divelab/Sys2Bench huggingface dataset:
Question: Shahrukh starts from Barabanki to Fatehpur , 1 hour after Ajay starts. Shahrukh meets Kajol 1.5 hours after Shahrukh starts. If the speed of Shahrukh is at least 20km/h faster than the speed of Kajol.
What is the minimum speed of Shahrukh to overtake Ajay, before he meets Kajol?
Options:
A)32
B)21
C)27
D)None of these
E)18
Rationale: Explanation:
Let t be the time after Kajol starts, when she meets Ajay, then
\inline t=\frac{300}{(x+y)}
This should be less than 2.5 or (x+y)>120
Since y= \inline \frac{3x}{2} \inline \Rightarrow y>72
This (y>72) is greater than 67.5 km/h and hence Shahrukh will always overtake Ajay before he meets Kajol.
Answer: D
Answer: D
Question: United Telephone charges a base rate of $8.00 for service, plus an additional charge of $0.25 per minute. Atlantic Call charges a base rate of $12.00 for service, plus an additional charge of $0.20 per minute. For what number of minutes would the bills for each telephone company be the same?
Options:
A)25 minutes
B)10 minutes
C)20 minutes
D)80 minutes
E)60 minutes
Rationale: Lets take number of minutesx.
Given that, 8+0.25x=12+0.2x ->0.05x=2 -> x=80minutes
ANS D
Answer: D
Question: The average mark of the students of a class in a particular exam is 90. If 3 students whose average mark in that exam is 40 are excluded, the average mark of the remaining will be 95. Find the number of students who wrote the exam?
Options:
A)25
B)35
C)23
D)22
E)33
Rationale: Let the number of students who wrote the exam be x.
Total marks of students = 90 x.
Total marks of (x - 3) students = 80(x - 3)
90x - (3 * 40) = 95(x - 3)
165 = 5x => x = 33
Answer: E
Answer: E
Question: Find the odd man out 3, 5, 7, 12, 13, 17, 19
Options:
A)3
B)5
C)7
D)12
E)13
Rationale: 12 is an even number while the others are odd
ANSWER:D
Answer: D
Question: From 6 positive numbers and 6 negative numbers, how many groups of 4 numbers, yielding a positive product, can be formed?
Options:
A)720
B)625
C)30
D)960
E)255
Rationale: When will the product of 4 numbers be positive? It is positive when the number of negative numbers in the product is even i.e. when we have 0 negative numbers or 2 negative numbers or 4 negative numbers.
3 cases:
- 0 negative numbers - All numbers are positive - Selected in 6C4 = 15 ways
- 2 negative numbers - 2 are positive and 2 are negative - Selected in 6C2*6C2 = 15*15 = 225 ways
- 4 negative numbers - All numbers are negative - Selected in 6C4 = 15 ways
Total number of ways = 15 + 225 + 15 = 255
Answer (E)
Answer: E
Question: How many prime numbers W exist such that 90 < W < 106 and W is a factor of 99999919?
Options:
A)1. Zero
B)2. One
C)3. Two
D)4. Three
E)5. More than three
Rationale: I found that considering the constraint..W is a prime num in between 90 to 106 not inclusive , only 3 numbers (91,97 and 101) are present but those numbers are not the factors of the number mentioned....Therefore, i doubt the answer.C
Answer: C
Question: If n is a natural number, then (6n2 + 6n) is always divisible by:
Options:
A)6 only
B)6 and 12 both
C)12 only
D)by 18 only
E)None
Rationale: EXPLANATION
(6n2 + 6n) = 6n(n + 1), which is always divisible by 6 and 12 both, since n(n + 1) is always even.
Answer B
Answer: B
Question: If a and b are distinct positive integers. The units digit of a^2 is equal to the units digit of a, and the units digit of b^2 is equal to the units digit of b. If the units digit of a·b is equal to neither the units digit of a nor the units digit of b, then what is the units digit of a·b?
Options:
A)0
B)1
C)4
D)5
E)6
Rationale: There are four digits which when squared give the same units digits: 0, 1, 5, 6
0^2 = 0
1^2 = 1
5^2 = 25
6^2 = 36
So a and b must take 2 of these values. They are positive integers so 0 is not possible.
If one of the digits is 1, when the other is multiplied by 1, you will get the same digit. 1*5 = 5
So 1 is out of the picture.
Then you have only two digits left 5 and 6. So out of a and b, one must be 5 and the other 6.
5*6 = 30 so units digit of their product = 0
Answer (A)
Answer: A
Question: A bag contains 6 black and 4 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
Options:
A)4
B)4/3
C)4/5
D)4/9
E)2/5
Rationale: Let number of balls = (6 + 4) = 10.
Number of white balls = 4.
P (drawing a white ball) = 4/10 = 2/5
Hence Answer is E
Answer: E
Question: The total age of A and B is 16 years more than the total age of B and C. C is how many years younger than A ?
Options:
A)12
B)16
C)21
D)18
E)11
Rationale: (A+B) - (B+C) = 16
A - C = 16.
C is younger than A by 16 years.
Answer: B
Answer: B
Question: In a recent election, Ms. Robbins received 7,200 votes cast by independent voters, that is, voters not registered with a specific political party. She also received 10 percent of the votes cast by those voters registered with a political party. If N is the total number of votes cast in the election and 60 percent of the votes cast were cast by independent voters, which of the following represents the number of votes that Ms. Robbins received?
Options:
A)0.06N + 3,200
B)0.1N + 7,200
C)0.04N + 7,200
D)0.1N + 8,000
E)0.06N + 8,000
Rationale: I will go with option C
According to question 60 percent of total votes (N) cas were cast by independent voters. This implies 40 percent of N are voters that belong to political party. And she received 7200 votes from independent voters and 10 percent from registered voters (i.e 0.1 * 0.4 * N = 0.04N). Hence total votes = 7200 + 0.04N ....option C
Answer: C
Question: Three friends neha, sabi and mahi divide $1100 amongs them in such a way that if $5, $8 and $4 are removed from the sums that neha, sabi and mahi received respectively, then the share of the sums that they got will be in the ratio of 2 : 8 : 6. How much did mahi receive?
Options:
A)$122
B)$152
C)$202
D)$107
E)$102
Rationale: Explanatory Answer
Let the sums of money received by A, B and C be x, y and z respectively.
Then x - 5 : y - 8 : z -4 is 2a : 8a : 6a
When $5, $8 and $4 are removed, we are removing a total of $17 from $1100.
Therefore, 2a + 8a + 6a = 1100 - 17 = 1093
i.e., 16a = 1093
or a = 68.
We know that z - 6 = 16a = 6 * 16 = 96
Therefore, z = 96+6 = $102
The correct choice is (E)
Answer: E
Question: The variables m and n are positive integers. When m is divided by 18, there is a remainder of 12, and when n is divided by 24, there is a remainder of 14. Which of the following are possible values of m + n?
I. 26
II. 70
III. 90
Options:
A)I only
B)III only
C)I and II
D)I​ and III
E)II and III
Rationale: m = 18k + 12 --> Values are 12, 30, 48, 66, 84
n = 24k + 14 --> Values are 14, 38, 62, 86
I. 26 --> 12 + 14 --> Possible
II. 70 --> Not possible
III. 90 --> Not possible
Answer: A
Answer: A
Question: Two letters from the word NOTHING are selected at random. What is the probability that at least one of the selected letters is a consonant?
Two letters from the word NOTHING are selected at random. What is the probability that at least one of the selected letters is a consonant?
Options:
A)A)1/500
B)B)1/28
C)C)27/28
D)D)124/125
E)E)499/500
Rationale: There are 5 consonants and 2 vowels in NOTHING .
probability that at least one of the selected letters is a consonant = 1 - (Probability of both vowels)
Probability of both vowels = 2C2/7C2 = 1/21
So, Answer is 1 - 1/21 = 20/21 ------> C.
Answer: C
Question: A and B start a business, with A investing the total capital of Rs.50000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.1500 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year?
Options:
A)59028
B)59010
C)59190
D)59000
E)92700
Rationale: Interest received by A from B = 10% of half of Rs.50000 = 10% * 25000 = 2500.
Amount received by A per annum for being a working partner = 1500 * 12 = Rs.18000.
Let 'P' be the part of the remaining profit that A receives as his share. Total income of A = (2500 + 18000 + P)
Total income of B = only his share from the remaining profit = 'P', as A and B share the remaining profit equally.
Income of A = Twice the income of B
(2500 + 18000 + P) = 2(P)
P = 20500
Total profit = 2P + 18000
= 2*20500 + 18000 = 59000
Answer:D
Answer: D
Question: If a large pizza has a radius that is 40% larger that that of a medium pizza, what is the percent increase in area between a medium and a large pizza?
Options:
A)40%
B)80%
C)96%
D)112%
E)124%
Rationale: Let the radius of medium pizza be r. Then the radius of large pizza is 1.4r.
The area of the medium pizza is pi*r^2
The area of the large pizza is pi*(1.4*r)^2 = 1.96*pi*r^2, an increase of 96%.
The answer is C.
Answer: C
Question: In case O is the only individual sewing on committee B, which among the following shouldserve on committee A?
Options:
A)V and U
B)V and T
C)U and S
D)P and Q
E)T and U
Rationale: P and Q should serve on A
ANSWER:D
Answer: D
Question: How many ONE letter words are formed using the letters of the word WALK?
Options:
A)1
B)16
C)7
D)4
E)2
Rationale: The number of letters in the given word is 4.
The number of ONE letter words that can be formed using these four letters is 4P1=4*1=4
Answer:D
Answer: D
Question: A can do a piece of work in 20 days and B alone can do it in 10 days. B works at it for 5 days and then leaves. A alone can finish the remaining work in
Options:
A)10days
B)6days
C)7.5days
D)8.5days
E)9days
Rationale: Explanation:
B's 5 days work =
1/10∗5=1/2
Remaining work =1−1/2=1/2
A can finish work =20∗1/2=10days
Option A
Answer: A
Question: An unbiased die is tossed .find the probability of getting a multiple of 3
Options:
A)4/5
B)1/3
C)3/2
D)4/3
E)5/2
Rationale: . Here S={1,2,3,4,5,6}
Let E be the event of getting the multiple of 3
then ,E={3,6}
P(E)=n(E)/n(S)=2/6=1/3
Ans: B
Answer: B
Question: A car covers a distance of 624 km in 3 1/5 hours. Find its speed?
Options:
A)104 kmph
B)195 kmph
C)109 kmph
D)174 kmph
E)101 kmph
Rationale: 624/3 1/5
=195 kmph
Answer:B
Answer: B
Question: The average of the marks of 12 students in a class is 36. If the marks of each student are doubled, find the new average?
Options:
A)72
B)55
C)66
D)11
E)67
Rationale: Sum of the marks for the 12 students = 12 * 36 = 432. The marks of each student are doubled, the sum also will be doubled.
The new sum = 432 * 2 = 864. So, the new average = 864/12 = 72.Answer: A
Answer: A
Question: Mangala completes a piece of work in 12 days, Raju completes the same work in 34 days. If both of them work together, then the number of days required to complete the work is?
Options:
A)8 3/4 days
B)10 1/4 days
C)11 1/4 days
D)12 2/3 days
E)14 1/4 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 12× 34/46= 8 3/4 days
A)
Answer: A
Question: Ella can fill K cans of water in 4 minutes. If there are T cans of water in one gallon, how many gallons can Ella fill in 36 minutes?
Options:
A)4T/K
B)4KT
C)9T/K
D)9K/T
E)9KT
Rationale: Ella can fill this number of cans in 36 minutes: (36/4)K = 9K.
One can is 1/T gallons.
Ella can fill 9K*(1/T) = 9K/T gallons of water in 36 minutes.
The answer is D.
Answer: D
Question: A box contains seven bulbs out of which 5 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good.
Options:
A)125/167
B)125/186
C)125/126
D)125/186
E)20/21
Rationale: Required probability
= 1 - 1/21
= 20/21
Answer: E
Answer: E
Question: A 240 meter long train crosses a man standing on the platform in 6 sec. What is the speed of the train?
Options:
A)228
B)144
C)1266
D)188
E)211
Rationale: S = 240/6 * 18/5 = 144 kmph
Answer: B
Answer: B
Question: Find the perimeter and area of the rectangle of length 17 cm and breadth 13 cm.
Options:
A)71 cm2
B)121 cm2
C)141 cm2
D)171 cm2
E)221 cm2
Rationale: length = 17 cm, breadth = 13 cm
Perimeter of rectangle = 2 (length + breadth)
= 2 (17 + 13) cm
= 2 × 30 cm
= 60 cm
We know that the area of rectangle = length × breadth
= (17 × 13) cm22
= 221 cm2
ANSWER : E
Answer: E
Question: An auction house charges a commission of 15% on the first $50,000 of the sale price of an item, plus 10% on the amount of of the sale price in excess of $50,000. What was the price of a painting for which the house charged a total commission of $24,000?
Options:
A)$115,000
B)$160,000
C)$215,000
D)$240,000
E)$365,000
Rationale: Say the price of the house was $x, then 0.15*50,000+0.1*(x-50,000)=24,000 --> x=$215,000 (15% of $50,000 plus 10% of the amount in excess of $50,000, which is x-50,000, should equal to total commission of $24,000).
Answer: C
Answer: C
Question: Felix earned 50% more per month than Oscar. If Felix’s salary is decreased 10% and Oscar’s salary is increased by 10%, then Felix would be earning what percent more than Oscar?
Options:
A)25%
B)9.09%
C)14%
D)22.73%
E)It cannot be determined from the information given.
Rationale: This Q is all about taking the correct BASE for taking %s..
the very first step requires taking some numbers for each..
ONE should be 100...
it is easy to take 50 and 100 here..
but the BASE is 100 here, so the salary can be 100 and 150..
100 increases 10% =110..
150 decreases 10%=135..
so the increase is 25..
again the BASE is 110, so answer 25/110 * 100= 22.73% D
without calculations,
answer cannot be equal to or greater than 25, as 25 is on 110..
so D is the only one left
Answer: D
Question: A box is in the shape of a semicircle with a radius of 12. What is the approximate perimeter of the semicircle?
Options:
A)54
B)62
C)25
D)34
E)60
Rationale: perimeter of a circle =2pi*r
perimeter of a semicircle = pi*r + 2r
aprox perimiter = 3.14*12 + 2*12 = 61.68 approximately 62
answer B
Answer: B
Question: a and b are positive integers less than or equal to 7. If a and b are assembled into the six-digit number ababab, which of the following must be a factor of ababab?
Options:
A)3
B)4
C)2
D)6
E)none of the above
Rationale: 686868 when divided by 2 gives the result 343434
CONCEPT: Rule of Divisibility of 2 isIf sum of the digits of the Number is divisible by 2 then the number will be divisible by 2
SUm of the digits of No. which is divisible by 2 hence the Number 686868 will be divisible by 2
Answer: A
Question: There are 50 students in a class. If 2 % are absent on a particular day, find the number of students present in the class.
Options:
A)43
B)36
C)28
D)49
E)11
Rationale: Number of students absent on a particular day = 1 % of 50
i.e., 2/100 × 50 = 1
Therefore, the number of students present = 50 - 1 = 49 students.
Answer:D
Answer: D
Question: A boat can move upstream at 22 kmph and downstream at 42 kmph, then the speed of the current is?
Options:
A)15
B)16
C)18
D)10
E)12
Rationale: US = 22
DS = 42
M = (42 - 22)/2 = 10 Answer:D
Answer: D
Question: If two numbers are in the ratio 2:3. If 10 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number?
Options:
A)10
B)20
C)24
D)26
E)29
Rationale: 2:3
2x + 10 : 3x + 10 = 3 : 4
4[2x + 10] = 3[3x + 10]
8x + 40 = 9x + 30
9x - 8x = 40 - 30
x = 10
Then smallest number is = 2
2x = 20
Short cut method:
a:b = 2:3
c:d = 3:4
1.Cross multiplication with both ratios
a * d ~ b * c = 2 * 4 ~ 3 * 3 = 8 ~ 9 = 1
2. If 10 is added both the number means 10 * 3 = 30 and 10 * 4 = 40,
Then 30 ~ 40 = 10
===> 1 -----> 10
===> 2 -----> 20
B
Answer: B
Question: Mr. Yutaro’s class contains 11 boys and 5 girls. If two students are chosen, one at a time, from the class, what is the probability that a boy and a girl are chosen?
Options:
A)11/24
B)9/20
C)11/28
D)27/48
E)13/16
Rationale: Probability of a girl being chosen first, then a girl:
5/16 * 11/15
Probability of a boy being chosen first, then a boy:
11/16 * 5/15
Probability of a boy and a girl being chosen:
(5*11+5*11) / (15*16)
=11+11/3*16
=22/48
=11/24,
Answer:A
Answer: A
Question: The average weight of a group of boys is 20 kg. After a boy of weight 31 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?
Options:
A)12
B)14
C)18
D)24
E)10
Rationale: Let the number off boys in the group originally be x.
Total weight of the boys = 20x
After the boy weighing 31 kg joins the group, total weight of boys = 20x + 31
So 20x + 31 = 21(x + 1) = > x = 10.
ANSWER:E
Answer: E
Question: On his drive to work, Leo listens to one of three radio stations A, B or X. He first turns to A. If A is playing a song he likes, he listens to it; if not, he turns it to B. If B is playing a song he likes, he listens to it; if not, he turns it to X. If X is playing a song he likes, he listens to it; if not, he turns off the radio. For each station, the probability is 0.30 that at any given moment the station is playing a song Leo likes. On his drive to work, what is the probability that Leo will hear a song he likes?
Options:
A)0.027
B)0.09
C)0.417
D)0.657
E)0.9
Rationale: Probability he hears a song is like:
Tune to A and likes what he is hearing = 0.3
Tune to A, don't find he like what they are airing, then tune to B and likes what he finds there = 0.7 * 0.3 = 0.21
Tune to A, finds crap there, Tune to B, hears a similar crap, Tune to X and finally falls in love with the program = 0.7^2 * 0.3 = 0.147
Total = 0.657
Ans D
Answer: D
Question: The fourth proportional to 10, 15 and 18 is?
Options:
A)21
B)27
C)55
D)88
E)61
Rationale: (15*18)/10
= 27
Answer:B
Answer: B
Question: Today John is 3 times older than Mark. If in 14 years, John will be one year younger than twice the age of Mark on that day, how old is John today?
Options:
A)13
B)33
C)36
D)38
E)39
Rationale: Given after 14yrs john will be 1 year younger than twice mark's age
i.e 3M+14 = 2(M+14)-1
M=13
=>John's current age = 3M = 39
Answer is E
Answer: E
Question: Which is a better offer out of (i) a cash payment now of Rs.8100 or (ii) a credit of Rs.8250 after 6 months(6.5% S.I)
Options:
A)(i)
B)(ii)
C)both (i) and (ii)
D)only (i)
E)NONE OF THESE
Rationale: Explanation:
PW=100*Amount / 100+(R+T)
ANSWER IS A
Answer: A
Question: If f(x) = x^4/(x^4 - 1), what is f(1/x) in terms of f(x)?
Options:
A)f(x)
B)1/-f(x)
C)-2/-f(x)
D)-3/-f(x)
E)-f(x)
Rationale: If x = 2 then f(x) = 16/15 and f(1/x) = -16/15 which is equal to -f(x)
answer E
Answer: E
Question: The number 0.5 is how much greater than 1/6 ?
Options:
A)1/3
B)2/10
C)1/50
D)1/500
E)2/500
Rationale: let x be the difference
then
.5-1/3=x
5/10-1/3=x
x=1/3
ans A
Answer: A
Question: M is 30% of Q. Q is 20% of P. N is 50% of P. Find M:N ratio
Options:
A)3:25
B)3:24
C)3:23
D)3:22
E)4:25
Rationale: Let p be 100
N = 50% of 100 (P=100) = 50
Q= 20% of 100 (P=100) = 20
M = 30% of 20 (Q=20) = 6
M:N = 6:50
M:N = 3:25
ANSWER:A
Answer: A
Question: A boatman goes 2 km against the current of the stream in 2 hour and goes 1 km along the current in 20 minutes. How long will it take to go 5 km in stationary water?
Options:
A)2 hr 30 min
B)2 hr
C)4 hr
D)1 hr 15 min
E)3 hr 15 min
Rationale: Explanation:
Speed upstream =2/2=1km/hr
Speed downstream =1/(20/60)=3km/hr
Speed in still water =1/2(3+1)=2km/hr
Time taken to travel 5 km in still water
=5/2=2(1/2)hours=2 hour 30mins
ANSWER IS A
Answer: A
Question: 10% of a 50% alcohol solution is replaced with water. From the resulting solution, again 10% is replaced with water. This step is repeated once more. What is the concentration of alcohol in the final solution obtained?
Options:
A)3%
B)20%
C)25%
D)36%
E)40%
Rationale: Since the numbers in the answers are pretty far apart. I just simplified and rounded.
Alcohol = 50%
Total - 10% * 3 = 70%
.5 * .7 = .35 (so that means 70% of 50% of the total is 35%)
Answer: D) 36
Answer: D
Question: Two boats start from opposite banks of river perpendicular to the shore. One is faster then the other. They meet at 720 yards from one of the ends. After reaching opposite ends they rest for 10mins each. After that they start back. This time on the return journey they meet at 400yards from the other end of the river. Calculate the width of the river.
Options:
A)1660 yard
B)1760 yard
C)1860 yard
D)1560 yard
E)1460 yard
Rationale: Let us assume that width of river d yards and speed of boats - x and y yards/min respectively.Hence the two equations are :1) (d-720)/x = 720/y2) (d/y+10+400/y) = (d/x + 10 + (d-400)/x)Solving the two equationsWe get d=1760 yard
ANSWER:B
Answer: B
Question: In an IT company, there are a total of 120 employees including 50 programmers. The number of male employees is 80, including 35 male programmers. How many employees must be selected to guaranty that we have 3 programmers of the same sex?
Options:
A)10
B)50
C)55
D)35
E)75
Rationale: You could pick 70 non-programmers, 2 male programmers, and 2 female programmers, and still not have 3 programmers of the same sex. But if you pick one more person, you must either pick a male or a female programmer, so the answer is 75.
E
Answer: E
Question: A train 360 m long is running at a speed of 48 km/hr. In what time will it pass a bridge 140 m long?
Options:
A)40 sec
B)11 sec
C)37.5 sec
D)19 sec
E)10 sec
Rationale: Speed = 48 * 5/18 = 40/3 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 3/40 = 37.5 sec
Answer: C
Answer: C
Question: If (18^a) * 9^(3a – 1)= (2^4)(3^b) and a and b are positive integers, what is the value of a?
Options:
A)22
B)11
C)9
D)6
E)4
Rationale: (18^a) * 9^(3a – 1)= (2^4)(3^b)
= 2^a . 9^a . 9^(3a – 1) = (2^4)(3^b)
Just compare powers of 2 from both sides
Answer = 4 = E
Answer: E
Question: A certain company expects quarterly earnings of $0.80 per share of stock, half of which will be distributed as dividends to shareholders while the rest will be used for research and development. If earnings are greater than expected , shareholders will receive an additional $0.04 per share for each additional $0.10 of per share earnings. If quarterly earnings are $1.10 per share, what will be the dividend paid to a person who owns 600 shares of the company's stock?
Options:
A)$92
B)$312
C)$104
D)$120
E)$240
Rationale: EPS Actual> EPS expected.
each gets and additional .12 per share.
Thus .52*600 --> $312
answer is B
Answer: B
Question: If Jake loses 8 pounds, he will weigh twice as much as his sister Kendra. Together they now weigh 293 pounds. What is Jake’s present weight, in pounds?
Options:
A)182
B)186
C)190
D)194
E)198
Rationale: J + K = 293 and so K = 293 - J
J - 8 = 2K
J - 8 = 2(293-J)
3J = 594
J = 198
The answer is E.
Answer: E
Question: Four dice are thrown simultaneously. Find the probability that all of them show the same face.
Options:
A)1/216
B)1/212
C)1/272
D)1/220
E)8/216
Rationale: Explanation:
The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:
=
n(S) =
Let X be the event that all dice show the same face.
X = { (1,1,1,1,), (2,2,2,2), (3,3,3,3), (4,4,4,4), (5,5,5,5), (6,6,6,6)}
n(X) = 6
Hence required probability
Answer: A) 1/216
Answer: A
Question: How many liters of 20% alcohol solution should be added to 40 liters of a 50% alcohol solution to make a 30% solution?
Options:
A)60 liters
B)70 liters
C)80 liters
D)90 liters
E)50 liters
Rationale: Let x be the quantity of the 20% alcohol solution to be added to the 40 liters of a 50% alcohol. Let y be the quantity of the final 30% solution. Hence
x + 40 = y
We shall now express mathematically that the quantity of alcohol in x liters plus the quantity of alcohol in the 40 liters is equal to the quantity of alcohol in y liters. But remember the alcohol is measured in percentage term.
20% x + 50% * 40 = 30% y
Substitute y by x + 40 in the last equation to obtain.
20% x + 50% * 40 = 30% (x + 40)
Change percentages into fractions.
20 x / 100 + 50 * 40 / 100= 30 x / 100 + 30 * 40 / 100
Multiply all terms by 100 to simplify.
20 x + 50 * 40 = 30 x + 30 * 40
Solve for x.
x = 80 liters
80 liters of 20% alcohol is be added to 40 liters of a 50% alcohol solution to make a 30% solution
Answer C
Answer: C