RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: If x dollars is invested at 12.5 percent for one year and y dollars is invested at 9.5 percent for one year, the annual income from the 12.5 percent investment will exceed the annual income from the 8 percent investment by $60. If $2500 is the total amount invested, how much is invested at 9.5 percent?
A.a. $1097.83
B.b. $1231.57
C.c. $1101.52
D.d. $1147.72
Answer: D.d. $1147.72
Explanation: 2 equations with 2 unknowns
12.5x / 100 - 9.5y / 100 = 60
and
x + y = 2500
Solving these 2 equations, x =1352.27 and y = 1147.72
Answer D.
Question: If the average (arithmetic mean) of a and b is 45 and the average of b and c is 80, what is the value of c − a?
A.25
B.60
C.90
D.140
Answer: B.60
Explanation: -(a + b = 90)
b + c=160
c-a=60
B. 60
Question: Rs. 6000 is lent out in two parts. One part is lent at 2% p.a simple interest and the other is lent at 10% p.a simple interest. The total interest at the end of one year was Rs. 450. Find the ratio of the amounts lent at the lower rate and higher rate of interest?
A.5:11
B.5:6
C.5:2
D.5:8
Answer: A.5:11
Explanation: Let the amount lent at 2% be Rs. x
Amount lent at 10% is Rs. (6000 - x)
Total interest for one year on the two sums lent
= 2/100 x + 10/100 (6000 - x) = 600 - 3x/100
=> 600 - 3/100 x = 450 => x = 1875
Amount lent at 10% = 4125
Required ratio = 5:11
Answer:A
Question: If y/x is an integer, which of the following must also be an integer?
I. xy
II. x/y
III. x
A.I alone
B.II alone
C.None of the above
D.I and III
Answer: C.None of the above
Explanation: Lets take X = 1/6 and Y = 2/3
Then Y/X = 4 which is an integer.
But XY = 1/6 * 2/3 = 1/9 --> Not an integer.
X/Y = 1/6 divided by 2/3 = 1/4 --> Not an integer.
X alone is 1/6. Not an integer.
Hence C. None of the above.
Question: Evaluate permutation
7P7
A.5010
B.5020
C.5030
D.5040
Answer: D.5040
Explanation: Explanation:
nPn=n!
7P7=7*6*5∗4∗3∗2∗1=5040
Option D
Question: The difference between a two-digit number and the number obtained by interchanging the digit is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1:2?
A.7
B.8
C.6
D.5
Answer: B.8
Explanation: Explanation:
Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit.
Let the ten's and unit's digits be 2x and x respectively.
Then, (10 * 2x + x) - (10x + 2x) = 36
9x = 36
x = 4
Required difference = (2x + x) - (2x - x) = 2x = 8.
Answer: B
Question: In a certain boys camp, 20% of the total boys are from school A and 30% of those study science. If there are 77 boys in the camp that are from school A but do not study science then what is the total number of boys in the camp?
A.550
B.245
C.150
D.35
Answer: A.550
Explanation: Since 30% of the boys from school A study science, then 70% of the boys from school A do NOT study science and since 20% of the total number of boys are from school A, then 0.2*0.7 = 0.14, or 14% of the boys in the camp are from school A and do not study science.
We are told that this number equals to 77, so 0.14*{total} = 77 --> {total} = 550.
Answer: A.
Question: An analyst will recommend a combination of 2 industrial stocks, 2 transportation stocks, and 2 utility stocks. If the analyst can choose from 5 industrial stocks, 4 transportation stocks, and 3 utility stocks, how many different combinations of 6 stocks are possible?
--
A.12
B.19
C.60
D.180
Answer: D.180
Explanation: 5C2 * 4C2 * 3C2 = 10*6*3 = 180.
Answer: D.
Question: In a certain code VOLITION is written as UMIEUKRR, MARTINET is written as LYOPJPMX. How is DESTROYS written in this code?
A.CCPPSQBW
B.CCPPSQBU
C.CCPPSQBV
D.CCPPSQBX
Answer: A.CCPPSQBW
Explanation: as per the sequence the
ans is D-1 = C
E-2 = C
S-3=P
T-4=P
R+1=S
O+2=Q
Y+3=B
S+4=W
ans is CCPPSQBW
ANSWER:A
Question: A manufacturer is using glass as the surface for the multi-touch screen of its smartphone. The glass on the manufactured phone has a 6% probability of not passing quality control tests. The quality control manager bundles the smartphone in groups of 10. If that bundle has any smartphone that does not pass the quality control test, the entire bundle of 10 is rejected.
What is the probability that a smartphone bundle that will be rejected by quality control?
A. 0.25
B. .05^10
C. 1-0.94^10
D. 1-0.05^10
Answer: C. 1-0.94^10
Explanation: Find the probability of the opposite event and subtract from 1.
The opposite event is that bundle will NOT be rejected by quality control, which will happen if all 10 phones pass the test, so P(all 10 phones pass test)=0.94^10.
P(at least one phone do not pass the test)=1- P(all 10 phones pass test)=1-0.94^10.
Answer: C.
Question: If the mean of a, b, c is M and ab + bc + ca = 0, then the mean of is :
A.3 M^9
B.3 M^2
C.3 M^6
D.3 M^1
Answer: B.3 M^2
Explanation: Explanation:
We have : ( a + b + c) / 3 = M or (a + b + c) = 3M.
Now. .
Answer: B) 3 M^2
Question: There are 5 candidates in an election and 3 of them are tobe elected. A voter can cast any number of votes but notmore than three. The number of ways in which he can cast his vote is
A.5
B.15
C.20
D.25
Answer: D.25
Explanation: Solution
The voter can cast one or two or three votes. So total number of ways in which he can cast his vote =5C1 + 5C2 + 5C3 = 5 + 10 + 10 = 25. Answer D
Question: If $30,000 interest is invested in x percent simple annual interest for n years, which of the following represents the total amount of interest, in dollars, that will be earned by this investment in the n years?
A.10,000(x^n)
B.30,000n(x/100)
C.10,000(1 + x/100)^n
D.30,000(x/100)^n
Answer: B.30,000n(x/100)
Explanation: Principal * no.of years * percentage of interest
Answer : B
Question: Excluding stoppages, the speed of a bus is 50 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
A.7 min
B.6 min
C.9 min
D.10 min
Answer: B.6 min
Explanation: Due to stoppages, it covers 5 km less.
Time taken to cover 5 km =(5/50)x60 = 6 min
answer : B
Question: If a = (1/6)b and c = 7a, then which of the following represents the average (arithmetic mean) of a, b, and c, in terms of a ?
A. a + 4
B. (11/3)a
C. (13/3)a
D. (4 1/7)a
Answer: C. (13/3)a
Explanation: Official Answer: C
The average of the three variables isa + b + c/3. However, we need to solve in terms of a, which means we must convert b and c into something in terms of a.
Were told that a =1/6b, which is equivalent to b = 6a. We can plug that in and simplify the average to:a + 6a + c/3
We also know that c = 7a, which we can plug directly into the average expression:
a + 6a + 7a/3
= 13a/3 = (13/3)a choiceC.
Question: A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long?
A.180
B.190
C.130
D.120
Answer: B.190
Explanation: L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (D)= 1900 m
T = D/S
T = 1900/10
T = 190 Sec
Answer: Option B
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are drawn at random, what is the probability that at least one is green?
A.23/35
B.23/36
C.23/33
D.23/31
Answer: A.23/35
Explanation: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
Probability that at least one green marble can be picked in the random draw of two marbles = Probability that one is green + Probability that both are green
= (⁶C₁ * ⁹C₁)/¹⁵C₂ + ⁶C₂/¹⁵C₂
= (6 * 9 * 2)/(15 * 14) + (6 * 5)/(15 * 14) = 36/70 + 1/7
= 46/70 = 23/35
Answer: A
Question: Sophia finished 2/3 of a book. She calculated that she finished 90 more pages than she has yet to read. How long is her book?
A.270
B.150
C.130
D.90
Answer: A.270
Explanation: Let x be the total number of pages in the book, then she finished 2/3*x pages.
Then she has x−2/3*x=1/3*x pages left.
2/3*x−1/3*x=90
1/3*x=90
x=270
So the book is 270 pages long.
Answer is A.
Question: In a division, divident is 689, divisior is 36 and quotient is 19. Find the remainder.
A.4
B.3
C.2
D.5
Answer: D.5
Explanation: Explanation:
689 = 36 x 19 + r
689 = 684 + r
r = 689 - 684 = 5
Answer: Option D
Question: A take 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 5 days. B can do the work alone in?
A.19
B.12
C.11
D.30
Answer: D.30
Explanation: Suppose A, B and C take x, x/2 and x/3 respectively to finish the work.
Then, (1/x + 2/x + 3/x) = 1/5
6/x = 1/5 => x = 30
So, B takes 15 hours to finish the work.
Answer: D
Question: Twenty percent of Country Y's yearly exports come from fruit exports. One-sixth of all fruit exports from Country Y are orange exports. If country Y generates $4.25 million from its orange exports, how much money does it generate from its yearly total of exports?
A.$21.25m
B.$25.5m
C.$106.25m
D.$127.5m
Answer: D.$127.5m
Explanation: 2/10*1/6*(total) = 4.25
1/30*(total) = 4.25
(total) = 4.25*30 = 127.5
Answer: D.
Question: A and B together can do a work in 6 days. If A alone can do it in 15 days. In how many days can B alone do it?
A.7
B.13
C.19
D.10
Answer: D.10
Explanation: 1/6 â€“ 1/15 = 1/10
B can do the work in 10 days
Answer: D
Question: Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate got?
A.55%
B.56%
C.57%
D.58%
Answer: C.57%
Explanation: Total number of votes polled = (1136 + 7636 + 11628) = 20400
So, Required percentage = 11628/20400 * 100 = 57%
ANSWER : C
Question: A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is?
A.50 m
B.150 m
C.200 m
D.300 m
Answer: B.150 m
Explanation: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 15 => y = x/15
(x + 100)/25 = x/15 => x = 150 m.
ANSWER:B
Question: Distances from you to Man united is written below.
CHELSEA and ARSENAL are 700 kms away
SPURS 1800 kms away
WOLVES 200 kms away
Based on the system , How far should it be to MANCITY ?
A.1100 miles.
B.3100 miles.
C.2100 miles.
D.5100 miles.
Answer: C.2100 miles.
Explanation: Solution:
2100 miles.
Each vowel equivalent to 500 and each consonant equivalent to -200
Answer C
Question: Amar takes as much time in running 18 meters as a car takes in covering 12 meters. What will be the distance covered by Amar during the time the car covers 1.6 km?
A.6200 m
B.2400 m
C.300 m
D.4300 m
Answer: B.2400 m
Explanation: B
2400 m
Distance covered by Amar = 18/1.2 (1.6km) = 3/8(1600) = 2400 m
Answer is B
Question: The sequence of numbers a1, a2, a3, ..., an is defined by an = 1/n - 1/(n+2) for each integer n >= 1. What is the sum of the first 40 terms of this sequence?
A.(1+1/2) + 1/40
B.(1+1/2) – 1/42
C.(1+1/2) – 1/40
D.(1+1/2) – (1/41 +1/ 42)
Answer: D.(1+1/2) – (1/41 +1/ 42)
Explanation: The answer would most certainly be[D]. But the question needs a slight modification.n>=1, since the answer does consider a1 under the sum.
The sequence is :
a1 = 1-1/3
a2 = 1/2 - 1/4
a3 = 1/3 - 1/5....
We can observe that the third term in the sequence cancels the negative term in the first. A similar approach can be seen on all the terms and we would be left with 1 + 1/2 from a1 and a2 along with -1/42 and -1/41 from a40 and a39 term which could not be cancelled.
Hence the sum = (1+1/2) – (1/41 +1/ 42)
Answer : D
Question: A train 120 meters long passes an electric pole in 12 seconds and another train of same length traveling in opposite direction in 8 seconds. The speed of the second train is
A.60 Km
B.66 Km
C.72 Km
D.62 Km
Answer: C.72 Km
Explanation: speed of first train=120/12=10 m/s
let speed of second train be x m/s. As they are approaching each other, relative speed is (10+x) m/s.
distance between each other is 120+120=240 m.
time of crossing each other is 8 sec
=>240/(10+x)=8
=>x=20m/s = 20*18/5 km/hr = 72 kmph
ANSWER:C
Question: Jack and Jill work at a hospital with 3 other workers. For an internal review, 2 of the 5 workers will be randomly chosen to be interviewed. What is the probability that Jack and Jill will both be chosen?
A. 1/3
B. 1/10
C. 1/15
D. 3/8
Answer: B. 1/10
Explanation: 1/5C2=1/10.
Answer: B.
Question: The ratio of the present age of two brothers is 1:2 and 5 years back, the ratio was 1:3. What will be the ratio of their ages after 5 years?
A.1:4
B.2:3
C.3:5
D.5:6
Answer: C.3:5
Explanation: Let the present ages of the two brothers be x and 2x years respectively.
Then, (x - 5)/(2x - 5) = 1/3
3(x - 5) = (2x - 5) => x = 10
Required ratio = (x + 5) : (2x + 5) = 15 : 25 = 3:5
ANSWER:C
Question: Albert borrowed a total of $ 6000 from Brian and Milton. He paid simple interest at the rate of 7 % Per yr and 9 % per yr respectively.At the end of three years he paid $ 1494 as total interest. What is the interest paid to Brian at the end of three years?
A.491
B.481
C.471
D.441
Answer: D.441
Explanation: Let x be the amount borrowed form Brian. So amount borrowed form Milton = 6000-x.
1494 = 21/100x + 27/100(6000-x)
=>x = 2100.
Interest paid = 3*7/100*2100 = 441.
D
Question: Find the average of first 5000 natural numbers?
A.2500
B.2500.5
C.2145.5
D.2005.5
Answer: B.2500.5
Explanation: Sum of first 100 natural numbers = 5000*5001/2 = 12502500
Required average = 12502500/5000 = 2500.5
Answer is B
Question: A father was as old as his son's present at the time of your birth. If the father's age is 38 years now, the son's age five years back was?
A.10 years
B.12 years
C.14 years
D.16 years
Answer: C.14 years
Explanation: Let the son's present age be x years. Then, (38 - x) = x
2x = 38.
x = 19.
Son's age 5 years back (19 - 5) = 14 years.
C
Question: In a school of 850 boys, 44% of Muslims, 28% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities?
A.125
B.627
C.153
D.721
Answer: C.153
Explanation: 44 + 28 + 10 = 82%
100 – 82 = 18%
850 * 18/100 = 153
Answer:C
Question: 8, 12, 18, 27, 40.5, (...)
A.60
B.60.75
C.58
D.89
Answer: B.60.75
Explanation: 8
(8×3)÷ 2 = 12
(12×3)÷ 2 = 18
(18×3)÷ 2 = 27
(27×3)÷ 2 = 40.5
(40.5×3)÷ 2 = 60.75
Answer is B
Question: If x≠4 and (x^2 - 16)/(2y) = (x - 4)/4, then in terms of y, x = ?
A.(y - 8)/2
B.(y - 3)/2
C.y - 3
D.y - 6
Answer: A.(y - 8)/2
Explanation: Since (x^2 – 16)=(x-4)(x+4) the original equation can be changed into 4*(x-4)(x+4) = 2y *(x-4).
By cancelling 2(x-3) (we can do it because x≠4) we get :
2*(x+4)=y.
So x=(y-8)/2. So the answer is A).
Question: Rectangular tile each of size 50cm by 40cm must be laid horizontally on a rectangular floor of size 120cm by 150cm,such that the tiles do not overlap and they are placed with edges jutting against each other on all edges. A tile can be placed in any orientation so long as its edges are parallel to the edges of floor. No tile should overshoot any edge of the floor. The maximum number of tiles that can be accommodated on the floor is:
A.9
B.15
C.12
D.11
Answer: A.9
Explanation: Area of tile = 50*40 = 2000
Area of floor = 120*150= 18000
No of tiles = 18000/2000 =9
So, the no of tile = 9
ANSWER:A
Question: A salt manufacturing company produced a total of 5000 tonnes of salt in January of a particular year. Starting from February its production increased by 100 tonnes every month over the previous months until the end of the year. Find its average monthly production for that year?
A.2989
B.2765
C.5550
D.2989
Answer: C.5550
Explanation: Total production of salt by the company in that year
= 5000 + 5100 + 5200 + .... + 6100 = 66600.
Average monthly production of salt for that year
= 66600/12
= 5550.
Answer:C
Question: In a survey of political preferences, 78% of those asked were in favour of at least one of the proposals: I, II and III. 50% of those asked favoured proposal I, 30% favoured proposal II, and 20% favoured proposal III. If 5% of those asked favoured all three of the proposals, what percentage Q of those asked favoured more than one of the 3 proposals.
A. 10
B. 12
C. 17
D. 22
Answer: C. 17
Explanation: Bunuel, my answer for exactly 2 people was 17 and this was my approach:
100%=(A+B+C)-(AnB+AnC+BnC)-5%+22% which leads me to
Q=100%=(50+30+20)-(at least 2 people)-5%+22%.C
Question: The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8339 for a computer table, then what was the cost price of the computer table?
A.Rs. 5725
B.Rs. 5275
C.Rs. 6275
D.Rs. 6725
Answer: D.Rs. 6725
Explanation: CP = SP * (100/(100 + profit%))
= 8339(100/124) = Rs. 6725.
ANSWER:D
Question: A river 2m deep and 45 m wide is flowing at the rate of 6 kmph the amount of water that runs into the sea per minute is?
A.4500 M3
B.4580 M3
C.9000 M3
D.4900 M3
Answer: C.9000 M3
Explanation: Explanation:
(6000 * 2 * 45)/60 = 9000 M3
Answer: Option C
Question: The present ratio of students to teachers at a certain school is 45 to 1. If the student enrollment were to increase by 50 students and the number of teachers were to increase by 5, the ratio of students to teachers would then be 25 to 1. What is the present number of teachers?
A.4
B.8
C.10
D.12
Answer: A.4
Explanation: We are given that the ratio of students to teacher is 45 to 1. We can rewrite this using variable multipliers.
students : teachers = 45x : x
We are next given that student enrollment increases by 50 and the number of teachers increases by 5. With this change the new ratio becomes 25 to 1. We can put all this into an equation:
Students/Teachers  25/1 = (45x + 50)/(x + 5)
If we cross multiply we have:
25(x + 5) = 45x + 50
25x + 125 = 45x + 50
3.75 = x
x~4
Since x is the present number of teachers, currently there are 4 teachers.
Answer A.
Question: If log 27 = 1.431, then the value of log 9 is :
A.0.934
B.0.945
C.0.954
D.0.958
Answer: C.0.954
Explanation: Solution
Log 27 = 1.431 ⇒ log (33) = 1.431 ⇒ 3 log 3 = 1.431
⇒ log 3 = 0.477
∴ log 9 = log (32) = 2 log 3 = (2 × 0.477) = 0.954. Answer C
Question: Ram purchased a TV and a DVD Player for Rs. 25000 and Rs. 5000 respectively. He sold the DVD Player at a loss of 4 percent and TV at a profit of 10 percent. Overall he make a.?
A.2200
B.2500
C.2800
D.2300
Answer: D.2300
Explanation: Let the SP of the TV and the DVD Player be Rs. r and Rs. m respectively.
r = 25000(1 + 10/100) = 25000 + 2500
m = 5000(1 - 4/100) = 5000 - 200
Total SP - Total CP = r + m - (25000 + 5000) = 2500 - 200 = Rs. 2300
As this is positive, an overall profit of Rs. 2300 was made.
Answer: D
Question: A = 10% of x, B = 10% of y, C = 10% of x + 10% of y. On the basis of the above equalities, what is true in the following?
A.A is equal to B
B.A is greater than B
C.B is greater than A
D.Relation cannot be established between A and B
Answer: D.Relation cannot be established between A and B
Explanation: The given information gives no indication regarding the comparison of x and y.
Answer D
Question: If after 100 grams of water were added to the 24%-solution of alcohol, the strength of the solution decreased by one-third, how much of the 24%-solution was used?
A.180 grams
B.200 grams
C.250 grams
D.350 grams
Answer: B.200 grams
Explanation: The 24% alcohol solution decreases by 1/3 once the 100 grams of water is added so 100/.08 =1250*.16% (2/3 of 24%) is 200 grams, thus answer is B.
Question: In a race of 1000 m, A can beat by 100 m, in a race of 800m, B can beat C by 100m. By how many meters will A beat C in a race of 600 m?
A.127.6
B.127.5
C.127.9
D.127.8
Answer: B.127.5
Explanation: When A runs 1000 m, B runs 900 m and when B runs 800 m, C runs 700 m.
When B runs 900 m, distance that C runs = (900 * 700)/800 = 6300/8 = 787.5 m.
In a race of 1000 m, A beats C by (1000 - 787.5) = 212.5 m to C.
In a race of 600 m, the number of meters by which A beats C = (600 * 212.5)/1000
= 127.5 m.
Answer: B
Question: What are the number of ways to select 3 men and 2 women such that one man and one woman are always selected?
A.80 ways
B.87 ways
C.30 ways
D.28 ways
Answer: C.30 ways
Explanation: The number of ways to select three men and two women such that one man and one woman are always selected = Number of ways selecting two men and one woman from men and five women
= ⁴C₂ * ⁵C₁ = (4 * 3)/(2 * 1) * 5
= 30 ways.
Answer: C
Question: X completes a work in 12 days and Y complete the same work in 24 days. If both of them work together, then the number of days required to complete the work will be ?
A.8 days
B.10 days
C.12 days
D.20 days
Answer: B.10 days
Explanation: If X can complete a work in x days and Y can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days
Therefore, here, the required number of days = 12 × 24/ 36 = 8 days.
B)
Question: How many possible integer values are there for x if |7x - 3| < 6 ?
A.One
B.Two
C.Three
D.Four
Answer: B.Two
Explanation: Solution: |7x-3| < 6
let 7x=a therefore we have |a-3| < 6 ==> read this as origin is at +3 and we have to move +6 to the right and -6 to the left
(the less than sign represents that the a must be within boundaries )
(3-6)----------3----------(3+6)
now, we have -3<a<9
but a =7x ==> -3<7x<9
dividing all values by +4 we have -0.46 <x < 1,2
Now question says Integer values (not rational ) therefore we have 0,1
Hence 2 B
Question: A alone can complete a work in 16 days and B alone can do in 12 days. StarƟng with A, they work on
alternate days. The total work will be completed in
A.1314
B.1312
C.1334
D.1344
Answer: C.1334
Explanation: ExplanaƟon:
A's 1 day work = 1/16
B's 1 day work = 1/12
As they are working on alternate day's
So their 2 days work = (1/16)+(1/12)
= 7/48
[here is a small technique, Total work done will be 1, right, then mulƟply numerator Ɵll denominator, as
7*6 = 42, 7*7 = 49, as 7*7 is more than 48, so we will consider 7*6, means 6 pairs ]
Work done in 6 pairs = 6*(7/48) = 7/8
Remaining work = 1-7/8 = 1/8
On 13th day it will A turn,
then remaining work = (1/8)-(1/16) = 1/16
On 14th day it is B turn,
1/12 work done by B in 1 day
1/16 work will be done in (12*1/16) = 3/4 day
So total days =
1334
Answer: C
Question: A Jar of marble contains 6 yellow and 4 blue marbles, and no other marbles. If four are pulled out of the jar, one after the other, without being replaced, what is the probability that exactly two of the four marbles will be yellow and two blue.
A
B
C
D 9
A.1/10
B.1/7
C.1/6
D.3/7
Answer: D.3/7
Explanation: 4 marbles out of the given 10 are pulled out of the jar, one after the other, without being replaced
The number of possible combinations (total events) = 10C4
We need to find the probability that exactly two of the four marbles will be yellow(out of 6) and two blue( out of 4).
Here the order in which the marbles are removed isn't asked. So no permutation reqd.
The number of possible combinations to such a specific event = 6C2 X 4C2
The Probability of the specific event = [ 6C2 X 4C2 ] / 10C4
= 15 X 6 / 210
= 3/7
Correct Option : D
Question: You collect baseball cards. Suppose you start out with 15. Maria takes half of one more than the number of baseball cards you have. Since you're nice, you give Peter 1 baseball card. Since his father makes baseball cards, Paul decides to triple your baseball cards. How many baseball cards do you have at the end?
A.17
B.18
C.19
D.20
Answer: B.18
Explanation: Solution
Start with 15 baseball cards.
Maria takes half of one more than the number of baseball cards you have. So Maria takes half of 15 + 1 which is 8,
so you're left with 15 - 8 = 7.
Peter takes 1 baseball card from you: 7 - 1 = 6 baseball cards.
Paul triples the number of baseball cards you have: 6 × 3 = 18 baseball cards.
So you have 18 at the end.
Correct answer : B
Question: A tank contains 10,000 gallons of a solution that is 3 percent sodium chloride by volume. If 4,000 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride?
A. 1.25%
B. 5%
C. 6.25%
D. 6.67%
Answer: B. 5%
Explanation: The remaining solution will be approximately what percent sodium chloride?means:what percent of the remaining solution is sodium chloride. Now, since the remaining solution is 10,000-4,000=6,000 gallons and sodium chloride is 300 gallons (3% of initial solution of 10,000 gallons) then sodium chloride is 300/6,000*100=5% of the remaining solution of 6,000 gallons.
Answer: B.