RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A class consists of 100 students, 30 of them are girls and 70 boys; 20 of them are rich and remaining poor; 40 of them are fair complexioned. The probability of selecting a fair complexioned rich girl is
A.3/125
B.1/59
C.1/56
D.1/54
Answer: A.3/125
Explanation: The probability of selecting girl is: 30/100 = 3/10
The probability of selecting rich is: 20/100 = 1/5
The probability of selecting fair complexioned is: 40/100 = 2/5
Three are independent;probability of rich and fair complexioned girl is:
(3/10) Ã—(1/5) Ã— (2/5) = 3/125
Answer: A
Question: For how many integers n is 1^n+5 = (n+5)^1?
A.1
B.2
C.None of these
D.3
Answer: C.None of these
Explanation: If n=0
1^0+5= (0+5)^1
1^5 = 1 ; 5^1 =5 not ok
If n=1
1^1+5 =1 ; (1+5)^1=6^1=6 not OK
So, Answer : C
Question: The first train leaves the station at 6:00 am with a speed of 60 km/hr. The second train leaves at 7:30 am, in the same direction from the same station, with a speed of 75 km/hr. What time will the second train catch the first train?
A.11:30 am
B.12:30 pm
C.1:30 pm
D.2:30 pm
Answer: C.1:30 pm
Explanation: In ninety minutes, the first train travels 90 km.
The second train catches the first train with a relative speed of 15 km/h.
The second train will catch the first train in 6 hours.
The second train will catch the first train at 1:30 pm.
The answer is C.
Question: A thief is spotted by a policeman from a distance of 200metres. When the policeman starts the chase, the thief also starts running. If the speed of the thief be 15km/hr and that of the policeman 20km/hr, how far the thief will have run before he is overtaken ?
A.A)1km
B.B)500m
C.C)600m
D.D)750m
Answer: C.C)600m
Explanation: Relative speed of the policeman = 20-15 = 5 km/hr
time taken by policeman to cover 200m = (200/1000)*(1/5) = 1/25 hr
In 1/25 hr the thief covers a distance of 15/25 km = 3/5 km = 600m
Answer is C
Question: 36, 34, 30, 28, 24, ?
A.26
B.23
C.22
D.20
Answer: C.22
Explanation: This is an alternating number subtraction series. The pattern is -2, -4, -2, ....
Answer : C.
Question: Seven years ago Anoop was P times as old as Kiran was. If Anoop is now 17 years old, how old is Kiran now in terms of P ?
A.10/P + 7
B.P/11 +7
C.17 - P/7
D.17/P
Answer: A.10/P + 7
Explanation: let's call Kiran's age seven years ago is x
so seven years ago Anoop was: 17-7 = 10 years old
and seven years ago Anoop was P times as old as Kiran was
=> 10/x = P
=> x = 10/P
=> Now Kiran's age will be : x+7 = 10/P+7
=> the answer is A
Question: The surface of a cube is 24sq cm. Find its volume?
A.8
B.7
C.6
D.5
Answer: A.8
Explanation: 6a2 = 24
a = 2 => a3 = 8cc
Answer: A
Question: A train travels from station A to station B. If it travels at a speed of 100 miles per hour, it ends up reaching the station 15 minutes late. If it travels at 120 miles per hour, it reaches the station 15 minutes early. What is the amount of time that the train is scheduled to take for the journey and what is the distance between the stations?
A.	2 hours, 225 miles
B.	3 hours, 350 miles
C.	4 hours, 450 miles
D.	2.75 hours, 325 miles
Answer: D.	2.75 hours, 325 miles
Explanation: Let t be the usual time and x be the distance between AB. So we need to find t and Distance x. The question gives us 2 combinations of speedtime, but the distance remains the same for both condition.
Equation 1 - x= 100 (t+.25) (converted 30 mins into hr) added .5 hrs because it is late or took more time than usual.
Equation 2 - x= 120 (t-.25) subtracted .25 hrs because it is early or took less time than usual.
Now equating 12 we get 100(t+.25)=120(t-.25)
=> 10t +2.5 = 12t - 3
=> 2t=5.5 => t= 2.75 hrs.
Hence x= 100(2.75+.5) =>100 X 3.25 => 325 miles.
Hence correct answer D
Question: The ratio of the number of females to males at a party was 1:2 but when 6 females and 6 males left, the ratio became 1:3. How many people were at the party originally?
A.24
B.28
C.32
D.36
Answer: D.36
Explanation: The total number of people are x females + 2x males.
3*(x-6) = 2x - 6
x = 12
There were 3x = 36 people at the party originally.
The answer is D.
Question: If A and B are two prime numbers bigger than 2, which of the following can be true?
(1) A + B is an even number.
(2) A x B is also a prime number.
(3) A^B is also a prime number.
A.1 only.
B.2 only.
C.3 only.
D.2 and 3 only.
Answer: A.1 only.
Explanation: Answer is D : 2 and 3 only
(1) A + B is an even number. : All primes beyond 2 are odd, so odd+odd = even, so true
(2) A x B is also a prime number. : Beats the property of primes, so false
(3) A^B is also a prime number. : Beats the property of primes, so false
Ans :A
Question: Three persons invested Rs.9000 in a joint business. The second person invested Rs.1000 more than the first and the third Rs.1000 more than second. After two years, they gained Rs.5400. How much third person will get?
A.Rs.2400
B.Rs.3600
C.Rs.2850
D.Rs.2000
Answer: A.Rs.2400
Explanation: First persons investment = x
Second persons investment = x + 1000
Third persons investments = x + 2000
x + x + 1000 + x + 2000 = 9000
3x = 6000
x = 2000
Ratio = 2000 : 3000 : 4000
2:3:4
4/9 * 54000 = 2400
ANSWER:A
Question: When 19 is divided by the positive integer k, the remainder is 3, for how many different values of k is this true?
A.1
B.2
C.3
D.4
Answer: C.3
Explanation: This means that 16 must be a multiple of k.
The factors of 16 are 1, 2, 4, 8, and 16.
Out of these, k can be 4, 8, and 16.
The answer is C.
Question: In what time will Rs. 1000 become Rs. 1331 at 10% per annum compounded annually?
A.2 years
B.3 years
C.4 years
D.5 years
Answer: B.3 years
Explanation: Principal = Rs. 1000; Amount = Rs. 1331; Rate = 10% p.a. Let the time be n years. Then,
[ 1000 (1+ (10/100))n ] = 1331 or (11/10)n = (1331/1000) = (11/10)3
n = 3 years.
ANSWER B 3 years
Question: A person traveled from P to Q at a speed of 40km/hr and return by increasing his speed by 50km/hr. What is his average speed for both the trips?
A.30km/hr
B.50km/hr
C.55km/hr
D.48km/hr
Answer: D.48km/hr
Explanation: Speed on return trip = 150% of 40 = 60kmph
Average = 2*40*60/(40+60) = 4800/100 = 48km/hr
Answer is D
Question: We had $2800 left after spending 30% of the money that we took for shopping. How much money did we start with?
A.$3700
B.$4000
C.$4300
D.$4600
Answer: B.$4000
Explanation: Let x be the amount of money we started with.
0.7x = 2800
x = 4000
The answer is B.
Question: What approximate value should come in place of the question mark (?) in the following equation ?
6⁄7 of 1596 + 3015 = ? – 2150
A.7200
B.48000
C.6530
D.58000
Answer: C.6530
Explanation: ? ≈ 6 × 230 + 3000 + 2150
= 1380 + 3000 + 2150 = 6530
Answer C
Question: When x is divided by 5, the quotient is y and the remainder is 1. When x is divided by 8, the quotient is z and the remainder is 6. Which of the following is the value of y in terms of z?
A.4z/7 + 5
B.(7z + 5) / 6
C.(6z + 7) / 4
D.(8z + 5) / 5
Answer: D.(8z + 5) / 5
Explanation: When x is divided by 5, the quotient is y and the remainder is 1: x = 5y + 1.
When x is divided by 8, the quotient is z and the remainder is 6: x = 8z + 6.
Equate those two:
5y + 1 = 8z + 6;
y = (8z + 5)/5.
Answer: D.
Question: Amar takes as much time in running 18 meters as a car takes in covering 48 meters. What will be the distance covered by Amar during the time the car covers 1.5 km?
A.375 m
B.200 m
C.300 m
D.400 m
Answer: A.375 m
Explanation: A
375 m
Distance covered by Amar = 18/4.8 (1.5km) = 3/8(1500) = 375 m
Question: Find the number of shares that can be bought for Rs.8200 if the market value is Rs.20 each with brokerage being 2.5%.
A.237
B.270
C.177
D.166
Answer: C.177
Explanation: Explanation:
Cost of each share = (20 + 2.5% of 20) = Rs.20.5
Therefore, number of shares = 8200/20.5 = 400
ANSWER:C
Question: If the line L passes through the point (3,n) and (n,3), where n is not equal to 3, which of the following must be true?
1. The slope of L is negative
2. Line L does pass the origin.
3. Line L must passes through the first quadrant
A.I only
B.II only
C.III only
D.I and II
Answer: A.I only
Explanation: Slope of the given line= 3-n/n-3
Given information is that n is not equal to 3, that means n <3 or n>3. In both these conditions the slope will be negative.
1) n<3 (n=2)
3-2/2-3= -1
2) n<3 (n= 0)
3-0/0-3= -1
3) n<3 (n=-3)
3+3/ -3-3= -2/3
4) n>3
3-4/4-3= -1
Answer A
Question: The price of a cycle is reduced by 25 % The new price is reduced by a further 20 %. The 2 reductions together are equal to a single reduction of
A.30
B.40
C.60
D.80
Answer: C.60
Explanation: Let the original price of the cycle be 100. After the first reduction the price will be 75.
This new price is then reduced by 20% = 0.8 x 75 = 60
60 represents a reduction of 40 percent on the original.
C
Question: Marco rode his dirt bike at 45 miles per hour (mph) for two hours. If he then continued to ride at a different constant rate for another three hours, and at the end of the three hours his average speed for the entire five hour ride was 30mph, what was his average speed over the three hour portion of his ride?
A.14 mph
B.20 mph
C.70/3 mph
D.80/3 mph
Answer: B.20 mph
Explanation: Average speed for first two hours, S1 = 45 mph
Distance travelled in these two hours, D1 = 90 miles
Average speed for the entire 5 hour ride, S = 30 mph
Total Distance traveller in the entire 5 hour ride, D = 30 x 5 = 150 miles.
Hence, distance traveller in the latter 3 hour period, D2 = D - D1 = 150 - 90 = 60
Average speed for the latter 3 hour period S2 = D2/3 = 60/3=20
Hence, the correct answer is B
Question: When working alone, painter W can paint a room in 2 hours, and working alone, painter X can paint the same room in z hours. When the two painters work together and independently, they can paint the room in 3/4 of an hour. What is the value of z?
A.3/4
B.1[1/5]
C.1[2/5]
D.1[3/4]
Answer: B.1[1/5]
Explanation: Rate*Time=Work
Let Painter W's rate be W and Painter X's rate be X
R*T = Work
W * 2 = 1 (If the work done is same throughout the question then the work done can be taken as 1) => W = 1/2
X * z = 1 => X = 1/z
When they both work together then their rates get added up
Combined Rate = (W+X)
R*T = Work
(W+X) * 3/4 = 1
=> W+X = 4/3
=> 1/2 + 1/z = 4/3
=> 1/z = (8-3)/6 = 5/6
=> z = 6/5 = 1[1/5]
Answer B
Question: A can do a job in 15 days and B can do it in 30 days. A and B working together will finish twice the amount of work in ------- days?
A.14 days
B.16 days
C.20 days
D.11 days
Answer: C.20 days
Explanation: C
1/15 + 1/30 = 1/10
10*2 = 20 days
Question: How many 7 in between 1 to 100?
A.18
B.20
C.22
D.23
Answer: B.20
Explanation: 7,17,27,37,47,57,67,
70,71,72,73,74,75,76,77(two 7's),78,79,87,97
20 7's between 1 to 100
ANSWER:B
Question: (1/5)^w * (1/4)^18 = 1/(2(10)^35). What is w?
A.17
B.18
C.34
D.35
Answer: D.35
Explanation: We need to arrive at a common base. -->
(5)^(-w) * 2^(-36) = 2^(-36)*5^(-35)
5^(-w)=5^(-35)
-w=-35
w=35=D
Question: A and B can finish a piece of work in 12 days and 18 days respectively. A begins to do the work and they work alternately one at a time for one day each. The whole work will be completed in
A.14 1/3 days
B.15 2/3 days
C.16 1/3 days
D.18 2/3 days
Answer: A.14 1/3 days
Explanation: Explanation:
Both of them together can finish the work (daily working) in 12 × 18/30 days = 36/5
= 7 1/5 days.
By working in alternate days, their 2 day’s work = 5/36
Their, 14 day’s work (because they take more than double of 7 days) = 5/36 × 7
= 35/36
Remaining work = 1 – 35/36 = 1/36
Because A started the work, the remaining work is finished by A
A’s 1 day’s work = 1/12
Therefore, the No. of days taken by A to finish 1/36 work = 1/36/1/12 = 1/3 days.
Therefore, the total work is completed in 14 + 1/3 = 14 1/3 days.
Answer: Option A
Question: if n>0 and x is n percent of y, then, in terms of n, y is what percent of x?
A.a)100n
B.b)1/100n
C.c)1/n
D.d)10^4/n
Answer: D.d)10^4/n
Explanation: Given (n*y)/100=x
to find (y/x)*100
Rearranging first equation
y/x*100 = 100*100/n
=10000/n
Answer D
Question: Sandy walks around a circular field at the rate of one round per hour while Molly runs around it at the rate of two rounds per hour. If they start in the same direction from the same point, how many minutes will it take until they meet again?
A.30
B.45
C.60
D.75
Answer: C.60
Explanation: Since Sandy and Molly move in the same direction along the circle, they will first meet each other when there is a difference of one round between the two.
The relative speed of Sandy and Molly is 2 - 1 = 1 round per hour.
The time required to complete one round at this speed 60 minutes.
The answer is C.
Question: When x is divided by y, the quotient is z with remainder s. Which of the following is equal to s?
A.yz – x
B.y/x−z
C.x – y – z
D.x – yz
Answer: D.x – yz
Explanation: (x/y)=z(+s)
(18/8)=2(+2)
x-yz
which is 18-(8*2)=2
Answer is D
Question: Cars emerging from a motorway arrive at a junction that splits the road into two separate lanes. The number of cars per hour that continue in either lane is constant. If 70 cars per hour were diverted from the left lane to the right lane, the number of cars entering the right lane per hour would be twice as big as the number of cars entering the left lane per hour. Alternatively, if 70 cars per hour were diverted from the right lane to the left lane, the number of cars entering the left lane per hour would be four times as great as the number of cars entering the right lane per hour. How many cars enter the left lane per hour?
A.140
B.170
C.210
D.265
Answer: B.170
Explanation: as per question 70 cars diverted from left lane to right lane. Thus we get equation R+70=2(L-70)
as per question 70 cars diverted from right lane to left lane .thus we get equation L+70=4(R-70)
by solving two equation i.e R +70 =2L-140 OR. R =2L -210 AND L+70= 4R -280 OR L= 4R -3500
BY SOLVING WE GET L= 4( 2L -210) -350 OR L= 8L -840-350 OR 1190 =7L THUS L =170
B
Question: When 40 per cent of a number is added to another number the second number increases to its 140 per cent. What is the ratio between the first and the second number?
A.1 : 1
B.4 : 3
C.3 : 2
D.Data inadequate
Answer: A.1 : 1
Explanation: Let the first and the second numbers be x and y respect then
y + 40% of x = 140% of y
or, y + 0.4x = 1.4y
or, 0.4x = 0.4y
∴ x : y = 0.4 : 0.4 = 1 : 1
Answer A
Question: If 3x + 7 = x2 + M = 7x + 5, what is the value of 120% of M?
A.8.9
B.9.9
C.9.98
D.Cannot be determined
Answer: B.9.9
Explanation: If 3x + 7 = x2 + M = 7x + 5
ie, 3x + 7 = 7x + 5
or, 4x = 2 ∴ x = 1⁄2
and 3x + 7 = x2 + M
or, 1⁄4 + M = 3⁄2 + 7 ⇒ M + 1⁄4 = 8 + 1⁄2
∴ M = 81⁄4
Answer B
Question: Apple costs L rupees per kilogram for first 30kgs and Q rupees per kilogram for each additional kilogram. If the price of 33 kilograms is 168 and for 36kgs of Apples is 186 then the cost of first 20 kgs of Apples is
A.3.69
B.3.66
C.3.6
D.100
Answer: D.100
Explanation: Ans: By framing equations we get
30L+3Q=168
30L+6Q=186
Eliminate Q by multiplying the first equation by 2 and subtracting second equation from the first
30 L = 150 => L = 5
Then we get L = 5
Cost of 20 kgs of apples = 20 x 5 =100
Answer:D
Question: A train speeds past a pole in 15 sec and a platform 110 m long in 25 sec, its length is?
A.50 m
B.165 m
C.200 m
D.300 m
Answer: B.165 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 + 110)/25 = x/15 => x = 165 m.
ANSWER:B
Question: Triangle A’s base is 10% greater than the base of triangle B, and A’s height is 10% less than the height of triangle B. The area of triangle A is what percent less or more than the area of triangle B?
A.9 % less
B.1 % less
C.Equal to each other
D.1 % more
Answer: B.1 % less
Explanation: Base of A = 11/10 * Base of B
Height of A = 9/10 * Height of B
Area of A = (1/2) * Base of A * Height of A = 11/10 * 9/10 * Area of B = 99/100 * Area of B
Area of A is 1% less than the area of B.
Answer (B)
Question: When the integer k is divided by 7, the remainder is 1. Which of the following expressions below when divided by 7, will have a remainder of 5?
I. 4k + 1
II. 6k + 6
III. 8k + 2
A.I only
B.II only
C.III only
D.I and II only
Answer: D.I and II only
Explanation: k = 7j + 1
4k + 1 = 28j + 4 + 1 = 28j + 5
6k + 6 = 42j + 6 + 6 = 42j + 7 + 5
8k + 2 = 56j + 8 + 2 = 56j + 7 + 3
The answer is D.
Question: If “&” implies “Add”, “@” implies “multiply”, “#” implies “subtract”, “$” implies “division”,
12 & 3 @ 2 # 32 $ 4 = ?
A.12
B.10
C.13
D.14
Answer: B.10
Explanation: Explanation:
Given:
12 & 3 @ 2 # 32 $ 4 = ?
By substituting appropriate mathematical symbols, we get,
12 + 3 * 2 – 32/4 = ?
12 + 3 * 2 – 8 = ?
12 + 6 – 8 = ?
18 – 8 = 10
ANSWER IS B
Question: what is next no. 11 23 47 83 131 ???
A.171
B.181
C.191
D.201
Answer: C.191
Explanation: 11+12*1=23
23+12*2=47
47+12*3=83
83+12*4=131
131+12*5=191
ANSWER:C
Question: Equal amount of water were poured into two empty jars of different capacities, which made one jar 1/7 full and other jar 1/6 full. If the water in the jar with lesser capacity is then poured into the jar with greater capacity, what fraction of the larger jar will be filled with water?
A.1/7
B.7/12
C.1/2
D.2/7
Answer: D.2/7
Explanation: Same amount of water made bigger jar 1/7 full, then the same amount of water(stored for a while in smaller jar) were added to bigger jar, so bigger jar is 1/7+1/7=2/7 full.
Answer: D.
Question: A can do a work in 15 days and B in 20 days. If they work on it together for 5 days, then the fraction of the work that is left is :
A.1/3
B.7/12
C.5/12
D.2/3
Answer: C.5/12
Explanation: Ans is:C
A's 1 day's work =1/15
B's 1 day's work =1/20
(A + B)'s 1 day's work =(1/15+1/20)=7/60
(A + B)'s 5 day's work =(7/60*5)=7/12
Therefore, Remaining work =(1-7/12)=5/12. Answer: C
Question: In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, what was the number of valid votes that the other candidate got?
A.2800
B.2700
C.2100
D.2500
Answer: B.2700
Explanation: Explanation :
Total number of votes = 7500
Given that 20% of Percentage votes were invalid
=> Valid votes = 80%
Total valid votes = 7500 × (80/100)
1st candidate got 55% of the total valid votes.
Hence the 2nd candidate should have got 45% of the total valid votes
=> Valid votes that 2nd candidate got = total valid votes × (45/100)
= 7500 × (80/100) × (45/100) = 75 × 45 × 45 = 75 × 4 × 9 = 300 × 9 = 2700
Answer : Option B
Question: In the first 10 overs of a cricket game, the run rate was only 3.8. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?
A.6.25
B.6.5
C.6.75
D.6.1
Answer: D.6.1
Explanation: 10 overs - run rate = 3.8
runs scored in first 10 overs = 38
remaining overs 40
total runs to be scored= 282
38 runs already scored 282-38=244
244 runs to be scored in 40 overs
let required runrate be x
40*x=244
x=244/40
x=6.1
the required runrate is 6.1
ANSWER:D
Question: A sum fetched a total simple interest of 4025.25 at the rate of 9 %.p.a. in 5 years. What is the sum?
A.5768
B.8925
C.2345
D.8945
Answer: D.8945
Explanation: Principal = (100 x 4025.25)/(9 x 5)
= 402525/45
= 8945.
ANSWER D
Question: A man buys an article for $110. and sells it for $125. Find the gain percent?
A.10%
B.13.6%
C.25%
D.20%
Answer: B.13.6%
Explanation: C.P. = $110
S.P. = $125
Gain = $15
Gain% = 15/110 *100 = 13.6%
Answer is B
Question: A car takes 6 hours to cover a distance of 540 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
A.55 Kmph
B.60 Kmph
C.65 Kmph
D.70 Kmph
Answer: B.60 Kmph
Explanation: Time = 6
Distence = 540
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 540/9 = 60 Kmph
B)
Question: The operation T is defined by x T y=1/x+1/y for all nonzero numbers x and y. If z is a number greater than 1, which of the following must be true.
I. z T (-z)=0
II. z T z/z-1=0
III. 2/z T 2/z=z
A.a.) I
B.b.) I and II only
C.c) I and III only
D.d) II and III only
Answer: C.c) I and III only
Explanation: Statement I is TRUE
Statement II is not TRUE
Statement III is TRUE
Answer : C
Question: How many odd numbers between 10 and 1,100 are the squares of integers?
A.12
B.13
C.14
D.15
Answer: D.15
Explanation: The square of an odd number is an odd number:
10 < odd < 1,000
10 < odd^2 < 1,000
3.something < odd < 31.something (by taking the square root).
So, that odd number could be any odd number from 5 to 31, inclusive: 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, and 31.
15 numbers.
Answer: D.
Question: Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is?
A.22
B.98
C.60
D.88
Answer: C.60
Explanation: Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(100 + 100)/8 = 3x => x = 25/3.
So, speed of the faster train = 50/3 = 50/3 * 18/5 = 60 km/hr.
Answer:C
Question: If the weight of 12 meters long rod is 14 kg. What is the weight of 6 meters long rod ?
A.8 kg.
B.10.8 kg.
C.7 kg.
D.18.0 kg
Answer: C.7 kg.
Explanation: Answer
∵Weight of 12 m long rod = 14 kg
∴ Weight of 1 m long rod = 14 / 12 kg
∴ Weight of 6 m long rod = 14 x 6 / 12
= 7 kg
Option: C
Question: Cost of 16 mirror and 8 comb is Rs.352 and the cost of 4 mirror and 4 comb is Rs.96. Find the cost of each mirror?
A.10
B.12
C.20
D.21
Answer: C.20
Explanation: Let the cost of each pen and pencil be 'p' and 'q' respectively.
16m + 8c = 352 --- (1)
4m + 4c = 96
8m + 8c = 192 --- (2)
(1) - (2) => 8p = 160
=> m = 20
C
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.23/39
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: If a randomly selected non-negative single digit integer is added to {2, 3, 4, 7}. What is the probability that the median of the set will increase but the range still remains the same?
A.0.2
B.0.3
C.0.4
D.0.5
Answer: C.0.4
Explanation: We are selecting from non-negative single digit integers, so from {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. These 10 digits represent the total number of outcomes.
Hence, the total number of outcomes is 10.
We need to find the probability that the median of the set will increase but the range still remains the same.
The median of the set is (3 + 4)/2 = 3.5, thus the number selected must be 4 or greater.
For the range to remain the same, the number must be between 2 and 7 inclusive.
To satisfy both conditions, the number selected must be 4, 5, 6, or 7.
The probability is 4/10 = 0.4
The answer is C.
Question: The denominator of a fraction is 2 less than twice the numerator. If the numerator and denominator are both increased by 1, the fraction becomes 3/5. Find the fraction?
A.A)2/3
B.B)3/5
C.C)4/9
D.D)5/9
Answer: C.C)4/9
Explanation: Let the numerator and denominator of the fraction be 'n' and 'd' respectively.
d = 2n - 2
(n + 1)/(d + 1) = 3/5
5n + 5 = 3d + 3
5n + 5 = 3(2n - 2 ) + 3 => n = -8
d = 2n - 2 => d = -18
Hence the fraction is : 4/9
ANSWER:C
Question: 99,996^2 - 4^2 =
A.10^10 - 2
B.(10^5 – 2)^2
C.10^5(10^5 – 8)
D.10^5(10^4 – 2)
Answer: C.10^5(10^5 – 8)
Explanation: (99,996)^2 - (4)^2 = (100,000 -4)^2 - (4)^2 = (100,000)^2 - 2*4*100,000 + 4^2-4^2=(10^5)^2 - 8*(10^5) = 10^10 - 8*(10^5)=10^5(10^5 - 8) Answer C
Question: Cassandra invested one part of her $10,000 at 7.5% per year and the other part at 8.5% per year. Her income from the two investment was $820. How much did she invest at each rate?
A.x = $2000 and y = $7000
B.x = $4000 and y = $7000
C.x = $3000 and y = $7000
D.x = $5000 and y = $7000
Answer: C.x = $3000 and y = $7000
Explanation: Let x and y be the amount invested at 7.5% and 8.5% respectively
Income = $820 = 7.5% * x + 8.5% * y
The total amount invested is also known
10,000 = x + y
Solve the system of the equations to find x and y.
x = $3000 and y = $7000
Answer C