MU-NLPC/Calc-aqua_rat huggingface dataset:
George takes 30 days to do a piece of work and Mark takes 45 days for the same work. For the first 15 days only George works. Then Mark also joins him. Find the time taken to complete the entire work.
Choose the correct choice from the following answers:  A) 23  B) 24  C) 25  D) 26  E) 27

Solution: George 1 day work= 1/30   Mark 1 day work= 1/45   George 15 day work= 15*1/30 =1/2   Work remaining= 1-1/2 =1/2   George + Mark 1 day work= 1/30 + 1/45 =1/18   Number of day required to complete 1/2 work= (1/2)/(1/18)= 
(1/2)/(1/18) = 9
9 days   So total days required to complete the work is  15+9= 
 15+9 = 24
24 days.   ANSWER:24
Answer: B
There are 54 people in a certain community who belong to the local golf club, tennis club or both clubs. If twice as many people belong to the tennis club as belong to the golf club, what could be the number of people who belong to both clubs? Choose one:
A) 1) 4  B) 2) 7  C) 3) 17  D) 4) 21  E) 5) 27

Solution: x -> Golf Club   2x -> Tennis Club   y -> both   x+2x-y = 51   3x - y =51   multiples of 3 greater than 51   57   60   63   66   69   72 - 21= 
72 - 21 = 51
51   IMO (4) 21)
Answer: D
The average age of 3 girls is 16 years and their ages are in the proportion 1:2:3. The age of the youngest girl is?
Pick one.
A) 12 years	B) 7 years	C) 9 years	D) 10 years	E) 8 years

Solution: Total age of 3 boys = 16*3= 
16*3 = 48
48   ratio of their ages= 1:2:3   Age of the youngest =48*1/6= 
48*1/6 = 8
8 years   Answer is 8 years
Answer: E
The H.C.F of two numbers is 23 and the other two factors of their L.C.M are 12 and 13. The larger of the two numbers is:	Choices.
A) 299 B) 278 C) 322 D) 231 E) 121

Solution: Clearly, the numbers are (23 * 12) and (23 * 13). Larger number   = (23 * 13)= 
(23 * 13) = 299
299.   299nswer: 299
Answer: A
One drier dries certain quantity of material in 24 minutes. Another drier does the same work in 2 minutes how much time will it take to do the same job when both driers are put to work ? Select the correct option:  A) 1.00 minutes  B) 1.20 minutes  C) 1.50 minutes  D) 1.85 min  E) 2.00 minutes

Solution: By guess it is clear that the time taken will be less than 2 minutes and more than 1.5 mintes Therefore, answer 1.85 minutes will be correct. Answer-1.85 min
Answer: D
A, B two inlet pipes takes 15,18 minutes to fill the tank and C an oulet pipe takes 45 minutes to empty the tank respectively. In what time the tank be filled if all of them are operated together?  Choose the correct option:
A) 11 minutes B) 10 minutes C) 12 minutes D) 13 minutes E) 14 minutes

Solution: LCM=90   No of days= [90/(90/15 + 90/18 - 90/45)   = [90/(6+5-2)]   = [90/9= 
90/9 = 10
10 minutes   ANSWER:10 minutes
Answer: B
A train 250 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: Choose the correct choice from the following: A) 95 km/hr B) 50 km/hr C) 54 km/hr D) 55 km/hr E) 56 km/hr

Solution: Speed of the train relative to man = (250/10) m/sec = 25 m/sec. [(25 * (18/5)] km/hr = 90km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 90 ==> x = 95 km/hr.   95 km/hrNSWER: 95 km/hr
Answer: A
If y is 50 percent greater than x, then x is what percent less than y?	Answers: A) 20% B) 25% C) 33% D) 50% E) 67%

Solution: y = 1.5x   x = y/1.5 = 10y/15 = y - (1/3)*y   1/3 is about 33%.   The answer is 33%.
Answer: C
The C.P of 15 books is equal to the S.P of 20 books. Find his gain% or loss%?  Answers:
A) 28% B) 25% C) 24% D) 23% E) 27%

Solution: explanation:   15 CP = 20 SP   20 --- 5 CP loss   100 --- ? => 25% loss   Answer: 25%
Answer: B
q, b, c, and d are positive integers. If the remainder is 9 when q is divided by b, and the remainder is 5 when c is divided by d, which of the following is NOT a possible value for b + d?	Choices:	A) 20	B) 19	C) 18	D) 16	E) 15

Solution: When q is divided by b remainder is 9 that means b is greater than or equals to 10, similarly d is greater than or equals to 6.   b + d cannot be 15, hence 15 is the answer.
Answer: E
If Juan takes 15 seconds to run y yards, how many seconds will it take him to run x yards at the same rate? Pick:  A) 15x/y  B) 15y/x  C) x/(15y)  D) 15/(xy)  E) xy/15

Solution: This problem is testing us on the Rate x Time = Distance relationship. This relationship also tells us that Rate = Distance/Time and Time = Distance/Rate.   Ultimately, we are looking for how many seconds it will take Juan to run x yards. Thus, the equation we’ll use is: Time = Distance/Rate. We know the distance is x yards, and we need to find Juan’s rate.   We can find Juan’s rate as follows: Rate = Distance/Time = y yards/15 seconds   Using that rate, we need to determine how long it takes him to run x yards at the same rate. So we have:   Time = Distance/Rate   Time = x yards/(y yards/15 seconds)   Time = (x yards) x (15 seconds/y yards)   Time = 15x/y seconds   15x/ynswer 15x/y.
Answer: A
Solve This
6 + 7 = 12
8 + 9 = 16
5 + 6 = 10
7 + 8 = 14
Then, 3 + 3 = ?? Choose the most appropriate option.
A) 11 B) 12 C) 5 D) 14 E) 18

Solution: 5   ANSWER:5
Answer: C
Walking 6/7 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school?	Pick one:  A) 28 m  B) 20 m  C) 22 m  D) 23 m  E) 24 m

Solution: Speed Ratio = 1:6/7 = 7:6   Time Ratio = 6:4   1 -------- 6   4 --------- ?   => 24 m   ANSW24 mR:24 m
Answer: E
If .003^4 is represented in its shortest possible decimal form, how many 0’s to the right of the decimal point does it contain?
Choose the most appropriate option:
A) 0
B) 8
C) 9
D) 10
E) 11

Solution: 0.003^4= (3*10^-3)^4 = 81*10^-12 = 0.81*10^-10 which would have 10 zeros to the right of the decimal point. The answer is 10.
Answer: D
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 $56 more. What was his original selling price? Select.
A) $880
B) $950
C) $1100
D) $1240
E) $1360

Solution: Let P be the original purchase price of the product.   Bill originally sold the product for 1.1*P.   In the second scenario, the purchase price is 0.9*P.   A 30% profit means the selling price would be 1.3*0.9*P = 1.17*P   Thus, according to the information in the question, 1.17P - 1.1P = 56   0.07 = 56   P = 800   The original selling price was  800*1.1= 
 800*1.1 = 880
880.   The correct answer is $880.
Answer: A
The side of a square is increased by 25% then how much % does its area increases? Choose the correct choice.
A) 56.28 %  B) 56.25 %  C) 56.28 %  D) 46.25 %  E) 56.21 %

Solution: a = 100 a2 = 10000   a = 125 a2 = 15625   ----------------   10000 --------- 5625   100 -------? => 56.25 %   Answer: 56.25 %
Answer: B
Little Texas Drilling Company has three wells, each producing oil at a constant rate. Well A produces one barrel every two minutes. Well B produces one barrel every three minutes. Well C produces one barrel every four minutes. How many hours does it take Little Texas Drilling Company to produce 100 barrels of oil? Pick one: A) 2 B) 3 C) 4 D) 18 E) 180

Solution: Well A produces 1/2 a barrel per minute.   Wells B and C produce 1/3 + 1/4 = 7/12 (a little more than half) a barrel per minute.   So all three wells combined produce a little more than 1 barrel per minute.   So for 100 barrels they will take a bit less than 100 mins which will be more than 1 hrs but less than 2 hrs.   2nswer (2)
Answer: A
In how many ways can an animal trainer arrange 5 lions and 4 tigers in a row so that no two lions are together?  Choose the correct choice
A) 1880 B) 2400 C) 2880 D) 3424 E) None

Solution: Solution   They have to be arranged in the following way: | L | T | L | T | L | T | L | T | L | The 5 lions should be arranged in the 5 places marked ‘L’. This can be done in 5! ways. The 4 tigers should be in the 4 places marked ‘T’. This can be done in 4! ways. Therefore, the lions and the tigers can be arranged in 5!*4!= 2880 ways   Answer 2880
Answer: C
The operation # is defined for all nonzero d and y by d#y = d + d/y. If a>0, then 1#(1#a) =
Pick:
A) a B) a+1 C) a/(a+1) D) (a+2)/(a+1) E) (2a+1)/(a+1)

Solution: d#y = d + d/y. If a>0, then 1#(1#a) =   You can see that a stands for y and 1 stands for d. I like to work with numbers so I did d=1 a=2 and a=y so y=2   1#a= 1+(1/2)= 
1+(1/2) = 3/2 = around 1.5
1.5 so now a is 1.5 --> 1+(1/1.5)=1 2/3 = 5/3   So now you can check by filling in a, which is 2:   A. a --> 2   B. a+1 --> 2+1=3   C. a/(a+1)-->2/(2+1)=2/3   D. (a+2)/(a+1)-->(2+2)/(2+1)=4/3   E. (2a+1)/(a+1)-->(2*2+1)/(2+1)=5/3   So (2a+1)/(a+1) is the answer.
Answer: E
A jogger running at 9 kmph alongside a railway track is 240 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction. In how much time will the train pass the jogger ?
Choose the most appropriate option.
A) 30 seconds
B) 32 seconds
C) 34 seconds
D) 36 seconds
E) 38 seconds

Solution: Explanation:   Speed of train relative to jogger = (45-9)= 
(45-9) = 36
36 kmph= 36*(5/18)= 
36*(5/18) = 10
10 m/sec   36 secondsistance to cover= 240 + 120= 
240 + 120 = 360
360 metres   Time= 36 secondsistance/Speed   So,   Time=360/10= 
360/10 = 36
36 Seconds   ANSWER IS 36 seconds
Answer: D
Can you replace the question mark with the correct number, given the pair of numbers exhibits similar relationship?
? : 3839 :: 11 : 1209 Pick
A) 15
B) 16
C) 17
D) 18
E) 19

Solution: Solution   16   Formular used :   pow(x,3) - pow(x,2) - 1   11*11*11 - 11*11 - 1   1331 - 121 - 1   1209   Similarly, we can solve   pow($x,3) - pow($x,2) - 1 = 3839   This condition holds true for number-16   Answer 16
Answer: B
In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl ande 2 boys are selected is:
Choose the correct choice.
A) 21/46
B) 25/117
C) 1/50
D) 3/25
E) 7/15

Solution: Let S be sample space and E be event of selecting 1 girl and 2 boys   Then n(S)=25c3   =2300   n(E)=10c1x15c2=1050   P(E)=2300/1050=21/46   21/46NSWER 21/46 21/46
Answer: A
A bowl contains pecans, cashews, and almonds in a ratio of 3 : 4 : 6, respectively. If some of the nuts of one of the three types are removed, which of the following could be the ratio of pecans to cashews to almonds remaining in the bowl? i. 1 : 2 : 3 ii. 2 : 3 : 4 iii. 4 : 7 : 10
Choose the correct choice
A) II only
B) I,II only
C) III only
D) I,III only
E) I only

Solution: i. The ratio 2 : 3 is the same as the given ratio 4 : 6. If one pecan were removed, the new ratio would be 2 : 4 : 6, or 1 : 2 : 3.   ii. None of the nuts currently have a ratio of 3 : 4. The cashews and almonds do have a ratio of 2 : 3, but there are not enough pecans in the bowl to complete the ratio.   iii. The ratio 4 : 10 is the same as the given ratio 6 : 15. To see this, multiply the ratio by 3/2 . The new ratio is 6 : 10.5 : 15. Unfortunately, this means that there are fewer cashews that this ratio would require. Removing cashews won’t create the desired ratio.   Answer : I only
Answer: E
There r 4 prime numbers in ascending order. The multiplication of first 3 is 385 and that of last 3is 1001. what is the last number is
Choose the most appropriate option:	A) 8	B) 10	C) 11	D) 13	E) 15

Solution: Explanation:   abcbcd=3851001=>ad=513   abcbcd=3851001=>ad=513   So d = 13   13
Answer: D
Machine A and Machine B can produce 1 widget in 3 hours working together at their respective constant rates. If Machine A's speed were doubled, the two machines could produce 1 widget in 2 hours working together at their respective rates. How many hours does it currently take Machine A to produce 1 widget on its own?	Choose the correct option:
A) 1/2 B) 2 C) 3 D) 5 E) 6

Solution: Given rate at which A & B works at normal pace to complete 1 widget is (1/3).   Hence A's rate = B's rate = half of (1/3).   Hence A's rate is (1/6), so to complete 1 widget A requires 6 hours.   1/2NSWER:1/2
Answer: A
The wages earned by Robin is 49% more than that earned by Erica. The wages earned by Charles is 60% more than that earned by Erica. How much % is the wages earned by Charles more than that earned by Robin?  Choose the correct choice from the following answers: A) 23% B) 18.75% C) 30% D) 50% E) 32.88%

Solution: Explanatory Answer   Let the wages earned by Erica be $100   Then, wages earned by Robin and Charles will be $149 and $160 respectively.   Charles earns $49 more than Robin who earns $149.   Therefore, Charles' wage is 49/149*100 = 32.88%.   The correct choice is (32.88%)
Answer: E
Based on this year's costs, a builder budgets P dollars for planing N new buildings next year. If the average cost of building each building were to increase 10% from this year's cost, then the greatest number of buildings that the builder could build next year using P dollars would be:
Answers.
A) 9% less than N B) 11% less than N C) Equal to N D) 9% greater than N E) 11% greater than N

Solution: Correct answer is (A).   This year, the price of a building is price1=P/N.   If this price increases by 50% it becomes Price2=P/N*1.1   Then with P dollars, you can build P/Price2 buildings i.e. P/(P/N*1.1) i.e. N/1.1 i.e. 0.91*N   Which is 9% less than N.
Answer: A
If any amount is distributed among A ,B and C so that the part of A is doubled that of the part of B and part of b is 6 time the part of C .Find the ratio among their parts.  Choose the correct choice from the following options:
A) 1:2:4
B) 1:4:1
C) 8:4:1
D) 12:6:1
E) 4:3:2

Solution: By the assumptions as mentioned we have A=2B and B=6C. So A=2(6C) and we get A=12C. We have, therefore, A:B:C = 12C:6C:C. By cancelling the ratio with C we have 12:6:1. The answer is, therefore, 12:6:1.
Answer: D
At present the ratio between the ages of Arun and Deepak is 2:3. After 5years, Arun's age will be 25 years. What is the age of Deepak at present?
Answers
A) 20 years
B) 30 years
C) 15 years
D) 25 years
E) 28 years

Solution: Let the present ages of Arun and Deepak be 2x years and 3x years respectively   2x+5 = 25   2x = 20   x = 10   Deepak's age = 3x = 30years   Answer is 30 years
Answer: B
It takes Machine A 32 minutes to fill a water tank.Another Machine B takes 6 minutes to fill the same water tank. If both machines are put to work , how long would it take to fill same water tank? Answers:
A) 3.0 minutes B) 4.5 minutes C) 5.1 minutes D) 6.0 minutes E) 6.5 minutes

Solution: By guess it is clear that the time taken will be less than 6 minutes and around 5 Therefore, answer 5.1 minutes will be correct. Answer-5.1 minutes
Answer: C
What will the ratio of simple interest earned by certain amount at the same rate of interest for 3 years and that for 15 years. Choose the correct choice from the following choices.
A) 5:2  B) 1:5  C) 1:2  D) 5:1  E) None of these

Solution: Explanation:   Let the principal be P and rate be R   then   ratio = [(P∗R∗3/100) /(P∗R∗15/100)]   =3PR /15PR=1:5   Option 1:5
Answer: B
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?  Choose the correct choice from the following:  A) 2%  B) 3%  C) 5%  D) 7%  E) None

Solution: increase in the population in 10 years   =   262500   −   175000   =   87500   =262500−175000=87500   percent increase in the population in 10 years   =   87500   175000   ×   100   =   8750   175   =   50   %   =87500175000×100=8750175=50%   average percent increase of population per year   =   50%/10   =   5%   Option 5%50 /10= 
50 /10 = 5
5%   Option 5%
Answer: C
A train runs across a post in 15 seconds and across a platform of length 100m in 25 seconds. Determine the length of this train:  Pick
A) 137 B) 150 C) 287 D) 167 E) 172

Solution: Explanation:   Let us assume for this question that the length of train is x metres and it is assumed to be running at the speed of y m/sec.   A pole is assumed as a point object.   =>Time taken by the train to pass the pole= x/y   =>15=x/y   =>y=x/15   Now, the train passes the platform which is 100 m in length in 25 seconds.   =>x+100/y=25   =>x+100/25=y   Equating speed generated from both cases:   x+100/25=x/15   Therefore x = 150 metres.   ANSWER: 150
Answer: B
The total cost of a vacation was divided among 3 people. If the total cost of the vacation had been divided equally among 4 people, the cost per person would have been $30 less. What was the total cost cost of the vacation? Answers.
A) $200  B) $360  C) $400  D) $500  E) $600

Solution: C for cost.   P price per person.   C= 3*P   C=4*P-120   Substituting the value of P from the first equation onto the second we get P = 120.   Plugging in the value of P in the first equation, we get C= 360. Which leads us to answer choice $360
Answer: B
The length of the bridge, which a train 475 metres long and travelling at 90 km/hr can cross in 30 seconds, is:	Choices.
A) 200 m	B) 225 m	C) 245 m	D) 250 m	E) 275 m

Solution: Speed = [90 X 5/18] m/sec = [25] m/sec   Time = 30 sec   Let the length of bridge be x metres.   Then, (475 + x)/30 = 25 => 475 + x= 750 => x = 275   Answer : 275 m
Answer: E
If y is 75% greater than x, than x is what % less than y?	Choose the correct option:
A) 30.6%
B) 34.4%
C) 38.7%
D) 42.9%
E) 46.5%

Solution: y = 1.75x   x = y/1.75 = 100y/175 = 4y/7   x is 3/7 less which is about 42.9% less than y.   The answer is 42.9%.
Answer: D
While planning their outing, Abhishek understood that their boat could travel with a speed of 12kmph in still water.The group decided to travel 24 minutes downstream. Aarti had prior experience in that route and mentioned that the speed of stream was 4kmph.How many kms will the group travel downstream? Choose the correct choice from the following choices.
A) 6.4 B) 3.2 C) 4 D) 4.8 E) 4.4

Solution: Downstream speed= boat speed in still water + speed of stream   Boat speed in Downstream = 12 + 4= 
12 + 4 = 16
16 km/h   Time spend= 24 min = 24/60 h = 2/5 h   Distance Travel = 16 * 2/5= 
16 * 2/5 = 32/5 = around 6.4
6.4 km   6.4nswer:a
Answer: A
A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is?
Choose the correct choice from the following answers:
A) 40 B) 48 C) 45 D) 50 E) 25

Solution: D = 540 + 180= 
540 + 180 = 720
720   S= 54 * 5/18= 
54 * 5/18 = 15
15 mps   T= 720/15= 
720/15 = 48
48 sec   ANSWER 48
Answer: B
Out of 6 consonants and 3 vowels, how many words of 4 consonants and 2 vowels can be formed?	Choose one.
A) 1050	B) 25200	C) 32400	D) 5800	E) 6800

Solution: Number of ways of selecting (4 consonants out of 6) and (2 vowels out of 3)   = 6C4 * 3C2   = 6C2 * 3C1   = 6*5 *3   2*1   = 15*3= 
15*3 = 45
45   Number of groups, each having 4 consonants and 2 vowels= 45.   Each group consists of 6 letters.   Number of ways of arranging 6 letters among themselves   = 6! = (6*5*4*3*2*1)= 
(6*5*4*3*2*1) = 720
720   Therefore, Required number of words= 45*720= 
45*720 = 32_400
32400   ANSWER:32400
Answer: C
The probability of Sam passing the exam is 1/4. The probability of Sam passing the exam and Michael passing the driving test is 1/7. What is the probability of Michael passing his driving test?  Select.
A) 1/24.
B) 1/2.
C) 4/7.
D) 2/3.
E) 2/5

Solution: 1/4 *1/m= 1/7 , 1/m = 4/7   Answer 4/7.
Answer: C
An old priest fell on a bottom of the well of a church.
The well is 15 inches deep.
At day time, the old priest climbs 5-inches but when at dark he slip back 4 inches.
In how many days priest will come out of the well ? Choose the correct choice from the following choices
A) 16-days  B) 14-days  C) 11-days  D) 19-days  E) 10-days

Solution: 11-days   11-days   In 10-days, he will climb 10-inch and when he climbs 5 inch more, he will be out of the well :-)
Answer: C
Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 2/3 were basic and the rest were deluxe. If it takes 6/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?
Choose the correct choice:
A) 6/16
B) 14/31
C) 7/15
D) 17/35
E) 1/2

Solution: # of basic stereos was 2/3 of total and # of deluxe stereos was 1/3 of total, let's assume total=15, then Basic=10 and Deluxe=5.   Now, if time needed to produce one Deluxe stereo is 1 unit than time needed to produce one Basic stereo would be 6/5 units. Total time for Basic would be  10*1= 
 10*1 = 10
10 and total time for Deluxe would be 5*6/5= 
5*6/5 = 6
6 --> total time for both of them would be 10+6= 
10+6 = 16
16 --> deluxe/total=6/16.   6/16nswer: 6/16.
Answer: A
If 6a = 7b = 20, then 84ab =	Choose one
A) 50
B) 100
C) 625
D) 800
E) 1250

Solution: 6a * 7b = 20 * 20= 
20 * 20 = 400
400   42 ab= 400   i.e. 84 ab = 800   Answer: Option 800
Answer: D
A gang of 8 boys goes on an tour in 2 cars, of which 1 canseat 5 & the other only 4. In how many ways can they travel?  Choices
A) 110 B) 123 C) 126 D) 154 E) 165

Solution: There are 8 students and the maximum capacity of the cars together is 9.   We may divide the 8 students as follows   Case I: 5 students in the first car and 3 in the second   Or Case II: 4 students in the first car and 4 in the second   Hence, in Case I: 8 students are divided into groups of 5 and 3 in8C3 ways.   Similarly, in Case II: 8 students are divided into two groups of 4 and 4 in 8C4ways.   Therefore, the total number of ways in which 8 students can travel is:   \inline {\color{Blue}8126_{3}+8126_{4}}=56 + 70= 
56 + 70 = 126
126   126
Answer: C
If a certain number is divisible by 25 and 38, it is NOT necessarily divisible by which of the following? Select: A) 5 B) 10 C) 19 D) 20 E) 95

Solution: If a certain number is divisible by 25 and 38, it is NOT necessarily divisible by which of the following?   let the certain number be 950, which is both divisible by 25 and 38.   950/20 = 95/2   D. 20
Answer: D
An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 1 hours, it must travel at a speed of: Choose the correct choice:	A) 150	B) 720	C) 160	D) 80	E) 12

Solution: Explanation:   Speed = Distance/Time   Speed =1200(5/3)km/hr   Required speed =(1200*(3/5))km/hr=720 km/hr   Answer 720
Answer: B
The sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter? Choose one.
A) 91.5 cm
B) 91.8 cm
C) 61.8 cm
D) 91.6 cm
E) 92.5 cm

Solution: Perimeter of the sector = length of the arc + 2(radius)   = (135/360 * 2 * 22/7 * 21) + 2(21)   = 49.5 + 42= 
49.5 + 42 = 91.5
91.5 cm   91.5 cmnswer:91.5 cm
Answer: A
The “d-number” of a number x is defined as the ones digit of 2^x. Antony rolls a die with 6 sides labeled with the integers from 1 to 6, each of which has an equal probability of landing face-up. He then takes 3^d, where d is the d-number of the result of his die roll, and plots 3^d on a number line as the point A. Finally, he repeats this entire process, this time plotting the result as the point B. What is the probability that the distance between A and B is greater than the value of B?	Choose the most appropriate option:
A) 3/8  B) 13/36  C) 17/36  D) 19/36  E) 23/36

Solution: If you calculate 3^d for 1st roll, all 6 results will be 9, 81, 6561, 729, 9, 81. This result is the same for 2nd roll. 9, 81, 6561, 729, 9, 81.   About distance: If the first result is 9 and the second is also 9, the distance is   9-9= 
  9-9 = 0
0 which is smaller than 9. If the first result is 9 and the second is 81, the distance is   81-9= 
  81-9 = 72
72 which is also smaller than B which has the value of 81. If the first result is 81 and the second is 9, the distance will be greater than B. Distance  81-9= 
 81-9 = 72
72>9.   On the first roll, the probability of getting result 9 is 2/6. In this case no other alternative values for second roll which would make the distance greater than B. So probability is 0. So next estimations are:   probability of getting 81 on the first roll (2/6) * probability of getting 9 on the second roll (2/6)= 1/9   probability of getting 729 on the first roll (1/6) * probability of getting 9, 81 on the second roll (4/6) = 1/9   probability of getting 6561 on the first roll (1/6) * probability of getting 9, 81, 729 on the first roll (5/6) = 5/36   All together: 1/9 + 1/9 + 5/36 = 13/36=13/36
Answer: B