MU-NLPC/Calc-aqua_rat huggingface dataset:
If a certain toy store's revenue in November was 2/5 of its revenue in December and its revenue in January was 1/3 of its revenue in November, then the store's revenue in December was how many times the average (arithmetic mean) of its revenues in November and January?	Choose the correct choice from the following choices:
A) 5/3	B) 5/4	C) 10/3	D) 15/4	E) 15/2

Solution: N = 2D/5   J = N/3 = 2D/15   The average of November and January is (N+J)/2 = 8D/15 / 2 = 4D/15   D is 15/4 times the average of November and January.   The answer is 15/4.
Answer: D
If x≠6 and (x^2 - 36)/(2y) = (x - 6)/4, then in terms of y, x = ?
Choose the correct choice from the following
A) (y - 6)/2  B) (y - 3)/2  C) y - 3  D) (y - 12)/2  E) (y + 6)/2

Solution: Since (x^2 – 36)=(x-6)(x+6) the original equation can be changed into 4*(x-6)(x+6) = 2y *(x-6).   By cancelling 2(x-6) (we can do it because x≠6) we get :   2*(x+6)=y.   So x=(y-12)/2. So the answer is (y - 12)/2).
Answer: D
How many 4 digit odd numbers do not use any digit more than once  Choose the correct answer
A) 1720  B) 2160  C) 224  D) 2460  E) None of these

Solution: The Way i solved it is   A B C D ( thousand , hundreds, tens, units)   D can be 1 3 5 7 9 ( any of the 5 digits )   A can be anything except (D or 0) so 8 possibilities   C can be anything execpt A and B so 8 possibilities   B can be anything execpt ( A D C ) so 7 possibilities   total ways are   8 * 7 * 8 * 5= 
  8 * 7 * 8 * 5 = 2_240
2240   Ans None of these
Answer: E
A and B walk around a circular track. They start at 8 a.m. from the same point in the opposite directions. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other before 9.30 a.m. ? Choose one.
A) 5	B) 6	C) 8	D) 7	E) 9

Solution: Relative speed = 2 + 3= 
2 + 3 = 5
5 rounds per hour.   So, they cross each other 5 times in an hour and 2 times in half an hour.   Hence, they cross each other 7 times before 9.30 a.m.   ANSWER:7
Answer: D
In a colony of 70 residents, the ratio of the number of men and women is 4:3. Among the women, the ratio of the educated to the uneducated is 1:4. If the ratio of the number of education to uneducated persons is 8:27, then find the ratio of the number of educated and uneducated men in the colony?	Choose one:	A) 1:9	B) 1:6	C) 1:3	D) 1:1	E) 1ratio 3

Solution: Number of men in the colony = 4/7 (70) = 40   Number of women in the colony = 3/7 (70) = 30   Number of educated women in the colony = 1/5 (30) = 6   Number of uneducated women in the colony = 4/5 (30) = 24   Number of educated persons in the colony = 8/35 (70) = 16   As 6 females are educated, remaining 10 educated persons must be men.   Number of uneducated men in the colony = 40 - 10= 
40 - 10 = 30
30   Number of educated men and uneducated men are in the ratio 10:30=> 1:3   Answer: 1ratio 3
Answer: E
The population of a town increase annually by 20% . If the present population is 2,00,000, then what is the difference in population after two years and three years  Choose the most appropriate option:
A) 63,250 B) 48,800 C) 60,800 D) 57,600 E) 67,600

Solution: M .F for 2Yrs = 120/100*120/100 =36/25   M .F for 3Yrs =120/100*120/100*120/100 =6/5*6/5*6/5 =216/125   Population after 2Yrs = 2,00,000*36/25 = 2,88,000   Population after 3 Yrs = 2,00,000*216/125 = 3,45,600   57,600ifference = 3,45,600 – 2,88,000 =57,600   ANSWER:57,600
Answer: D
A shopkeeper sold an article offering a discount of 5% and earned a profit of 23.5%. What would have been the percentage of profit earned if no discount had been offered?  Choose the correct choice from the following answers:
A) 28.5 B) 27.675 C) 30 D) Data inadequate E) None of these

Solution: Giving no discount to customer implies selling the product on printed price. Suppose the cost price of the article is 100.   Then printed price = 100×(100+23.5)/(100−5)   = 100×247/190=130   Hence, required % Profit = 130 – 100 = 30%   Answer 30
Answer: C
The C.P of 8 books is equal to the S.P of 16 books. Find his gain% or loss%?
Choose the most appropriate option
A) 60% B) 50% C) 70% D) 90% E) 55%

Solution: explanation:   8 CP = 16 SP   16 --- 8 CP loss   100 --- ? => 50% loss   Answer: 50%
Answer: B
A train is running at a speed of 4040 km/hr and it crosses a post in 1818 seconds. What is the length of the train? Choose the correct choice from the following answers
A) 190 metres	B) 160 metres	C) 200 metres	D) 120 metres	E) 150 metres

Solution: Explanation:   Speed =40 km/hr =40 km/hr =40Ã—518=1009 m/s=40Ã—518=1009 m/s   Time =18=18 seconds   Distance 200 metresovered =1009Ã—18=200 m=1009Ã—18=200 m   Therefore, length of the train =200 m   ANSWER IS 200 metres
Answer: C
You are given with two ropes with variable width. However if we start burning both the ropes, they will burn at exactly same time i.e. an hour. The ropes are non-homogeneous in nature. You are asked to measure 45 minutes by using these two ropes.
How can you do it?
Please note that you can’t break the rope in half as it is being clearly stated that the ropes are non-homogeneous in nature.	Options:
A) 45 minutes B) 40 minutes C) 35 minutes D) 55 minutes E) 60 minutes

Solution: A   45 minutes   All you have to do is burn the first rope from both the ends and the second rope from one end only simultaneously. The first rope will burn in 30 minutes (half of an hour since we burned from both sides) while the other rope would have burnt half. At this moment, light the second rope from the other end as well. Where, the second rope would have taken half an hour more to burn completely, it will take just 15 minutes as we have lit it from the other end too.   Thus you have successfully calculated   30+15= 
  30+15 = 45
45 minutes with the help of the two given ropes.
Answer: A
The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres?  Choose the correct choice from the following answers.
A) 23	B) 27	C) 28	D) 12	E) 25

Solution: Speed of the boat downstream = 15 + 3= 
15 + 3 = 18
18 kmph= 18 * 5/18= 
18 * 5/18 = 5
5 m/s   Hence time taken to cover 60 m= 60/5= 
60/5 = 12
12 seconds.   Answer:12
Answer: D
List K consists of 12 consecutive integers. If -3 is the least integer in list K, what is the range of the positive integers in list K? Choices: A) 5 B) 6 C) 7 D) 11 E) 12

Solution: Answer = 7 =7   If least = -3, then largest = 8   Range = 8 - 1= 
8 - 1 = 7
7
Answer: C
A train running at the speed of 162 km/hr crosses a pole in 9 seconds. Find the length of the train. Choices: A) 150 meter B) 286 meter C) 186 meter D) 405 meter E) 265 meter

Solution: Speed = 162*(5/18) m/sec   = 45 m/sec   Length of Train (405 meteristance)   = Speed * Time     (45) * 9= 
  (45) * 9 = 405
405 meter   Answer:405 meter
Answer: D
Which of these following integers is the square of an integer?
Select the correct option
A) 49981101542
B) 49206101137
C) 49471101241
D) 49859101723
E) 49323101988

Solution: The unit digit of any perfect square can not be 2, 3, 7, or 8.   The answer is 49471101241.
Answer: C
A soccer store typically sells replica jerseys at a discount of 60 percent to 50 percent off list price. During the annual summer sale, everything in the store is an additional 20 percent off the original list price. If a replica jersey's list price is $80, approximately what percent of the list price is the lowest possible sale price? Choose the correct choice from the following answers:  A) 20  B) 25  C) 30  D) 40  E) 50

Solution: Let the list price be 2x   for min sale price, the first discount given should be 50%, 2x becomes x here   now, during summer sale additional 20% off is given ie sale price becomes 0.8x   it is given lise price is $80   => 2x = 80   => x = 50   and 0.8x = 32   so lowest sale price is 32, which is 40% of 80   hence, 50 is the answer
Answer: E
A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 36 hrs and a machine of type S does the same job in 18 hours. If the company used the same number of each type of machine to do the job in 3 hours, how many machines of type R were used? Choose the correct choice.
A) 3  B) 4  C) 6  D) 9  E) 12

Solution: Rate of machine R = 1/36   Rate of machine S = 1/18   Rate of R+S = 1/12   To finish the work in 3 hrs, the combined rate needs to be 1/3.   x * 1/12 = 1/3   x = 4   The answer is 4.
Answer: B
One-seventh of the light switches produced by a certain factory are defective. Four-fifths of the defective switches are rejected and 1/15 of the non defective switches are rejected by mistake. If all the switches not rejected are sold, what percent of the switches sold by the factory are defective?	Choose the correct choice from the following answers:
A) 2.3%
B) 3.4%
C) 4.5%
D) 5.6%
E) 6.7%

Solution: 1/7 of the switches are defective.   The defective switches that are not rejected are 1/5*1/7 = 1/35 = 3/105 of all switches.   The non defective switches that are sold are 6/7*14/15 = 84/105 of all switches.   The percent of switches sold that are defective is 3/87 which is about 3.4%.   The answer is 3.4%.
Answer: B
Find large no. from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 30 as remainder  Choose the correct choice from the following answers:
A) 1235	B) 1456	C) 1567	D) 1632	E) 1635

Solution: Let the smaller number be x. Then larger number = (x + 1365).   x + 1365 = 6x + 30   5x = 1335   x = 267   Large number = 267+1365= 
267+1365 = 1_632
1632   1632
Answer: D
The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 75 sq. cm. Find the length of the rectangle. Answers:	A) 10 cm	B) 20 cm	C) 30 cm	D) 40 cm	E) 50 cm

Solution: Let breadth = x. Then, length = 2x. Then,   (2x - 5) (x + 5) - 2x * x = 75 <=> 5x - 25 = 75 <=> x = 20.   :. Length of the rectangle = 20 cm.   ANSWER 20 cm 20 cm
Answer: B
A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 150 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?  Pick
A) 39  B) 27  C) 36  D) 88  E) 12

Solution: Speed of train relative to jogger = 45 - 9= 
45 - 9 = 36
36 km/hr.= 36 * 5/18= 
36 * 5/18 = 10
10 m/sec.   Distance to be covered= 240 + 150= 
240 + 150 = 390
390 m.   Time taken= 390/10= 
390/10 = 39
39 sec.   39nswer: 39
Answer: A
Stacy and Heather are 20 miles apart and walk towards each other along the same route. Stacy walks at constant rate that is 2 mile per hour faster than heather's constant rate of 5 miles/hour. If Heather starts her journey 24 minutes after Stacy, how far from the original destination has Heather walked when the two meet?  Choose the correct choice from the following options.
A) 5miles
B) 7 miles
C) 9 miles
D) 10 miles
E) 12 miles

Solution: Original distance between S and H = 20 miles.   Speed of S = 5+2= 
5+2 = 7
7 mph, Speed of H= 5 mph.   Time traveled by H = t hours ---> time traveled by S = t+24/60 = t+2/5 hours.   Now, the total distances traveled by S and H = 20 miles ---> 7*(t+2/5)+5*t=20 ---> t= 86/60 hours. Thus H has traveled for 86/60 hours giving you a total distance for H = 5*86/60 = 7 miles.   B is thus the correct answer.   P.S.: based on the wording of the question, you should calculatehow far from theoriginal destination has Heather walkedwhen the two meet. 'Original destination' for H does not make any sense. Original destination for H was situated at a distance of 20 miles.
Answer: B
Two interconnected, circular gears travel at the same circumferential rate. If Gear A has a diameter of 80 centimeters and Gear B has a diameter of 50 centimeters, what is the ratio of the number of revolutions that Gear A makes per minute to the number of revolutions that Gear B makes per minute?
Choose the correct option.
A) 8:5  B) 9:25  C) 5:8  D) 25:9  E) Cannot be determined from the information provided

Solution: Same circumferential rate means that a point on both the gears would take same time to come back to the same position again.   Hence in other words, time taken by the point to cover the circumference of gear A = time take by point to cover the circumference of gear B   Time A = 2*pi*25/Speed A   Time B = 2*pi*40/Speed B   Since the times are same,   50pi/Speed A = 80pi/Speed B   SpeedA/Speed B = 50pi/80pi = 5/8   5:8orrect Option: 5:8
Answer: C
By using the numbers 1, 2, 3, 5 and 7 only once, how many five digit numbers can be made that are divisible by 20?	Options
A) Not possible	B) 9	C) 4	D) 6	E) 8

Solution: A number to be divisible by 50 must end with 00 or 50.   So, not possible.   Not possiblenswer: Not possible.
Answer: A
Kamal obtained 76, 60, 82, 67 and 85 marks(out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
Choose the correct choice from the following:
A) 65
B) 69
C) 74
D) 75
E) NOne

Solution: Sol.   Average   = 76 + 60 + 82 + 67 + 85 / 5)   = (375 / 5)   = 74.   Answer 74
Answer: C
Tom wants to buy items costing $25.35, $50.69, and $95.96. He earns $6.50 an hour doing
odd jobs. If ten percent of his income is put aside for other purposes, how many hours must he
work to earn the money he needs for his purchases? Round your answer to the nearest whole
hour. Select the correct option:  A) 29 hours  B) 48 hours  C) 38 hours  D) 18 hours  E) 28 hours

Solution: $6.50 x .10 = $.65 is 10% of his hourly income   $  6.50 - .65= 
  6.50 - .65 = 5.85
$5.85 hourly amount available to spend   $25.35 + $50.69 + $95.96 = $172 total needed   $172 ÷ $5.85  25.35 +  50.69 +  95.96= 
 25.35 +  50.69 +  95.96 = 172
$172 total needed   $172 ÷ $5.85= 29.4... rounds to 29 hours   correct answer 29 hours
Answer: A
A sum of money is to be distributed among A, B, C, D in the proportion of 5:2:4:3. If C gets Rs. 500 more than D, what is B's share?  Options:
A) A)8239
B) B)2900
C) C)1000
D) D)2393
E) E)2009

Solution: Let the shares of A, B, C and D be 5x, 2x, 4x and 3x Rs. respectively.   Then, 4x - 3x = 500 => x = 500.   B's share = Rs. 2x = 2 * 500 = Rs. 1000.   Answer: 1000
Answer: C
If a square and a rhombus stand on the same base, then the ratio of the areas of the square and the rhombus is:	Choose the correct choice from the following choices
A) 1:1
B) 1:2
C) 1:3
D) 1:4
E) 1:6

Solution: 1:1 square and a rhombus on the same base are equal in area 1:1nswer: 1:1
Answer: A
500 is increased by 30%. Find the final number.  Options:
A) 550
B) 500
C) 650
D) 600
E) 700

Solution: ExplanationFinal number = Initial number + 30%(original number) = 500 + 30%(500) = 500 + 150= 
500 + 150 = 650
650.Answer 650
Answer: C
Find the cost of fencing around a circular field of diameter 28 m at the rate of Rs.1.50 a meter?	Choose the correct option
A) 288  B) 132  C) 772  D) 592  E) 261

Solution: 2 * 22/7 * 14= 
2 * 22/7 * 14 = 88
88   88 * 1 1/2= Rs.132   Answer: 132
Answer: B
If the President and Vice President must sit next to each other in a row with 4 other members of the Board, how many different seating arrangements are possible?	Choose the correct choice from the following options
A) 120  B) 240  C) 300  D) 360  E) 720

Solution: We need to take President and VP as one unit. Therefore we have 5 people to arrange=5! ways   Also, we both President and VP can be arranged in 2 ! ways.   Reqd no of ways=5!*2!=240 ways   Answer 240
Answer: B
Find the average of first 10 natural numbers.	Choices
A) A)10.5	B) B)9.9	C) C)7.5	D) D)6.6	E) E)5.5

Solution: Sum of first n natural numbers = n(n+1)/2   sum of first 10 natural numbers = 10*11/2= 
10*11/2 = 55
55   average= 55/10= 
55/10 = 11/2 = around 5.5
5.5   Answer is 5.5
Answer: E
A store sells four different kinds of shirts. If we want to buy two different kinds of shirts, how many possible combinations of two shirts can we buy?	Select the correct option:
A) 5
B) 6
C) 7
D) 8
E) 9

Solution: 4C2=6.   The answer is 6.
Answer: B
A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
Choose the most appropriate option:
A) 30  B) 35  C) 36  D) 37  E) 38

Solution: Speed of train relative to jogger = 45 - 9= 
45 - 9 = 36
36 km/hr.= 36 * 5/18= 
36 * 5/18 = 10
10 m/sec.   Distance to be covered= 240 + 120= 
240 + 120 = 360
360 m.   Time taken= 360/10= 
360/10 = 36
36 sec.   Answer: Option 36
Answer: C
A train covers a distance of 12 km in 5 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?	Choose the most appropriate option
A) 120m
B) 180m
C) 240m
D) 220m
E) 280m

Solution: Speed = (12/5 * 60) km/hr = (144 * 5/18) m/sec = 40 m/sec.   Length of the train = 40 * 6= 
40 * 6 = 240
240 m.   ANSWER:240m
Answer: C
The prime sum of an integer n greater than 1 is the sum of all the prime factors of n, including repetitions. For example , the prime sum of 12 is 7, since 12 = 2 x 2 x 3 and 2 +2 + 3 = 7. For which of the following integers is the prime sum greater than 36 ? Select the correct option:
A) 440
B) 512
C) 550
D) 620
E) 750

Solution: Large numbers are made in two ways:   Either by taking small prime numbers and raising them to higher powers or taking large prime numbers in the first place.   31*2= 
31*2 = 62
62 (large prime number)   2^6= 64 (many small prime numbers)   To get a sum as large as 36 or more, you would need some large prime numbers. So options such as 512, 700 and 750 which have small prime numbers as factors should be ignored first. 440 also splits into 11, 4( which is 2*2), 2, 5 - relatively small prime numbers.   You are left with 620 which is 31*2*2*5 (sum greater than 36)   Answer (620)
Answer: D
Two years ago, Arthur gave each of his five children 20 percent of his fortune to invest in any way they saw Fit. In the first year, three of the children, Alice, Bob, and Carol, each earned a profit of 50 percent on their Investments, while two of the children, Dave and Errol, lost 40 percent on their investments. In the second Year, Alice and Bob each earned a 30 percent profit, Carol lost 60 percent, Dave earned 25 percent in profit, And Errol lost all the money he had remaining. What percentage of Arthur's fortune currently remains?  Choose the correct choice from the following answers.
A) 93%  B) 97%  C) 100%  D) 105%  E) 120%

Solution: Say Arthur's fortune was $100. Then:   A = 20*1.5*1.3= 
20*1.5*1.3 = 39
39   B= 20*1.5*1.3= 
20*1.5*1.3 = 39
39   C= 20*1.5*0.4= 
20*1.5*0.4 = 12
12   D= 20*0.6*1.25= 
20*0.6*1.25 = 15
15   E= 0   Total 39 + 39 + 12 + 15= 
39 + 39 + 12 + 15 = 105
105.   Answer: 105%.
Answer: D
How many words can be formed from the letters of the word ‘DIRECTOR’ So that the vowels are always together?  Choose the correct choice from the following:
A) 2160
B) 2162
C) 2161
D) 2163
E) 2134

Solution: In the given word, we treat the vowels IEO as one letter.   Thus, we have DRCTR (IEO).   This group has 6 letters of which R occurs 2 times and others are different.   Number of ways of arranging these letters = 6!/2! = 360.   Now 3 vowels can be arranged among themselves in 3! = 6 ways.   Required number of ways = (360x6) = 2160.   2160nswer 2160.
Answer: A
At a restaurant, glasses are stored in two different-sized boxes. One box contains 12 glasses, and the other contains 16 glasses. If the average number of glasses per box is 15, and there are 16 more of the larger boxes, what is the total number of glasses R at the restaurant? (Assume that all boxes are filled to capacity.) Choose the correct choice:
A) 96 B) 240 C) R=256 D) R=384 E) R=480

Solution: Most Test Takers would recognize thesystemof equations in this prompt and just do algebra to get to the solution (and that's fine). The wording of the prompt and the 'spread' of the answer choices actually provide an interesting 'brute force' shortcut that you can take advantage of to eliminate the 4 wrong answers....   We're told that there are 2 types of boxes: those that hold 12 glasses and those that hold 16 glasses. Since the AVERAGE number of boxes is 15, we know that there MUST be at least some of each. We're also told that that there are 16 MORE of the larger boxes.   This means, at the minimum, we have...   1 small box and 17 large boxes = 1(12) + 17(16) = 12 + 272= 
12 + 272 = 284
284 glasses at the MINIMUM   Since the question asks for the total number of glasses, we can now eliminate Answers A, B and C....   The difference in the number of boxes MUST be 16 though, so we could have....   2 small boxes and 18 large boxes   3 small boxes and 19 large boxes   etc.   With every additional small box + large box that we add, we add   12+16= 
  12+16 = 28
28 MORE glasses. Thus, we can justadd 28suntil we hit the correct answer....   284+28= 
284+28 = 312
312   312+28= 
312+28 = 340
340   340+28= 
340+28 = 368
368   368+28= 
368+28 = 396
396   At this point, we've 'gone past' Answer D, so the correct answer MUST be Answer E.....But here's the proof....   396+28= 
396+28 = 424
424   424+28= 
424+28 = 452
452   452+28= 
452+28 = 480
480   Final Answer:   R=480
Answer: E
There are 9 teams in a certain league and each team plays each of the other teams exactly twice. If each game is played by 2 teams, what is the total number of games played?  Choose the correct option
A) 15  B) 16  C) 28  D) 56  E) 72

Solution: Every team plays with 8 teams...so total no of matches = 9 x 8 = 72.   Now, each match is played twice => 72 x 2   But 2 teams play a match => 72 x 2 /2 = 72.   Answer: 72
Answer: E
A factory that employs 1000 assembly line workers pays each of these workers $5 per hour for the first 40 hours worked during a week and 1½ times that rate for hours worked in excess of 40. What was the total payroll for the assembly-line workers for a week in which 30 percent of them worked 25 hours, 50 percent worked 40 hours, and the rest worked 50 hours?	Answers
A) $180,000
B) $185,000
C) $180,000
D) $200,000
E) $192,500

Solution: 30% of 1000 = 300 worked for 20 hours   Payment @ 5/hr   Total Payment = 300*25*5= 
300*25*5 = 37_500
37500   50 % of 1000= 500 worked for 40 hours   Payment @ 5/hr   Total payment = 500*40*5= 
500*40*5 = 100_000
100000   Remaining 200 worked for 50 Hours   Payment for first 40 Hours @ 5 /hr   Payment= 200*40*5= 
200*40*5 = 40_000
40000   Payment for next 10 hr @ 7.5/hr   Payment= 200 * 10 * 7.5= 
200 * 10 * 7.5 = 15_000
15000   Total Payment= 37500+100000 + 40000 +15000= 
37500+100000 + 40000 +15000 = 192_500
192500   Hence , answer is $192,500
Answer: E
The instructions state that Deepthi needs 4/17 square yards of one type of material and 3/10 square yards of another type of material for a project. She buys exactly that amount. After finishing the project, however, she has 9/30 square yards left that she did not use. What is the total amount of square yards of material Deepthi used?  Pick:
A) 1/12
B) 4/17
C) 2/3
D) 1 1/9
E) 2 1/9

Solution: Total bought = 4/17+3/10   left part 9/30--->3/10   so used part 4/17+3/10-3/10=4/17   ANSWER:4/17
Answer: B
A dishonest dealer uses a scale of 85 cm instead of a metre scale and claims to sell at cost price. His profit is	Pick.
A) 17.65%
B) 10%
C) 12%
D) None of these
E) Cannot be determined

Solution: Solution   Gain%	= (15 / 85 x 100)%   = 17.65%   17.65%nswer 17.65%
Answer: A
If 42.12 = k(14 + m/50), where k and m are positive integers and m < 50, then what is the value of k + m ?  Choices.
A) 5 B) 7 C) 8 D) 9 E) 10

Solution: 42.12 = 14K + Km/50...we can rewrite the number as follows:   42+ 0.12= 14K + Km/50........Since K is integer, then 42=14K..........K=3   0.12=Km/50......12/100=3m/50......m=2   k+m=3+2= 
3+2 = 5
5   5nswer: 5
Answer: A
(68-a)(68-b)(68-c)(68-d)(68-e)=725.wat is the value of a+b+c+d?
Options:	A) 230	B) 231	C) 232	D) 233	E) 234

Solution: factors of 725= 5,5 29   so (68-63)= 
(68-63) = 5
5 ,(68-63)=5,(68-39)=29, (68-67)=1 ,(69-67)=1   so a+b+c+d= 232   ANSWER:232
Answer: C
If the integer n has exactly four positive divisors, including 1 and n, how many positive divisors does n^2 have?  Choose the correct choice.
A) 4 B) 5 C) 6 D) 8 E) 9

Solution: take the example of 6...   it has 4 positive divisors (1,2,3,4)   Now, take the example of 36...   it has only 9 divisors..   so 9 is the ans
Answer: E