RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A man can row 9 1/3 kmph in still water and finds that it takes him thrice as uch time to row up than as to row down the same distance in the river. The speed of the current is:
A.3 1/2 km/hr
B.2 1/3 km/hr
C.4 1/2 km/hr
D.4 2/3 km/hr
Answer: D.4 2/3 km/hr
Explanation: Sol.
Let speed upstream be x kmph. Then, speed downstream = 3x kmph.
Speed in still water = 1/2(3x + x) kmph = 2x kmph.
∴ 2x = 28/3 ⇒ x = 14/3
So, Speed upstream = 14/3 km/hr; Speed downstream = 14/hr.
Hence, speed of the current = 1/2 [14 - 14/3] km/hr = 14/3 km/hr = 4 2/3 km/hr.
Answer D
Question: If selling price is doubled, the profit triples. Find the profit percent:
A.170
B.320
C.100
D.280
Answer: C.100
Explanation: C
100%
Let C.P. be Rs. x and S.P. be Rx. y.
Then, 3(y - x) = (2y - x) => y = 2x
Profit = (y - x) = Rs. (2x - x) = Rs. x
Profit % = x/x * 100 = 100%.
Question: The difference of the squares of two consecutive even integers is divisible by which of the following integers ?
A.8
B.4
C.12
D.16
Answer: B.4
Explanation: Explanation:
Let the two consecutive even integers be 2n and (2n + 2). Then,
(2n + 2)2 = (2n + 2 + 2n)(2n + 2 - 2n)
= 2(4n + 2)
= 4(2n + 1), which is divisible by 4.
Answer B
Question: What is the units digit of (5!*4! + 6!*5!)/3?
A.4
B.3
C.2
D.0
Answer: D.0
Explanation: (5!*4! + 6!*5!)/3
=5!(4! + 6!)/3
=120 ( 24 + 720)/3
=(120 * 744)/3
= 120 * 248
Units digit of the above product will be equal to 0
Answer D
Question: Monika purchased a pressure cooker at 9/10th of its selling price and sold it at 8% more than its Selling Price. Find her gain percent.
A.10
B.20
C.25
D.15
Answer: B.20
Explanation: Let the Selling Price be $X. then Cost Price = $9x/10, Receipt=108% of $x= $27x/25 Gain=$(27x/25*9x/10)=$(108x-90x/100)=$18x/100
Gain%=(18x/100*10/9x*100)%=20%
Answer B) 20.
Question: In how many ways letters of the word CORPORATION be arranged?
A.125879
B.3326400
C.369
D.1698
Answer: B.3326400
Explanation: CORPORATION has 11 letters, out of which O repeated 3 times, R repeated 2 times. Hence total ways = 11! / (3!*2!) = 3326400 ways
B
Question: 279936, 46656, 7776, 1296, 216, ?
A.60
B.46
C.36
D.66
Answer: C.36
Explanation: Explanation :
Go on dividing by 6 to the next number
Answer : Option C
Question: 12.1212+17.0005 - 9.1102 = ?
A.20.0015
B.20.0105
C.20.0115
D.20.1015
Answer: C.20.0115
Explanation: Solution
Given expression
=(12.1212+17.0005)-9.1102
= (29.1217 - 9.1102)
=20.0115.
Answer C
Question: Find the wrong number below mentioned series
13,60,100,500,850
A.13
B.60
C.100
D.500
Answer: A.13
Explanation: 13 is the only prime number or odd number in the series.
ANSWER:A
Question: How many of the following numbers are divisible by 3 but not by 9 ?
2133, 2343, 3474, 4131, 5286, 5340, 6336, 7347, 8115, 9276
A.5
B.6
C.7
D.8
Answer: B.6
Explanation: Marking (/) those which are are divisible by 3 by not by 9 and the others by (X), by taking the sum of digits, we get:s
2133 9 (X)
2343 12 (/)
3474 18 (X)
4131 9 (X)
5286 21 (/)
5340 12 (/)
6336 18 (X)
7347 21 (/)
8115 15 (/)
9276 24 (/)
Required number of numbers = 6.
Answer: B
Question: If x≠0 and x=√4xy−4y^2, then, in terms of y, x =
A.2y
B.y
C.y/2
D.-(4y^2)/(1-2y)
Answer: A.2y
Explanation: Well it means :
Squaring we get:
x^2 =4y(x-y)
Assume X^2=m >>>>>>>>>>>1
Than ,m=4y(m^1/2-y)
on solving:m-4y(m)^1/2+4y^2=0 >> quadratic in y s solve for y.
Y comes out to be =(m^1/2)/2
Hence,put m =x^2 from 1.
So x=2y
ANSWER:A
Question: How many times are the hands of a clock at right angle in a day?
A.22
B.24
C.44
D.48
Answer: C.44
Explanation: In 12 hours, they are at right angles 22 times.
In 24 hours, they are at right angles 44 times.
Answer: Option C
Question: Find the 2nd greatest number of five digits which is exactly divisible by 12, 15 and 18?
A.A)13050
B.B)12960
C.C)14090
D.D)16200
Answer: B.B)12960
Explanation: The largest five digit numbers are
16200,14090,13050,12960,12080,
16200 is divisible by 12, 15 and 18 ------(1st largest no)
14090 is not divisible by 12
13050 is not divisible by 12
12960 is divisible by 18, 12 and 15 -------(2nd largest)
12080 is not divisible by 12
ANSWER:B
Question: If line L passes through point (m, n) and (– m, – n), where m and n are not 0, which of the following must be true?
I.	L exactly passes through 2 quadrants
II.	The slope of L is negative
III.	The slope of L is positive
A.I only
B.II only
C.III only
D.I and II only
Answer: A.I only
Explanation: Let (m,n) = (2,3)
(-m,-n) = (-2,-3)
Slope = (3+3)/(2+2) = 6/4 = 3/2
So II may not be true
Let (m,n) = (2,-3) then (-m,-n) = (-2,3)
So slope = (3 +3)/(-2-2) = -3/2
so III may not be true
So such a line would be -> (y - 3) = 3/2(x - 2)
=> 2y - 6 = 3x - 6
=> 2y - 3x = 0, hence no x or y intercept, so it passes through origin.
I is true.
Answer - A
Question: A cube is painted red on all faces. It is then cut into 27 equal smaller cubes. How many P cubes are painted on only 2 faces?
A.12
B.8
C.6
D.10
Answer: A.12
Explanation: 1) Draw a simple cube
2) Draw 9 squares on each face of the cube (so that it looks like a Rubik's Cube) - this is what the cube will look like when it's cut into 27 equal smaller cubes.
3) Remember that the OUTSIDE of the cube is the part that's painted....
The mini-cubes with 2 painted sides are ALL on the edge of the cube, in themiddleof the edge. There are 4 in front, 4 in back and 4 more on thestripthat runs around the left/top/right/bottom of the cube. P=4 + 4 + 4 = 12. Answer A
Question: The average runs of a cricket player of 10 innings was 20. How many runs must he make in his next innings so as to increase his average of runs by 4?
A.12
B.42
C.64
D.76
Answer: C.64
Explanation: Explanation:
Average after 11 innings = 24
Required number of runs = (24 * 11) – (20 * 10)
= 264 – 200 = 64
ANSWER C
Question: Eighty percent of the lights at Hotel California are on at 8 p.m. a certain evening. However, forty percent of the lights that are supposed to be off are actually on and ten percent of the lights that are supposed to be on are actually off. What percent E of the lights that are on are supposed to be off?
A.22(2/9)%
B.16(2/3)%
C.11(1/9)%
D.10%
Answer: D.10%
Explanation: Is the Answer D.
let me try..
Let the light which are supposed to be OFF = SO
Let the light which are supposed to be ON = SN
Let the light which are ACTUALLY OFF = AO
Let the light which are ACTUALLY ON = AN
Let the total no. of lights be 100,
So ACTUALLY ON lights = 80
And ACTUALLY OFF lights = 20
Also given >> forty percent of the lights that are supposed to off are actually on >>> (40/100)*SO are ACTUALLY ON
it means >>> (60/100)*SO are ACTUALLY OFF
Also given >> ten percent of the lights that are supposed to be on are actually off >>> (10/100)*SN are ACTUALLY OFF
it means >>> (90/100)*SN are ACTUALLY ON
So, Total ACTUALLY ON lights = (40/100)*SO + (90/100)*SN = 80
and Total ACTUALLY OFF lights = (60/100)*SO + (10/100)*SN = 80
From here we get SO = 20
we need to find: What percent of the lights that are on are supposed to be off >>> So light ACTUALLY ON are 80 and light which are ACTUALLY ON, which are supposed to be OFF = (40/100)*SO = 8.
So (8/80)*100 E= 10%.D
Question: If 315,214 football shoes need to be placed in boxes and each box can contain at most 2 pair of football shoes. How many pair of football shoes will be in the last unfilled box?
Options:
A.1football shoes
B.0 football shoes
C.4 football shoes
D.7 football shoes
Answer: B.0 football shoes
Explanation: The number of football shoes that can be placed in boxes of 2 football shoes is the last number that is divisible by 2 that occurs before 315,214.
In order to divide the sum in 2 parts, the last number must be divisible by 2
Divisibility rule of 2: The last digit must be divisible by 2
last digit of 315,214 is 4 and 4 is divisible by 2.
Hence, there is no unfilled box.
Correct Option: B
Question: John can row at 5 kmph and still water. He takes 5 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?
A.28 km
B.12 km
C.16 km
D.30 km
Answer: B.12 km
Explanation: Let the distance between A and B be x km.
Total time = x/(5 + 1) + x/(5 - 1) = 5
=> x/6 + x/4 = 4 => (2x + 3x)/12 = 5 => x = 12 km.
ANSWER:B
Question: Read the following three equations:
5 ~ 4 ~ 3 ~ 9 = 4215
6 ~ 9 ~ 2 ~ 6 = 3816
4 ~ 7 ~ 3 ~ 3 = 1122
Now based on the rule that has been used, solve the following equation:
6 ~ 2 ~ 7 ~ 4 = ____
A.2414
B.2910
C.2940
D.3749
Answer: A.2414
Explanation: A
2414
2414
The rule that is being followed here is
P ~ Q ~ R ~ S = [first digit of (P * S)] [last digit of (Q * R)] [first digit of (Q * R)] [last digit of (P * S)]
Using the same rule in the incomplete equation,
6 ~ 2 ~ 7 ~ 4 = [first digit of (6 * 4)] [last digit of (2 * 7)] [first digit of (2 * 7)] [last digit of (6 * 4)]
= 2414
Thus 2414 is the missing number.
Question: The population of a town increased from 1,75,000 to 2,62,500 in a decade. What is the average percent increase of population per year?
A.5%
B.6%
C.7%
D.2%
Answer: A.5%
Explanation: increase = 262500 - 175000 = 87500
% increase in 10 yrs
= 87500/175000*100 = 50%
avg = 50/10 = 5%
ANSWER A
Question: A store reported total sales of $385 million for February of this year. If the total sales for the same month last year was $320 million, approximately what was the percent increase R in sales?
A. 2%
B. 17%
C. 20%
D. 65%
Answer: C. 20%
Explanation: Last year's sales = $320 million;
This year's sales = $385 million;
Increase R = $65 million.
Now, 20% of $320 million is $64 million, which is very close to actual increase of $65 million.
Answer: C.
Question: A shopkeeper purchased 70 kg of potatoes for Rs. 420 and sold the whole lot at the rate of Rs. 6.50 per kg. What will be his gain percent?
A.8 1/9 %
B.8 9/3 %
C.8 1/3 %
D.32 1/3 %
Answer: C.8 1/3 %
Explanation: C.P. of 1 kg = 420/7 = Rs. 6
S.P. of 1 kg = Rs. 6.50
Gain % = 0.50/6 * 100 = 25/3 = 8 1/3 %
Answer: C
Question: A and B together can do a work in 4 days. If A alone can do it in 20 days. In how many days can B alone do it?
A.11
B.5
C.6
D.8
Answer: B.5
Explanation: B
5
1/4 â€“ 1/20 = 1/5 => 5
Question: If a and b are positive integers and a/b=0 then which of the following give positive Numbers and CANNOT be zero?
A.ab/ba
B.a/b-b/a
C.b/a-a/b
D.(a^2 -b^2)/ab
Answer: C.b/a-a/b
Explanation: (D) (a^2 -b^2)/ab = a/b-b/a gives negative value.
The option C is Answer.
(C)a/b-b/a
If a/b=0, b/a gives positive numbers.(a and b are positive integers)
Question: In the decimal notation of number (223)3(223)3, what is the third digit to the right of the decimal point?
A.0
B.1
C.2
D.4
Answer: A.0
Explanation: Because (2/23)3<(2/20)3=(1/10)3=0.001, the third digit to the right of the decimal point in the decimal notation of (2/23)3 is 0.
Answer: A
Question: A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 2500. The difference between the profit shares of A and C is?
A.621
B.276
C.236
D.1000
Answer: D.1000
Explanation: Explanation:
Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6
And also given that, profit share of B is Rs. 2500
=> 5 parts out of 15 parts is Rs. 2500
Now, required difference is 6 - 4 = 2 parts
Required difference = 2/5 (2500) = Rs. 1000
Answer: D
Question: If 15% of A is the same as 40% of B, then A : B is :
A.5:4
B.8:3
C.7:16
D.2:17
Answer: B.8:3
Explanation: Expl : 15% of A I= 40 % of B =15A/100 = 40B/100 = 8/3 = 8:3
Answer:B
Question: If y exceeds x by 20%, then x is less than y by?
A.16 8/3%
B.16 9/3%
C.16 2/3%
D.16 2/9%
Answer: C.16 2/3%
Explanation: X=100	y=120
120------20
100-------? => 16 2/3%
Answer:C
Question: A train crosses a platform of 120 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.88
C.270
D.62
Answer: C.270
Explanation: Length of the train be â€˜Xâ€™
X + 120/15 = X + 250/20
4X + 480 = 3X + 750
X = 270m
Answer: C
Question: z is a positive integer and multiple of 2; v = 4^z, what is the remainder when v is divided by 10?
A.10
B.6
C.4
D.0
Answer: B.6
Explanation: It is essential to recognize that the remainder when an integer is divided by 10 is simply the units digit of that integer. To help see this, consider the following examples:
4/10 is 0 with a remainder of 4
14/10 is 1 with a remainder of 4
5/10 is 0 with a remainder of 5
105/10 is 10 with a remainder of 5
It is also essential to remember that the z is a positive integer and multiple of 2. Any integer that is a multiple of 2 is an even number. So, z must be a positive even integer.
With these two observations, the question can be simplified to:what is the units digit of 4 raised to an even positive integer?
The units digit of 4 raised to an integer follows a specific repeating pattern:
4^1 = 4
4^2 = 16
4^3 = 64
4^4 = 256
4^(odd number) --> units digit of 4
4^(even number) --> units digit of 6
There is a clear pattern regarding the units digit. 4 raised to any odd integer has a units digit of 4 while 4 raised to any even integer has a units digit of 6.
Since z must be an even integer, the units digit of v=4^z will always be 6. Consequently, the remainder when v=4^z is divided by 10 will always be 6.
In case this is too theoretical, consider the following examples:
z=2 --> v=4^z=16 --> v/10 = 1 with a remainder of 6
z=4 --> v=4^z=256 --> v/10 = 25 with a remainder of 6
z=6 --> v=4^z=4096 --> v/10 = 409 with a remainder of 6
z=8 --> v=4^z=65536 --> v/10 = 6553 with a remainder of 6
Answer: B.
Question: The CI on Rs. 30,000 at 7% per year is Rs. 4347. The period is?
A.1 year
B.2 years
C.3 years
D.4 years
Answer: B.2 years
Explanation: Amount = Rs. (30000 + 4347) = Rs. 34347.
Let the time be n years.
Then, 30000 1 +	7 n	= 34347
100
107 n	=	34347	=	11449	= 107 2
100	30000	10000	100
n = 2 years
B
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
A.37 km/hr
B.50 km/hr
C.36 km/hr
D.26 km/hr
Answer: B.50 km/hr
Explanation: Speed of the train relative to man = 125/10 = 25/2 m/sec.
= 25/2 * 18/5 = 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 5 = 45 => x = 50 km/hr.
Answer:B
Question: Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
A.11
B.12
C.77
D.88
Answer: B.12
Explanation: Speed of the first train = 120/10 = 12 m/sec.
Speed of the second train = 120/5 = 8 m/sec.
Relative speed = 12 + 8 = 20 m/sec.
Required time = (120 + 120)/20 = 12 sec.Answer: B
Question: A contractor undertook to do a piece of work in 9 days. He employed certain number of laboures but 6 of them were absent from the very first day and the rest could finish the work in only 15 days. Find the number of men originally employed .
A.15
B.6
C.13
D.9
Answer: A.15
Explanation: Let the number of men originally employed be x.
9x = 15(x – 6)
or x = 15
Answer A
Question: If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is ?
A.1/5
B.1/2
C.1/9
D.1/8
Answer: B.1/2
Explanation: The number of exhaustive outcomes is 36.
Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2
P(E) = 1 - 1/2 = 1/2.
Answer: B
Question: 10 speakers gathered to deliver speeches on two topics. Even though 10 speeches were initially planned to be delivered, due to lack of time only 2 speeches were finally decided to be delivered. Topics are to be spoken in a specific order and the speeches differ with respect to speaker or topic. How many such two speeches are possible?
A.2
B.20
C.50
D.100
Answer: D.100
Explanation: 1)there are 10 speeches in ONE topic and 10 in OTHER..
2)there is a specific order for topics, so
a) both the topics are to be spoken on- so ONE from each
b) the order does not matter since there is ONLY one specific order..
so 10C1∗10C1=10∗10=100
ANSWER:D
Question: In how many ways can 4 indistinguishable red balls and 2 different blue balls be arranged in a line?
A.6!
B.30
C.40
D.6!/2!
Answer: B.30
Explanation: The total number of ways in which a total N items, out of which p are identical of one type, q are identical of another type and rest are different, can be arranged in a line is N!/{p!q!}
In the given problem, we have 6 balls out of which 4 are identical.
Hence the number of arrangements possible are 6!/4! = 30
Ans B
Question: To be eligible for retirement benefits at the Sieman Corporation, the sum of an employee's age, in years, and the number of years employment must be at least 64. If x, where x <64, is a certain employee's age when hired and y is the minimum number of years of employment required for the employee to be eligible for retirement benefits, which of the following equations represents the relationship between x and y?
A.x+2y=64
B.xy=64
C.2x+y=64
D.x+y=64
Answer: A.x+2y=64
Explanation: We are told that when a certain employee was hired he was x years old and that the he needed minimum y years to be eligible for benefits.
Now,after y years of employment, when the employee will be be eligible for benefits, the employee will be x+y years old and will have y years of employment, thus{age after y years}+{employment years}=(x+y)+y=x+2y=64.
Answer: A
Question: Barbara has 8 shirts and 12 pants. How many clothing combinations does Barbara have, if she doesn’t wear 2 specific shirts with 3 specific pants?
A.126
B.120
C.101
D.112
Answer: A.126
Explanation: 8 shirts
9 pants
we can combine 2 shirts with (12-3) pants
2*9=18
we can combine the other shirts (6) with any pants (9)
9*12=54
Thus total :108+18=126	ANS:A
Question: In the first 20 overs of a cricket game, the run rate was only 4.2. What should be the run rate in the remaining 30 Overs to reach the target of 324 runs?
A.7.25
B.8.5
C.8
D.9.15
Answer: C.8
Explanation: Explanation :
Required run rate = (324 - 4.2 20 ) = 240/ 30 = 8.
Answer : C
Question: In how many ways can 5 letters be posted in 3 post boxes, if any number of letters can be posted in all of the three post boxes?
A.25
B.40
C.35
D.60
Answer: C.35
Explanation: The first letter can be posted in any of the 3 post boxes. Therefore, we have 3 possibilities.
Similarly, the second, the third, the fourth and the fifth letter can each be posted in any of the 3 post boxes.
Each of the 5 letters has 3 possibilities because we can post any number of letters in all of the boxes.
Therefore, the total number of ways the 5 letters can be posted in 3 boxes is
3 * 3 * 3 * 3 * 3 = 35
Ans: C
Question: A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively.The length of the train is:
A.35M
B.45M
C.55M
D.50M
Answer: D.50M
Explanation: 2 kmph = ( 2 x 5/18) m/sec = 5/9 m/sec.
4 kmph = ( 4 x 5/18)m/sec = 10/9 m/sec.
Let the length of the train be x metres and its speed by y m/sec.
Then, ( x / y-5) = 9 and x / (y-10/ 9) = 10.
Therefore 9y - 5 = x and 10(9y - 10) = 9x
=9y - x = 5 and 90y - 9x = 100.
On solving, we get: x = 50 ANSWER : D
Question: 36, 34, 30, 28, 24, 22, 18, 16, ?
A.12
B.10
C.8
D.6
Answer: A.12
Explanation: This is an alternating number subtraction series. The pattern is -2, -4, -2, ....
The answer is A.
Question: A and B started a partnership business investing Rs. 20,000 and Rs. 15,000 respectively. C joined them with Rs. 20,000 After six months. Calculate B's share in total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?
A.7500
B.8500
C.9000
D.8000
Answer: A.7500
Explanation: Explanation :
A : B : C = 20000*24 : 15000*24 : 20000*18 = 20*4 : 15*4 : 20*3
= 4*4 : 3*4 : 4*3
= 4:3:3
B's Share = 25000 * 3/10 = 7500. Answer : Option A
Question: There were two candidates in an election. Winner candidate received 54% of votes and won the election by 288 votes. Find the number of votes casted to the winning candidate?
A.776
B.1944
C.2199
D.2157
Answer: B.1944
Explanation: W = 54% L = 46%
54% - 46% = 8%
8% -------- 288
54% -------- ? => 1944
Answer:B
Question: A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 400 m long?
A.266 Sec
B.160 Sec
C.776 Sec
D.166 Sec
Answer: B.160 Sec
Explanation: L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (D)= 1600 m
T = D/S
T = 1600/10
T = 160 Sec
Answer: B
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow?
A.3/98
B.2/28
C.2/21
D.2/29
Answer: C.2/21
Explanation: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = ³C₂/¹⁵C₂ = (3 * 2)/(15 * 14) = 1/35
Probability that both are yellow = ²C₂/¹⁵C₂ = (2 * 1)/(15 * 14) = 1/105
Probability that one blue and other is yellow = (³C₁ * ²C₁)/¹⁵C₂ = (2 * 3 * 2)/(15 * 14) = 2/35
Required probability = 1/35 + 1/105 + 2/35
= 3/35 + 1/105 = 1/35(3 + 1/3)
= 10/(3 * 35) = 2/21
Answer:C
Question: How many numbers can be made with digits 0, 7, 8 which are greater than 0 and less than a million?
A.496
B.486
C.1084
D.728
Answer: D.728
Explanation: The number of single digit numbers = 2
The number of 2 digit numbers = 2 × 3 = 6
The number of 3 digit numbers = 2 × 3 × 3 = 18
The number of 4 digit numbers = 2 × 3 × 3 × 3 = 54
The number of 5 digit numbers = 2 × 3 × 3 × 3 × 3 = 162
The number of 6 digit numbers = 2 × 3 × 3 × 3 × 3 × 3 = 486
Therefore, the total numbers = 728
ANSWER:D
Question: A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?
A.10 / 21
B.11 / 21
C.2 / 7
D.5 / 7
Answer: A.10 / 21
Explanation: Total number of balls = (2 + 3 + 2) = 7.
Let S be the sample space.
Then, n(S)	= Number of ways of drawing 2 balls out of 7
= 7C2 `
=(7 x 6)/(2 x 1)
= 21.
Let E = Event of drawing 2 balls, none of which is blue.
n(E)	= Number of ways of drawing 2 balls out of (2 + 3) balls.= 5C2 =	(5 x 4)/(2 x 1) = 10.
P(E) =	n(E)/n(S)	=	10/21
Answer: A.
Question: There are 750 male and female participants in a meeting. Half the female participants and one-quarter of the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female?
A.150
B.135
C.160
D.125
Answer: D.125
Explanation: Explanation :
Let m be the number of male participants and f be the number of female articipants in the meeting.
Thetotal number of participants is given as 750.
Hence, we have m+f= 750
Now, we have that half the female participants and one-quarter of the male participants are
Democrats.
Let d equal the number of the Democrats.
Then we have the equation f/2 + m/4 =d
Now, we have that one-third of the total participants are Democrats. Hence, we have the equation
=> d = 750/3 = 250
Solving the three equations yields the solution
=> f = 250,m= 500, and d= 250.
The number of female democratic participants equals half the female participants equals
=> 250/2 = 125.
Hence (D) is the correct answer.
Answer : D
Question: On the first day of her vacation, Louisa traveled 100 miles. On the second day, traveling at the same average speed, she traveled 175 miles. If the 100-mile trip took 3 hours less than the 175-mile trip, what was the average speed, in miles per hour?
A.27
B.28
C.25
D.30
Answer: C.25
Explanation: (time)*(rate) = (distance)-->(rate) = (distance)/(time)--> given:(rate) = 100/t = 175/(t+3)-->4/t = 7/(t+3)-->4t+12=7t ---->3t= 12 . t= 4 ---->(rate ) = 100/4 = 25
Answer: C
Question: The instructions state that Cheryl needs 5/11 square yards of one type of material and 2/3 square yards of another type of material for a project. She buys exactly that amount. After finishing the project, however, she has 25/55 square yards left that she did not use. What is the total amount of square yards of material Cheryl used?
A.1/12
B.1/9
C.1 2/3
D.2/3
Answer: D.2/3
Explanation: total bought = 5/11+2/3
left part 25/55--->5/11
so used part 5/11+2/3-5/11=2/3
Ans D