Answer: B.2^11
Explanation: Fix the third coin as H. The remaining 11 coins have 2^11 outcomes.
B
Question: The instructions state that Cheryl needs 4/19 square yards of one type of material and 2/13 square yards of another type of material for a project. She buys exactly that amount. After finishing the project, however, she has 4/26 square yards left that she did not use. What is the total amount of square yards of material Cheryl used?
A.4/19
B.1/9
C.2/3
D.1 1/9
Answer: A.4/19
Explanation: Total bought = 4/19+2/13
left part 4/26--->2/13
so used part 4/19+2/13-2/13=4/19
ANSWER:A
Question: A takes twice as much time as B or thrice as much time to finish a piece of work. Working together, they can finish the work in 2 ays, can do the work alone in
A.10 days
B.11 days
C.15 days
D.12 days
Answer: D.12 days
Explanation: work as x,x/2,x/3
==(1/x+2/x+3/x)
=1/2==>6/x=1/2
==>12
ANSWER D