MU-NLPC/Calc-aqua_rat huggingface dataset:
Find large number 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 15 as remainder  Choices:  A) 1234  B) 1345  C) 1564  D) 1670  E) 1635

Solution: Let the smaller number be x. Then larger number = (x + 1365).   x + 1365 = 6x + 15   5x = 1350   x = 270   Large number = 270+1365= 
270+1365 = 1_635
1635   1635
Answer: E
There is a sequence An for a positive integer n such that when An-2 is divided by An-1 the remainder is An. If A3=6, A4=0, which of the following can be the value of A1?  Select:	A) 48	B) 50	C) 52	D) 56	E) 58

Solution: When 481/482, Remainder = 483 = 6 --> 481 = x482 + 6   When 482/483, Remainder = 484 = 0 --> 482 = y483   481 = xy483 + 6 = k483 + 6 = 6(k + 1) --> 481 must be a multiple of 6   Only option 48 is a multiple of 6   48nswer: 48
Answer: A
In a colony of 70 residents, the ratio of the number of men and women is 5: 2. Among the women, the ratio of the educated to the uneducated is 1 : 4. If the ratio of the number of educated to uneducated persons is 8 : 27, then find the ratio of the number of educated to uneducated men in the colony?  Choose the most appropriate option:
A) A)1:5
B) B)1:1
C) C)1:8
D) D)1:9
E) E)1:3

Solution: Number of men in the colony = 5/7 * 70= 
5/7 * 70 = 50
50.   Number of women in the colony= 2/7 * 70= 
2/7 * 70 = 20
20.   Number educated women in the colony= 1/5 * 30= 
1/5 * 30 = 6
6.   Number of uneducated women in the colony= 4/5 * 50 = 24.   Number of educated persons in the colony = 8 /35 * 70= 
8 /35 * 70 = 16
16.   As 6 females are educated, remaining 10 educated persons must be men.   Number of uneducated men in the colony= 50 - 10= 
50 - 10 = 40
40.   Number of educated men and uneducated men are in the ratio 10 : 40 i.e., 1:4.   1:5nswer:1:5
Answer: A
Keats Library purchases a number of new books, all in the category of biography, and the library does not acquire any other books. With the addition of the new biographies, the biography collection of the library amounts to 32% of the total number of books in the library. If prior to the purchase, only 20% of the books in Keats Library were biographies, by what percent has the number of biographies in the library increased?	Choose the correct option:
A) 60%  B) 72%  C) 88%  D) 95%  E) 110%

Solution: Let x be the number of new biographies added to the library.   Let b be the original number of biographies, so the original number of books was 5b.   0.32(5b+x) = b+x   0.6b = 0.68x   x = 0.88b   The answer is 88%.
Answer: C
Which of the following is the best approximation for y?
1/2−1/3+1/6−1/10+1/12−1/14+1/16
Choose the correct answer
A) 0.1 B) 0.31 C) 0.35 D) 0.4 E) 0.6

Solution: 1/2 - 1/3 +1/6-1/10+1/12-1/14+1/16   => 1/2 [1+1/3-1/5+1/6-1/7+1/8] - 1/3   => 0.5 [ 1+0.33-0.2+0.167-0.142+0.125] - 0.33   => 0.31   Option 0.31
Answer: B
The students of a particular class were given two tests for evaluation. Twenty Five percent of the class cleared both the tests and forty five percent of the students were able to clear the first test.
You have to calculate the percentage of those students who passed the first test and were also able to pass the second test. How will you do it?  Select.
A) 48%
B) 55%
C) 60%
D) 71%
E) 80%

Solution: C   60%   In all such cases where you have to find out the probability of anything with an already given situation, you have to use the formula for conditional probability.   In this case, you have to find out the probability that the second test was passed by a student given that he passed the first test already.   Therefore, P(Second/First) = P (First and Second)/ P (First)   = 0.25/0.42   =0.60   =60 %
Answer: C
How many different possible arrangements can be obtained from the letters G, M, A, T, I, I, and T, such that there is at least one character between both I's? Choose the most appropriate option:
A) 360
B) 720
C) 900
D) 1800
E) 5040

Solution: A= all possible permutations = 7!/2!2!   B= permutations with II together = 6!/2!   A-B = 900   ANSWER:900
Answer: C
Caleb spends $70.50 on 50 hamburgers for the marching band. If single burgers cost $1.00 each and double burgers cost $1.50 each, how many double burgers did he buy?
Choose the correct choice from the following answers:
A) 5  B) 10  C) 20  D) 41  E) 45

Solution: Solution -   Lets say, Single hamburgersxand Double hamburgersy   Given that,   x+y=50 and 1x+1.5y=70.50. By solving the equations y=41. ANS 41.
Answer: D
A tourist purchased a total of $1,700 worth of traveler’s checks in $10 and $50 denominations, During the trip the tourist cashed 7 checks and then lost all of the rest. If the number of $10 checks cashed was one more or one less than the number of $50 checks cashed, what is the minimum possible value of the checks that were lost?	Select
A) $1,430  B) $1,310  C) $1,290  D) $1,470  E) $1,150

Solution: since total cashed checks = 7 ans $10 check cashed = one less or more than $50 checks   Therefore either $10 checks = 3 and $50 checks = 4 OR $10 checks = 4 and $50 checks = 3   using this information 1st option gives us the maximum cashed value therefore if we negate this value from total value we will get minimum value of which checks have lost   Therfore   1700 - 230= 
  1700 - 230 = 1_470
1470 hence answer is $1,470
Answer: D
The least number which when divided by 2,3, 4 and 6 leaves a remainder 3, but when divided by 9 leaves no remainder, is
Pick one: A) 17 B) 27 C) 25 D) 33 E) None of these

Solution: Explanation:   L.C.M of 2, 3, 4, 6= 12   therefore Required Number is of the form 12k+3.   Least value of k for which (12k+3) is divisible by 9 is k = 2   therefore Required Number = (12 x 2+3)=27. Answer: 27
Answer: B
A customer bought a product at the shop. However, the shopkeeper increased the price of the product by 20% so that the customer could not buy the required amount of the product. The customer managed to buy only 70% of the required amount. What is the difference in the amount of money that the customer paid for the second purchase compared to the first purchase?
Choose the correct choice from the following answers: A) 16% B) 18% C) 20% D) 22% E) 24%

Solution: Let x be the amount of money paid for the first purchase.   The second time, the customer paid 0.7(1.2x)=0.84x.   The difference is 16%.   The answer is 16%.
Answer: A
If (A-B-C+D = 12) and (A+B-C-D = 6), what is the value of (B-D)^2? Choose the correct choice:
A) 4.
B) 9.
C) 12.
D) 16.
E) 64.

Solution: EQ1: A - 9. - C + D = 12   EQ2: A + 9. - C - D = 6   (1) Subtract EQ1 from EQ2   A - 9. - C + D = 12   - A +9. - C - D = 6   ------------------------   -29. + 2D = 6   (2) Simplify   -9. + D = 3   9. - D = -3   (9.-D)^2 = (-3)^2 = 9   My answer: 9.
Answer: B
Of the families in City X in 2001, 25 percent owned a personal computer. The number of families in City X owning a computer in 2008 was 15 percent greater than it was in 2001, and the total number of families in City X was 6 percent greater in 2008 than it was in 2001. what percent of the families in City X owned a personal computer in 2008?  Choose the correct choice from the following choices
A) 27.12%  B) 23.12%  C) 25.55%  D) 31.22%  E) 56.22%

Solution: Say a 100 families existed in 1994 then the number of families owning a computer in 1994 - 25   Number of families owning computer in 1998 = 25 * 115/100= 
25 * 115/100 = 115/4 = around 28.75
28.75   Number of families in 1998= 106   The percentage = 28.75/106 * 100 = 27.12%.   27.12%NSWER:27.12%
Answer: A
A rectangular cube has a volume of 9 cubic feet. If a similar cube is twice as long, twice as wide, and twice as high, then the volume, in cubic feet of such cube is?
Choices	Choose the correct option:	A) 24	B) 48	C) 81	D) 72	E) 100

Solution: Lets say the sides of the rectangular cube are x, y and z. Problem states volume is 9.   i.e,   x*y*z = 9 .   If every side is increased twice as before. then new volume is   2x*2y*2z = 9*(x*y*z) = 8*9= 
8*9 = 72
72.   Answer is 72
Answer: D
John throws a coin until a series of seven consecutive heads or three consecutive tails appears. What is the probability that the game will end after the eighth throw?
Choose the correct choice from the following answers:	A) 1/128	B) 2/16	C) 3/16	D) 7/16	E) 9/16

Solution: Let's consider the routes that would lead to ending the game on the fourth toss. In order to be a win at that point, tosses #2#3#4 would all have to be the same, either H or T, and in order for the game NOT to end on the third toss, the first toss would have to be different from the other four. Thus, the only two possible sequences are   H-T-T-T--T-T-T-T ----> P = (1/2)^8 = 1/256   T-H-H-H-H-H-H-H ----> P = (1/2)^8 = 1/256   Either one of these would satisfy the condition, so we could have one or the other. OR means add in probability.   1/256 + 1/256 = 2/256 = 1/128   1/128nswer(1/128).
Answer: A
Bhajan Singh purchased 120 reams of paper at Rs 80 per ream. He spent Rs 280 on transportation, paid octroi at the rate of 40 paise per ream and paid Rs 72 to the coolie. If he wants to have a gain of 8 %, what must be the selling price per ream?
Choose the correct choice from the following choices:
A) 90
B) 89
C) 87.48
D) 86
E) 85

Solution: Explanation:   Total investment = Rs. (120 * 80 + 280 + (40/100) * 120 + 72).   = Rs. (9600 + 280+48 + 72) = Rs, 10000.   Sell price of 120 reams = 108% of Rs. 10000 = Rs. 10800.   Sell Price per ream = Rs. [10800/120] = Rs. 90. 90nswer: 90
Answer: A
Seed mixture X is 40% ryegrass and 60% bluegrass by weight; seed mixture Y is 25% ryegrass and 75% fescue. If a mixture of X and Y contains 34% ryegrass, what percent of the weight of the mixture is from mixture X? Choose the correct choice from the following options
A) 25%	B) 40%	C) 50%	D) 60%	E) 75%

Solution: 34% is 9%-points above 25% and 6%-points below 40%.   Thus the ratio of mixture Y to mixture X is 2:3.   The percent of mixture X is 3/5 = 60%.   The answer is 60%.
Answer: D
The H.C.F of two numbers is 11 and their L.C.M is 7700. If one of the numbers is 275 , then the other is Select.
A) 344
B) 387
C) 308
D) 299
E) 882

Solution: Explanation:   other number = \inline \fn_jvn \left ( \frac{11\times 7700}{275} \right ) = 308   Answer: 308) 308
Answer: C
Find the greatest number, which will divide 260, 281 and 303, leaving 7, 5 and 4 as remainders respectively.  Choose the correct answer
A) 23 B) 24 C) 25 D) 26 E) 27

Solution: 23ns: We have to find the HCF of (260 - 7, 281 - 5, 303 - 4) = HCF (253, 276, 299) = 23   23nswer 23
Answer: A
Find out the C.I on Rs.5000 at 4% p.a. compound half-yearly for 1 1/2 years.
Options:
A) 893.09 B) 392.98 C) 306.04 D) 830.48 E) 345.91

Solution: A = 5000(51/50)3   = 5306.04   5000   -----------   306.04   Answer:306.04
Answer: C
In a certain brick wall, each row of bricks above the bottom row contains one less brick than the row just below it. If there are 6 rows in all and a total of 135 bricks in the wall, how many bricks does the bottom row contain ?
Choose one:
A) 21	B) 20	C) 22	D) 19	E) 24

Solution: The bottom row has x bricks   x+x-1+x-2+x-3+x-4+x-5 = 135   6x-15=135   6x=120   x= 20   Answer:20
Answer: B
The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 57 kmph, find the speed of the stream?	Pick:
A) 19
B) 88
C) 14
D) 12
E) 17

Solution: The ratio of the times taken is 2:1.   The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1)= 
(2+1)/(2-1) = 3
3/1= 
3/1 = 3
3:1   Speed of the stream= 57/3= 
57/3 = 19
19 kmph.   19nswer:19
Answer: A
In how many ways can you line up 7 wrestlers in a row if one of them, Houdidi, cannot be in the middle or at the either end? Choose the correct choice
A) 1,850  B) 929  C) 828  D) 724  E) 2,880

Solution: Since Houdini cannot be placed in the middle or at either end (3 spots), then he can choose 4 spots to sit. The remaining 6 apples can be placed in in 6! ways. Thus the # of arrangements is 4*6! = 2,880.   Answer: 2,880.
Answer: E
A total of 115 homes within Verde county were damaged during a terrible storm. The county had an emergency fund of $509,862.50 to be disbursed among households that incurred damage. The funds were distributed so that two story homes received $6,219.70 whereas one story homes received $3109.85. What was the number of damaged one story homes?	Choices.
A) 75 B) 80 C) 95 D) 100 E) 115

Solution: Let x = two story homes   115 - x = one story homes   6219.70x + 3109.85(115 - x) = 590862.50   6219.70x + 357623.75 - 3109.85x = 590862.50   3109.85x = 233238.75   x = 75   75nswer: 75
Answer: A
If the area of circle is 960 sq cm then its circumference?
Select the correct option.
A) 11
B) 88
C) 99
D) 266
E) 110

Solution: 22/7 r2 = 960 => r = 17.5   2 * 22/7 * 17.5= 
2 * 22/7 * 17.5 = 110
110 Answer: 110
Answer: E
How many arrangements can be made out of the letters of the word 'ENGINEERING'? Pick one:
A) 277200 B) 92400 C) 69300 D) 23100 E) 85600

Solution: The word 'ENGINEERING' contains 11 letters, namely 3E, 3N, 2G, 2I and 1R.   Required number of arrangements =11!/(3!)(3!)(2!)(2!)(1!)=277200   277200nswer is 277200
Answer: A
If x, y, and z are consecutive positive integers greater than 1, not necessarily in that order, then which of the following is (are) true?
I. x > z
II. 5x+ 5y >5z
III. yz > xz
IV. xy > y + z  Choose one
A) I only
B) II only
C) II and III only
D) II and IV only
E) III and IV only

Solution: we do not know the values or the relative values but that the three are consecutive..   so the max difference in any two number is 2 and min 1..   lets see the choices..   I. x > z...   we do not know the values or the relative values... need not be true..   II. 5x+ 5y >5z or x+ y > z   we take the worst case that z is teh largest and x and y are lowest possible..... so 2+3>4.. 5>4.. always true   III. yz > xz   we do not know the values or the relative values between x and y..need not be true   IV. xy > y + z   xy-y>z or y(x-1)>z...   again lets take the worst scenario..   we take the worst case that z is the largest and x and y are lowest possible..... so (2-1)3>4.. 3>4.. not true   only ii is true   ans II only
Answer: B
On a map the distance between two mountains is 310 inches. The actual distance between the mountains is 136 km. Ram is camped at a location that on the map is 34 inch from the base of the mountain. How many km is he from the base of the mountain? Choose the correct choice from the following answers.
A) 14.83	B) 14.81	C) 14.91	D) 14.82	E) 14.12

Solution: Explanation:   Since 310 inch = 136 km   So 1 inch = 136/310 km   So 34 inch = (136 Ã— 34)/ 310 = 14.91 km   Answer: 14.91
Answer: C
If the fraction 9/6 is equivalent to 6/a, then a is
Pick:	A) 4	B) 5	C) 6	D) 7	E) 8

Solution: Solution:   If the fractions are equivalent, then 9 × a = 36   a = 36 ÷ 9 = 4   4nswer 4
Answer: A
Rectangle A has sides a and b, and rectangle B has sides c and d. If a/c=b/d=2/5, what is the ratio of rectangle A’s area to rectangle B’s area?	Choose the correct option:
A) 2/5	B) 2/25	C) 5/2	D) 5/4	E) 4/25

Solution: The area of rectangle A is ab.   c=5a/2 and d=5b/2.   The area of rectangle B is cd=25ab/4.   The ratio of rectangle A's area to rectangle B's area is ab / (25ab/4) = 4/25.   The answer is 4/25.
Answer: E
The sum of four consecutive even numbers is 52, Find the third number ?
Choices:
A) 14 B) 10 C) 12 D) 16 E) 20

Solution: Let the first number be n   Let the second number be n + 2   Let the third number be n + 4   Let the third number be n + 6   n + n + 2 + n + 4 + n + 6 = 52   Combine like terms:   4n + 12 = 52   4n + 12 = 52   4n = 52 - 12   4n = 40   n = 10   n + 2 = 12   n + 4 = 14   n + 6 = 16   The third number is 14   14nswer: 14
Answer: A
An insect leaps 48 centimeters in 1.2 seconds. What is its speed?
Answers:
A) 0.4 meters per second B) 4 meters per second C) 40 meters per second D) 4 centimeters per second E) 0.4 centimeters per second

Solution: 48 / 1.2= 
48 / 1.2 = 40
40 cm/s= 0.4 m/s   The answer is 0.4 meters per second.
Answer: A
A man sells two articles for Rs.3600 each and he gains 40% on the first and loses 40% on the next. Find his total gain or loss?	Choose the correct option
A) 16% loss  B) 400  C) 4000  D) 324  E) 8% LOSS

Solution: (40*40)/100= 
(40*40)/100 = 16
16%loss   16% lossNSWER:16% loss
Answer: A
If x and y are integers and x divided by y is 22.15, then which of the following integers is a possible value for the remainder when x is divided by y? I. 15 II. 5 III. 3  Choices
A) II,III only B) I,III only C) I,II only D) I only E) III only

Solution: x=22.15y from which x = 22y + 15y/100 or x = 22y + 3y/20.   Since x and y are integers, 3y/20 must also be an integer. 3 is not divisible by 20, then y must be divisible by 20, and therefore, y/20 is an integer and 3y/20 is an integer which is a multiple of 3. From the given answers, only 15 and 3 are divisible by 3.   Answer I,III only
Answer: B
The price of an item is discounted 6 percent on day 1 of a sale. On day 2, the item is discounted another 6 percent, and on day 3, it is discounted an additional 10 percent. The price of the item on day 3 is what percentage of the sale price on day 1?	Choose the correct choice from the following options: A) 82.3% B) 84.6% C) 85.6% D) 89.6% E) 79.2%

Solution: Let initial price be 100   Price in day 1 after 6% discount = 94   Price in day 2 after 6% discount = 88.36   Price in day 3 after 10% discount = 79.52   So, Price in day 3 as percentage of the sale price on day 1 will be = 79.52//94*100 => 84.6%   Answer will definitely be (84.6%)
Answer: B
In a recent head-to-head run-off election, 12,000 absentee ballets were cast. 1/2 of the absentee ballets were thrown out and 1/2 of the remaining absentee ballets were cast for Candidate A. How many absentee votes did Candidate B receive?
Choose the correct choice from the following
A) 2,000  B) 3,000  C) 6,000  D) 8,000  E) 9,000

Solution: 1/2 * 1/2 (total absentee votes) = 1/4 (total votes)=1/4*12000= 
1/4*12000 = 3_000
3000   Answer is 3,000
Answer: B
A person covered one-fourth of the total distance at 22 kmph and remaining distance at 24 kmph. What is the average speed for the total distance?  Choose the correct choice from the following answers
A) 21 (7/8)kmph
B) 23 (7/15)kmph
C) 23 (7/3)kmph
D) 27 (1/13)kmph
E) 21 (1/8)kmph

Solution: Let the total distance be x km   total time taken = (x/4)/22 + (3x/4)/24 = x/88 + x/32 = 15x/352   Average speed = x/(15x/352) = 352/15kmph   = 23 (7/15)kmph.   Answer:23 (7/15)kmph
Answer: B
In what time will a train 120 m long cross an electric pole, it its speed be 160 km/hr?  Choose the most appropriate option.
A) 2.5 sec B) 2.9 sec C) 2.7 sec D) 8.7 sec E) 8.5 sec

Solution: Speed = 160 * 5/18 = 44 m/sec   Time taken = 120/44 = 2.7 sec.   Answer: 2.7 sec
Answer: C
A person travels equal distances with speeds of 50km/hr,100km/hr and 120km/hr and takes a total time of 23 minutes. The total distance is?	Select the correct option:
A) 15km B) 30km C) 45km D) 50km E) 60km

Solution: Let the total distance be 3x km   x/50 + x/100 + x/120 = 23/60   23x/600 = 23/60   23x = 230   x = 10km   Total distance = 3x = 30km   Answer is 30km
Answer: B
The price of a book is increased from $300 to $360. What is the % of increase in its price?	Choose the correct choice from the following answers:  A) 10%  B) 20%  C) 40%  D) 50%  E) 60%

Solution: Explanation: Change in the price = Rs 360 – Rs 300   = Rs 60   Percentage of increase = Change in the price Initial Price   * 100.   Percentage increase in price =( 60 300   ) *100 = 20%   20%
Answer: B
A rabbit on a controlled diet is fed daily 300 grams of a mixture of two foods, food X and food Y. Food X contains 10 percent protein and food Y contains 15 percent protein. If the rabbit`s diet provides exactly 38 grams of protein daily, how many grams of food X are in the mixture?  Choose the correct choice from the following:
A) 100	B) 140	C) 150	D) 160	E) 200

Solution: Let there be X and Y gm of food.   0.10 X + 0.15 Y = 38   or 10 X + 15 Y = 3800 -----(1)   X + Y = 300 ---------(2)   1) + 2) Eliminating Y, we get   X = 140 gm   ANSWER:140
Answer: B
Of the science books in a certain supply room, 50 are on botany, 65 are on zoology, 90 are on physics. 40 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science? Select:	A) 81	B) 159	C) 166	D) 285	E) 314

Solution: I solve it using the tough luck technique:   According to question: What is the least number of books you should pick so as to get at least 80 books of the same science subject.   80 books of the same science subjects is possible only for two subjects: Physics=90>80 OR Chemistry=110>80   Now, we need to be certain that out of the books we picked, there are either at least 80 physics books or 80 chemistry books   What if we pick the first 80 books and none of them is either Physics or Chemistry. Possible. Thus, we first count all our negatives.   We picked:   50 Botany Books   65 Zoology Books   40 Geology Books   Now, any book we pick will be either Chemistry or Physics. But unfortunately, we can't be lucky enough to pick 80 books and all of them will be Physics, right!!   Thus, in order to make sure that we have 80 books of either of these 2 subjects, we must pick   79*2+1 books   Because, we could have picked the books in following order;   1st book picked: Physics   2nd book picked: Chemistry   3rd book picked: Physics   Thus, Total= 50+65+40+79*2+1=155+1+158= 
155+1+158 = 314
314   Ans:314
Answer: E
The time a passenger train takes to cross another freight train is twice when the passenger train crosses the freight train running in opposite directions. What is the ratio of their speeds?  Choose the correct choice from the following choices:
A) 1:3
B) 3:1
C) 1:4
D) 4:1
E) 1:5

Solution: let speed of freight train=x and speed of passenger train=y, and sum of their length =s so time=s/(x-y),when both are in same direction and time=s/(x+y) when oppsite direction.from question,s/(x-y)=2.s/(x+y) so solving this we get, x/y=3/1.= 
3/1. = 3
3:1   ANSWER:3:1
Answer: B
A person took some amount with some interest for 3 years, but increase the interest for 1%, he paid Rs.240/- extra, then how much amount he took?  Choose the most appropriate option
A) Rs.8000/-  B) Rs.6000/-  C) Rs.4000/-  D) Rs.7000/-  E) None of these

Solution: Explanation:3 years = Rs.240/-year = 240/3Rate of Interest = 1%100/1% × 240/3 = Rs.8000/-P = Rs.8000/- Rs.8000/-nswer: Option Rs.8000/-
Answer: A
The present worth of a sum due sometime hence is Rs.576 and the banker’s gain is Rs.16.The true discount is
Choose the most appropriate option
A) Rs.36
B) Rs.72
C) Rs.48
D) Rs.96
E) None

Solution: Solution   T.D	= √P.W xB.G   = √576 x 16   = 96.   Answer Rs.96
Answer: D
In a certain school, 25% of students are below 8 years of age. The number of students above 8 years of age is 2/3 of the number of students of 8 years of age which is 36. What is the total number of students in the school? Answers:
A) 72
B) 80
C) 120
D) 150
E) 100

Solution: Explanation: Let the number of students be x.   Then, Number of students above 8 years of age = (100 - 25)= 
(100 - 25) = 75
75% of x.   75% of x= 36 + 2/3 of 36   75/100x = 60   x = 80.   Answer: Option 80
Answer: B
If 1+2+3+...+n=n (n+1), then
3 (1+3+5+....+99)=?	Choose the most appropriate option: A) 7000 B) 7250 C) 7500 D) 7750 E) 6750

Solution: Explanation :   To solve this use the formula of AP,   Sn= (n/2)(a+l) ................(1)   To find n, use   => Tn= a+(n-1)d   => 99=1+(n-1)2   => n=50   Use value of n in (1)   then,   Sn = (50/2)(1+99) = 2500   Ans:- 3(Sn) = 7500   Answer : 7500
Answer: C