MU-NLPC/Calc-aqua_rat huggingface dataset:
The temperature of a certain cup of coffee 15 minutes after it was poured was 120 degrees Fahrenheit. If the temperature F of the coffee t minutes after it was poured can be determined by the formula F = 120*2^(-at) + 60, where F is in degrees Fahrenheit and a is a constant. Then the temperature of the coffee 30 minutes after it was poured was how many degrees Fahrenheit?	Choose the correct choice from the following
A) 65  B) 75  C) 80  D) 85  E) 90

Solution: First, we have to find a.   We know that after t=15 minutes the temperature F=120 degrees.   Hence:   120 = 120*(2^-15a)+60   60 = 120*(2^-15a)   60/120 = 2^-15a   1/2 = 2^-15a   2^-1 = 2^-15a   -1 = -15a   1/15 = a   Now we need to find F after t=30 minutes:   F = 120*(2^-1/15*30)+60   F = 120* (2^-2) +60   F = 120* (1/2^2) +60   F = 120*1/4 +60   F = 30+60= 
30+60 = 90
90   Answer 90!
Answer: E
A certain series is defined by the following recursive rule: Sb=K(Sb-1) , where k is a constant. If the 1st term of this series is 64 and the 25th term is 192, what is the 9th term?
Choices:
A) ROOT 2  B) ROOT 3  C) 64*ROOT 3  D) 64*3^1/3  E) 64*3^24

Solution: Ans...D   No need for any GP formula here   The rule is that bth term is K times the (b-1)th term.   1st = 64   2nd = k.64   3rd = k^2.64   .   .   .   9th term = k^8 *64   .   .   .   so 25th = k^24*64   Using this solve for k and substitute k in the equation for the 9th term
Answer: D
1903 x 1903 = ?	Answers:
A) A)3623216
B) B)3624216
C) C)3624316
D) D)3621409
E) E)3625216

Solution: 1903 x 1903 = (1903)2   = (1900 + 3)2   = (1900)2 + (3)2 + (2 x 1900 x 3)   = 3610000 + 9 + 11400.= 
3610000 + 9 + 11400. = 3_621_409
3621409.   3621409)
Answer: D
To make 552185 divisible by 8, what is the least whole number that should be added to it?  Choose the correct option
A) 3
B) 7
C) 9
D) 6
E) 4

Solution: A number is divisible by 8 if the number formed by the last three digits is divisible by 8.   Here, 552185=185(no formed by last three digit)   the next multiple of 8 is 192   7 must be added to 552185 to make it divisible by 8   7
Answer: B
Two horses begin running on an oval course at the same time. One runs each lap in 9 minutes; the other takes 18 minutes to run each lap. How Many minutes after the start will the faster horse have a one lap lead?  Choices:  A) 36  B) 18  C) 9  D) 4  E) 3

Solution: The rate of the faster horse is 1/9 lap/minute;   The rate of the slower horse is 1/18 lap/minute;   Their relative rate is 1/9-1/18=1/18 lap/minute;   The faster horse to gain one full lap will need time=distance/rate=1/(1/18)= 
1/(1/18) = 18
18 minutes.   Answer: 18
Answer: B
45 girls and 60 boys are present at a party. There are 17 girl-boy are in relationship among them. If a girl and a boy is selected at random, what is the probability that they will be not a couple? Pick one:
A) 17/ 2900	B) 2683/2700	C) 2496/2700	D) 2369/2700	E) 198/270

Solution: In how many ways we can select a girl and a boy from 45 lady and 60 gentlemen? In 45*60 = 2,700 ways.   We have a total of 17 couples so, the probability of selecting a couple is 17/2,700 = 17/2700.   Probability of there will not be a couple = 1 - (17/2700)   = 2683 / 2700   Ans- 2683/2700
Answer: B
For what value(s) of k is the following equation satisfied: 3k-9-2k = 5k+6-4k Choose the correct choice from the following choices:
A) a. -5	B) b. 0 only	C) c. 5/2 only	D) d. No value	E) e. Any value

Solution: 3k-9-2k = 5k+6-4k   k - 9 = k + 6   -9 = 6, which is false.   So, no k satisfies given equation.   Answer: d. No value.
Answer: D
A 270 m long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds.What is the length of the other train?
Answers
A) 230 m
B) 240 m
C) 260 m
D) 320 m
E) 350 m

Solution: speed of first train= (120 * 5/18)m/sec   = 100/3 m/sec   speed of other Train= (80 * 5/18)m/sec   = 200/9 m/sec   time to cross each other= 9 sec   Let x be the length of 2nd train   therefore 9 = (270+ x)/(100/3 +200/9)   500 = 270 + x   230m = x   230 mNSWER:230 m
Answer: A
A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?  Choose the correct choice from the following choices:
A) 328
B) 375
C) 279
D) 269
E) 276

Solution: CP1 = 100 SP1 = 120   CP2 = 80 SP2 = 80 * (125/100)= 
80 * (125/100) = 100
100   20 ----- 100   75 ----- ?=> 375   Answer: 375
Answer: B
Dhoni rented a power tool from a rental shop. The rent for the tool was $10 for the first hour and $4 for each additional hour. If Dhoni paid a total of $38, excluding sales tax, to rent the tool, for how many hours did she rent it?	Choose the correct answer:
A) 6 B) 10 C) 12 D) 13 E) 8

Solution: 10 + 4n = 38   n = 7   Total time = n+1 hrs = 7+1= 
7+1 = 8
8 hrs   Answer : 8
Answer: E
What day will be 61 days after today, if today is Monday? Choose the correct choice from the following options
A) Tuesday	B) Thursday	C) Saturday	D) Friday	E) Monday

Solution: Explanation:   The basic concept in a problem involving days is finding the number of odd days. In 61 days:   => 7 x 8 + 5 = 5 odd days   => Monday + 5 days = Saturday   Hence 61 days from today will be a Saturday.   ANSWER Saturday
Answer: C
The angles of a triangle are in the ratio 1:3:8. Find the measures of the three angles of this triangle.  Options:
A) 15° ,45° ,110°  B) 15° ,45° ,130°  C) 15° ,45° ,110°  D) 15° ,35° ,110°  E) 25° ,45° ,110°

Solution: Solution   If the ratio of the three angles is 1:3:8, then the measures of these angles can be written as x, 3x and 8x. Also the sum of the three interior angles of a triangle is equal to 180°. Hence   x + 3x + 8x = 180   Solve for x   12x = 180   x = 15   The measures of the three angles are   x = 15°   3x = 3 × 15 = 45°   8x = 8 × 15 = 120°   ANSWER IS 15° ,45° ,110°
Answer: C
Rajesh can finish 1/5 of his home work in one hour. Seema can finish 3/7 of
her homework in 90 minutes and Ramya can finish 3/4 of her homework in
three and a half hours. If all of them start their home work at 12.00 PM and can
go to play as soon as they all finish their homework. When can they start to
play, if they take a break at 3.30 PM for 30 minutes?  Options.
A) 4:30pm  B) 5:30pm  C) 6:30pm  D) 5:10pm  E) 3:30pm

Solution: ajesh can finish his work in 5 hr,   ramya can finish her work in 4.7 hr   seema can finish in 3.5 hr   so 5:30pm they can go to play   ANSWER:5:30pm
Answer: B
A dealer offers a cash discount of 10% and still makes a profit of 35% when he further allows 20 articles to be sold at the cost price of 15 articles to a particular sticky bargainer. How much percent above the cost price were his articles listed?  Choose the correct choice from the following choices
A) 80%	B) 100%	C) 120%	D) 60%	E) 90%

Solution: Given   Cash Discount - 10%   Profit - 35%   Items Sold - 20   Price Sold at = List Price of 15   Assume List price = $20   Total Invoice = $300   -10% Cash Discount = $270   Let cost price of 20 items be x   So total cost = 20*x   Given the shopkeeper had a profit of 20%   20 * x * 135/100 = 270   or x = $10   Which means his products were listed at $20 which is a 100% markup over $10   Answer 100%
Answer: B
James rode his bike 5 miles against the wind in 50 minutes and back 5 miles with the wind in 25 minutes. How strong is the wind in miles/hr (mph)?
Choose the correct choice from the following options
A) 1 mph B) 2 mph C) 3 mph D) 4 mph E) 5 mph

Solution: Explanation:   speed against the wind = (5/50) X 60 = 6 mph   with the wind = (5/25) X 60 = 12 mph   strength of wind = 1/2(12 - 6) = 6/2= 
6/2 = 3
3 mph   Answer: Option 3 mph
Answer: C
A man purchased a cow for Rs. 3000 and sold it the same day for Rs. 3600,allowing the buyer a credit of 2 years. If the rate of interest be 10% per annum, then the man has a gain of :  Options
A) 0%  B) 5%  C) 7.5%  D) 10%  E) 40%

Solution: Solution   C.P. = Rs. 3000. S.P. = Rs. [ 3600x 100/100+( 10x2 ) ] = Rs. 3000   Gain = 0 %.   0%nswer 0%
Answer: A
What least value must be given to * so that the number 451*603 is exactly divisible by 9? Choose the correct choice from the following choices:
A) 2
B) 5
C) 7
D) 8
E) 9

Solution: Sum of digits=(4+5+1+x+6+0+3)=19+x divisible by 9   Clearly x(4+5+1+ +6+0+3)= 
(4+5+1+ +6+0+3) = 19
19+x divisible by 9   Clearly x=9   ANSW9R 9 9
Answer: E
List S consists of 12 consecutive integers. If -4 is the least integer in list S, what is the range of positive integers in list S?  Choose the correct answer:
A) 5 B) 6 C) 7 D) 11 E) 12

Solution: Since -4 is the least integer in list S, then 7 is the largest integer in that list. Thus the range of the positive integers in the list is   7-1= 
  7-1 = 6
6.   Answer: 6.
Answer: B
In a club with 310 peopl, 138 play tennis, 255 play baseball, and 94 people play both sports. How many people do not pla a sport? Choose the most appropriate option:
A) 9
B) 8
C) 4
D) 10
E) 11

Solution: Take 94 off the baseball players-->161   then   161 + 138= 
  161 + 138 = 299
299 play either baseball or tennis    310 - 299= 
 310 - 299 = 11
11   Answer is 11
Answer: E
David used part of $100,000 to purchase a house. Of the remaining portion, he invested 1/3 of it at 4 percent simple annual interest and 2/3 of it at 6 percent simple annual interest. If after a year the income from the two investments totaled $320, what was the purchase price of the house?
Choose the correct choice from the following answers
A) $96,000	B) $94,000	C) $88,000	D) $75,000	E) $40,000

Solution: Of all the answer choices, (A) and (D) do not offer a number divisible by 3. (E) can be eliminated easily because when you invest 1/3 of $60,000 ($20,000) @ 4% interest rate, you earn $800 interest, which is definitely more than $320. But, if you calculate 2/3 of $60,000 ($40,000) @ 6% interest rate, you earn $2400 interest. Total interest when $60,000 is the remaining amount: $800 + $2400 = $3200. We need $320. It means the remaining amount should be $6000. Therefore, ($94,000) is the answer.800 +  2400= 
800 +  2400 = 3_200
$3200. We need $320. It means the remaining amount should be $6000. Therefore, ($94,000) is the answer.
Answer: B
Sandy is younger than Molly by 8 years. If their ages are in the respective ratio of 7:9, how old is Molly? Pick
A) 18 B) 27 C) 36 D) 45 E) 54

Solution: S = M - 8   S / M = 7/9   9S = 7M   9(M-8) = 7M   M = 36   The answer is 36.
Answer: C
A dealer offers a cash discount of 16% and still makes a profit of 25% when he further allows 60 articles to be sold at the cost price of 50 articles to a particular sticky bargainer. How much percent above the cost price were his articles listed? Select: A) 50% B) 60% C) 70% D) 75% E) 78+(4/7)%

Solution: Given   Cash Discount - 16%   Profit - 25%   Items Sold - 60   Price Sold at = List Price of 50   Assume List price = $10   Total Invoice = $500   -16% Cash Discount = $420   Let cost price of 60 items be x   So total cost = 60*x   Given the shopkeeper had a profit of 25%   60 * x * 125/100 = 420   or x = $7*4/5=$28/5   Which means his products were listed at $10 which is a 78+(4/7)% markup over $28/5   Answer 78+(4/7)%
Answer: E
Rs.8000 become Rs.9261 in a certain interval of time at the rate of 5% per annum of C.I. Find the time?
Pick one:
A) 6 YEARS  B) 7  C) 5  D) 3  E) 4

Solution: Explanation:   9261 = 8000(21/20)N   (21/20)3 = (21/20)N => N = 3   Answer: Option 3
Answer: D
The two trains of lengths 400 m, 600 m respectively, running at same directions. The faster train can cross the slower train in 180 sec, the speed of the slower train is 48 km. then find the speed of the faster train?  Pick one:  A) 65  B) 68  C) 69  D) 67  E) 64

Solution: Length of the two trains = 600m + 400m   Speed of the first train = X   Speed of the second train= 48 Kmph   1000/X - 48 = 180   1000/x - 48 * 5/18 = 180   50 = 9X - 120   X = 68 Kmph   Answer: Option 68
Answer: B
A candidate got 35% of the votes and lost to the rival by 1650 votes. How many votes were cast?	Choose the correct choice from the following options
A) 5000 B) 5500 C) 6000 D) 6500 E) 7000

Solution: 35%-----------L   65%-----------W   ------------------   30% = 1650   10% = 550   100% of the votes = 5500   Answer: 5500
Answer: B
The average monthly salary of 8 workers and one supervisor in a factory was 430.@SSWhen@SSthe@SSsupervisor@CC@SSwhose@SSsalary@SSwas@SS430.@SSWhen@SSthe@SSsupervisor@CC@SSwhose@SSsalary@SSwas@SS430.Whenthesupervisor,whosesalarywas430. When the supervisor, whose salary was 870 per month, retired, a new person was appointed and then the average salary of 9 people was $$440 per month. The salary of the new supervisor is:
Choose one:
A) 233	B) 960	C) 287	D) 771	E) 191

Solution: Explanation:   Total salary of 8 workers and supervisor together = 9 Ã— 430 = 3870   Now total salary of 8 workers = 3870 âˆ’ 870 = 3000   Total salary of 9 workers including the new supervisor = 9 Ã— 440 = 3960   Salary of the new supervisor = 3960 âˆ’ 3000 = 960   Answer: 960
Answer: B
Two third of three- fifth of one fourth of a number is 24, what is 30% of that number?
Choose the most appropriate option:	A) 22	B) 72	C) 91	D) 12	E) 17

Solution: Explanation:   x * 2/3 * 3/5 * 1/4 = 24   x = 240   240 * 30/100= 
240 * 30/100 = 72
72'   Answer: 72
Answer: B
Total dinning bill for 7 people was $211.00.If they add 15% tip and divided the bill evenly ,approximate.What was each persons find share
Choose the correct option:	A) $30.14	B) 45.14	C) 34.66	D) 32.29	E) 33.16

Solution: 211*15= 
211*15 = 3_165
3165/100= 
3165/100 = 633/20 = around 31.65
31.65   211+31.65= 
211+31.65 = 242.65
242.65   242.65/7=34.66   ANSWER:34.66
Answer: C
Convert the following unit:
2.0 hectares in ares	Pick one.
A) 200 ares.  B) 210 ares.  C) 220 ares.  D) 230 ares.  E) 240 ares.

Solution: 2.0 hectares in ares   1 hectare = 100 ares   Therefore, 2.0 hectares = 2.0 × 100 ares   = 200 ares.   200 ares.NSWER : OPTION 200 ares.
Answer: A
In what time will a train 100 m long cross an electric pole, it its speed be 162 km/hr?  Choose the correct answer.
A) 2.5 sec  B) 2.8 sec  C) 8.5 sec  D) 2.2 sec  E) 4.5 sec

Solution: Speed = 162 * 5/18= 
162 * 5/18 = 45
45 m/sec   Time taken= 100/45   = 2.2 sec.   Answer:2.2 sec
Answer: D
The sum of the present ages of a father and his son is 52 years. Six years ago, father's age was four times the age of the son. After 6 years, son's age will be: Choose the correct answer.
A) 14 B) 16 C) 18 D) 20 E) 22

Solution: Let the present ages of son and father be x and (52 - x) years respectively.   Then, (52 - x) - 6 = 4(x - 6)   46 - x = 4x - 24   x = 14   The son's age after 6 years will be 20.   The answer is 20.
Answer: D
Ram sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles?
Select the correct option.
A) Rs.2000  B) Rs.2029  C) Rs.2068  D) Rs.2297  E) Rs.2025

Solution: (10*10)/100= 
(10*10)/100 = 1
1%loss   100 --- 99   ? --- 1980=>   Rs.2000   Rs.2000nswer:Rs.2000
Answer: A
|9 - 4| - |12 - 14| = ?  Choose the correct option: A) 3 B) 2 C) 1 D) 0 E) 4

Solution: |9 - 4| - |12 - 14| = | 5 | - | -2 | = 5 - 2= 
5 - 2 = 3
3   correct answer 3
Answer: A
A invested $300 in a business and B invested $400 in a business. At the end of the year they got $350 as the profit. Find their share? Options
A) $150,$200	B) $250,$300	C) $125,$250	D) $130,$150	E) $180,$220

Solution: $150,$200:B = 300:400   $150,$200:B = 3:4   $150,$200's share = 350*3/7= 
350*3/7 = 150
$150   B's share= 350*4/7= 
350*4/7 = 200
$200   $150,$200nswer is $150,$200
Answer: A
In the first 1000 natural numbers, how many integers exist such that they leave a remainder 4 when divided by 7, and a remainder 9 when divided by 11?	Choose one
A) 11
B) 14
C) 12
D) 13
E) 10

Solution: Explanatory Answer   Step 1: Find the first number common to both the sequences.   The first sequence: Numbers leaving a remainder of 4 when divided by 7: 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, ....   The second sequence: Numbers leaving a remainder of 9 when divided by 11: 9, 20, 31, 42, 53, 64, .....   From the listing of the two sequences we can identify the first number that is a part of the both the sequences is 53.   Step 2: Compute common difference of terms common to both sequences and find number of terms.   The common difference of the first sequence is 7 and that of the second sequence is 11.   Elements common to both the sequences will have a common difference that is the LCM of 7 and 11.   77 is the LCM of 7 and 11.   Every 77th number after 53 will satisfy both the conditions.   The terms that are common to both the arithmetic sequences can be expressed as 77k + 53.   Because we are interested in the first 1000 natural numbers, k will take values from 0 to 12.   i.e., a total of 13 values.   Choice 13 is the correct answer.
Answer: D
Two cogged wheels of which one has 32 cogs and other 54 cogs, work into each other. If the latter turns 80 times in three quarters of a minute, how often does the other turn in 8 seconds?	Choose the most appropriate option:
A) 22
B) 24
C) 99
D) 27
E) 17

Solution: Explanation:   Less Cogs more turns and less time less turns   Number of turns required=80 × × = 24 times   Answer: 24) 24
Answer: B
tom and Bonnie are opposing participants in an online auction. Each has a constant bidding strategy: tom always bids up by raising $40 over any previous bid. Bonnie always bids up by doubling any previous bid. The auction begins with an initial bid by a third player, and progresses as follows: tom bids up first, and Bonnie follows. tom bids up again, and Bonnie follows and raises the bid to a final $600. What was the dollar value of the initial price?
Choose the correct option
A) 90 B) 45 C) 46 D) 255 E) 466

Solution: Initial bid = p$   tom = p+40   Bonnie = 2p   The sequence is R---> B ---> R -----> B ---> 600   Thus per the sequence we have: p+40, 2(p+40), 2p+80+40 , 2(2p+120)   Now given, 2(2p+120) = 600----> p =90$. Thus 90 is the correct answer.
Answer: A
The average weight of 20 boys sitting in a boat had some value. A new person added to them whose weight was 50 kg only. Due to his arrival, the average weight of all the boys decreased by 8 kg. Find the average weight of first 20 boys?	Answers.
A) 150
B) 154
C) 218
D) 182
E) 192

Solution: 20x + 50 = 21(x â€“ 8)   x = 218   218
Answer: C
Difference between the length&breadth of a rectangle is 23m. If its perimeter is 206m, then its area is?? We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103? Answers
A) 2430 m^2 B) 2640 m^2 C) 2520 m^2 D) 2650 m^2 E) 2570 m^2

Solution: Solving the two equations, we get: l = 63 and b = 40.   Area = (l x b) = (63 x 40) m2 = 2520 m^2   2520 m^2
Answer: C
It takes printer A 4 more minutes more than printer B to print 40 pages. Working together, the two printers can print 50 pages in 6 minutes. How long will it take Printer A to print 120 pages? Choose the correct choice from the following answers:
A) 12
B) 18
C) 20
D) 24
E) 36

Solution: If it takes 4 more minutes for A to print 40 pages than it takes B,   it takes 5 more minutes for A to print 50 pages than it takes B.   Thus if b is the number of minutes than B takes to print 50 pages,   we can write:   1/b+1/(b+5)=1/6 (since in 1 minute, they print 1/6th of the 50 page job)   6(2b+5)=b(b+5)   b^2-7b-30=0   (b-10)(b+3)=0   b=10   Thus it takes A 15 minutes to print 50 pages and   15*120/50= 
  15*120/50 = 36
36 minutes to print 120 pages (ANSW36R 36)
Answer: E
The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is:	Select.
A) 31 kg	B) 32 kg	C) 33 kg	D) 34 kg	E) None of these

Solution: Explanation:   Let A, B, C represent their respective weights. Then, we have:   A + B + C = (45 x 3) = 135 …. (i)   A + B = (40 x 2) = 80 …. (ii)   B + C = (43 x 2) = 86 ….(iii)   Adding (ii) and (iii), we get: A + 2B + C = 166 …. (iv)   Subtracting (i) from (iv), we get : B = 31.   B’s weight = 31 kg.   31 kgnswer: 31 kg
Answer: A
What is the ratio of 4/7 to the product 2*(7/3)? Select
A) 6:49	B) 1:3	C) 3:21	D) 1:7	E) 3:49

Solution: 4/7 / 14/3 = 6/49...   IMO option 6:49.
Answer: A
45 men working 8 hours per day dig 30 m deep. How many extra men should be put to dig to a depth of 50 m working 6 hours per day?
Choose the correct choice from the following answers
A) 77 B) 77 C) 66 D) 55 E) 77

Solution: (45 * 8)/30   = (x * 6)/50   => x =100   100 – 45   = 55   Answer:55
Answer: D
George's drawer has 7 loose black socks, 11 loose blue socks, and 8 loose white socks. If George takes socks out of the drawer at random, how many would he need to take out to be sure that he had at least two matching pairs of socks in two different colors?  Options.
A) 10  B) 12  C) 14  D) 16  E) 18

Solution: The worst case scenario is choosing 11 blue socks. Then he would need 3 more socks to be sure of a matching pair of black socks or white socks.   The answer is 14.
Answer: C
What is the greatest prime factor of 11!10! + 10!9! ? Pick:
A) 11	B) 17	C) 29	D) 37	E) 41

Solution: 11!10! + 10!9! = 10!9!(11*10+1) = 10!*9!*111 = 10!*9!*3*37   The answer is 37.
Answer: D
In a bag, there are coins of 25 p, 10 p and 5 p in the ratio of 1 : 2 : 3. If there is Rs. 30 in all, how many 5 p coins are there?	Choose one:	A) 50	B) 100	C) 150	D) 200	E) 250

Solution: Let the number of 25 p, 10 p and 5 p coins be x, 2x, 3x respectively.   25p of x,10p of 2x,5p of 3x;   25p=25/100=1/4;   10p=10/100=1/10;   5p=5/100=1/20;   1x/4 + 2x/10 + 3x/20=30;   5x+4x+3x=600;   12x=600 (3*50)   x=150 answer : 150
Answer: C
The amount of water (in ml) that should be added to reduce 9 ml. Lotion, containing 50% alcohol, to a lotion containing 30% alcohol, is?  Pick one:
A) 5  B) 2  C) 3  D) 4  E) 6

Solution: 4.5 4.5   30% 70%   30% ----- 4.5   70% ------? => 10.5 - 4.5= 
10.5 - 4.5 = 6
6 ml   ANSW6R 6
Answer: E
What is the perimeter of a regular polygon with sides of length 10 cm and internal angles measuring 140° each?	Choose the correct choice from the following choices
A) 90 cm B) 108 cm C) 120 cm D) 132 cm E) 144 cm

Solution: Sum of all interior angles is given by:   180(n-2) = n is number of sides   180(n-2) = 140*n   from here   n = 9   So perimeter becomes 10*9= 
10*9 = 90
90   90 cmnswer: 90 cm
Answer: A
If n = 2×3×5×7×11×13×18, then which of the following statements must be true?
I. n^2 is divisible by 600
II. n + 19 is divisible by 19
III. (n + 4)/2 is even
Select
A) I only
B) II only
C) III only
D) I and III
E) None of the above

Solution: Statement I: this is true.   Statement 2 this is NOT true.   Statement 3: (n+4)/2 = n/2 + 2, So this is true.   Hence option (I and III).
Answer: D
If $x is invested at a constant annually compound interest rate of k percent, what is the ratio of the total amount including interest after 6n years to that after 3n years?	Choose the correct answer
A) (1+n/100)^k  B) (1+k)^n  C) (1+kn/100)  D) (1+k/100)^3n  E) (1+kn)

Solution: Amount after 6n years will be = x ( 1 + k/100)^6n   Amount after 3n years will be = x ( 1 + k/100)^3n   So, required ratio will be -   { x ( 1 + k/100)^6n } / {x ( 1 + k/100)^3n } = (1+k/100)^3n   Hence answer will be a. (1+k/100)^3n   (1+k/100)^3n
Answer: D
What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 30%?
Choose one:
A) 20%	B) 26%	C) 42%	D) 5%	E) 22%

Solution: SP2 = 2/3 SP1   CP = 100   SP2 = 70   2/3 SP1 = 70   SP1 = 105   100 --- 5 => 5%   Answer: 5%
Answer: D
A can complete the job in 3 hours and B can complete the same job in 3 hours. A works for 1 hour and then B joins and both complete the job. What fraction of the job did B complete Select the correct option:
A) 1/6
B) 3/10
C) 1/2
D) 5/6
E) 8/9

Solution: 1/6=1/6
Answer: A
Twelve machines, each working at the same constant rate, together can complete a certain job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the Job in 8 days?	Choices
A) 2
B) 3
C) 4
D) 6
E) 8

Solution: Another solution which is faster is Since each machine works at a constant rate. The time needs to bought down from 12 to 8. So the new time is 2/3 of the original time. Thus to achieve this we need the rate to be 3/2 of original.   So 3/2*12= 
3/2*12 = 18
18   So we need   18-12= 
  18-12 = 6
6 more machines.   Answer : 6
Answer: D