MU-NLPC/Calc-aqua_rat huggingface dataset:
What is the probability Q of randomly selecting an arrangement of the letters of the wordMEDITERRANEANin which the first letter is E and the last letter is R?  Answers:
A) 1/13
B) 1/20
C) 1/26
D) 1/50
E) 1/100

Solution: Why do you calculate the total combinations and everything, it is much easier to calculate as follows:   3/13 * 1 * 1 * 1 * 1 ..... * 2/12 = 6/156 = 1/26   This is because 3/13 = Probability that first letter will be E and 2/12 = probability that thefirstletter will be R. Between everything else cuts down to 1*1*1... e.g. probability Q of the second letter is 11/11= 
11/11 = 1
1, > we do not care what's in between.1/26
Answer: C
There r 4 prime numbers in ascending order. The multiplication of first 3 is 385 and that of last 3is 1001. what is the last number is	Choose the correct choice from the following options:	A) 8	B) 10	C) 11	D) 13	E) 14

Solution: Explanation:   abcbcd=3851001=>ad=513   abcbcd=3851001=>ad=513   So d = 13   13
Answer: D
Charles’s and Sarah’s current ages are C years and S years, respectively. If 6 years from now, Charles will be at least as old as Sarah was 2 years ago, which of the following must be true?  Select
A) C + 6 < S − 2	B) C + 6 ≤ S + 2	C) . C + 6 = S − 2	D) C + 6 > S − 2	E) C + 6 ≥ S − 2

Solution: Now: Charles = C, Sarah = S   in 6Y: C+6≥S−2,   Answer C + 6 ≥ S − 2
Answer: E
Real-estate salesman Z is selling a house at a 30 percent discount from its retail price. Real-estate salesman X vows to match this price, and then offers an additional 15 percent discount. Real-estate salesman Y decides to average the prices of salesmen Z and X, then offer an additional 40 percent discount. Salesman Y's final price is what fraction of salesman X's final price?  Options
A) 39/6	B) 62/11	C) 11/61	D) 21/61	E) 20/61

Solution: Let the retail price be = x   Selling price of Z = 0.7x   Selling price of X = 0.85*0.7x = 0.60x   Selling price of Y = ((0.7x + 0.6x)/2)*0.60 = 0.65x * 0.60 = 0.39x   0.39x 0.65  * 0.60= 
0.65  * 0.60 = 0.39
0.39x   0.39x= k * 0.60x   k = 0.39/0.6 = 39/6   39/6nswer: 39/6
Answer: A
A jar is filled with red, white, and blue tokens that are equivalent except for their color. The chance of randomly selecting a red token, replacing it, then randomly selecting a white token is the same as the chance of randomly selecting a blue token. If the number of tokens of every color is a multiple of 8, what is the smallest possible total number of tokens in the jar? Choose the correct choice from the following:  A) 9  B) 12  C) 15  D) 18  E) 21

Solution: (Red / Total Coins)*(White / Total Coins) = (Blue / Total Coins)   í.ẹ. Red*White = Blue*Total Coins   Let, Red = 3a   White = 3b   Blue = 3c   Total Coins = 3(a+b+c)   í.ẹ. 3a * 3b = 3c*3(a+b+c)   í.ẹ. a*b = c*(a+b+c)   For smallest values of a, b and c   2*3 = 1*(1+2+3)   í.ẹ. Minimum Total 15oins = 3*(1+2+3) = 15   Answer: Option 15
Answer: C
A conical vessel, whose internal radius is 12 cm and height 50 cm, is full of liquid. The contents are emptied into a cylindrical vessel with internal radius 10 cm. Find the height to which the liquid rises in the cylindrical vessel. Choose the most appropriate option.
A) 24 cm  B) 14 cm  C) 20 cm  D) 37 cm  E) 17 cm

Solution: Volume of the liquid in the cylindrical vessel   = Volume of the conical vessel   = ((1/3)* (22/7)* 12 * 12 * 50) )cm3 = (22 *4 *12 * 50)/7 cm3.   Let the height of the liquid in the vessel be h.   Then (22/7)*10*10*h =(22*4*12*50)/7 or h = (4*12*50)/100= 
(4*12*50)/100 = 24
24 cm   24 cmNSWER 24 cm 24 cm
Answer: A
When processing flower-nectar into honey bees' extract, a considerable amount of water gets reduced. How much flower-nectar must be processed to yield 1kg of honey, if nectar contains 50% water, and the honey obtained from this nectar contains 40% water?
Choose the correct choice:	A) 1.2 kg	B) 1.5 kg	C) 1.7 kg	D) 1.9 kg	E) None of these

Solution: Explanation :   Flower-nectar contains 50% of non-water part.   In honey this non-water part constitutes 60% (100-40).   Therefore 0.5 X 1.2 kgmount of flower-nectar = 0.60 X 1.2 kgmount of honey = 0.60 X 1 kg   Therefore amount of flower-nectar needed =   (0.60/0.51)kg=1.2 kgs   1.2 kgnswer : 1.2 kg
Answer: A
A hollow iron pipe is 21 cm long and its external diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weighs 8 g/cm3, then the weight of the pipe is:
Pick one
A) 3.6 kg
B) 3.696 kg
C) 36 kg
D) 36.9 kg
E) None

Solution: Solution   External radius = 4 cm,   Internal radius = 3 cm.   Volume of iron	=(22/7×(42)-(32)×21)cm3   = (22/7×7 ×1×21)cm3   = 462 cm3.   Weight of iron = (462 x 8) gm = 3696 gm = 3.696 kg.   Answer 3.696 kg
Answer: B
A bread merchant declares a 20% discount after 8 P.M. Each bread costs Rs.40 when it is not on sale. Sam goes before 8 P.M. to buy 4 pieces of bread. Max goes after 8 P.M. with the same amount of money that Sam had to buy bread. How many pieces did Max get over Sam?	Choose the correct choice from the following.
A) 1
B) 2
C) 3
D) 4
E) 5

Solution: Explanation:   Sam: 4 pieces * 40 = 160   Max: Max had 160. 160 / (40*(1-20%)) = 160 / (40*0.80) = 160 / 32= 
160 / 32 = 5
5 pieces   Max - Sam= 5 - 4= 
5 - 4 = 1
1   Correct Option: 1
Answer: A
A courtyard is 18 meter long and 12 meter board is to be paved with bricks of dimensions 12 cm by 6 cm. The total number of bricks required is :	Choose the correct choice:
A) 16000
B) 18000
C) 20000
D) 30000
E) None of these

Solution: Explanation:   Number of bricks =Courtyard area /1 brick area   =(1800Ã—1200 /12Ã—6)=30000   Option 30000
Answer: D
The cube root of .000216 is:  Choose one:
A) .6 B) .06 C) 77 D) 87 E) 89

Solution: Explanation:   (.000216)1/3	= [216/(10)6	]	1/3 = 6/100= 
6/100 = 3/50 = around 0.06
0.06   ANSWER IS .06
Answer: B
Find k if 64 / k = 4.
Answers.
A) 16  B) 17  C) 18  D) 14  E) 13

Solution: Since 64 /k = 4 and   64/ 16= 
  64/ 16 = 4
4, then   k= 16 correct answer 16
Answer: A
A train 120 meter long passes an electric pole in 12 seconds and another train of same length traveling in opposite direction in 8 seconds. The speed of the second train is  Choose the correct choice
A) 10m/s	B) 20m/s	C) 30m/s	D) 40m/s	E) 50m/s

Solution: speed of 1st train=120/12= 
120/12 = 10
10m/s   let the speed of 2nd is v   then   240/(v+10)=8   8v=160   v=20m/s   ANSWER:20m/s
Answer: B
A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?	Select the correct option
A) 378  B) 240  C) 772  D) 281  E) 213

Solution: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train   = (15 x 20)m   = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36   = 15 ==> x + 300 = 540   ==> x   = 240 m.   Answer: 240
Answer: B
How many words with or without meaning, can be formed by using all the letters of the word, ‘ORANGE’, using each letter exactly once?  Choose the correct choice from the following answers:	A) 700	B) 720	C) 750	D) 800	E) 820

Solution: The word ‘ORANGE’ contains 6 different letters.   Therefore, Required number of words= Number of arrangement of 6 letters, taken all at a time   =6P6   = 6!   = 6*5*4*3*2*1= 
6*5*4*3*2*1 = 720
720   ANSWER:720
Answer: B
The average age of three boys is 12 years and their ages are in the proportion 2 : 6 : 8. The age of the youngest boy is:  Choose the correct option:
A) 21 years
B) 8.75 years
C) 6.75 years
D) 9 years
E) None of these

Solution: Total age of 3 boys = (12 Ã— 3) years = 36 years. Ratio of their ages = 2 : 6 : 8.   Age of the youngest = (36 Ã— 3â„16) years = 6.75 years.   Answer 6.75 years
Answer: C
Square RSTU shown above is rotated in a plane about its center in a clockwise direction the minimum number of degrees necessary for R to be in the position where T is now shown. The number of degrees through which RSTU is rotated is Choose the correct choice from the following answers:
A) 135 degree B) 180 degree C) 225 degree D) 270 degree E) 315 degree

Solution: From the options, I am assuming the positioning of T and R relative to each other to be as shown. To replace T by R, focus on OR. Say, you rotate OR clockwise (and with it the entire square) and bring it in place of OT. How many degrees did you go? You covered 2 right angles i.e. 180 degrees.   Answer : 180 degree
Answer: B
Set M contains number that satisfy the condition that, if integer x is in the set then x + 6 will also be in the set M. If -4 is one value in the set, which of the following values must also be present in the set M? I) -10 II) 2 III) 8  Choose the correct choice from the following answers:	A) I only	B) II only	C) I and II only	D) II and III only	E) I, II and III

Solution: Since -4 is in the set, then the set must also include 2, 8, 14, 20, etc...   Depending on whether -4 is the starting element in the set or not, we can have -10...or not.   The answer is II and III only.
Answer: D
Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in?	Choose the correct choice from the following choices
A) 6	B) 5	C) 7	D) 9	E) 2

Solution: 1/10 + 1/15 - 1/x   = 1/18   x = 9   Answer:9
Answer: D
Cereal A is 10% sugar by weight, whereas healthier but less delicious Cereal B is 2% sugar by weight. To make a delicious and healthy mixture that is 6% sugar, what should be the ratio of Cereal A to Cereal B, by weight?	Choose the correct choice from the following options
A) 2:9  B) 2:7  C) 1:6  D) 1:4  E) 1:1

Solution: Ratio of A / Ratio of B = (Average Wt of Mixture - Wt of B)/(Wt of A - Average Wt of Mixture)   => Ratio of A / Ratio of B = (6 - 2)/(10 - 6) =4/4   So they should be mixed in the ratio 1:1   Answer - 1:1
Answer: E
What is the sum of all remainders obtained when the first 130 natural numbers are divided by 9?
Choices:
A) 397
B) 401
C) 403
D) 412
E) 399

Solution: A positive integer can give only the following 9 remainders when divided by 9: 1, 2, 3, 4, 5, 6, 7, 8, and 0.   1 divided by 9 gives the remainder of 1;   2 divided by 9 gives the remainder of 2;   ...   8 divided by 9 gives the remainder of 8;   9 divided by 9 gives the remainder of 0.   We'll have 11 such blocks, since  99/9= 
 99/9 = 11
11. The last will be:   91 divided by 9 gives the remainder of 1;   92 divided by 9 gives the remainder of 2;   ...   98 divided by 9 gives the remainder of 8;   99 divided by 9 gives the remainder of 0.   The last number, 100, gives the remainder of 1 when divided by 9, thus the sum of all remainders will be:   11(1+2+3+4+5+6+7+8+0)+1=412.   Answer: 412.
Answer: D
A merchant marks his wares 40% more than the real price and allows 20% discount. His profit is:	Select
A) 20% B) 18% C) 16% D) 12% E) None of these

Solution: Let the CP = 100 Rs.   Mark Price = 140   12%iscount = 20%   Selling price 80/100 × 140   Hence profit = 12%   Answer: 12%.
Answer: D
The smallest fraction, which each of 6/7, 5/14, 10/21 will divide exactly is?  Choose the correct choice from the following answers
A) 30/7 B) 30/9 C) 30/2 D) 30/3 E) 30/6

Solution: Required fraction = L.C.M of 6/7, 5/14, 10/21   = (L.C.M of 6, 5, 10) / (H.C.F of 7, 14, 21) = 30/7   30/7nswer:30/7
Answer: A
Rhoda tosses a coin 5 times. Find the probability of getting exactly 4 heads.
Answers.
A) 5/32	B) 6/32	C) 5/16	D) 4/32	E) 8/32

Solution: Exactly 4 heads out of 5 would be: HHHHT, HHTHH, or many other combinations.   therefore, no. of possible combinations are 5!/4!*1! = 5   Probability = 5/2^5 = 5/32   5/32NSWER:5/32
Answer: A
A trader sold two items for Rs.2500 each, if he made a profit of 28% from the first item and a loss of 20% from the second item, calculate his total gain or loss.
Choose the most appropriate option.
A) 2.6	B) 12.6	C) 3.6	D) 7.6	E) 5.6

Solution: (28*20)/100= 
(28*20)/100 = 28/5 = around 5.6
5.6%   Answer: 5.6
Answer: E
While working alone at their constant rates, computer X can process 240 files in 4 hours, and computer Y can process 240 files in 6 hours. If all files processed by these computers are the same size, how many hours would it take the two computers, working at the same time at their respective constant rates, to process a total of 240 files?  Pick one:
A) 2
B) 2.2
C) 2.4
D) 2.6
E) 2.8

Solution: Both computers together process files at a rate of 240/4 + 240/6 = 60+40= 
60+40 = 100
100 files per hour.   The time required to process 240 files is  240/100= 
 240/100 = 12/5 = around 2.4
2.4 hours   The answer is 2.4.
Answer: C
A sum of Rs. 1530 has been divided among A, B and C such that A gets of what B gets and B gets of what C gets. B’s share is:  Choose the correct choice from the following options:  A) Rs. 120  B) Rs. 160  C) Rs. 270  D) Rs. 300  E) None

Solution: EXPLANATION   Let C’s share = Rs. x   Then, B’s share = Rs. x/4 , A’s share = Rs. (2/3 x x/4 ) = Rs. x/6   =x/6 + x/4 + x = 1530   => 17x/12 = 1530   => 1530 x 12/ 17 = Rs.1080   Hence, B’s share = Rs. (1080/4) = Rs. 270.   Answer Rs. 270
Answer: C
The average amount with a group of seven numbers is Rs. 30. If the newly joined member has Rs. 55 with him, what was the average amount with the group before his joining the group? Pick:
A) s. 25.6
B) s. 155/6
C) s. 16.6
D) s. 260/6
E) s. 25

Solution: Total members in the group = 7   Average amount = Rs. 30   Total amount with them = 7 * 30 = Rs. 210   One number has Rs. 55. So, the amount with remaining 6 people = 210 - 55= Rs. 155   The average amount with them = 155/6   ANSWER:s. 155/6
Answer: B
Three of the sides of a rectangular prism have areas of 91, 39, and 21. What is the volume of the rectangular prism?
Select:
A) 252
B) 269
C) 273
D) 920
E) 1911

Solution: One easy way to get the answer for this question is just multiply the unit's digits of these three numbers, i.e (1*9*1 = 9) (Why the multiplication is needed?, you can see the solution suggested by Bunuel in the above post)   Now look out for the answer whose square gives us a 9 in the unit place.   So, it is easy to pic (273) 273 whose square will give us a 9 in the unit place( 3*3), and hence this is the answer.
Answer: C
If a randomly selected positive single digit multiple of 3 is multiplied by a randomly selected prime number less than 20, what is the probability E that this product will be a multiple of 45? Choose the most appropriate option:	A) 1/32	B) 1/28	C) 1/24	D) 1/16	E) 1/14

Solution: There are 3 single digit multiple of 3, that is, 3,6,9.   There are 8 prime nos less than 20 - 2,3,5,7,11,13,17,19   Total outcome - 8*3 = 24   Favourable outcome = 1 (9*5)   Hence required probability E= 1/24. Answer 1/24.
Answer: C
At a conference, the only events scheduled for the day are seminars and breaks. All seminars are the same length and are 10 times as long as each break. A break must be between two consecutive seminars. If the first seminar begins at 9:00 a.m. and the third one ends at 11:00 a.m., how long will the conference last if there are a total of 6 seminars that day?
Choices:  A) hours and 15 minutes  B) hours and 20 minutes  C) hours and 25 minutes  D) hours and 30 minutes  E) hours and 35 minutes

Solution: Well its like this S B S B S B S B S B S   the interval between 9 am to 11:40 am is 160 min having 3 seminars and 2 breaks .If 1 break is of 5 min than time for 3 seminars = 160 - 2*5= 
160 - 2*5 = 150
150   Time of 1 seminar=150 /3= 
150 /3 = 50
50 min .   So calculating for 6 seminars and 5 breaks ,total time comes out to be 5 hrs and 35 min .   Answer is hours and 35 minutes.
Answer: E
The average of 13 result is 60. Average of the first 7 of them is 57 and that of the last 7 is 61. Find the 8th result?  Answers:
A) 35  B) 37  C) 46  D) 48  E) 50

Solution: Sum of all the 13 results = 13 * 60= 
13 * 60 = 780
780   Sum of the first 7 of them= 7 * 57= 
7 * 57 = 399
399   Sum of the last 7 of them= 7 * 61= 
7 * 61 = 427
427   So, the 8th number= 427 + 399 - 780= 
427 + 399 - 780 = 46
46.   46
Answer: C
What sum of money will produce Rs.60 as simple interest in 4 years at 3 1/2 percent?	Choose the correct choice from the following:
A) 337
B) 429
C) 266
D) 288
E) 211

Solution: 60 = (P*4*7/2)/100   P = 429   Answer: 429
Answer: B
The sum of ages of 5 children born at the intervals of 3 years each is 70 years. What is the age of the youngest child?	Choose the correct choice from the following options
A) 3 years B) 4 years C) 6 years D) 7 years E) 8 years

Solution: Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.   Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 70   5x = 40   x = 8.   Age of the youngest child = x = 8 years.   8 years)
Answer: E
A and B go around a circular track of length 600 m on a cycle at speeds of 36 kmph and 54 kmph. After how much time will they meet for the first time at the starting point?	Choose one:
A) 120 sec
B) 165 sec
C) 186 sec
D) 167 sec
E) 168 sec

Solution: Time taken to meet for the first time at the starting point   = LCM { length of the track / speed of A , length of the track / speed of B}   = LCM { 600/ (36 * 5/18) , 600/ (54 * 5 /18) }   = LCM (60, 40)   =120 sec.   120 secnswer:120 sec
Answer: A
How long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 170 m in length?	Choose the correct choice from the following answers:
A) 16.5 B) 16.0 C) 16.4 D) 16.8 E) 16.1

Solution: 16.8 = 110 + 170= 
110 + 170 = 280
280 m   S= 60 * 5/18 = 50/3   T = 280 * 3/50= 
280 * 3/50 = 84/5 = around 16.8
16.8 sec   Answer: 16.8
Answer: D
What are the last two digits of 55*34*86*47*23*51?	Choose one:
A) 18 B) 20 C) 23 D) 25 E) 57

Solution: 55*34*86*47*23*51=   We have to focus on the last two digits only, so 55*34=70*86=20*47=40   40*23=20 therefore 20*51=20   Hence Answer is 20
Answer: B
A sum of money is put out at compound interest for 2 years at 20%. It would fetch Rs.482 more if the interest were payable half-yearly, then it were pay able yearly. Find the sum.  Choose the correct choice from the following
A) 277  B) 277  C) 2877  D) 2000  E) 2711

Solution: P(11/10)4 - P(6/5)2 = 482   P = 2000   Answer: 2000
Answer: D
The daytime telephone rate between two cities is 60 cents for the first 3 minutes and c cents for each additional minute. The total charge is reduced 40 percent on calls made after 10:00 P.M. The cost, in dollars, of a 35-minute call made at 10:30 P.M. between these two cities is:
Choose the correct choice from the following answers:
A) 0.4(0.60) + 35c
B) 0.4(0.60 + 0.32c)
C) 0.4(0.60 + 9c)
D) 0.6(0.60 + 32c)
E) 0.6(0.60 + 0.35c)

Solution: For first three minutes = 60 cents   Remaining minutes = 35 -3= 
35 -3 = 32
32   charge for 32 minutes= 32c   total cost (if the call was made in daytime) = 0.60 + 32c   40% chargereducedon night calls => 60% charge   =>0.6(0.60 + 32c)   Hence, Answer is 0.6(0.60 + 32c)
Answer: D
A cube of side 5cm is painted on all its side. If it is sliced into 1 cubic centimer cubes, how many 1 cubic centimeter cubes will have exactly one of their sides painted?  Choose the correct answer
A) 9
B) 61
C) 98
D) 54
E) 64

Solution: Look at the image below:   Little cubes with exactly one painted side will be those 3*3= 
3*3 = 9
9, which are in the center of each face. (6 faces)*(9 per each)= 54.   Answer: 54.
Answer: D
A mathematics teacher tabulated the marks secured by 35 students of 8th class. The average of their marks was 72. If the marks secured by Reema was written as 36 instead of 86 then find the correct average marks up to two decimal places. Choices.
A) 73.41	B) 74.31	C) 72.43	D) 73.43	E) Cannot be determined

Solution: Correct average = 35x72+(86-36)/35   ≈   72 + 1.43= 
  72 + 1.43 = 73.43
73.43   Answer 73.43
Answer: D
A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500? Options:	A) Rs. 4991	B) Rs. 5991	C) Rs. 6991	D) Rs. 6001	E) None of these

Solution: Explanation:   Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.   Required sale = Rs. [ (6500 x 6) - 34009 ]   = Rs. (39000 - 34009)   = Rs. 4991.   Rs. 4991nswer: Rs. 4991
Answer: A
A machine P completes a certain amount of work in 12 hrs and machine Q completes the same work in x hrs if both machines works together to complete the same work in 8 hrs then what is x? Choose the correct choice from the following answers
A) 12 hrs  B) 18 hrs  C) 24 hrs  D) 32 hrs  E) 34 hrs

Solution: Explanation:   P’s 1hr work = 1/12   Q’s 1 hr work = 1/x   (A+B)’s 1 hr work = 1/8 = 1/12+1/x   => x = 24 hrs   Answer: Option 24 hrs
Answer: C
In the first 20 overs of a cricket game, the run rate was only 4.3. What should be the run rate in the remaining 30 overs to reach the target of 264 runs?
Select the correct option:
A) 5.93
B) 6.5
C) 6.75
D) 7
E) 8

Solution: Explanation :   Required run rate = (264 - (4.3 x 20))/30 = 178/30 = 5.93   5.93nswer : 5.93
Answer: A
The difference between the two digit number and the number obtained by interchanging its digits is 54. The difference between the digits is?
Choose one:
A) 7 B) 6 C) 5 D) 1 E) 41

Solution: Explanation:   (10x + y) â€“ (10y + x) = 54   x â€“ y = 6   Answer: 6
Answer: B
If a 7 cm cube is cut into 1 cm cubes, then what is the percentage increase in the surface area of the resulting cubes?  Choose the correct choice.
A) 140%	B) 350%	C) 450%	D) 600%	E) 700%

Solution: The area A of the large cube is 7*7*6= 
7*7*6 = 294
294 square cm.   The area of the 343 small cubes is 7*7*7*6= 7A, an increase of 600%.   The answer is 600%.
Answer: D
Population of a city in 2004 was 1000000. If in 2005 there is an increment of 35% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city at the end of the year 2007  Choose the correct option
A) 967532 B) 977522 C) 984424 D) 997454 E) 1272375

Solution: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)   = P (1 + 35/100)(1 - 35/100)(1 + 45/100)   = 1272375   1272375
Answer: E
Out of n consecutive natural numbers, four numbers are selected such that the differences of all the possible pairs are distinct. What is the least value of n for which this is possible? Pick one:	A) 6	B) 7	C) 8	D) 9	E) 10

Solution: Explanation :   Let the 4 numbers be X1, X2, X3, X4 where X1<X2<X3<X4. Let X1 + a1 = X2, X2 + a2 1 +  1= 
1 +  1 = 2
X2, X2 + a2= X3, X3 + a3 = X4. The difference of X1 and each of the other three, of X2 and each of the greater two, of X3 and X4 are tabulated.   X1	X2	X3   X2	a1   X3	a1+a2	a2   X4	a1+a2+a3	a2+a3	a3   We require that n be minimized and these 6 expressions have distinct values. Let X1 = 1   Now, n = 1+a1+a2+a3. Now a1, a2, a3 can be chosen as the least possible values i.e. 1,2 and 3. However the order of chosing should be such that the six expressions (differences) should all be distinct.   By little trial and error (a1, a2, a3) can be (1, 3, 2) or (2, 3, 1) in which case n = 7 and the four numbers can be (1, 2, 5, 7) or (1, 3, 6, 7) respectively.   Hence the minimum value of n is 7.   Answer : 7
Answer: B
A pipe takes a hours to fill the tank. But because of a leakage it took 5 times of its original time. Find the time taken by the leakage to empty the tank  Choose one:	A) 50 min	B) 60 min	C) 90 min	D) 80 min	E) 75 min

Solution: pipe a can do a work 60 min.   lets leakage time is x;   then   1/60 -1/x=1/300   x=75 min   ANSW75 minR:75 min
Answer: E
A person is traveling at 65 km/hr and reached his destiny in 3 hr then find the distance? Options:
A) 205 km B) 195 km C) 295 km D) 115 km E) 215 km

Solution: T = 3 hrs   D= T*S = 65*3= 
65*3 = 195
195 km   Answer is 195 km
Answer: B
The number of boys in the class is 8 more than the number of girls in the class, which is five times the difference between the number of girls and boys in the class.How many boys are there in the class?  Choose the correct choice from the following options
A) 20 B) 30 C) 40 D) 50 E) 60

Solution: 8+y=5(x-y); y=no of girlz & x=boys   so, y=32 & x=8+y ie 40   40 ans.   ANSWER:40
Answer: C