RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: The average of 35 numbers is 25. If each number is multiplied by 5, find the new average?
A.125
B.772
C.821
D.912
Answer: A.125
Explanation: Sum of the 35 numbers = 35 * 25 = 875
If each number is multiplied by 5, the sum also gets multiplied by 5 and the average also gets multiplied by 5.
Thus, the new average = 25 * 5 = 125.
Answer:A
Question: If GCD of two numbers (both integers, greater than 1) is 1, then which of the following must be true?
1. They are prime.
2. They are consecutive.
3. They do not have a common prime factor
4. They do not have a common factor other than 1
A.Only 1
B.Only 2
C.Only 3 and 4
D.Only 1 and 4
Answer: C.Only 3 and 4
Explanation: 15,16 are not prime numbers, but GCD for them is 1. so statement one is incorrect.
2,7 have 1 as GCD, but they are not consecutive numbers.
Statement 3 and 4 are correct. Since GCD is 1, we can't have a common prime factor or a common factor other than 1 for the two numbers
ANSWER:C
Question: The ratio of men to women in the Snyder community choir is 4 to 5. The ratio of men to women in the Leigh community choir is 5 to 6. If the two choirs merged, the ratio of men to women in the combined choir would be 22 to 27. If Snyder has 4 more men and 6 more women than Leigh, how many women are in the Snyder choir?
A.20
B.24
C.30
D.32
Answer: C.30
Explanation: Use simultaneous equations / By combination
4x = 5y + 4
5x = 6y + 6
Multiply (1) by 6
Multiply (2) by -5
Get rid of y, and x = 6
Then 5x = 30
ANSWER:C
Question: Bill made a profit of 10% by selling a product. If he had purchased that product for 10% less and sold it at a profit of 30%, he would have received $ 49 more. What was his original selling price?
A.$770
B.$660
C.$700
D.$1100
Answer: A.$770
Explanation: Let the original purchase price be X
So original selling price at 10% profit = 1.1X
If product is purchased at 10% less of original = 0.9X
Profit of 30% on this price = 1.3(0.9X)
He would have received $49 more in second scenario => 1.3(0.9X) - 1.1X = 49
=> 0.07X = 49
=> X = $700
Original purchase price = $700
Hence, original selling price (at 10% of profit) = 1.1(700) = $770
Option A
Question: The speed of a boat in still water is 60kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
A.75
B.40
C.77
D.26
Answer: B.40
Explanation: Speed downstream = 60 + 20 = 80 kmph
Speed upstream = 60 - 20 = 40 kmph.Answer: B
Question: If both 5^2 and 3^3 are factors of the number a*4^3*6^2*13^11, then what is the smallest possible value of a?
A.49
B.75
C.150
D.225
Answer: B.75
Explanation: The number a must include at least 3*5^2 = 75
The answer is B.
Question: Three cubes of metal whose edges are 9, 12 and 15 cm respectively, are melted and one new cube is made. Find the edge of the new cube?
A.28
B.77
C.66
D.18
Answer: D.18
Explanation: 93 + 123 + 153 = a3 => a
= 18
Answer: D
Question: 20 beavers, working together in a constant pace, can build a dam in 3 hours. How many hours Z will it take 12 beavers that work at the same pace, to build the same dam?
A.2.
B.Z=4.
C.Z=5.
D.6.
Answer: C.Z=5.
Explanation: C. 5 hrs
If there were 10 beavers it qould have taken double Z= 6hrs.. so closest to that option is 5.
Question: If six persons sit in a row, then the probability that three particular persons are always together is?
A.1/8
B.1/2
C.1/5
D.1/1
Answer: C.1/5
Explanation: Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability
= 3!4!/6!
= 1/5
Answer:C
Question: Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent?
A.16%
B.88%
C.18%
D.14%
Answer: C.18%
Explanation: Total CP = Rs. 42000 + Rs. 13000
= Rs. 55000 and SP
= Rs. 64900
Profit(%) = (64900 - 55000)/55000 * 100
= 18%
Answer:C
Question: A and B go around a circular track of length 600 m on a cycle at speeds of 30 kmph and 54 kmph. After how much time will they meet for the first time at the starting point?
A.120 sec
B.360 sec
C.178 sec
D.187 sec
Answer: B.360 sec
Explanation: Time taken to meet for the first time at the starting point
= LCM { length of the track / speed of A , length of the track / speed of B}
= LCM { 600/ (30 * 5/18) , 600/ (54 * 5 /18) }
= 360 sec.
Answer: 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 seconds. The speed of the train is?
A.12
B.50
C.27
D.28
Answer: B.50
Explanation: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr
= 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: how many internal diagonals does a heptagon (seven sided polygon) have?
A.7
B.9
C.14
D.20
Answer: C.14
Explanation: Number of diagonals in any polygon can be found using this formula: n(n-3)/2
Here n = 7
No. of diagonals = 7(7 - 3)/2
= 14
Ans C
Question: From among the 36 students in a class, one leader and one class representative are to be appointed. In how many ways can this be done?
A.1360
B.1260
C.1060
D.1160
Answer: B.1260
Explanation: There are 36 students and every one has equal chance of being selected as a leader. Hence, the leader can be appointed in 36 ways. When one person is appointed as leader, we are left with 35 students. Out of these 35 teachers, we can select one class representative. So, a class representative can be selected in 35 ways. Hence, the number of ways in which a leader and class representative can be selected = 36 x 35 = 1260
ANSWER:B
Question: The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?
A.5:7
B.3:9
C.21:22
D.1:2
Answer: C.21:22
Explanation: Explanation:
Originally, let the number of boys and girls in the college be 7x and 8x respectively.
Their increased number is (120% of 7x) and (110% of 8x).
(120/100*7x) and(110/100*8x)
42x/5 and 44x/5
The required ratio =(42x/5:44x/5)=21:22
Answer:C
Question: In what time will a train 95 m long cross an electric pole, it its speed be 214 km/hr?
A.1.6 sec
B.2.9 sec
C.2.7 sec
D.8.7 sec
Answer: A.1.6 sec
Explanation: Speed = 214 * 5/18 = 59 m/sec
Time taken = 95/59 = 1.6 sec.
Answer: A
Question: Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?
A.2:3:4
B.6:7:8
C.6:7:9
D.8:9:7
Answer: A.2:3:4
Explanation: Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively.
Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x).
140	x 5x , 150	x 7x and 175	x 8x
100	100	100
7x,	21x	and 14x.
2
The required ratio = 7x :	21x	: 14x
2
14x : 21x : 28x
2 : 3 : 4.
so the answer is option A)
Question: I have a few sweets to be distributed. If I keep 2, 3 or 4 in a pack, I am left with one sweet. If I keep 5 in a pack, I am left with none. What is the minimum number of sweets I have to pack and distribute ?
A.5
B.7
C.23
D.4
Answer: A.5
Explanation: Clearly, the required number would be such that it leaves a remainder of 1 when divided by 2, 3 or 4 and no remainder when divided by 5.
Answer: A
Question: Find the average of all the numbers between 40 and 80 which are divisible by 3.
A.15
B.70
C.20
D.60
Answer: D.60
Explanation: Sol.
Average = (42+ 45+ 48+ 51+ 54+ 57+ 60+ 63+ 66+ 69+ 72+ 75+ 78 / 13) = 780 / 5 = 60.
Answer D
Question: When a stone is dropped from a building 200 m high, its speed is proportional to the time elapsed after dropping. The distance traveled is proportional to the square of the time elapsed. After 1 second the speed of the train was 10 m/sec and it was 190 m above the ground. When its speed is 25 m/sec, what would be its distance from the ground?
A.140 m
B.137.5 m
C.125.75 m
D.142.5 m
Answer: B.137.5 m
Explanation: v= x*t and s= y*t^2
10 = x*1, hence x=10 units
(200-190) = y*1*1
y=10
when speed = 25m/sec, time elapsed = 25/10 = 2.5 sec
distance travelled by stone = 10*(2.5)^2 = 62.5 mts
so distance of stone above ground = 200-62.5 = 137.5 mtrs
ANSWER:B
Question: Find the largest number which divides 62, 132 and 237 to leave the same remainder in each case.
A.45
B.25
C.15
D.35
Answer: D.35
Explanation: Required number = H.C.F. of (132 - 62), (237 - 132) and (237 - 62)
= H.C.F. of 70, 105 and 175 = 35.
Answer is D.
Question: In the quadratic equation ax2 - 11x + 40 = 0, if the sum of two roots is 1.1, what is the product of the two roots?
A.4
B.4.2
C.8
D.9
Answer: A.4
Explanation: Explanation:
The sum of the roots of the quadratic equation ax2 - bx + c = 0 are (-b/a) and the product of the roots are (c/a).
Thus, in the equation ax2 - 11x + 40 = 0, where a = a, b = - 11 and c = 40.
we get, sum of the roots = - (- 11) / a = 1.1
a = 11 / 1.1 = 10
Product of the roots = 40 / 10 = 4
ANSWER: A
Question: The current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is?
A.5 kmph
B.1 kmph
C.6 kmph
D.2 kmph
Answer: C.6 kmph
Explanation: The current of a stream = 1
The speed of the motor boat in still water= x
Speed downstream = x + 1
Speed upstream = x - 1
since distance = speed Ã— time, we have
35/(x + 1) + 35/(x - 1) = 12 kmph=6 kmph
Answer : Option C
Question: The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 5 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?
A.Rs.4599
B.Rs.4528
C.Rs.4527
D.Rs.4530
Answer: D.Rs.4530
Explanation: Area of the four walls = 2h(l + b)
Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.
Total cost = 906 * 5 = Rs.4530
Answer:D
Question: What will be the compound interest on a sum of Rs. 25,000 after 3 years at the rate of 12% p.a.?
A.Rs:10123.19
B.Rs:10123.29
C.Rs:10123.20
D.Rs:10123.28
Answer: C.Rs:10123.20
Explanation: Amount
= [25000 * (1 + 12/100)3]
= 25000 * 28/25 * 28/25 * 28/25
= Rs. 35123.20
C.I. = (35123.20 - 25000)
= Rs:10123.20
Answer: C
Question: Jaime earned enough money by selling seashells at 30 cents each to buy several used paperback books at 55 cents each. If he spent all of the money he earned selling seashells to buy the books, what is the least number of seashells he could have sold ?
A.5
B.22
C.17
D.25
Answer: B.22
Explanation: Let's TEST Answer B: 22 seashells...
With 22 seashells, Jamie would have 22(30) = 660 cents. This would allow him to buy 12 books for 660 cents total, with no money left over. This is an exact MATCH for what we were told, so this MUST be the answer.
Final Answer:
[Reveal]Spoiler:
B
Question: 3889 + 12.952 - ? = 3854.002
A.47.095
B.47.752
C.47.932
D.47.95
Answer: D.47.95
Explanation: Let 3889 + 12.952 - x = 3854.002.
Then x = (3889 + 12.952) - 3854.002
= 3901.952 - 3854.002
= 47.95.
Answer = D
Question: Bill has a small deck of 10 playing cards made up of only 2 suits of 5 cards each. Each of the 5 cards within a suit has a different value from 1 to 5; thus, there are 2 cards in the deck that have the same value. Bill likes to play a game in which he shuffles the deck, turns over 5 cards, and looks for pairs of cards that have the same value. What is the chance that Bill finds at least one pair of cards that have the same value?
A.25/33
B.35/43
C.45/53
D.55/63
Answer: D.55/63
Explanation: P(no pairs) = 8/9*6/8*4/7*2/6 = 8/63
P(at least one pair) = 1 - 8/63 = 55/63
The answer is D.
Question: If x is 20 percent greater than 55, then x =
A.68
B.70.4
C.86
D.66
Answer: D.66
Explanation: X is 20% greater than 55 means X is 1.2 times 55 (in other words 55 + 20/100 * 55 = 1.2 * 55)
Therefore, X = 1.2 * 55 = 66
ANSWER:D
Question: A 290 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
A.230 m
B.210 m
C.260 m
D.320 m
Answer: B.210 m
Explanation: Relative speed = (120 + 80) km/hr
=	(200 x(5/18))m/sec
=	(500/9)m/sec.
Let the length of the other train be x metres.
Then,	(x + 290)/9 = 500/9
x + 290 = 500
x = 210.
B
Question: The odds in favour of an event are 3 : 5. The probability of occurrence of the event is ?
A.3/5
B.3/8
C.1/3
D.1/5
Answer: B.3/8
Explanation: Number of cases favourable of E = 3
Total Number of cases = (3 + 5 ) = 8
∴ P(E) = 3/8
Answer : B
Question: A person purchases 90 watches and sells 40 watches at a gain of 10% and 50 watches at a gain of 20%. If he sold all of them at a uniform profit of 15%, then he would have got $ 40 less. The cost price of each clock is:
A.70
B.90
C.80
D.60
Answer: C.80
Explanation: C
80
Let C.P. of clock be $ x.
Then, C.P. of 90 watches = $ 90x.
[(110% of 40x) + (120% of 50x)] - (115% of 90x) = 40
44x + 60x - 103.5x = 40
0.5x = 40 => x = 80
Question: 49 pumps can empty a reservoir in 13/2 days, Working 8 hours a day. If 196 pumps are used for 5 hours each day, then the same work will be completed in:
A.2 days
B.5/2 days
C.13/5 days
D.3 days
Answer: C.13/5 days
Explanation: Explanation :
Let the required number of days be x. Then,
More pumps, Less days (Indirect Proportion)
Less working hrs / day, More days (Indirect Proportion)
Pumps 196 : 49
Working Hrs / Day 5 : 8 :: 13/2 : x
96 x 5 x x = 49 x 8 x 13/2
x = 49 x 8 x 13/2 x 1 / (196 x 5)
x = 13/5
Answer C
Question: If it takes 6 identical printing presses exactly 4 hours Q to print 5,000 newspapers, how long would it take 3 of these presses to print 3,000 newspapers?
A.3 hours, 20 minutes
B.4 hours, 20 minutes
C.4 hours, 48 minutes
D.5 hours, 48 minutes
Answer: C.4 hours, 48 minutes
Explanation: 6 presses - 5,000 newspapers - 4 hours ;
3 presses - 2,500 newspapers - 4 hours ;
3 presses - 3,000 newspapers - 4 hours + 1/5*4 hours = 4 hours, 48 minutes (since 2,500+1/5*2,500=3,000) =Q.
Answer: C.
Question: Rohan spends 40% of his salary on food, 20% on house rent, 10% on entertainment and 10% on conveyance. If his savings at the end of a month are Rs. 2500. then his monthly salary is
A.Rs. 12500
B.Rs. 1000
C.Rs. 8000
D.Rs. 6000
Answer: A.Rs. 12500
Explanation: Sol.
Saving = [100 - (40 + 20 + 10 + 10]% = 20%.
Let the monthly salary be Rs. x.
Then, 20% of x = 2500
â‡” 20 / 100x = 2500
â‡” x = 2500 Ã— 5 = 12500.
Answer A
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.75 km and 1.10 km respectively. The time taken by the slower train to cross the faster train in seconds is?
A.48
B.9
C.7
D.66
Answer: D.66
Explanation: :
Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 1.75 + 1.10 = 2.75 km = 2750 m.
Required time = 2750 * 3/125
= 66 sec.
Answer: D
Question: A small water pump would take an hour to fill an empty tank. A larger pump would take 1/4 hour to fill the same tank. How many hours would it take both pumps, working at their respective constant rates, to fill the empty tank if they began pumping at the same time?
A.1/7
B.1/4
C.1/5
D.1/6
Answer: C.1/5
Explanation: Rate of the small pump is 1 tank/hour
Rate of the larger pump is 1/(1/4) or 4 tank/hour;
Combined rate of the two pumps is 1+4=5 tank/hour, together they will fill the empty tank in 1/5 hours (time=job/rate).
Answer: C
Question: A thief goes away with a SANTRO car at a speed of 20 kmph. The theft has been discovered after half an hour and the owner sets off in a bike at 50 kmph when will the owner over take the thief from the start?
A.5/3 hours
B.2/7 hours
C.2/3 hours
D.1/3 hours
Answer: C.2/3 hours
Explanation: -----------20--------------------|
50 20
D = 20
RS = 50 – 20 = 30
T = 20/30 = 2/3 hours
ANSWER:C
Question: In what ratio must water be mixed with milk to gain 16 2/3% on selling the mixture at cost price ?
A.1:9
B.1:1
C.1:2
D.1:6
Answer: D.1:6
Explanation: Required ratio is cheaper quantity : dearer quantity = (d-m) : (m-c) Answer with Explanation: Step i) Let C.P of 1 litre of mild be Rs.1 And S.P of1 litre of mild be Rs.1 Gain = 50/3 per cent
 C.P of 1 litre of mixture =
     
     

1
3 50
100
100
x
= Re. 100 x 3/350 x 1 = 6/7 (Mean price) Step (ii) By the rule of allegation I. C.P of 1 liter of water = 0 II. C.P of 1 liter of milk = 1 III. Mean price (p) = 6/7 IV. d – m = 1 – 6/7 = 1/7 V. m – c = 6/7 - 0 = 6/7  ratio of water and milk = 1/7 : 6/7 = 1 : 6
Answer:D
Question: Find the compound ratio of (2:3), (6:11) and (11:4) is
A.3:2
B.2:1
C.1:1
D.4:5
Answer: C.1:1
Explanation: Required ratio = 2/3 * 6/11 * 11/4 = 2/1 = 1:1
Answer is C
Question: Sonika deposited Rs.8000 which amounted to Rs.10200 after 3 years at simple interest. Had the interest been 2% more. She would get how much?
A.9680
B.10680
C.2999
D.2774
Answer: B.10680
Explanation: (8000*3*2)/100 = 480
10200
--------
10680
Answer:B
Question: Ajay bought 15 kg of dal at the rate of Rs 14.50 per kg and 10 kg at the rate of Rs 13 per kg. He mixed the two and sold the mixture at the rate of Rs 15 per kg. What was his total gain in this transaction ?
A.Rs 1.10
B.Rs 11
C.Rs 16.50
D.Rs 27.50
Answer: D.Rs 27.50
Explanation: Explanation:
Cost price of 25 kg = Rs. (15 x 14.50 + 10 x 13) = Rs. 347.50.
Sell price of 25 kg = Rs. (25 x 15) = Rs. 375.
profit = Rs. (375 — 347.50) = Rs. 27.50.
Answer: D
Question: The calendar for the year 2007 will be the same for the year:
A.2014
B.2016
C.2017
D.2018
Answer: D.2018
Explanation: Count the number of odd days from the year 2007 onwards to get the sum equal to 0 odd day.
Year : 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
Odd day : 1 2 1 1 1 2 1 1 1 2 1
Sum = 14 odd days 0 odd days.
Calendar for the year 2018 will be the same as for the year 2007.
Answer: Option D
Question: Which of the following best approximates the value of q if 5^25+5^15=5^q ?
A.40
B.26
C.25
D.24
Answer: C.25
Explanation: We have: 5^25+5^15=5^q
==> because 5^15 > 0 --> 5^q MUST be equal or greater than 5^25 ==>q MUST be equal or greater than 25
==> Option D and E are out immediately.
Divide both sides by 5^q and q >= 25
We have:
5^(25-q) + 5^15/5^q = 1
Because q >= 25 ==>5^15/5^q = 0.0000xyz, that is very small,we can ignore it.
Thus, 5^(25-q) must be approximately 1
==> 25-q = 0 ==> q is approximately 25
C is the answer.
Question: Matt is touring a nation in which coins are issued in two amounts, 2¢ and 5¢, which are made of iron and copper, respectively. If Matt has twu iron coins and twu copper coins, how many different sums from 1¢ to 14¢ can he make with a combination of his coins?
A.8
B.11
C.9
D.4
Answer: A.8
Explanation: The total sum is 2*2 + 2*5 = 14¢. If you can make each sum from 1 to 14 (1¢, 2¢, 3¢, ..., 14¢), then the answer would be 14 (maximum possible).
Now, with 2¢ and 5¢ we cannot make 1¢ and 3¢. We also cannot make 13¢ and 11¢ (since total sum is 14¢ we cannot remove 1¢ or 3¢ to get 13¢ or 11¢).
Also discarded 6 and 8, for lack of even numbers after 4
So, out of 14 sums 6 are for sure not possible, so the answer must be 14 - 6 = 8 sums or less. Only A fits.
Answer: A.
Question: A factory has three types of machines, each of which works at its own constant rate. If 7 Machine As and 11 Machine Bs can produce 261 widgets per hour, and if 8 Machine As and 22 Machine Cs can produce 600 widgets per hour, how many widgets could one machine A, one Machine B, and one Machine C produce in one 8-hour day?
A.408
B.475
C.550
D.625
Answer: A.408
Explanation: Let Machine A produce A widgets per hour. B produce B widgets per hour and C produce C widgets per hour.
7A+11B=261 ---(1)
8A+22C=600 ---(2)
Dividing (2) by 2
4A+11C=300.....(3)
Adding (1)(3)
11A+11B+11C = 561
A+B+C=51 per hour
So for eight hrs = 51*8 = 408 = Answer = A
Question: What is the least number should be added to 1156, so the sum of the number is completely divisible by 25?
A.19
B.2
C.5
D.6
Answer: A.19
Explanation: (1156 / 25) gives remainder 6
6 + 19 = 25, So we need to add 19
Answer : A
Question: Find value of X: (323^23 + 73^44 + 413^30) - (317 × 91) = ?
A.34455
B.35546
C.52150
D.68542
Answer: C.52150
Explanation: It's speed and accuracy which decides the winner. You can use various methods including Vedic mathematics to do calculations quickly.
(32323+7344+41330)−(317×91)=80997−28847=52150
C
Question: In one can of mixed nuts, 30% is peanuts. In another can of mixed nuts that is one-half the size of the first one, 40% is peanuts. If both cans are emptied into the same bowl, what percentage of the mixed nuts in the bowl is peanuts?
A.16 2/3%
B.20%
C.25%
D.33 1/3%
Answer: D.33 1/3%
Explanation: Let number of mixed nuts in first can = 100
Number of peanuts in first can = (30/100)*100 = 30
Since second can is one- half of first , number of mixed nuts in second can = 50
Number of peanuts in second can = (40/100)*50 = 20
Total number of peanuts in both cans = 30+20 = 50
Total number of mixed nuts in both cans = 100+50 = 150
% of peanuts if both cans are mixed = (50/150) *100% = 33.33 %
Answer D
Question: Jim and Joe split the bill based on the amount of space they take up in their apartment. Jim pays for two-fifths of it and Joe pays the rest. If Jim pays 30 dollars, how much will Joe have to pay?
A.45
B.50
C.55
D.40
Answer: A.45
Explanation: 30 x (5/2) = 150/2 = 75
150 - 30 = 45
Answer is A
Question: What is the units digit of 3333^(333)*3333^(222)?
A.0
B.2
C.4
D.6
Answer: D.6
Explanation: Each of the other explanations to this question has properly explained that you need to break down the calculation into pieces and figure out the repeatingpatternof the units digits.
Here's another way to organize the information.
We're given [(2222)^333][(3333)^222]
We can 'combine' some of the pieces and rewrite this product as....
([(2222)(3333)]^222) [(2222)^111]
(2222)(3333) = a big number that ends in a 6
Taking a number that ends in a 6 and raising it to a power creates a nice pattern:
6^1 = 6
6^2 = 36
6^3 = 216
Etc.
Thus, we know that ([(2222)(3333)]^222) will be a gigantic number that ends in a 6.
2^111 requires us to figure out thecycleof the units digit...
2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32
2^6 = 64
2^7 = 128
2^8 = 256
So, every 4powers, the pattern of the units digits repeats (2, 4, 8, 6.....2, 4, 8, 6....).
111 = 27 sets of 4 with a remainder of 3....
This means that 2^111 = a big number that ends in an 8
So we have to multiply a big number that ends in a 6 and a big number that ends in an 8.
(6)(8) = 48, so the final product will be a gigantic number that ends in an 6.
Final Answer:
D
Question: If H = {1, 7, 18, 20, 29, 33}, how much less is the mean of the numbers in H than the median of the numbers in H?
A. 1.0
B. 1.5
C. 2.0
D. 2.5
Answer: A. 1.0
Explanation: This is a good question to understand the difference between mean and median.
Mean: Average of all the numbers. (Sum of all the elements divided by the number of elements)
Median: Arrange the elements of the set in increasing order. If the number of terms is odd, the middle term is the median. If the number of terms is even, the average of middle two terms is the median
Coming to this question,
Mean = (1 + 7 + 18 + 20 + 29 + 33)/6 = 18
Median = (18 + 20)/2 = 19
Difference = 1
Option A
Question: A dog is tied to a tree by a long nylon cord. If the dog runs from the due North side of the tree to the due South side of the tree with the cord extended to its full length at all items, and the dog ran approximately 30 feet, what was the approximate length of the nylon cord L in feet?
A.30
B.25
C.15
D.10
Answer: D.10
Explanation: Because the cord was extended to its full length at all items, the dog ran along a semi-circular path, from north to south.
The circumference of a full circle is 2*pi*r, but since we only care about the length of half the circle, the semi-circle path is pi*r.
L=pi*r = 30. Round pi = 3, then r = 10.
Chord is about 10 feet long.D