MU-NLPC/Calc-aqua_rat huggingface dataset:
A magician has five animals in his magic hat: 3 doves and 2 rabbits. If he pulls two animals out of the hat at random, what is the chance X that he will have a matched pair? Choose the correct choice from the following
A) X=2/5  B) X=3/5  C) X=1/5  D) 1/2  E) 7/5

Solution: P(both doves) + P(both rabbits) = p(matched pair)   (3/5)*(2/4) + (2/5)*(1/4) = 2/5   Hi How did you get the probability 2/4 and 1/4???   You have 3 doves and 2 rabbits i.e. a total of 5 animals.   The probability that you pick a dove on your first pick is 3/5 (since there are 3 doves)   The probability that you pick a dove on your second pick too is 2/4 (because now only 2 doves are left after we picked a dove in the first pick. ALso only 4 animals are left to choose from)   Similarly,   The probability that you pick a rabbit on your first pick is 2/5 (since there are 2 rabbits)   The probability that you pick a rabbit on your second pick too is 1/4 (because now only 1 rabbit is left after we picked a rabbit in the first pick. X=2/5lso only 4 animals are left to choose from)   Probability of picking a matched pair = 3/5 * 2/4 + 2/5 * 1/4 = 2/5
Answer: A
Two trains each 250 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 40 kmph respectively. In what time will they cross each other completely?
Choices: A) 15 sec B) 19 sec C) 12 sec D) 10 sec E) 11 sec

Solution: Explanation:   D = 250 m + 250 m = 500 m   RS = 80 + 40= 
80 + 40 = 120
120 * 5/18= 100/3   T = 500 * 3/100= 
500 * 3/100 = 15
15 sec   15 secnswer: Option 15 sec
Answer: A
In shop contains 500 articles each of a cost of $10. He sold them at a price of $15. If the shop keeper has a order of 200 articles, how much profit he will get?
Choose the correct option:
A) A)200 B) B)2000 C) C)1500 D) D)1000 E) E)600

Solution: Total money after selling articles = 200*15= 
200*15 = 3_000
3000   cost price= 200*10= 
200*10 = 2_000
2000   profit= 1000   correct option is 1000
Answer: D
A bag contains 12 red marbles. If someone were to remove 2 marbles from the bag, one at a time, and replace the first marble after it was removed, the probability that neither marble would be red is 36/49. How many marbles are in the bag? Choose the correct choice from the following choices:
A) 24
B) 48
C) 84
D) 72
E) 80

Solution: ok let me see if i can explain what went on in the previous post   lets say i have x marbles in the bag in total --> out of them 12 are red   so the probability of pulling a non-red marble is (x -12) / x   now the marble is placed back in the bag and we have x marbles again, of which again 12 are red. so the probability of pulling a non-red marble out is (x-12) / x   probability theorm states that if the probability of event A occuring is m and the probability of event B occuring is n then the probability of both A and B occuring is m*n   so therefore the probability of 2 non-red marbles getting pulled out is [(x-12)/x ] * [(x-12)/x]   this is given as 36/49   -->(x-12)^2= 36/49   x^2   square rooting u have x-12/x = 6/7 or 7x-6x =84 or x =84   84
Answer: C
What is the smallest positive perfect square that is divisible by 9, 15, and 25? Choose the correct choice from the following
A) 100 B) 225 C) 900 D) 1,600 E) 4,900

Solution: The number needs to be divisible by 3^2, 3*5, and 5^2.   The smallest such perfect square is 3^2*5^2 = 225   The answer is 225.
Answer: B
10 play kabadi, 25 play kho kho only, 5 play both gmaes. Then how many in total?	Choose the correct choice from the following:
A) 30 B) 35 C) 38 D) 40 E) 45

Solution: 10 play kabadi =>n(A)=10,   5 play both gmaes.=> n(An35)=5   25 play kho kho only,=>n(35)=n(35 only)+n(An35)=25+5= 
25+5 = 30
30   Total=> n(AU35)= n(A)+n(35)-n(An35)   = 10+30-5= 
10+30-5 = 35
35   ANSWER:35
Answer: B
A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is?	Choose the correct choice from the following answers:  A) 100  B) 150  C) 160  D) 170  E) 180

Solution: Let the length of the train be x m and its speed be y m/sec.   Then, x/y = 15 => y = x/15   (x + 100)/25 = x/15 => x = 150 m.   Answer: Option 150
Answer: B
The area of a parallelogram is 98sq m and its altitude is twice the corresponding base. Then the length of the base is?
Choose the correct choice from the following options
A) 8  B) 9  C) 7  D) 62  E) 2

Solution: 2x * x = 98 => x= 7   Answer: 7
Answer: C
A certain amount earns simple interest of Rs. 1750 after 6 years. Had the interest been 2% more, how much more interest would it have earned?
Choose the correct choice from the following.
A) Rs. 350  B) Rs. 35  C) Rs. 245  D) Cannot be determined  E) None of these

Solution: We need to know the S.I., principal and time to find the rate. Since the principal is not given, so data is inadequate.   ANSWER:Cannot be determined
Answer: D
Twenty percent of Country Y's yearly exports come from fruit exports. One-fourth of all fruit exports from Country Y are orange exports. If country Y generates $20 million from its orange exports, how much money does it generate from its yearly total of exports?	Choose the correct choice from the following answers:
A) $21.25m B) $25.5m C) $106.25m D) $400m E) $153m

Solution: 20/100*1/4*(total) = 20   1/20*(total) = 20   (total) = 20*20= 
20*20 = 400
400   Answer: $400m.
Answer: D
The present population of a town is 240. Population increase rate is 10% p.a. Find the population of town after 1 years?	Select the correct option: A) 100 B) 120 C) 200 D) 220 E) 264

Solution: P = 240   R = 10%   Required population of town = P*(1 + R/100)^T   = 240*(1 + 10/100)   = 240*(11/10)= 
240*(11/10) = 264
264   Answer is 264
Answer: E
The average of runs of a cricket player of 10 innings was 34. How many runs must he make in his next innings so as to increase his average of runs by 4 ?	Pick:
A) 78	B) 79	C) 85	D) 87	E) 89

Solution: Explanation:   Average = total runs / no.of innings = 34   So, total = Average x no.of innings = 34 x 10 = 340.   Now increase in avg = 4runs. So, new avg = 34+4= 
34+4 = 38
38runs   Total runs= new avg x new no. of innings = 38 x 11 = 418   Runs made in the 11th inning = 418 - 340= 
418 - 340 = 78
78 78nswer: 78
Answer: A
In one can of mixed nuts, 60% is peanuts. In another can of mixed nuts that is one-half the size of the first one, 40% is peanuts. If both cans are emptied into the same bowl, what percentage of the mixed nuts in the bowl is peanuts?	Choose the correct option
A) 16 2/3%	B) 20%	C) 25%	D) 53 1/3%	E) 35%

Solution: Can 1: size 1; 60% nuts   Can 2: size 0.5 and 40% nuts   (1x0.6+0.5x0.4)/1.5=53.33   53 1/3%
Answer: D
The difference between compound interest and simple interest on a sum for two years at 8% per annum, where the interest is compounded annually is Rs.16. if the interest were compounded half yearly , the difference in two interests would be nearly Choose the correct choice from the following answers.
A) 24.64
B) 24.69
C) 24.62
D) 24.6
E) 24.61

Solution: Explanation:   For 1st year S.I =C.I.   Thus, Rs.16 is the S.I. on S.I. for 1 year, which at 8% is thus Rs.200   i.e S.I on the principal for 1 year is Rs.200   Principle = = Rs.2500   Amount for 2 years, compounded half-yearly   C.I = Rs.424.64   Also,   Hence, [(C.I) - (S.I)] = Rs. (424.64 - 400) = Rs.24.64   24.64nswer:24.64
Answer: A
If the quantity 8^2+ 8^4 + 8^6 is written as (a + b)(a – b), in which both a and b are integers, which of the following could be the value of b?  Choices.
A) 51	B) 64	C) 49	D) 29	E) 37

Solution: (a+b)(a-b) = a^2 - b^2   8^2+ 8^4 + 8^6 = 8^2 (1+8^2+8^4)   if the above expression is solved even then every term of the expression will remain a multiple of 8^2 which is out of parenthesis   hence, b must be a multiple of 8^2 i.e. 64   Answer: option 64
Answer: B
A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 370 m long platform? Select:
A) 19
B) 27
C) 29
D) 47
E) 49

Solution: Let the length of the train be x m.   When a train crosses an electric pole, the distance covered is its own length.   So, x = 12 * 36 * 5 /18= 
12 * 36 * 5 /18 = 120
120 m.   Time taken to cross the platform= (120 +370)/ 36 * 5/18   = 49 min.   Answer:49
Answer: E
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 30 ? Choose the most appropriate 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 30 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 30)   Answer (620)
Answer: D
A, B and C enter into a partnership investing Rs 35000, Rs 45000 and Rs 55000 resp. The respective share of A,B and C in an annual profit of Rs 40500 are.	Choose the correct answer.
A) Rs. 11500, Rs. 13500, Rs. 16500	B) Rs. 10500, Rs. 12500, Rs. 16500	C) Rs. 10500, Rs. 13500, Rs. 15500	D) Rs. 10500, Rs. 13500, Rs. 16500	E) None of these

Solution: Explanation:   A:B:C = 35000:45000:55000   = 7:9:11   Now we are having the ratio.   to get the share, first make total of above ratio.   then get each share.   A's Share=40500∗7/27=Rs.10500   B's Share=40500∗927=Rs.13500   B's Share=40500∗1127=Rs.16500   Option Rs. 10500, Rs. 13500, Rs. 16500
Answer: D
Employees of a certain company are each to receive a unique 5-digit identification code consisting of the digits 0, 1, 2, 3, and 4 such that no digit is used more than once in any given code. In valid codes, the second digit in the code is exactly twice the first digit. How many valid codes are there?  Choose the correct answer: A) 10 B) 12 C) 14 D) 16 E) 18

Solution: There are 3! ways to make codes starting with 12.   There are 3! ways to make codes starting with 24.   The number of codes is 2*3! = 12.   The answer is 12.
Answer: B
x^2 + rx + 72 = 0 has two distinct integer roots; how many values are possible for r?	Choose the correct choice from the following answers:
A) 3
B) 6
C) 8
D) 12
E) 24

Solution: For a quadratic equation ax^2+rx+c=0, we know that -r/a is sum of roots and c/a is product of roots.   The quadratic equation here is x^2 + rx + 72 = 0, where product of roots is 72.   If we find all the factors of 72, we have the answer.   By prime factorization, we get 72= 2^3*3^2.   We know that total factors are  (3+1)*(2+1)= 
 (3+1)*(2+1) = 12
12 (Reason: with 2^n, we have n+1 possibilities. n^0 to n^n. so n+1)=12
Answer: D
An investor opened a money market account with a single deposit of $6000 on Dec. 31, 2001. The interest earned on the account was calculated and reinvested quarterly. The compound interest for the first 3 quarters of 2002 was $125, $130, and $145, respectively. If the investor made no deposits or withdrawals during the year, approximately what annual rate of interest must the account earn for the 4th quarter in order for the total interest earned on the account for the year to be 10 percent of the initial deposit?
Pick:
A) 3.1%
B) 9.3%
C) 10.0%
D) 10.5%
E) 12.5%

Solution: We know 10% of 6000 is 600   already earned is Rs. 400 in 3 quarters   balance to be earned is 200 on amount of 6400 (6000+400 intt)   we get quarterly Rate of Interest as 3.125% (200/6400).   annually it would be 3.125*4= 
3.125*4 = 12.5
12.5%   ANSW12.5%R:12.5%
Answer: E
If the remainder is 10 when the integer n is divided by 18, what is the remainder when 2n is divided by 9?  Choose the correct option:
A) 0  B) 1  C) 2  D) 3  E) 4

Solution: n = 18k+10   2n = 2(18k+10) = 4k*9 + 20 = 4k*9 + 2*9 + 2 = 9j + 2   The answer is 2.
Answer: C
Find the compound ratio of (1:2), (1:3) and (3:5) is
Choose the correct choice from the following choices
A) 1:10
B) 2:3
C) 3:4
D) 4:5
E) 3:2

Solution: Required ratio = 1/2 * 1/3 * 3/5 = 1/10 = 1:10   1:10nswer is 1:10
Answer: A
Four of the following five parts numbered (a), (b), (c), (d) and (e) are exactly equal. The number of the part which is not equal to the other four parts is your answer.
Select the correct option:  A) 85 ÷ 17 × 110  B) 45 × 6 + 75 × 4  C) 175 ÷ 25 × 75 + 5(2)  D) 36 × 4 + 21(2) – 7 × 5  E) 65 × 12 – 46 × 5

Solution: Except it, others are equal to 550.   Answer 45 × 6 + 75 × 4
Answer: B
A small, rectangular park has a perimeter of 560 feet and a diagonal measurement of 100 feet. What is its area, in square feet?  Options
A) 4,800	B) 19,600	C) 20,000	D) 20,400	E) 20,800

Solution: you can avoid a lot of work in this problem by recognizing that, with the info provided, the diagonal forms a triangle inside the rectangle with sides that have a 3:4:5 ratio.   diagonal = 200   2x + 2y = 560, or x + y = 280   a^2 + b^2 = c^2 for each the sides of the triangle   using the ratio 3:4:5 for sides, and knowing c = 100, you can deduce the following   a=60   b=80   60x80=4,800   4,800 is the answer.
Answer: A
A security guard at a certain store is instructed to check the receipt of one out of every five customers as they are leaving the store. If, on the guard's shift, 10 customers leave the store, how many different samples of customers could have been selected to have their receipts checked?  Choose the correct choice from the following choices
A) 20 B) 45 C) 59 D) 90 E) 100

Solution: If the guard is instructed to select 1 of every 5 receipts and the question is asking how many different sets of customers could be selected out of 10 then the guard will select 2 of the 10 customers to review.   10C2 = 45.   ANS:45
Answer: B
The average weight of 6 students decreases by 3 kg when one of them weighing 80 kg is replaced by a new student. The weight of the student is	Pick one:
A) 62 kg  B) 60 kg  C) 70 kg  D) 72 kg  E) None of these

Solution: Explanation :   Let the weight of student be x kg.   Given, Difference in average weight = 3 kg   => (80-x)/6 = 3   => x = 62   62 kgnswer : 62 kg
Answer: A
A sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 45 paisa and Z gets 30 paisa. If the share of Y is RS. 45, what is the total amount?
Pick one:
A) 166
B) 105
C) 175
D) 177
E) 169

Solution: x:y:z = 100:45:30   20:9:6   9 --- 45   35 --- ? => 175   Answer: 175
Answer: C
How many 6 digit even numbers can be formed from digits 1, 2, 3, 4, 5, 6, and 7 so that the digit should not repeat and the second last digit is even?
Choose the correct choice
A) 6480	B) 320	C) 2160	D) 720	E) 620

Solution: 5x4x3x2x2x3= 720   last digit can be 2 or 4 or 6 ie 3ways since the no is even   and second last digit 2 ways bcz no cannot be repeated similarly remaining 5,4,3,2 ways   multipling all we get 720   ANSWER:720
Answer: D
The price of a T.V. set worth Rs. 70000 is to be paid in 20 installments of Rs. 1000 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be?	Choose the correct choice from the following options:
A) 22678
B) 26699
C) 69000
D) 19000
E) 26711

Solution: Money paid in cash = Rs. 1000   Balance payment = (70000 - 1000) = Rs. 69000   Answer: 69000
Answer: C
One year ago, the ratio of Sooraj's and Vimal's age was 6:7 respectively. Four years hence, this ratio would become 7:8. How old is Vimal?
Choose the correct choice from the following choices:	A) 35	B) 36	C) 37	D) 38	E) 39

Solution: 1 year ago   Age of Sooraj and Vimal, 6x and 7x respectively.   After 4 years ratio would become 7:8   (6x+5):(7x+5)=7:8   8(6x+5)=7(7x+5)   48x+40=49x+35   x=5 Vimal's present age   =7x+1=7×5+1=36   answer :36
Answer: B
Solve for X, log10X + log√10 X + log3√100 X = 27.
Choose the correct choice from the following options.
A) 1 B) 106 C) 104 D) 10 E) 15

Solution: Changing the base to 10, we get   log√10 X = log10X / log10√10 = 2log10X   log3√X = log10X / log103√100 = 3log10X / 2.   Thus, log10X + 2log10X + 3/2 log10X = 27   => 9/2 log10X = 27   => log10X = 6   ANSWER:106
Answer: B
A sum of Rs.4600 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years. Options:
A) Rs.2990
B) Rs.3120
C) Rs.3320
D) Rs.2760
E) None of these

Solution: Let A be the amount received at the end of the three years.   Rs.2990 = 4600[1 + 10/100][1 + 20/100][1 + 25/100]   Rs.2990 = (4600 * 11 * 6 * 5)/(10 * 5 * 4)   Rs.2990 = Rs.7590   So the interest = 7590 - 4600 = Rs.2990   Rs.2990NSWER:Rs.2990
Answer: A
Rs.160 contained in a box consists of one rupee, 50 paisa and 25 paisa coins in the ratio 4:5:8. What is the number of 25 paisa coins?
Choose the correct choice from the following answers:
A) 100  B) 110.14  C) 140.24  D) 120.34  E) 170.64

Solution: 4x 5x 8x   100 50 25   400x + 350x + 200x = 16000   x = 21.33   6x = 170.64   ANSW170.64R:170.64
Answer: E
Henry eats X scones in X percent of the time it takes Rachel to eat Y scones. If Rachel eats four scones in ten minutes, then the number of minutes it takes Henry to eat 20 scones must be equal to which of the following?	Choose one:  A) Y/2  B) 20/Y  C) 100Y/(15X)  D) XY/250  E) Y/(5X)

Solution: Rachel eats 4 scones/10 minutes = 2/5 scones per minute   The time for Rachel to eat 1 scone is 5/2 minutes.   The time for Rachel to eat Y scones is 5Y/2 minutes.   The time for Henry to eat X scones is 5YX/200 minutes.   The time for Henry to eat 1 scone is 5Y/200 minutes.   The time for Henry to eat 20 scones is 100Y/200 = Y/2 minutes.   The answer is Y/2.
Answer: A
Jill works as a waitress at the local diner where she earns an hourly wage of $4.00 per hour and a standard tip rate of 15% of the cost of the orders she serves. If she worked one 8-hour shifts this week and averaged $40 in orders per hour, how much did Jill earn this week?
Select:
A) 280	B) 300	C) 80	D) 350	E) 400

Solution: Jill earns 4 dollars/hour and the hourly tip is (3/20)*40.   Jill thus earns 4*8+8*2*3 per day(or 4(8)+6(8)=10(8)=80).   Jill has worked for 1 days -> 80*1=80.   This matches answer choice 80.
Answer: C
Annie has 3 times the number of stamps that Doris does and Jane has 7 stamps more than Doris does. If Annie, Doris, and Jane each increase their number of stamps by 4, which of the following must be true after each person increases her number of stamps?
Annie has more stamps than Jane.
Jane has 3 more stamps than Doris.
The sum of the numbers of stamps that Annie and Doris have is a multiple of 4.	Choices:  A) None  B) IIIonly  C) and III only  D) and III only  E) II, and III

Solution: Given that:   A=3D;   J=D+7;   After increase:   Alice: A=3D+4;   Jane: J=D+11;   Doris: D+4.   Analyze each option:   Alice has more stamps than Jane.   3D+4>D+11 --> D>7/3=3.5. Thus this statement will be true if D is more than or equal to 4. Since we don't know that, then this statement is not always true.   Jane has 3 more stamps than Doris.   D+11=(D+4)+3. This is not true for ANY value of D.   The sum of the numbers of stamps that Alice and Doris have is a multiple of 4.   The sum of the numbers of stamps that Alice and Doris have is (3D+4)+(D+4)=4D+8=4(D+2). So, this sum is a multiple of 4 for ANY value of D, which smeans that this statement is always true.   Answer: IIIonly (III only).
Answer: B
Two equal triangles constitute rhombus A. If the diagonals of rhombus are 15cm and 20cm long. What is the area of each triangle?  Choose the correct choice from the following choices.
A) 300  B) 150  C) 75  D) 40  E) 20

Solution: Area of rhombus =0.5 x 15 x 20   =150 cmÂ²   Area of triangle= 150/2= 
150/2 = 75
75 cmÂ²   Answer: 75
Answer: C
If Ryan and Smith car ratio is 5:8. Ryan bought 6 new car and Smith bought 2 new car. Now,Smith has 18 car.what is their car ratio now?
Select the correct option:
A) 5:4  B) 3:2  C) 8:9  D) 6:5  E) 7:5

Solution: current no. of Smith car=8x+2=18,8x=16,x=2.   current car ratio= 10+6/18=16/18=8:9.   answer 8:9
Answer: C
Rs.1170 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?
Choose the correct choice from the following choices:
A) Rs.528
B) Rs.542
C) Rs.528
D) Rs.540
E) Rs.549

Solution: A+B+C = 1170   4A = 3B = 2C = x   A:B:C = 1/4:1/3:1/2 = 3:4:6   6/13 * 1170 = Rs.540   Answer: Rs.540
Answer: D
The banker's discount on Rs.1550 due a certain time hence is Rs.155. Find the true discount and the banker's gain.
Choices
A) 14 B) 15 C) 18 D) 21 E) None

Solution: Solution   Sum	=B.D x T.D/ B.D - T.D   = B.D x T.D/ B.G   T.D / B. G	=Sum / B.D   = 1550 / 155= 
1550 / 155 = 10
10 / 1   If B.D is Rs. 11,T.D= Rs.10.   If B.D is Rs.155,   T.D	= Rs.(10 / 11 x 155)   = Rs.140.   And, B.G	= Rs(155 - 140)   = Rs.14.   14nswer 14
Answer: A
What number should replace the question mark? 2, 16, 4, 14, 6, 12, ---?  Choose the correct choice from the following choices.
A) 8 B) 10 C) 12 D) 14 E) 16

Solution: 8nswer: 8   2, 16, 4, 14, 6, 12, 8?   There are two alternate sequences: +2 and -2.
Answer: A
In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 4 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 the correct choice:  A) 40  B) 44  C) 48  D) 22  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 - 4)   After adding milk, quantity of milk in the mixture = 6/11 T.   6T/11 - 4 = 4/9(T - 4)   10T = 396 - 176 => T = 22.   ANSWER:22
Answer: D
Total dinning bill for 8 people was $211.00.If they add 15% tip and divided the bill evenly ,approximate.What was each persons find share	Choices
A) $30.14  B) 45.14  C) 34.66  D) 32.29  E) 30.33

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   242.65/8=30.33   ANSW30.33R:30.33
Answer: E
Which of the following can be a perimeter e of a triangle inscribed in a circle of radius 1?
I. 0.001
II. 0.010
III. 0.100 Choices.
A) I only	B) III only	C) II and III only	D) I, II, and III	E) Not I, II, or III

Solution: Yes,the length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.   But how do you use the above property to solve the question?   The lower limit of the perimeter of an inscribed triangle in a circle of ANY radius is 0: e>0.   Answer is I, II, and III.
Answer: D
By selling 100 pencil, a trader gains the cost of 30 Pencil. Find his gain percentage?  Answers.
A) 26 1/3% B) 51 1/3% C) 30% D) 53 1/3% E) 34 1/3%

Solution: C   30%   Let the CP of each pencil be Rs. 1.   CP of 100 pens = Rs. 100   Profit = Cost of 30 pencil = Rs. 30   Profit% = 30/100 * 100= 
30/100 * 100 = 30
30%
Answer: C
If $ 5,000 is invested in an account that earns 6% interest compounded semi-annually, then the interest earned after one year would be how much greater than if the $ 5,000 had been invested at 8% simple yearly interest? Pick one
A) $ 6 B) $ 8 C) $ 12 D) $ 16 E) $ 432

Solution: $ 6NS $ 6   Solution   $ 6mount (CI) = P+(1+r/n)^nt = 5000+(1+0.06/2)^2= 5406   $ 6mount (SI) = P+PTR/100 = 5000+(5000*1*8/100)= 
5000+(5000*1*8/100) = 5_400
5400   Difference= 5406-5400= 
5406-5400 = 6
6 $   $ 6
Answer: A
80% of Ram's marks is equal to 20% of Rahim's marks which percent is equal to 30% of Robert's marks. If Robert's marks is 80, then find the average marks of Ram and Rahim?	Select the correct option.
A) 70
B) 97
C) 87
D) 90
E) 75

Solution: Given, 80% of Ram's marks = 20% of Rahim's marks = 30% of Robert's marks.   Given, marks of Robert = 80   30% of 80 = 30/100 * 8 = 24   Given, 80% of Ram's marks = 24.   => Ram's marks = (24 * 100)/80= 
(24 * 100)/80 = 30
30   Also, 20% of Rahim's marks= 24   => Rahim's marks = (24 * 100)/20= 
(24 * 100)/20 = 120
120   Average marks of Ram and Rahim= (30 + 120)/2= 
(30 + 120)/2 = 75
75.   Answer:75
Answer: E