MU-NLPC/Calc-aqua_rat huggingface dataset:
When positive integer N is divided by positive integer J, the remainder is 5. If N/J = 105.20, what is value of J?
Choose the correct choice from the following options:
A) 10  B) 50  C) 30  D) 15  E) 25

Solution: When a number is divided by another number, we can represent it as : Dividend = Quotient * Divisor + Remainder   So, Dividend/Divisor = Quotient + Remainder/Divisor   Given that N/J = 105.20   Here 105 is the quotient.   Given that Remainder = 5   So, 105.20 = 105 + 5/J   So, J = 25   Answer: 25
Answer: E
Two trains 161 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?  Choose the correct choice from the following.
A) 6.18  B) 7.12  C) 7.1  D) 8.09  E) 8.11

Solution: T = (161 + 165)/ (80 + 65) * 18/5   T = 8.09   Answer:8.09
Answer: D
Twenty four meters of wire is available to fence off a flower bed in the form of a circular sector. What must the radius of the circle in meters be, if we wish to have a flower bed with the greatest possible surface area?	Select the correct option: A) 2√2 B) 2√5 C) 6 D) 4√2 E) none of these

Solution: Area of Sector, A = x/360*pi*r^2   6ircumference of the sector = 24   => x/360*2*pi*r +2r= 24   => 2A/r+2r=24   => A= r12-r^2   = r12-r^2   We will now max using derivations   Max value of A will found at A=0   i.e 12-2r=0   r=6   6
Answer: C
In how many a committee of 5 members can be selected from 6men
5 ladies consisting of 3 men and 2 ladies
Pick one:
A) 30	B) 150	C) 50	D) 250	E) 200

Solution: (3 men out of 6) and (2 ladies out of 5) are to be chosen   Required number of ways   =(6C3 * 5C2)   = 200   ANSW200R 200 200
Answer: E
A and B can do a work in 10 days and 15 days respectively. A starts the work and B joins him after 2 days. In how many days can they complete the remaining work? Answers:
A) 6 days
B) 2 days
C) 4 4/5 days
D) 3 days
E) 9 days

Solution: Work done by A in 2 days = 2/10 = 1/5   Remaining work = 4/5   Work done by both A and B in one day = 1/10 + 1/15 = 5/30 = 1/6   Remaining work = 4/5 * 6/1 = 24/5 = 4 4/5 days.   Answer: 4 4/5 days
Answer: C
Salesperson A's compensation for any week is $350 plus 6 percent of the portion of A's total sales above $1,000 for that week. Salesperson B's compensation for any week is 8 percent of A's total sales for that week. For what amount of total weekly sales would both salepeople earn the same compensation?  Choose the correct choice
A) $21,000
B) $18,000
C) $15,000
D) $ 14,500
E) $4,000

Solution: sometime, setting up an equation is an easy way to go with:   350 + 0.06 (x - 1000) = 0.08 x   x = 14,500   Ans : $ 14,500
Answer: D
You are renting an apartment and you need √900 for each side, how many feet are you looking to measure?	Pick one.
A) 21  B) 22  C) 23  D) 25  E) 30

Solution: Try filling the numbers into the answer y x y =   Find the closest to 900.   Answer 30
Answer: E
After working for 6 days, Ashok finds that only 1/3 rd of the work has been done. He employs Ravi who is 60% as efficient as Ashok. How many days more would Ravi take to complete the work? Choose the correct option
A) 22 days	B) 77 days	C) 20 days	D) 17 days	E) 18 days

Solution: 1/3 ---- 6   1 -------? A = 18   R = 1/18 * 60/100 = 1/30   1 ----- 1/30   2/3 ----? => 20 days   Answer:20 days
Answer: C
In order to obtain an income of Rs. 650 from 10% stock at Rs. 96, one must make an investment of :  Choices:
A) Rs. 3100
B) Rs. 6240
C) Rs. 6500
D) Rs. 9600
E) Rs. 9800

Solution: Solution   To obtain Rs. 10, investment = Rs. 96.   To obtain Rs. 650, investment = Rs.(96/10x650) = Rs. 6240.   Answer Rs. 6240
Answer: B
Maths, Physics and chemistry books are stored on a library shelf that can accommodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books. Among all the books, 12 books are soft cover and the remaining are hard-cover. If there are a total of 7 hard-cover books among the maths and physics books. What is the probability E, that a book selected at random is either a hard cover book or a chemistry book? Answers:  A) 1/10  B) 3/20  C) 1/5  D) 1/4  E) 9/20

Solution: First phase of this problem requires you to determine how many mathematics and chemistry books are even on the shelf. To do so, you have the equations:   m + p + c = 20 (since 4/5 of the 25 spots are full of books)   m = 2p   p = 4 + c   From that, you can use Substitution to get everything down to one variable.   c = p - 4   m = 2p   p = p   Then (p - 4) + 2p + p = 20, so 4p = 24 and p = 6. That means that there are 12 math, 6 physics, and 2 chemistry books on the shelf.   With those numbers, you also know that there are 8 total hardcovers, 1 of which is chemistry. So if your goal is to get either a hardcover or a chemistry, there are 9 ways towin- either one of the 7 hardcovers that aren't chemistry or the two chemistry books. So out of the 20 total, 9/20=9 provide the desired outcome, making the answer 9/20.
Answer: E
Carmen made a sculpture from small pieces of wood. The sculpture is 2 feet 10 inches tall.Carmen places her sculpture on a base that is 8 inches tall. How tall are the sculpture andbase together?  Pick one:
A) 3.1 feet
B) 3.2 feet
C) 3.3 feet
D) 3.4 feet
E) 3.5 feet

Solution: we know 1 feet =12 inch then   2 feet =24 inch     24+10= 
  24+10 = 34
34 then     34+8= 
  34+8 = 42
42   42/12= 
42/12 = 7/2 = around 3.5
3.5 feet   ANSW3.5 feetR:3.5 feet
Answer: E
What is the compound interest paid on a sum of Rs.1500 for the period of 2 years at 10% per annum. Pick:
A) 230  B) 175  C) 225  D) 315  E) None of these

Solution: Solution= Interest % for 1st year= 10   Interest % for 2nd year= 10+ 10% of 10= 10+ 10 *10/100= 
10+ 10 *10/100 = 11
11   Total % of interest= 10 + 11= 
10 + 11 = 21
21   Total interest= 21 % 1500 = 1500 * (21/100)= 
1500 * (21/100) = 315
315   Answer 315
Answer: D
A invested Rs 76000 in a business. After few months, B joined him with Rs 57000. The total profit was divided between them in the ratio 2 : 1 at the end of the year. After how many months did B join?  Choose one:
A) 2 B) 3 C) 4 D) 5 E) 6

Solution: Explanation:   Suppose B was there in the business for xx months. Then   A: B =76000×12:57000×x   Therefore,   76000×12:57000×x=2:1   76×12:57x=2:1   76×12×1=57x×2   76×4=19x×2   4×4=x×2   x=8   Hence B was there in the business for 8 months, or joined after   12-8= 
  12-8 = 4
4 months   Answer: Option 4
Answer: C
The average height of 35 boys in a class was calculated as 184cm. It has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (Round off your answer to two decimal places).?  Pick one
A) 178.27 cm  B) 182.29 cm  C) 978.29 cm  D) 178.89 cm  E) 176.29 cm

Solution: Calculated average height of 35 boys = 184 cm.   Wrong total height of 35 boys = 184 * 35 cm. This was as a result of an actual height of 106 cm being wrongly written as 166 cm. Correct total height of 35 boys = 184 cm - (166 cm - 106 cm)/35   = 184 cm - 60 /35 cm   = 184 cm - 1.71 cm = 182.29 cm.   Answer: 182.29 cm
Answer: B
The distance between 2 cities A and B is 1000km. A train starts from A at 1 p.m. and travels towards B at 100 km/hr. Another starts from B at 2 p.m. and travels towards A at 150 km/hr. At what time do they meet? Choose the correct choice:
A) 11am. B) 6p.m. C) 3pm. D) 2p.m. E) 1p.m.

Solution: Suppose they meet x hrs after 1 p.m.   Distance moved by first in x hrs + Distance moved by second in (x-1)hrs = 1000   100x + 150 (x-1) = 1000   x = 4.60 = 5 hrs   They meet at   1+5= 
  1+5 = 6
6 p.m.   Answer is 6p.m.
Answer: B
in a tennis match the probability for A to win the match is 2/3 and he has to win 3 sets to win the match so what is the probability for A to win the match  Pick.
A) 182/243 B) 172/243 C) 162/243 D) 192/243 E) 292/243

Solution: The sequence of winning as follows:   Sequence Probability   ----------------- -----------   W W L W 8/81   W W L L W 8/243   W W W 8/27   W L L W W 8/243   W L W L W 8/243   W L W W 8/81   L L W W W 8/243   L W L W W 8/243   L W W L W 8/243   L W W W 8/81   Thus, by adding all the above probabilities, we get the probability for A to win the match as : 192/243   ANSWER:192/243
Answer: D
Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is? Pick one
A) 10 B) 11 C) 12 D) 10.8 E) 13

Solution: Relative speed = 60 + 40= 
60 + 40 = 100
100 km/hr.= 100 * 5/18 = 250/9 m/sec.   Distance covered in crossing each other = 140 + 160= 
140 + 160 = 300
300 m.   Required time= 300 * 9/250 = 54/5= 
54/5 = 54/5 = around 10.8
10.8 sec.   Answer: Option 10.8
Answer: D
A small pool filled only with water will require an additional 300 gallons of water in order to be filled to 80% of its capacity. If pumping in these additional 300 gallons of water will increase the amount of water in the pool by 30%, what is the total capacity of the pool in gallons?	Select.
A) 1000  B) 1250  C) 1300  D) 1600  E) 1625

Solution: Since pumping in additional 300 gallons of water will increase the amount of water in the pool by 30%, then initially the pool is filled with 1,000 gallons of water.   So, we have that 1,000 + 300 = 0.8*{total} --> {total} = 1,625.   Answer: 1625.
Answer: E
For all integers a and b, a%b = (a + b)(a - b). If 7%x = 13, then which of the following could be a value of x?  Pick one:
A) -6
B) -5
C) 2
D) 3
E) 6

Solution: 7%x = (7+x)(7-x)   49-x^2 = 13   x^2 = 36   x=-6,6   -6ns: -6
Answer: A
A firm is comprised of partners and associates in a ratio of 2:61. If 75 more associates were hired, the ratio of partners to associates would be 4:137. How many partners are currently in the firm? Choices.
A) 12 B) 14 C) 16 D) 18 E) 20

Solution: The ratio 2:61 = 4:122 so the ratio changed from 4:122 to 4:137.   137-122= 
137-122 = 15
15 which is 1/5 of the increase in 75 associates.   The ratio changed from 20:610 to 20:685.   Thus the number of partners is 20.   The answer is 20.
Answer: E
The distance that light travels in one year is approximately 5,870,000,000,000 miles. The distance light travels in 10000 years is:
Select:
A) 111 × 1827 miles
B) 999× 1238 miles
C) 587 x 10^14 miles
D) 247 × 1012 miles
E) 587 × 1012 miles

Solution: The distance of the light travels in one years is:   5,870,000,000,000 = 587 * 10 ^10   The distance of the light travels in 10000 years is:   = 587 * 10^10 x 10 ^4 = 587 x 10^14 miles   Answer :587 x 10^14 miles
Answer: C
John bought a shirt on sale for 25% off the original price and another 25 % off the discounted price. If the final price was $16, what was the price before the first discount?
Choices.
A) $28.44 B) $38.44 C) $48.44 D) $58.44 E) $68.44

Solution: let x be the price before the first discount. The price after the first discount is   x - 25%x (price after first discount)   $28.44 second discount of 25% of the discounted price after which the final price is 16   (x - 25%x) - 25%(x - 25%x) = 16   Solve for x   x = $28.44   correct answer $28.44
Answer: A
On a game show, a contestant is given three keys, each of which opens exactly one of three identical boxes. The contestant assigns each key to one of the boxes and wins the amount of money contained in any box that is opened by the key assigned to it. The first box contains $1.5, the second $150, and the third $1500. What is the probability that a contestant will win more than $1500?  Answers
A) 1/9	B) 2/3	C) 1/6	D) 1/3	E) 1/2

Solution: Let's call the boxes that contain $1.5, $150, and $1500, respectively, Box A, Box B, Box C. These are opened, respectively, by Key A, Key B, and Key C.   We want to know the probability of winning more than $1500. Notice that if the distribution of keys is:   Box A = Key B   Box B = Key A   Box C = Key C   then the contestant wins exactly $1500, not more than $1500. The only configuration that leads to winning more than $1000 is:   Box A = Key A   Box B = Key B   Box C = Key C   i.e., getting all three keys correct. That's the only way to be more than $1500. So, really, the question can be rephrased: what is the probability of guessing the order of keys so that each key matches the correct box?   Well, for a set of three items, the number of possible permutations is 3! = 3*2*1= 
3*2*1 = 6
6.   Of those 6 possible permutations, only one of them leads to all three keys being paired with the right box. So, the answer is   Probability= 1/6   Answer = 1/6
Answer: C
The three competitors in a race have to be randomly chosen from a group of three men and three women. How many different such trios contain at least one woman?  Choose the correct option
A) 13 B) 15 C) 17 D) 19 E) 21

Solution: The total number of ways to choose three runners 6C3 = 20   The number of trios with only males is 3C3 = 1   The number of trios which include at least one woman is 19.   The answer is 19.
Answer: D
For a race a distance of 224 meters can be covered by P in 28 seconds and Q in 32 seconds. By what distance does P defeat Q eventually?	Choose the correct choice from the following answers:
A) 32m
B) 38m
C) 34m
D) 31m
E) 36m

Solution: Explanation:   This is a simple speed time problem. Given conditions:   =>Speed of P= 224/28= 
224/28 = 8
8m/s=>Speed of Q=224/32= 
224/32 = 7
7m/s=>Difference in time taken = 4 seconds   Therefore, Distance covered by P in that time= 8m/s x 4 seconds = 32 metres   32mNSWER: 32m
Answer: A
If B and C are digits and 8BC is a 3-digit number that is divisible by 7, which of the following is a possible product of B and C?	Choose the most appropriate option: A) 1 B) 2 C) 5 D) 6 E) 14

Solution: Try with the options -   A. If BC = 1 , both B and C must be 1   B. If BC = 2 , either B or C must be 1 or 2 ; In that case sum of the digits will be 8 + 1 + 2= 
8 + 1 + 2 = 11
11 which is not divisible by 3   C. If BC= 5 , either B or C must be 1 or 5 ; In that case sum of the digits will be 8 + 1 + 5= 
8 + 1 + 5 = 14
14 which is not divisible by 3   D. If BC= 6 , then we can have the following possibilities   i. Either B or C must be 2 or 3 ; In that case sum of the digits will be 8 + 2 + 3= 
8 + 2 + 3 = 13
13 which is not divisible by 3   ii. Either B or C must be 1 or 6 ; In that case sum of the digits will be 8 + 1 + 6= 
8 + 1 + 6 = 15
15 which is divisible by 3   E. If BC= 14 , then either B or C must be 2 or 7 ; In that case sum of the digits will be 8 + 2 + 7= 
8 + 2 + 7 = 17
17 which is not divisible by 7   Thus answer is (14)
Answer: E
Ratio of two numbers x and y is 3:7. If x is increased by 50% and y is increased by 2 then the new ratio becomes 1:2. What is the ratio 2y:(2x+6)
Choose the most appropriate option:
A) 16:15
B) 4:5
C) 7:12
D) 4:9
E) 6:5

Solution: Let:   x = 3n   y = 7n   4.5n/(7n+5) = 1/2   9n = 7n+2   n = 1   So, x =3; y=7   2y/(2x+6) = 14/12 = 7:6   Answer = 7:12
Answer: C
The difference between a two-digit number and the number after interchanging the position of the two digits is 27. What is the difference between the two digits of the number? Pick.
A) 4  B) 6  C) 3  D) Cannot be determined  E) None of these

Solution: Let the two-digit no. be l0x + y.   Then, (10x + y) â€“ (10y + x) = 27   or, 9(x â€“ y) = 27   or, x â€“ y = 3   Answer 3
Answer: C
The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %?	Pick one:  A) 18  B) 99  C) 77  D) 66  E) 55

Solution: 1500 ---- 270   100 ---- ? => 18%   18nswer: 18
Answer: A
The speed of a train is 90 kmph. What is the distance covered by it in 10 minutes?  Choose the correct choice from the following answers
A) 277  B) 266  C) 300  D) 767  E) 211

Solution: 1/2:1/3:1/4 = 6:4:3   3/13*1300= 
3/13*1300 = 300
300   Answer:300
Answer: C
When positive integer m is divided by positive integer n, the remainder is 12. If m/n = 24.2, what is the value of n ?  Choose one:  A) 120  B) 60  C) 30  D) 24  E) 12

Solution: n = decimal part of 24.2 * remainder i.e. (12)   Hence 0.2 * n = 12   n = 60.60
Answer: B
There are 15 members in a family. it takes 180 days for a women to complete the work, however man completes in 120 days. They take 17days to complete the work if men work on alternate days and women work every third day. if all of them started together on the 1st day, then how many men are there in the family Choose one.
A) 9	B) 10	C) 11	D) 12	E) 13

Solution: Let the number of men be m and so the number of women = 15-m   Out of 17 days, men and women work together on 1,4,7,10,13,16th days (Total of 6 days) from the start.   Men work on alternate days, that is 1,3,5,7,9,11,13,15,17th days (Total of 9 days).   Let the total work be 360 units (LCM of 180 and 120).   1 man does  360/120= 
 360/120 = 3
3 units per day   1 woman does 360/180= 
360/180 = 2
2 units per day   Based on above facts,   Total work by men + women in these 17 days= 360 units   m*9*3 + (15-m)*6*2 = 360,   27m + 180 -12m = 360, Solving m=12.   Num of men = 12   ANSWER:12
Answer: D
In a mixture of milk and water, the proportion of milk by weight was 80%. If, in a 180 gm mixture, 36 gms of pure milk is added, what would be the percentage of milk in the mixture formed?  Choose the correct choice from the following options:
A) 83.33
B) 84
C) 85
D) 76
E) 80

Solution: Percentage of milk in the mixture formed = [80/100 (180) + 36] / (180 + 36) * 100% = (144 + 36)/216 * 100% = 5/6 * 100% = 83.33%.   83.33NSWER 83.33
Answer: A
A person purchased a TV set for Rs. 1600 and a DVD player for Rs. 625. He sold both the items together for Rs. 31150. What percentage of profit did he make?  Choose the correct option:  A) 1250%  B) 35%  C) 1300%  D) 1200%  E) None of these

Solution: The total CP = Rs. 1600 + Rs. 625= Rs. 2225 and SP = Rs. 31150   Profit(%) = (31150 - 2225)/2225* 100= 
(31150 - 2225)/2225* 100 = 1_300
1300%   ANSWER:1300%
Answer: C
A 340-liter solution of Kola is made from 75% water, 5% concentrated Kola and the rest is made from sugar. If 3.2 liters of sugar, 12 liter of water and 6.8 liters of concentrated Kola were added to the solution, what percent of the solution is made from sugar?  Options:
A) 6%.
B) 7.5%.
C) 19.6%.
D) 10.5%.
E) 11%.

Solution: Denominator:   340+12+3.2+6.8= 
340+12+3.2+6.8 = 362
362   Numerator:   340(1-.75-.05)+3.2   340(0.2)+3.2   68+3.2   71.2   Ratio:   71.2/362=0.196   Answer: 19.6%.
Answer: C
There are three vessels of equal capacity .Vessel A contains Milk and water in the ratio 4:3 ;Vessel B contains Milk and water in the ratio 2:1 and Vessel C contains Milk and water in the ratio 3:2 .If the mixture in all the three vessels is mixed up.What will be the ratio of milk and water ?  Choose the correct choice from the following choices
A) 9:6  B) 3:2  C) 118:126  D) 193:122  E) 201:132

Solution: m=portion of milk in solution   m=(4/7+2/3+3/5)/3➡193/315   315-193= 
315-193 = 122
122   122/315=portion of water in solution   ratio of milk to water=193/122   ANSWER:193:122
Answer: D
The Avg age of a class of 22 subject areas in 21 years. The avg increased by one when the lecturer’s age also involved. What is the age of the Lecturer?
Choose the correct choice from the following choices:
A) 48 years  B) 45 years  C) 46 years  D) 47 years  E) 44 years

Solution: 44 years   44 years   Average * Subject Areas = Total Age   So => 21 years x 22 numbers = 462 years … (1)   => 22 years x 23 numbers = 506 years … (2)   Therefore Lecturer’s age = 44 yearsqn(2) – 44 yearsqn(1)   = 506 – 462   = 44 Years.
Answer: E
If log 27 = 1.437, then the value of log 9 is: Choose the correct choice from the following choices.
A) 0.934 B) 0.945 C) 0.954 D) 0.958 E) 0.987

Solution: log 27 = 1.437   log (33 ) = 1.437   3 log 3 = 1.437   log 3 = 0.479   log 9 = log(32 ) = 2 log 3 = (2 x 0.479) = 0.958.   Answer: Option 0.958
Answer: D
Find the least number of complete years in which a sum of money put out at 25% compound interest will be more than double of itself?	Choose the correct choice from the following answers
A) 12
B) 33
C) 6
D) 4
E) 7

Solution: 4 years   Answer:4
Answer: D
A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 according to the following constraints. The first digit cannot be 0 or 1, the second digit must be 0 or 1, and the second and third digits cannot both be 0 in the same code. How many different codes are possible?
Select the correct option:
A) 119	B) 152	C) 160	D) 168	E) 176

Solution: The first digit can be filled in 7 ways   For second digit , it can either be 0 or 1   Case 1 -   If second digit is 1 ,Third digit can take 10 values   number of codes = 7 * 1 * 9= 
7 * 1 * 9 = 63
63   Case 2 -   If second digit is 0,Third digit can take 8 values ( Third digit can't be zero)   number of codes= 7 * 1 * 8= 
7 * 1 * 8 = 56
56   Total number of codes= 119   119nswer 119
Answer: A
A envelop weight 8.5 gm,if 850 of these envelop are sent with an advertisement mail. How much wieght?
Choose the correct choice from the following answers:
A) 6.6kg	B) 7.225kg	C) 6.7kg	D) 6.9kg	E) 7.8kg

Solution: 850*8.5   7225.0gm   7.225kg   ANSWER:7.225kg
Answer: B
Find the ratio in which rice at Rs.7.20 a kg be mixed with rice at Rs.5.70 a kg to produce a mixture worth Rs.6.30 a kg?  Choose the most appropriate option:
A) 1 : 3
B) 2 : 3
C) 3 : 4
D) 4 : 5
E) None of these

Solution: Solution   Required ratio = 60 : 90 = 2 : 3   Answer 2 : 3
Answer: B
A tank is filled in 10 hours by three pipes A, B and C. Pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?
Choose the correct choice from the following answers:
A) 70 hours B) 30 hours C) 35 hours D) 50 hours E) 40 hours

Solution: Efficiency of pipes A,B,C =1:2:4   Therefore, in 10 hours, part of the tank filled by A =17   Therefore, pipe A alone requires 10×7=70 hours to fill the tank.   70 hoursnswer: Option 70 hours
Answer: A
In a psychology school the grade of the students is determined by the following method: At the end of the first year the grade equals to twice the age of the student. From then on, the grade is determined by twice the age of the student plus half of his grade from the previous year. If Joey’s grade at the end of the first year is 32, what will be his grade at the end of the third year?  Options
A) 44	B) 51	C) 62	D) 75	E) 80

Solution: Cool question!   There's a lot of information given here, so let's eat slow here.   Joey scores a 32 at the end of his first year. That means that he's currently 16 years old (since given per instruction, after the first year one's grade is determined by doubling his/her age).   Now, come next year, or his second year at this psychology school, he's technically 17 years old. To find out the second year's grade, we want to double his age PLUS half of his previous grade.   Well, his second year is then going to be 17(2) + 16 = 50.   Now let's tackle the main question: what's his grade going to be the third year?   Well, he will be at an age of 18 on his third year at this school. Again, to find out his third year's grade, you're going to double his age (18x2), plus half of his previous year's grade (as calculated for his second year, his grade is 50; therefore, 50/2)   Having said that, the final answer would be 18(2) + 50/2 = 36 + 25 = 51 --> (51)
Answer: B
Bill likes long bike rides. On one ride, he goes biking for seven hours. For the first hour, he bikes
at a speed of 16 miles per hour. For the next two hours, he bikes at a speed of 12 miles per
hour. He remembers biking 112 miles over the seven hours. Compute the average speed, in miles
per hour, Bill biked during the last four hours of his trip.  Choose the correct choice from the following.
A) 18	B) 14	C) 22	D) 27	E) 35

Solution: He has to travel 112 - 16 - 12 * 2= 
112 - 16 - 12 * 2 = 72
72 miles in 4 hours   72 / 4= 
72 / 4 = 18
18 miles per hour   correct answer 18
Answer: A