MU-NLPC/Calc-aqua_rat huggingface dataset:
When all the students in a school are made to stand in rows of 50, 25 such rows are formed. If the students are made to stand in rows of 30, how many such rows will be formed ?
Choose the correct answer:
A) 41  B) 36  C) 38  D) 19  E) 21

Solution: Explanation:   Total number of students = 50 x 25   When arranged in rows of 30, number of rows formed are,   = 41.   41nswer: 41
Answer: A
A cement mixture is composed of 3 elements. By weight, 1/3 of the mixture is sand, 1/4 of the mixture is water, and the remaining 10 pounds of the mixture is gravel. What is the weight of the entire mixture in pounds?  Options
A) 24	B) 26	C) 28	D) 30	E) 36

Solution: Let the total weight be x.   Sand content= (1/3)x   Water content= (1/4)x   Gravel=x-(1/3)x-(1/4)x=(5/12)x=10   x=24   Then answer will be 24=24
Answer: A
Find the least number of 5 digits, which is exactly divisible by 89.  Choose the correct choice from the following choices:  A) 27  B) 37  C) 932  D) 12  E) 91

Solution: 27NSWER:27
Answer: A
If a sequence of 8 consecutive odd integers with increasing values has 5 as its 7th term, what is the sum of the terms of the sequence?
Choose the correct choice from the following options:
A) -8 B) -4 C) 0 D) 4 E) 8

Solution: Let x be the first term.   Then x + 12 = 5 and x = -7   The sum is: x + (x+2) +...+ (x+14) =   8x + 2(1+2+...+7) = 8x + 2(7)(8) / 2 = 8(-7) +56 = 0   The answer is 0.
Answer: C
A clock store sold a certain clock to a collector for 25 percent more than the store had originally paid for the clock. When the collector tried to resell the clock to the store, the store bought it back at 55 percent of what the collector had paid. The shop then sold the clock again at a profit of 70 percent on its buy-back price. If the difference between the clock's original cost to the shop and the clock's buy-back price was $125, for how much did the shop sell the clock the second time?	Choose the correct choice from the following answers.
A) $500 B) $467.5 C) $935 D) $525.5 E) $465.5

Solution: Now, in the question above, lets say the original cost of the clock to store was C$ and then it sold the same to the collector at 25% profit.   This means the clocks' selling price was C (1.25) and this becomes cost price for the collector.   Now, when the collector tries to sell the same clock to the store, the store buys it for 55% the price at which the collector bought it.   Thus, you get = 1.25*0.55*C = 0.6875 C   Furthermore, the store sells the clock for the second time for 70% profit and thus the selling price of the clock becomes = cost price of the clock for the store at buy-back * 1.7 = 1.7 * 0.6875 C   Finally given that C - 0.6875 C = 125 ----> C = 400$   Thus, the cost of the clock the second time around = 1.7*0.6875 C = 1.7 * 0.6875 * 400= 
1.7 * 0.6875 * 400 = 467.5
467.5$. Hence $467.5 is the correct answer.
Answer: B
Which one of the following is equal to 3.14×10(6)?
Choose one
A) 314
B) 3140
C) 3140000
D) None of these
E) Cannot be determined

Solution: Solution   Given, 3.14 ×106	=3.140000×1000000   = 3140000.   Answer 3140000
Answer: C
A four digit number divisible by 7 becomes divisible by 3 when 16 is added to it. The largest such number is :
Choose one:
A) 8847
B) 8853
C) 8871
D) 8856
E) 8897

Solution: Out of all the 5 options, only 8897 is NOT divisible by 3. All others are divisible   So Answer = 8897 (No further calculation required)   Addition of any two non-divisible numbers by 3 gives the resultant divisible by 3   16 is non-divisible by 3; we are adding a number to that so that the resultant becomes divisible by 3   Applying the above rule,It means that the number which we are going to add should be non-divisible by 3   So comes the answer = 8897   Answer : 8897
Answer: E
Marts income is 60 percent more than Tims income and Tims income is 40 percent less than Juans income. What percentage of Juans income is Marts income Choose one:  A) 124%  B) 120 %  C) 96 %  D) 80 %  E) 64 %

Solution: Tim=100   Mary's income is 60 percent more than tims income;   Mary's Income = T+0.6T = 1.6T = 1.6*100= 
1.6*100 = 160
160   Tims income is 40 percent less than juans income .   100 is 40% less than Juan's Income   100=J-0.4J   100=0.6J   J = 100/0.6=1000/6   What percentage of juans income is marts income   (160/(1000/6))*100 = (160*6*100)/1000= 
(160*6*100)/1000 = 96
96%   ANSWER:96 %
Answer: C
A woman begins bicycling with a pace of 8 kmph and she increases her pace every two hours by 2 kmph. She does not increase her pace as soon as her pace reaches her maximum speed of 12 kmph. How many hours did she bicycle if she traveled 64 kms?  Choose the correct choice from the following options.
A) 6 1â„7 hours B) 6 2â„7 hours C) 8 2â„7 hours D) Cannot be determined E) None of these

Solution: Distance covered in first two hours = 8 Ã— 2 = 16 km   Distance covered in next two hours = 10 Ã— 2 = 20 km   Distance covered in next two hours = 12 Ã— 2 = 24 km   Distance covered in first six hours     16 + 20 + 24= 
  16 + 20 + 24 = 60
60 km   Remaining distance= 64 â€“ 60 = 4 km.   Now, this distance will be covered at the speed of 12 km/hr.   âˆ´ Time taken = 4â„12 = 1â„3 hour.   Total time= 6 + 1â„3 = 6 1â„3 hour   Answer None of these
Answer: E
In a school there are 4 sections in LKG. Average students of the section is 30. A, B, C sections have 28, 30, 34 students respectively. Therefore how much students in section D? Select:
A) 30
B) 29
C) 35
D) 32
E) 28

Solution: 28XPLANATION   Total students of 3 sections = (28 + 30 + 34)= 
(28 + 30 + 34) = 92
92   Students of section D= [ (30 x 4) – 92 ]   = (120 – 92)   = 28   Answer 28
Answer: E
A does 4/5th of a work in 20 days. He then calls in B and they together finish the remaining work in 3 days. How long B alone would take to do the whole work?
Choose the correct choice from the following:  A) 23 days  B) 37 days  C) 37 ½ days  D) 40 days  E) 41 days

Solution: Explanation:   A can finish the whole work in 20 × 5/4 days = 25 days   A and B together finish the whole work in 5 × 3 days = 15 days   Therefore, B can finish the whole work in 25 B/ 25 + B = 15   25 B = 15 ( 25 + B)= 375 + 15B   10B = 375 and B = 375/10 = 37 ½ days.   Answer: Option 37 ½ days
Answer: C
Two dogsled teams raced across a 500-mile course in Alaska. Team A finished the course in 5 fewer hours than team B. If team A’s average speed was 5 miles per hour greater than that of team B, what was team B’s average speed, in miles per hour?
Pick one:
A) 12	B) 15	C) 18	D) 20	E) 25

Solution: Let v be team B's average speed.   Time = Distance/Rate and the time difference was 5 hours.   500/v - 500/(v+5)= 5   500v + 2500 - 500v = 5(v)(v+5)   500 = (v)(v+5)   (20)(25) = (v)(v+5)   v = 20 mph   The answer is 20.
Answer: D
Robert is travelling on his cycle andhas calculated to reach point A at 2 PM. if he travels at 10 kmph, he will reach there at 12Pm if he travels at 15kmph. At what speed must he travel to reach A at 1 PM? Choose the correct choice from the following answers: A) 10 kmph B) 11 kmph C) 12 kmph D) 14 kmph E) 16 kmph

Solution: Let the distance travelled by x km.   Then, x - x = 2   10 15   3x - 2x = 60   x = 60 km.   Time taken to travel 60 km at 10 km/hr = 60 hrs = 6 hrs.   10   So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M.   Required speed = 60 kmph. = 12 kmph.   5   12 kmph
Answer: C
The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is: Choose the correct choice from the following options
A) 152600m2 B) 153500m2 C) 153600m2 D) 153800m2 E) 153700m2

Solution: Explanation:   Question seems to be typical, but trust me it is too easy to solve, before solving this, lets analyse how we can solve this.   We are having speed and time so we can calculate the distance or perimeter in this question.   Then by applying the formula of perimeter of rectangle we can get value of length and breadth, So finally can get the area. Lets solve it:   Perimeter = Distance travelled in 8 minutes,   => Perimeter = 12000/60 * 8= 
12000/60 * 8 = 1_600
1600 meter. [because Distance= Speed * Time]   As per question length is 3x and width is 2x   We know perimeter of rectangle is 2(L+B)   So, 2(3x+2x) = 1600   => x = 160   So Length = 160*3= 
160*3 = 480
480 meter   and Width= 160*2= 
160*2 = 320
320 meter   Finally, Area= length * breadth   = 480 * 320= 
480 * 320 = 153_600
153600   ANSWER IS 153600m2
Answer: C
The average age of 6 men increases by 2 years when two women are included in place of two men of ages 20 and 24 years. Find the average age of the women? Choose the correct choice.
A) 24
B) 25
C) 26
D) 27
E) 28

Solution: 20 + 24 + 6 * 2= 
20 + 24 + 6 * 2 = 56
56/2= 
56/2 = 28
28   ANSW28R:28
Answer: E
In how many different number of ways 4 boys and 4 girls can sit on a bench? Choose the correct answer:
A) 40320
B) 42345
C) 23456
D) 40567
E) 34567

Solution: npn = n!   8p8 = 8 x 7 x 6 × 5 × 4 × 3 × 2 × 1 = 40320   40320)
Answer: A
A can finish a work in 18 days and B can do same work in half the time taken by A. then working together, what part of same work they can finish in a day
Choose the correct choice from the following answers:
A) 1/6 B) 1/9 C) 1/11 D) 1/3 E) None

Solution: 1/6's 1 day work = 1/18   B's 1 day work = 1/9   (1/6+B)'s one day work = (1/18+1/9)=1/6   1/6nswer: 1/6
Answer: A
If x ≠ 0 and (−y^2 + xy)/x=y+x, which of the following expressions is equal to its opposite?
Choose the most appropriate option.
A) x^2	B) x^2 + y^2	C) y^2	D) (y + x)^2	E) (x – y)^2

Solution: (−y^2 + xy)/x=y+x   => −y^2 + xy = xy +x^2   => x^2 + y^2 +  2= 
+  2 = 2
> x^2 + y^2= 0   Answer x^2 + y^2
Answer: B
x varies inversely as square of y. Given that y=3 for x=1. The value of x for y = 2 will be equal to:
Options:
A) 3	B) 6	C) 1/9	D) 1/3	E) 9/4

Solution: Explanation :   Solution: Given x = k/y^2, where k is constant. Now, y=3 and x =1 gives k = 9.   .'. x = 9/y^2   => x =9 /2^2 = 9/4   Answer : 9/4
Answer: E
A dishonest dealer marks up the price of his goods by 20% and gives a discount of 10% to the customer. He also uses a 900 gram weight instead of a 1 kilogram weight. Find his percentage profit due to these maneuvers?	Pick one.
A) 8% B) 12% C) 20% D) 16% E) None

Solution: Solution: He sells only 900 grams when he takes the money for 1 kg.   and   he sells at a 8% profit (20% markup, 10% discount).   Hence, his selling price is Rs. 108 for 900 grams.   % profit = (18/90)*100= 
(18/90)*100 = 20
20%.   Answer: Option 20%
Answer: C
Number of handshakes in a party is 28.Find the number of people present in the party altogether?	Answers.
A) 5  B) 6  C) 7  D) 8  E) 9

Solution: no. of handshakes (ie) n(n-1)/2= 28   therefore no. of people present   n(n-1)=56   n2-n-56=0   n=8   No. of people present = 8   ANSWER:8
Answer: D
If the time is currently 1:30pm, what time will it be in exactly 239 hours? Choose the correct choice from the following:
A) 12:30am  B) 1:30am  C) 12:30pm  D) 2:30pm  E) 10:30pm

Solution: Every 24 hours will bring us to the same 1:30pm. 240 is divisible by 24 (10*24=240), so if it were 240 hours we would have 1:30pm, but since it's 239 hours then it will be 1 hour less, so 12:30pm.   Answer: 12:30pm.
Answer: C
A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?  Choose the correct choice from the following options:
A) Rs. 375  B) Rs. 400  C) Rs. 600  D) Rs. 800  E) Rs. 900

Solution: Explanation:   C's 1 day's work =1/3-(1/6+1/8)=1/3-7/24=1/24   A's wages : B's wages : C's wages =1/6:1/8:1/24=4:3:1   C's share (for 3 days) = Rs.(3X1/24X3200)=Rs. 400   ANSWER IS Rs. 400
Answer: B
An agent buys a T.V. set listed at Rs. 10000 and gets 10% and 20% successive discounts. He spends 10% of his C.P. on transport. At what price (in rupees) should he sell the T.V. set to earn a profit of 10%? Choose one.
A) 8692  B) 8702  C) 8712  D) 8722  E) None of these

Solution: Net price after two discounts=80% of 90% of Rs. 10000=Rs. 7200.   Net C.P.=(7200+10% of Rs. 7200)=7920.   Therefore, S.P. =110% of Rs. 7920=Rs. 8712.   ANSWER:8712
Answer: C
A certain quantity is measured on two different scales, the R scale and the S scale, that are related linearly. Measurements on the R scale of 6 and 24 correspond to the measurements on the S scale of 30 and 60 respectively. What measurement on the R scale corresponds to a measurement of 90 on the S scale?	Pick one
A) 32
B) 36
C) 42
D) 48
E) 54

Solution: A change of +18 on the R scale is a change of +30 on the S scale.   R = (18/30)*S + K = 3S/5 + K   6 = 3(30)/5 + K   K = -12   R = 3S/5 - 12   R = 3(90)/5 - 12 = 54-12= 
54-12 = 42
42   The answer is 42.
Answer: C
In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 14 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can?  Choose one:  A) 40  B) 77  C) 48  D) 52  E) None of these

Solution: Let the capacity of the can be T litres.   Quantity of milk in the mixture before adding milk = 4/9 (T - 14)   After adding milk, quantity of milk in the mixture = 6/11 T.   6T/11 - 14 = 4/9(T - 14)   10T = 1386 - 616 => T = 77.   ANSWER:77
Answer: B
The sum of three consecutive even numbers is 87. Find the middle number of the three? Choose the correct choice from the following answers.
A) 31	B) 21	C) 29	D) 22	E) 12

Solution: Middle number =87/3= 
87/3 = 29
29   Ans 29
Answer: C
Rs.460 was divided among 41 boys and girls such that each boy Rs.12 and each girl got Rs.8. What is
the number of boys?	Select the correct option
A) 33	B) 30	C) 36	D) 28	E) 26

Solution: Explanation :   -------------------------------------------------------------------   Solution 1   -------------------------------------------------------------------   33ssume that the number of boys = b and number of girls is g   number of boys + number of girls = 41   => b + g = 41 ------------ (Equation 1)   Given that each boy got Rs.12 and each girl got Rs.8 and Total amount = Rs.460   => 12b + 8g = 460 -------- (Equation 2)   Now we need solve Equation 1 and Equation 2 to get b and g   (Equation1)×8=>8b+8g=8×41=328−−−−−−−−(Equation3)   (Equation 2) - (Equation 3) = 4b = 460 - 328= 
460 - 328 = 132
132=>b=1324=33   -------------------------------------------------------------------   Solution 2   -------------------------------------------------------------------   Given that 33mount received by a boy = Rs.12 and   33mount received by a girl =Rs.8   Total amount = 460   Given that number of boys + Number of girls = 41   Hence mean amount = 460/41   By the rule of alligation, we have   33mount received by a boy 33mount received by a girl   12 8   Mean amount   460/41   460/41 - 8 =132/41 12 - 460/41 = 32/41   Number of boys : Number of girls = 132/41 : 32/41 = 132 : 32 = 66 : 16 = 33 : 8   Given that number of boys + Number of girls = 41   Hence number of boys = 41×3341=33   33nswer : Option 33
Answer: A
Vijay bought 160 shirts at the rate of Rs. 215 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%? Pick one
A) Rs. 258	B) Rs. 270	C) Rs. 273	D) Rs. 285	E) None of these

Solution: Total CP per shirt = 215 + 1400/160 + 1.75 + 320/160 = Rs. 227.5   SP = CP[(100 + profit%)/100]   = 227.5 * [(100 + 20)/100] = Rs. 273.   ANSWER:Rs. 273
Answer: C
Three candidates contested an election and received 45990, 20008 and 34884 votes respectively. What percentage of the total votes did the winning candidate get ?  Pick one:
A) 57.25%	B) 45.54%	C) 75.20%	D) 45.59%	E) 58%

Solution: Explanation :   Total number of votes polled = (45990 + 20008 + 34884 )   = 61200.   Required percentage = (45990/ 100882) x 100%   = 45.59%.   Answer : 45.59%
Answer: D
The number of stamps that P and Q had were in the ratio of 5:3 respectively. After P gave Q 10 stamps, the ratio of the number of P's stamps to the number of Q's stamps was 9:7. As a result of the gift, P had how many more stamps than Q?  Pick one: A) 20 B) 30 C) 40 D) 60 E) 90

Solution: P started with 5k stamps and Q started with 3k stamps.   (5k-10)/(3k+10) = 9/7   35k - 27k = 160   k = 20   P has 5(20) - 10 = 90 stamps and Q has 3(20)+10 = 70 stamps.   The answer is 20.
Answer: A
the first flight out of Phoenix airport had a late departure. If the next three flights departed on-time, how many subsequent flights need to depart from Phoenix on-time, for the airport's on-time departure rate to be higher than 90%?
Select the correct option.
A) 6
B) 7
C) 9
D) 10
E) 11

Solution: We need on-time departure rate to be higher than 9/10, so it should be at least 10/11 which means that 10 out of 11 flights must depart on time. Since for now 3 out of 4 flights departed on time then 10−3=7 subsequent flights need to depart on-time.   Answer: 7
Answer: B
If the sum of a number and its square is 20, what is the number? Select
A) 15	B) 26	C) 28	D) 4	E) none of these

Solution: Let the number be x. Then,   x + x2 = 20   (x + 5)(x - 4) = 0   x = 4   ANSWER:4
Answer: D
If population of certain city increases at the rate of 5%. If population in 1981 was 370440, then population in 1978 was?
Choose the correct choice from the following answers:
A) 320000 B) 120029 C) 187899 D) 178968 E) 789698

Solution: X * (105/100) * (105/100) * (105/100) = 370440   X = 370440/1.157625= 
370440/1.157625 = 320_000
320000   320000nswer:320000
Answer: A
Set Q consists of the following five numbers: Q = {5, 8, 13, 21, 32}. Which of the following sets has the same standard deviation as Set Q?
I. {35, 38, 43, 51, 64}
II. {10, 16, 26, 42, 68}
III. {46, 59, 67, 72, 75} Pick:
A) I only
B) III
C) IIII
D) IIIII
E) I, II,III

Solution: (1)	Multiplying all the numbers change Standard Deviation   (2)	Adding and subtracting all the numbers with the same number keeps the standard deviation same.   If you observe Set I and III are added versions of Set Q .   Set I: 5 has been added to the Set Q   Set III: Subtract each element from 80 and you would find a number there in the Set Q.   Set II: elements are multiplied by 2 and standard deviation changes.   Hence the answer is IIIII.
Answer: D
If x and y are integers and x=50y + 2, which of the following must be odd?	Choose the correct choice from the following choices:
A) none of the following
B) x + y
C) x + 2y
D) 3x-1
E) xy

Solution: x = 50y + 2, since y is integer, 50y will always be even hence 50y + 2 will be even hence x = even   you don't know whether Y is even or odd, so you need to try.   E: even * even = even ; ->not true   B: even + even = even ; > not true   C: even + 2*even = even ;   none of the following
Answer: A
During the past week, a local medical clinic tested N individuals for two infections. If 1/2 of those tested had infection A and, of those with infection A, 1/6 also had infection B, how many individuals did not have both infection A and B?  Select the correct option: A) N/12 B) 4N/15 C) 14N/12 D) 11N/12 E) 4N/5

Solution: 1/3 of tested had infection A, thus N/2 had infection A;   Of those with infection A, 1/6 also had infection B, thus 1/2*N/6 = N/12 had both infections A and B.   Therefore, N - N/12 = 11N/12 did not have both infection A and B.   Answer: 11N/12.
Answer: D
A and B invests Rs.8000 and Rs.9000 in a business. After 4 months, A withdraws half of his capital and 2 months later, B withdraws one-third of his capital. In what ratio should they share the profits at the end of the year?
Choose the correct option
A) 32:45 B) 32:37 C) 32:41 D) 32:47 E) 32:48

Solution: 32:45 : B   (8000*4)+(4000*8) : (9000*6)+(6000*6)   64000 : 90000   32 : 45   32:45nswer: 32:45
Answer: A
If 4<x<8<y<12, then what is the greatest possible positive integer difference of x and y? Choose the correct choice from the following:
A) 3
B) 4
C) 5
D) 6
E) 7

Solution: Let x=4.1 and y=11.1   Greatest possible difference=11.1-4.1= 
11.1-4.1 = 7
7   Answer 7
Answer: E
Two pipes A and B can separately fill a cistern in 60 minutes and 75 minutes respectively. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 50 minutes. In how much time, the third pipe alone can empty the cistern? Choose the correct option
A) 90 min	B) 100 min	C) 110 min	D) 120 min	E) None

Solution: Solution   Work done by the third pipe in 1 min.	= 1/50 - (1/60+1/75)   = (1/50 - 3/100)   = -1/100.   Therefore, the third pipe alone can empty the cistern in 100 min.   Answer 110 min
Answer: C
A shop has 3000 cycles. It sells 10% of the cycles daily. How many cycles remain after 2 days?  Choose the correct choice from the following choices.
A) 2500 B) 2600 C) 2450 D) 2430 E) 2250

Solution: Formula :   ( After =100 denominator   Ago = 100 numerator)   3000 Ã— 90/100 Ã— 90/100 = 2430   2430
Answer: D
By selling 33 metres of wire, a shopkeeper gains the price of 11 metres of wire. His gain per cent is	Choose the correct choice.
A) 7%  B) 50%  C) 20%  D) 22%  E) 32%

Solution: Suppose S.P of 33 meters of cloth = Rs 33   Therefore, Gain = Rs 11 => C.P = Rs 22   Gain % = 11/22 x 100 = 50%   Gain = 50%   ANSWER:50%
Answer: B
For each month of a given year except December, a worker earned the same monthly salary and donated one-tenth of that salary to charity. In December, the worker earned N times his usual monthly salary and donated one-fourth of his earnings to charity. If the worker's charitable contributions totaled one-eighth of his earnings for the entire year, what is the value of N?
Select the correct option:	A) 8/5	B) 5/2	C) 3	D) 22/10	E) 4

Solution: Let monthly salary for each of the 11 months except 22/10ecember was x, then   11x*1/10 + Nx*1/4 = 1/8(11x + Nx);   11/10 + N/4 = 1/8(11 + N) => 44+10N/40= 11+N/8   352+80N = 440+40N => 40N = 88   N =88/40 =22/10   Answer: 22/10.
Answer: D
A clock is set right at 5 a.m. The clock loses 16 minutes in 24 hours.What will be the true time when the clock indicates 10 p.m. on 4th day? Choose the correct answer.
A) 11 B) 66 C) 88 D) 55 E) 18

Solution: Time from 5 am. on a day to 10 pm. on 4th day = 89 hours.   Now 23 hrs 44 min. of this clock = 24 hours of correct clock.   356/15 hrs of this clock = 24 hours of correct clock   89 hrs of this clock = (24 x 31556 x 89) hrs of correct clock.   = 90 hrs of correct clock.   So, the correct time is 11 p.m.   11nswer: 11) 11pm
Answer: A
A parking garage rents parking spaces for $15 per week or $30 per month. How much does a person save in a year by renting by the month rather than by the week? Select:	A) $140	B) $160	C) $220	D) $420	E) $260

Solution: 10$ per week!   An year has 52 weeks.   Annual charges per year = 52* 15= 
52* 15 = 780
780$   30$ per month!   An year has 12 months.   Annual charges per year= 12 * 30= 
12 * 30 = 360
360$    780 - 360= 
 780 - 360 = 420
420   Ans $420
Answer: D
3, k, 20, m, 4, n
In the list above, k, m, and n are three distinct positive integers and the average (arithmetic mean) of the six numbers in the list is 8. If the median of the list is 6.5, which of the following CANNOT be the value of k, m, or n ?  Choose the correct choice from the following answers.
A) 9
B) 8
C) 7
D) 6
E) 5

Solution: Since median is 6.5, the first options I will try are 6 and 7 - two numbers will be eliminated if I can find a case where this works.   3, 4, 6, 7, 20 - the avg of these numbers is 8. If the last number is also 8, the mean will remain 8 as desired. So in fact, we eliminated 3 options here. k, m and n can be 6, 7 and 8.   Let's try 5 now, not 9 because 9 is more complicated. 9 gives us two number less than 6.5 and 2 more than 6.5. So there will be many different options. If instead 5 is in the list, we now have 3 numbers less than 6.5, so the other 3 numbers must be greater than 6.5 and the average of one of those numbers with 5 must be 6.5. So the fourth number should be 8 on the list to give the median 6.5. These 5 numbers (3, 4, 5, 8, 20) give an average of 8. The sixth number must be 8 to keep the average 8 but numbers must be distinct. So this is not possible. Hence none of k, m and n can be 5.   Answer (5)
Answer: E