RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A car travels the first 1/3 of certain distance with a speed of 10km/hr the next 1/3 distance with a speed of 12 km/hr, and the last 1/3 distance with a speed of 60 km/hr. the average speed of the car for the whole journey is?
A.12km/hr
B.15km/hr
C.89km/hr
D.52km/hr
Answer: B.15km/hr
Explanation: Let the whole distance travelled be x km
and the average speed of the car for he whole journey be y km/hr
then (x/3)/10+(x/3)/12+(x/3)/60=x/y
x/30+x/36+x/180=x/y
1/15y=1
y=15km/hr
Answer(B)
Question: A store owner estimates that the average price of type A products will increase by 25% next year and that the price of type B products will increase by 20% next year. This year, the total amount paid for type A products was $4500 and the total price paid for type B products was $8300. According to the store owner's estimate, and assuming the number of products purchased next year remains the same as that of this year, how much will be spent for both products next year?
A.$14,755
B.$15,585
C.$16,000
D.$16,225
Answer: B.$15,585
Explanation: cost of type A products next year = 1.25 * 4500 = 5625
cost of type B products next year = 1.2 * 8300 = 9960
total 5625 + 9960 = 15585 option B
Question: 5⁄7 of 4⁄15 of a number is 8 more than 2⁄5 of 4⁄9 of the same number. What is half of that number?
A.630
B.315
C.210
D.105
Answer: D.105
Explanation: Let the number be x.
∴ 5⁄7 × 4⁄15 × x - 2⁄5 × 4⁄9 × x = 8
or, x = 8×31512=2108×31512=210
∴ Half of the number = 105
Answer D
Question: If a(a + 5) = 6 and b(b + 5) = 6, where a ≠ b, then a + b =
A. −48
B. −5
C. 2
D. 46
Answer: B. −5
Explanation: a(a + 5) = 6
=> we have a = 1 or -6
also b(b + 2) = 6
=> b = 1 or -6
given a ≠ b
1) when a =1, b= -6 and a + b = -5
1) when a = -6, b= 1 and a + b = -5
Answer choice B
Question: The ratio 5 : 4 expressed as a percent equals
A.12.5%
B.40%
C.80%
D.125%
Answer: D.125%
Explanation: Solution
5 : 4	= 5/ 4
= (5 / 4 x 100)%.
= 125 %.
Answer D
Question: Two trains start simultaneously from opposite ends of a 175-km route and travel toward each other on parallel tracks. Train X, traveling at a constant rate, completes the 175-km trip in 4 hours. Train Y, travelling at a constant rate, completes the 175-km trip in 3 hours. How many kilometers had Train X traveled when it met Train Y?
A.66
B.69
C.72
D.75
Answer: D.75
Explanation: If the two trains cover a total distance D, then Train X travels (3/7)*D while Train Y travels (4/7)*D. If the trains travel 175 km to the meeting point, then Train X travels (3/7)*175 = 75 km. The answer is D.
Question: If three distinct positive divisors of 128 are randomly selected, what is the probability that their sum will be less than 64?
A.1/3
B.3/7
C.5/14
D.9/28
Answer: C.5/14
Explanation: The positive divisors are 1, 2, 4, 8, 16, 32, 64, 128.
If any of the first six are chosen, the sum will be less than 64.
P(sum is less than 64) = 6/8 * 5/7 * 4/6 = 20/56 = 5/14
The answer is C.
Question: A train is running at a speed of 40 km/hr and it crosses a post in
18 seconds. What is the length of the train?
A.190 m
B.150 m
C.200 m
D.140 m
Answer: C.200 m
Explanation: speed = 40 km/hr = 40 * 5/18 = 100/9 m/s
time = 18 sec
distance covered = 100/9 * 18 = 200 m
so length of the train is = 200 m
ANSWER C
Question: Joseph’s grade was in the 80th percentile out of 100 grades in his class. In another class of 60 students there were 15 grades higher than Joseph’s. If nobody had Joseph’s grade, then Joseph’s was what percentile of the two classes combined?
A.80
B.78
C.75
D.60
Answer: B.78
Explanation: Being in 80% percentile out of 100 grades means Joseph was 81st (from the least grade) in the class (as long as nobody had Joseph’s grades), he outscored 80.
In another class his grade would rank him 46 (from the least grade out of 61, 60+Joseph), 45 had the grades lower than Amy.
So in combined classes he outscored 80+45=125. There are 160 students 125/160=0.78
Answer: B (78%)
Generally being in x% means that x% has the grades less than you.
Joseph in 80% --> he outscored 80% of of 100=80 (Joseph is 81st).
Of the 60 grades from another class, 15 were higher than Joseph 's, and the rest were lower --> rest is 45, hence Amy outscored 45.
So out of total 100+60=160, Joseph outscored 80+45=125. Hence he is in 125/160=78%.
Answer: B
Question: ramu sells gud for 27 per kg. but he has two plates for wighting one plate is 10% shorter then other.. he put 1 kg weight on shorter plat and apple on other plat.. at the end their is no profit no loss..what is cost price of apple
A.30
B.35
C.40
D.45
Answer: A.30
Explanation: ramu is making profit of 10% on weight because he puts 1 kg on shorter site.
to balance this profit if there is decrease of 1/10 in weight then there should be increse of 1/9 in price so 1/9 of 27=3
cost price=27+3=30
ans=30
ANSWER:A
Question: The number obtained by interchanging the two digits of a two-digit number is less than the original number by 45. If the sum of the two digits of the number so obtained is 13, then what is the original number?
A.49
B.94
C.83
D.38
Answer: B.94
Explanation: Let the number be in the form of 10a + b
Number formed by interchanging a and b = 10b + a.
a + b = 13 --- (1)
10b + a = 10a + b - 45
45 = 9a - 9b => a - b = 5 --- (2)
Adding (1) and (2), we get
2a = 18 => a = 9 and b = 4
The number is: 94.
ANSWER:B
Question: Cereal A is 11% sugar by weight, whereas healthier but less delicious Cereal B is 2% sugar by weight. To make a delicious and healthy mixture that is 3% sugar, what should be the ratio of Cereal A to Cereal B, by weight?
A.2:9
B.3:7
C.2:5
D.1:8
Answer: D.1:8
Explanation: 2% is 1%-points below 3% and 11% is 8%-points above 3%.
The ratio of A:B should be 1:8.
The answer is D.
Question: The compound interest earned by Sunil on a certain amount at the end of two years at the rate of 8% p.a. was Rs.2828.80. Find the total amount that Sunil got back at the end of two years in the form of principal plus interest earned?
A.Rs.19828.87
B.Rs.19828.80
C.Rs.19828.18
D.Rs.19828.97
Answer: B.Rs.19828.80
Explanation: Let the sum be Rs.P
P{ [ 1 + 8/100]2 - 1 } = 2828.80
P(8/100)(2 + 8/100)
= 2828.80 [a2 - b2 = (a - b) ( a + b)] P = 2828.80 / (0.08)(2.08)
= 1360/0.08
= 17000 Principal + Interest
= Rs.19828.80
Answer: B
Question: Out of 9 fruits in a basket, 2 are rotten. If two fruits are drawn at random from the basket, the probability of both being rotten is
A.1/36
B.10/36
C.20/36
D.11/36
Answer: A.1/36
Explanation: The number of exhaustive events = 9C2 = 36.
Let E be event of the 2 fruits being rotten. The number of favourable cases are
2C2 = 1 way.
Required probability = 1/36.
ANSWER:A
Question: Tom and Bob have a total of 49 toys. If Bob has 5 more toys than Tom, how many toys does each one have?
A.27
B.32
C.43
D.54
Answer: A.27
Explanation: If 5 toys are taken out of 49 toys and the remaining ones distributed to Tom and Bob, they will both have equal numbers of toys
49 - 5 = 44 for Tom and Bob
If distributed equally, each one will have
44 / 2 = 22 toys
Bob has 5 more toys than Tom, so Bob has
22 + 5 = 27 toys
correct answer A
Question: If an amount of Rs 26000 is divided equally among
76 students, approximately how much amount will
each student get?
A.Rs 206
B.Rs 400
C.Rs 420
D.Rs 218
Answer: B.Rs 400
Explanation: Amount received by each student = 26000/65 â‰ˆ Rs
400
Answer B
Question: Pipe A can fill a tank in 6 hours. Due to a leak at the bottom, it takes 9 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank?
A.87
B.16
C.18
D.19
Answer: C.18
Explanation: Let the leak can empty the full tank in x hours 1/6 - 1/x = 1/9
=> 1/x = 1/6 - 1/9 = (3 - 2)/18 = 1/18
=> x = 18.
Answer: C
Question: On a store counter are exactly two boxes containing only purple marbles and yellow marbles. Box A has 30 purple marbles and 20 yellow marbles; box B has 15 purple marbles and 35 yellow marbles. If Melanie randomly selects one of the boxes and then randomly selects one marble from the box, what is the probability that the marble selected will be purple?
A.3/20
B.3/10
C.9/20
D.3/5
Answer: C.9/20
Explanation: The question asks us to select a purple marble from either of the boxes. Here we need to select a box first(either A or B) and then select the marble from the box. So these events are AND events i.e. both need to be done to select a purple marble from the box. For an AND event we multiply the probability of the events. Hence the probability equation can be written as:
P(Selecting a purple marble) = P(selecting a box) * P(selecting purple marble from the selected box)
The probability of selecting either of the box is the same = 1/2
=1/2∗30/50+1/2∗15/50=9/20.
Answer:C
Question: By selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 5 p.c?
A.91887
B.38000
C.38002
D.38027
Answer: B.38000
Explanation: CP + CP/8 = 45000
CP = 40000
SP = 40000*(95/100)
=38000
Answer: B
Question: If the function f(x) is defined for all real numbers x as the maximum value of 2x + 4 and 16 + 6x, then for which one of the following values of x will f(x) actually equal 2x + 4 ?
A.–4
B.–5
C.–6
D.–7
Answer: A.–4
Explanation: Since f(x) defines maximum of 2x + 4 and 16 + 6x,
to find those x when 2x+4 has greater value,
2x + 4 > 16 + 6x
or x < -3
Only value that satisfy this is -4.
Answer is (A),
Question: Which greatest possible length can be used to measure exactly 15 meter 75 cm, 11 meter 25 cm and 7 meter 65 cm
A.45cm
B.255cm
C.244cm
D.55cm
Answer: A.45cm
Explanation: Explanation:
Convert first all terms into cm.
i.e. 1575 cm, 1125cm, 765cm.
Now whenever we need to calculate this type of question, we need to find the HCF. HCF of above terms is 255.
Option A
Question: A grocery store bought some mangoes at a rate of 5 for a dollar. They were separated into two stacks, one of which was sold at a rate of 3 for a dollar and the other at a rate of for a dollar. What was the ratio of the number of mangoes in the two stacks if the store broke even after having sold all of its mangoes?
A.1:4
B.16:9
C.2:3
D.1:2
Answer: B.16:9
Explanation: The cost price of a mango = 1/5 dollars.
The selling price of a mango from the first stack = 1/3 dollars --> the profit from one mango = 1/3 - 1/5 = 2/15 = 4/30 dollars.
The selling price of a mango from the second stack = 1/8 dollars --> the loss from one mango = 1/5 - 1/8 = 3/40
dollars.
The profit from one mango from the first stack is 4 times the loss from one mango from the second stack. the ratio is
4/30*40/3 =16/9
B
Question: A man traveled a total distance of 1200 km. He traveled one-third of the whole trip by plane and the distance traveled by train is two-thirds of the distance traveled by bus. If he traveled by train, plane and bus, how many kilometers did he travel by bus?
A.400
B.440
C.480
D.520
Answer: C.480
Explanation: total distance traveled = 1200 km.
distance traveled by plane = 400 km.
distance traveled by bus = x
distance traveled by train = 2x/3
x + 2x/3 + 400 = 1200
5x/3 = 800
x = 480 km
The answer is C.
Question: Rajeev wants to reach Mankar station exactly at 11 am. At 9.15 am, his train departs from Howrah Station. The speed of the train is 100 km per hour and distance between Howrah and Mankar is 150 kilometre. At what time will Rajeev actually reach Mankar?
A.10.45 am
B.11.00 am
C.11.15 am
D.11.30 am
Answer: A.10.45 am
Explanation: Speed of the train is 100 km per hour. To cover 150 km, train will take 60/100x150=90 minutes. So, the train will reach Mankar after 90 minutes from 9.15 am, that is 10.45 am.
Answer: A.
Question: Shaun invests a certain sum of money at 18.75% p.a. simple interest. After how many years will the sum of money become three times its principal?
A.10 years, 6 months, 20 days
B.10 years 8 months
C.10 years 9 months
D.12 years
Answer: B.10 years 8 months
Explanation: Solution:
B=A[1+ (tr/100)]; where A is principal amount, B final amount, t time in years and r interest rate
after putting the values 18.75= 75/4
3= [1+(75t/400)]
t= 32/3 which is (30+2)/3= 10 + 2/3 means 10 years and (12*2)/3 = 8 months.
total time 10 years 8 months
Ans: B
Question: A train running at the speed of 6 km/hr crosses a pole in 2 seconds. Find the length of the train?
A.150
B.872
C.3.33
D.3.21
Answer: C.3.33
Explanation: Speed = 6*(5/18) m/sec = 5/3 m/sec
Length of Train (Distance) = Speed * Time
5/3) * 2 = 3.33 meter
Answer:C
Question: If 0.6:1.4 :: 2:4:x, then x=?
A.56
B.5.6
C.0.56
D.0.056
Answer: B.5.6
Explanation: Explanation:
0.6 × x = 2.4 × 1.4
x = (2.4 × 1.4)/0.6 = 24/10 × 17/10 × 1/(6/10)
24/10 × 14/10 × 10/6
2/5 × 14 = 28/5 = 5.6
Answer: Option B
Question: On January 1, 2010, David invests 40% of his retirement savings in Antarctic largecap stocks, 20% in Antarctic midcaps, and 40% in Antarctic smallcaps. In 2010, largecaps rise 10%, midcaps rise 20%, and smallcaps rise 5% in the Antarctic stock market; however, in 2011, largecaps fall 5% and midcaps fall 10%, while smallcaps rise x% in Antarctica. If, on January 1, 2012, David has the same total amount of retirement savings as he did two years before, then x is between
A.0 and 5
B.5 and 10
C.10 and 15
D.15 and 20
Answer: C.10 and 15
Explanation: Pick a smart number for the total retirement savings David starts with—say, $10,000. (If you pick $100, you’ll wind up needing to track decimals, so give yourself more zeros to start with.)
Here are the starting values:
L = $4000
M = $2000
S = $4000
Apply the first year’s changes, so that you have these numbers on 1/1/2012:
Newer L = $4000+ 10% = $4400
Newer M = $2000 + 20% = $2400
Newer S = $4000 + 5% = $4200
Now apply the second year’s changes to L and M:
Newest L = $4400– 5% = $4400– $220 = $4180
Newest M = $2400– 10% = $2400– $240 = $2160
Add these to get $6340. So the newest S must be $10,000 (the target final total of David ’s retirement savings) minus $6340, $3660
The dollar change in S from 1/1/12 to 1/1/13 is $4200 – $540 = $3660. So the question is this: what percent change does $540 represent, from a starting point of $4200? Since $4200 is a nasty divisor, switch to benchmarks:
5% of $4200 = $210.
So 10% is just double that, or $420.
15% is $630.
And so on.
From this $540 lies between $420and $630
The correct answer is C.
Question: Mangala completes a piece of work in 10 days, Raju completes the same work in 40 days. If both of them work together, then the number of days required to complete the work is
A.4 days
B.6 days
C.8 days
D.10 days
Answer: C.8 days
Explanation: 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 = 10 × 40/50 = 8 days.
C)
Question: A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is:
A.12 kg
B.60 kg
C.72 kg
D.96 kg
Answer: B.60 kg
Explanation: Volume of water displaced	= (3 x 2 x 0.01) m3
= 0.06 m3.
Mass of man	= Volume of water displaced x Density of water
= (0.06 x 1000) kg
= 60 kg.Answer: Option B
Question: Mary and Joe are to throw three dice each. The score is the sum of points on all three dice. If Mary scores 10 in her attempt what is the probability that Joe will outscore Mary in his?
A.24/64
B.32/64
C.36/64
D.40/64
Answer: B.32/64
Explanation: Expected value of one die is 1/6*(1+2+3+4+5+6)=3.5.
Expected value of three dice is 3*3.5=10.5.
Mary scored 10 so the probability to get the sum more then 10 (11, 12, 13, ..., 18), or more then the average, is the same as to get the sum less than average (10, 9, 8, ..., 3) = 1/2 = 32/64.
That's because the probability distribution is symmetrical for this case:
The probability of getting the sum of 3 (min possible sum) = the probability of getting the sum of 18 (max possible sum);
The probability of getting the sum of 4 = the probability of getting the sum of 17;
The probability of getting the sum of 5 = the probability of getting the sum of 16;
...
The probability of getting the sum of 10 = the probability of getting the sum of 11;
Thus the probability of getting the sum from 3 to 10 = the probability of getting the sum from 11 to 18 = 1/2.
Answer: B.
Question: January 1, 2007 was Monday. What day of the week lies on Jan. 3, 2008?
A.Monday
B.Thursday
C.Wednesday
D.Friday
Answer: B.Thursday
Explanation: The year 2007 is an ordinary year. So, it has 1 odd day.
day of the year 2007 was Monday
day of the year 2008 will be 3 days beyond Monday
Hence, It will be Thursday. answer : B
Question: The ratio between the present ages of A and B is 3.5:3 respectively. The ratio between A's age 4 years ago and B's age 4 years hence is 1:1. What is the ratio between A's age 4 years hence and B's age 4 years ago?
A.14:4
B.13:0
C.15:11
D.13:12
Answer: C.15:11
Explanation: Let the present ages of A and B be 3.5x and 3x years respectively.
Then, (3.5x - 4)/(3x + 4) = 1/1
0.5x = 8 => x = 16
Required ratio = (5x + 4):(3x - 4) = 60:44 = 15:11.Answer: C
Question: A glass was filled with 10 ounces of water, and 0.02 ounce of the water evaporated each day during a 20-day period. What percent of the original amount of water evaporated during this period?
A.0.004%
B.0.02%
C.0.2%
D.4%
Answer: D.4%
Explanation: We are given that 0.02 ounces of water evaporated EACH DAY. Furthermore, we know that this process happened over a 20-DAY PERIOD. To calculate the total amount of water that evaporated during this time frame we need to multiply 0.02 by 20. This gives us:
0.02 x 20 = 0.4 ounces
Finally, we are asked for “What percent” of the original amount of water evaporated during this period. To determine this percentage, we have to make sure we translate the expression correctly. We can translate it to:
(Amount Evaporated/Original Amount) x 100%
(0.4/10) x 100%
(4/100) x 100% = 4%
Answer D
Question: A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?
A.1
B.4
C.7
D.9
Answer: A.1
Explanation: DS = 6
US = 4
S = ?
S = (6 - 4)/2 = 1 kmph
Answer: A
Question: If the terms of a series are either2or24and the sum of all the terms B of the series is 124, then which of the following could be the number of2sin the series?
A.26
B.29
C.35
D.40
Answer: A.26
Explanation: Ans: A
Solution: we are not certain how many 2 or 24 are there. but as given sum of all the terms B is 124 means 24*5= 120 so number of 24 can't be more than 5
so 24x +2y = 124
24*5 + 2y =124 then y=2
24*4 + 2y = 124 then y=14
24*3 +2y = 124 then y= 26
24*2 +2y =124 then y = 38
24 +2y = 124 then y= 50
26 is the ans.A
Question: Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 10 cm.
A.287 cm2
B.190 cm2
C.180 cm2
D.785 cm2
Answer: B.190 cm2
Explanation: Explanation:
Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them) = 1/2 (20 + 18) * (10) = 190 cm2
Answer: Option B
Question: Sandy is younger than Molly by 16 years. If the ratio of their ages is 7:9, how old is Sandy?
A.42
B.49
C.56
D.63
Answer: C.56
Explanation: Let Sandy's age be 7x and let Molly's age be 9x.
9x - 7x = 16
x = 8
Sandy is 56 years old.
The answer is C.
Question: If a and b are integers and (2^a)(3^b) is a factor of 600^40, what is the largest possible value of ab?
A.a
B.5a
C.20a
D.40a
Answer: A.a
Explanation: (2^a)(3^b) is a factor of 600^40
We need to find the largest possible value of ab.
We know that 600 = 2^3*5^2*3^1
Therefore 600^40 will have one powers of 3 in it.
Hence in (2^a)(3^b), b has to 1
Therefore value of ab = a
Correct Option: A
Question: Jim is able to sell a hand-carved statue for $620 which was a 25% profit over his cost. How much did the statue originally cost him?
A.$496.00
B.$512.40
C.$555.40
D.$574.90
Answer: A.$496.00
Explanation: 620 = 1.25*X
X = 620/1.25 = 496.00
which rounds to $496.00, which is (A).
Question: A train has a length of 150 meters . it is passing a man who is moving at 4 km/hr in the same direction of the train, in 3 seconds. Find out the speed of the train.
A.182 km/hr
B.184 km/hr
C.152 km/hr
D.169 km/hr
Answer: B.184 km/hr
Explanation: Explanation:
Length of the train, l = 150m
Speed of the man , Vm= 4 km/hr
Relative speed, Vr = total distance/time = (150/3) m/s = (150/3) × (18/5) = 180 km/hr
Relative Speed = Speed of train, Vt - Speed of man (As both are moving in the same direction)
=> 180 = Vt - 4
=> Vt = 180 + 4 = 184 km/hr
Answer: Option B
Question: What is the next number in the sequence : 15,21,24,30,33,39,51,57__?
A.69
B.71
C.67
D.65
Answer: A.69
Explanation: next no. = previous + (sum of digits)
15 + (1+5) = 21
21 + (2+1) = 24
24 + (2+4) = 30
30 + (3+0) = 33
33 + (3+3) = 39
39 + (3+9) = 51
51 +(5+1) = 57
57 + (5+7) = 69
ANSWER:A
Question: The true discount on a bill of Rs.270 is Rs.45.The banker's discount is
A.54
B.55
C.56
D.57
Answer: A.54
Explanation: Solution
P.W	= Rs.(270 - 45)
= Rs. 225
S.I on Rs. 270	=Rs.(45/225 x 270)
= Rs. 54.
Answer A
Question: what is the value of (4)^-5 ?
A.1/602
B.1/120
C.1/650
D.1/1024
Answer: D.1/1024
Explanation: 4^-5= 1/(4)^5= 1/1024
ANSWER:D
Question: One hundred gallons of fuel are purchased at $0.70 per gallon. The fuel is consumed at a rate of $0.50 worth of fuel per hour. At this rate, how many hours are required to consume the 100 gallons of fuel?
A.100
B.120
C.140
D.160
Answer: C.140
Explanation: The fuel is consumed at this rate: $0.50/$0.70 = 5/7 gallons per hour.
The time it takes to consume 100 gallons is: 100 / (5/7) = 140 hours.
The answer is C.
Question: If a certain toy store's revenue in November was 3/5 of its revenue in December and its revenue in January was 1/3 of its revenue in November, then the store's revenue in December was how many times the average (arithmetic mean) of its revenues in November and January?
A.5/2
B.7/2
C.10/3
D.15/4
Answer: A.5/2
Explanation: N = 3D/5
J = N/3 = D/5
The average of November and January is (N+J)/2 = 4D/5 / 2 = 2D/5
D is 5/2 times the average of November and January.
The answer is A.
Question: Gregory grossed $750 one week by working 60 hours. His manager pays him time-and-a-half for all hours worked in excess of 30 hours. What is Gregory's regular hourly wage?
A.11
B.12
C.10
D.20
Answer: C.10
Explanation: Denote by x the regular hourly wage.
Then 1.5x is the hourly overtime wage.
For 30 hours, Andrew received a salary of 30x.
For 60-30=30 hours, he received 30(1.5x)=45x
Total salary: 30x+45x=75x which equals $750.
75x=750 implies x=10 (he receives $10 per hour)
Answer C 10.
Question: If (18^a) * 9^(3a – 1)= (2^6)(3^b) and a and b are positive integers, what is the value of a?
A.22
B.11
C.9
D.6
Answer: D.6
Explanation: (18^a) * 9^(3a – 1)= (2^6)(3^b)
= 2^a . 9^a . 9^(3a – 1) = (2^6)(3^b)
Just compare powers of 2 from both sides
Answer = 6 = D
Question: In how many ways can 3 boys and 3 girls be seated on 8 chairs so that no two girls are together?
A.5760
B.14400
C.480
D.56
Answer: C.480
Explanation: Let us take opposite of the constraint.
2 girls sitting together:	:
1 case is GGBGBBBB.
Total number of ways=3!*5!*5 with just shifting the rightmost girl.
Then the 2 leftmost girls can shift one position , and using the above reasoning, the total number of ways = 3!*5!*4 and so on till the rightmost girl has 1 position.
So total number of ways = 3!*5!(5+4+3+2+1)=120*90=10800
Similarly another case is:
GBGGBBBB.
Using the above reasoning, the total number of cases is: 3!*5!*(15) =10800
Let us take 3 girls sitting together
GGGBBBBB
There are 3! *5! Ways. The 3 leftmost girls can shift 6 positions. So there are a total of 3!*5!*6=4320 ways
So total is 2*10800 + 4320=25920
The total number of possibilities = 8! Ways =40,320
Answer is 40320-25920=480
Hence C.
Question: Three candidates contested an election and received 3644 votes, 7606 votes, and 13750 votes respectively. What percentage of the total votes did the winning candidate receive?
A.55%
B.56%
C.57%
D.58%
Answer: A.55%
Explanation: The total number of votes polled = (3644 + 7606 + 13750) = 25000
The winner's percentage = 13750/25000 * 100 = 55%
The answer is A.