MU-NLPC/Calc-aqua_rat huggingface dataset:
x, y and z are consecutive positive integers such that x < y < z; which of the following must be true?
1. xyz is divisible by 8
2. (z-x)(y-x+1) = 4
3. xy is odd
Pick one:
A) I and II
B) II only
C) III only
D) I and II only
E) I, II, and III

Solution: Since x, y and z are consecutive integers such that x < y < z, we can say x = y-1 and Z = y+1   Statement 1 would be true as at least one of the three numbers is divisible by 2 and one by 4 so xyz would be divisible by 8.   Statement 2 can be simplified if we write everything in terms of y as ((y+1)-(y-1))*(y-(y-1)+1) = 2*2= 
2*2 = 4
4 So, always true   Statement 3 talks about xy Since x and y are consecutive integers one of them is odd and other is even so product would always be even and hence not true.   So, I and II are always true and hence answer   I and II
Answer: A
When a certain number X is divided by 143, the remainder is 45. Which of the following numbers, if added to X, would result in a number divisible by 19? Choose the correct choice:
A) 7 B) 21 C) 13 D) 47 E) 55

Solution: Số thẻ number given is N = 143Q + 45   If this number is divided by 13, the remainder would be R[(143Q + 45)/13]   Since 143 is divisible by 13 , the product 143Q gives no remainder   This means the remainder of 45/13 should be the remainder of the entire number N   which is 6   To make it divisible by 13 , the smallest number that can be added = 19 - 6= 
19 - 6 = 13
13   13orrect Option : 13
Answer: C
(3164 + 6160) / 28  Choose the most appropriate option.
A) 380	B) 350	C) 333	D) 310	E) None of these

Solution: Explanation:   As per BODMAS rule, first we will solve the equation in bracket then we will go for division   = (9324)/28= 
(9324)/28 = 333
333   Option 333
Answer: C
There are 193 items that are members of set U. Of these items, 47 are members of set B, 59 are not members of either of set A or set B, and 23 are members of both sets A and B. How many of the members of set U are members of set A ? Pick:
A) 72	B) 85	C) 94	D) 106	E) 108

Solution: You had the answer almost right. The x = 83 refers to ONLY set A.   However what's being asked is how many members are part of set A. This will include:   1. Only Set A   2. Set A and Set B   So the answer is Set A = 85 + Set AB = 83+23= 
83+23 = 106
106   106
Answer: D
A batsman in his 12th innings makes a score of 75 and thereby increases his average by 1 runs. What is his average after the 12th innings if he had never been ‘not out’?
Choose the correct choice from the following choices
A) 42 B) 43 C) 44 D) 64 E) 46

Solution: Let ‘x’ be the average score after 12 th innings   ⇒ 12x = 11 × (x – 1) + 75   ∴ x = 64   Answer 64
Answer: D
One morning after sunrise, Suresh was standing facing a pole. The shadow of the pole fell exactly to his right. To which direction was he facing?	Choose the correct choice from the following answers
A) East B) West C) South D) North E) 2891

Solution: Explanation:   Sun rises in the east in the morning. Since the shadow of Suresh falls to his right. So he is facing South.   Answer: South) South
Answer: C
A certain drink of type A is prepared by mixing 4 parts milk with 3 parts fruit juice. Another drink of type B is prepared by mixing 4 parts of fruit juice and 3 parts of milk. How many liters of fruit juice must be added to 105 liters of drink A to convert it to drink B?	Choose the most appropriate option:	A) 14	B) 21	C) 28	D) 35	E) 42

Solution: In 105 liters of drink A, there are 60 liters of milk and 45 liters of juice.   With 60 liters of milk, we need a total of 80 liters of juice to make drink B.   We need to add 35 liters of juice.   The answer is 35.
Answer: D
Given positive even integer x, which of the following CAN NOT be evenly divisible by x?	Choose the correct option:
A) x + 1
B) x + 2
C) 2x + 4
D) 3x − 2
E) 7x

Solution: This can be easily solved by substituting values:   Assume x to be 2   A. x + 1: 3 is not evenly divisible by 2   B. x + 2: 4 is evenly divisible by 2   C. 2x + 4: 8 is evenly divisible by 2   D. 3x − 2: 4 is evenly divisible by 2   E. 7x: 14 is evenly divisible by 2   Option x + 1
Answer: A
The avg weight of A,B & C is 84 kg. If D joins the group, the avg weight of the group becomes 80 kg.If another man E who weights is 3 kg more than D Replaces A, Then the avgof B,C,D&E becomes 79 kg. What is the weight of A?  Choose one:
A) 56  B) 65  C) 75  D) 89  E) 90

Solution: A + B + C = 3 *84= 
3 *84 = 252
252   A + B + C + D= 4 * 80= 
4 * 80 = 320
320 ---- (i)   So, D= 68& E = 68 + 3= 
68 + 3 = 71
71   B + C + D +E= 79 * 4= 
79 * 4 = 316
316 --- (ii)   From Eq. (i) & (ii)   A-E= 320 – 316 = 4   A = E +4 = 71 + 4= 
71 + 4 = 75
75   75
Answer: C
A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in:  Pick:  A) 4 days  B) 6 days  C) 8 days  D) 10 days  E) 12 days

Solution: Suppose A, B and C take x,x/2 and x/3	days respectively to finish the work.   Then,	1/x+2/x+3/x=1/2   6/x = 1/2   x = 12.   So, B takes (12/2)= 
(12/2) = 6
6 days to finish the work.   answer :6 days
Answer: B
My grandson is about as many days as my son in weeks, and my grandson is as many months as I am in years. My grandson, my son and I together are 150 years. Can you tell my son age in years? Pick one:
A) 63 years  B) 60 years  C) 50 years  D) 53 years  E) 46 years

Solution: Let m be my age in years. If s is my son's age in years, then my son is 52s weeks old. If g is my grandson's age in years, then my grandson is 365g days old. Thus,365g = 52s.Since my grandson is 12g months old,12g = m.Since my grandson, my son and I together are 150 years,g + s + m = 100.The above system of 3 equations in 3 unknowns (g, s and m) can be solved as follows:52s / 365 + s + 12 x (52s / 365) = 150 or52s + 365s + 365 x (624s / 365) = 365 x 150 ors = 54,750 / 1,041 = 53 yearsAnswer = 53 years
Answer: D
A boy is travelling from his home to school at 5km/hr and reached 5min late. Next day he travelled at 10km/hr and reached 10min early. Distance between home and school?  Choose the correct choice from the following answers: A) 2.5km B) 3km C) 4km D) 5.6km E) 6.5km

Solution: Let the distance be x   T1 = x/5 hr   T2 = x/10hr   Difference in time = 5+10= 
5+10 = 15
15=1/4hr   x/5-x/10 = 1/4   x/10 = 1/4   x = 2.5 km   2.5kmnswer is 2.5km
Answer: A
If the average of 16x and 8y is greater than 80, and x is twice y, what is the least integer value of x ? Choose the correct choice.
A) 8  B) 9  C) 10  D) 11  E) 12

Solution: Substitution can be used in the following way:   Always start with the equation: x = 2y. It is more straight forward to manage as compared to the inequality.   Substitute y = x/2, not the other way because you need to find the minimum value of x. So you can get rid of y.   Now go on to the inequality. So 8y = 8x/2 = 4x   Now average of 16x and 4x is greater than 80. Average of 16x and 4x is 10x. So,   10x > 80   x > 8   8nswer : 88 /2= 
8 /2 = 4
4x   Now average of 16x and 4x is greater than 80. Average of 16x and 4x is 10x. So,   10x > 80   x > 8   8nswer : 8
Answer: A
A circular path of 13 m radius has marginal walk 2 m wide all round it. Find the cost of leveling the walk at 25p per m2?  Select
A) 22  B) 77  C) 44  D) 88  E) 12

Solution: π (152 - 132) = 176   176 * 1/4 = Rs.44   Answer: 44
Answer: C
A person lent a certain sum of money at 4% per annum at simple interest and in 8 years the interest amounted to Rs.340 less than the sum lent. What was the sum lent?	Choose the correct choice from the following answers:  A) Rs. 500  B) Rs 569  C) Rs478  D) Rs369  E) Rs178

Solution: Explanation:   P - 340 = (P*4*8)/100   P =Rs. 500   Rs. 500nswer: Rs. 500
Answer: A
Find the smallest number which should be multiplied with 520 to make it a perfect square
Choose the correct choice from the following:
A) 337 B) 297 C) 266 D) 116 E) 130

Solution: Explanation:   520 = 26 * 20 = 2 * 13 * 22 * 5 = 23 * 13 * 5   Required smallest number = 2 * 13 * 5= 
2 * 13 * 5 = 130
130   130 is the smallest number which should be multiplied with 520 to make it a perfect square.   Answer: 130
Answer: E
Each shelf of a bookcase contained 12 books. If the librarian took out 21 books and rearranged the remaining books so that all shelves but the last one contained 8 books and that last shelf contained 15 books, how many shelves does the bookcase have?
Pick one
A) 5	B) 6	C) 7	D) 8	E) 9

Solution: Let x be the number of shelves.   12x - 21 = 8(x-1) + 15   4x = 28   x= 7   The answer is 7.
Answer: C
The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is	Choose the most appropriate option:
A) 35.2  B) 36.1  C) 36.2  D) 36.5  E) None

Solution: Solution   Correct sum	= (36x50+48-23)   = 1825.   ∴ Correct mean	= 1825 / 50   = 36.5.   Answer 36.5
Answer: D
A trade analyst announced 10% reduction in the unit price of bike. As a result, the sales volume went up by 10%. What was the net effect on the sales revenue? Choose the correct choice:  A) no change  B) decreases by 1%  C) increases by 1%  D) increases by 10%  E) None of these

Solution: Explanation :   Reduction of price = (100 -10)= 
(100 -10) = 90
90%= 0.9   Increase of sale = (100+10)= 
(100+10) = 110
110%= 1.1   Total effect = 0.9 X 1.1 = 99%, Decreases by 1%   Answer : decreases by 1%
Answer: B
Tough and Tricky questions: Combinations.
Two contestants representing four different countries advance to the finals of a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded?  Answers:
A) 6  B) 7  C) 12  D) 16  E) 24

Solution: Number of ways First-place medal can be awarded to four contestants = 2   Number of ways Second-place medal can be awarded to contestants after awarding First-place medal =3   Therefore number of possibilities = 2 *3= 
2 *3 = 6
6   6nswer:6
Answer: A
The sale price at which a store sells an article is 25% more than its cost price. If the sale price is an integer, which of the following cannot be the cost price?	Choose the correct choice from the following:
A) $64	B) $80	C) $96	D) $112	E) $123

Solution: Sale Price = (5/4)*(Cost Price)   If the sale price is an integer, then the cost price must be divisible by 4.   The answer is $123.
Answer: E
The W train leaves station A moving at a constant speed, and passes by stations B and C, in this order. It takes the W train 7 hours to reach station B, and 5 additional hours to reach station C. The distance between stations A and B is m kilometers longer than the distance between stations B and C. What is the distance between stations A and C in terms of m?	Select the correct option:
A) 1.8m B) 6m C) 7m D) 9m E) 12m

Solution: The reason it is failing for you is that you chose incorrect numbers. If the question says it W took 7 hrs to reach from A to B and 5 hrs to reach from B to C at a constant speed. It shows that distance AB and BC should be in ratio of 7/5.   If you take such numbers you can solve problem.   A6m = 7, 6mC=5   Therefore   A6m-6mC = 2   6mut from question, A6m-6mC =m   => m=2   Now total distance = A6m+6mC= 12   Substitute 12 to get answer in terms of m   Total distance 6 +6= 
6 +6 = 12
12   Substitute 12 to get answer in terms of m   Total distance=12 =6m   Ans 6m
Answer: B
Given the positive integer x, which of the following must be divisible by 3?
Choose the correct option
A) x(x^2−2)	B) (x−1)*x*(x+1)	C) x(x+2)^3	D) x^2*(x−5)	E) x^2*(x−5)

Solution: option B) (x−1)*x*(x+1) which represents the product of three consecutive integers, which will always be divisible by 3. hence answer should be (x−1)*x*(x+1)
Answer: B
Which of the following is a prime number ?	Select the correct option:
A) 9  B) 8  C) 4  D) 2  E) 1

Solution: Explanation :   2 is a prime number   A prime number is a natural number greater than 1 which has no positive divisors   other than 1 and itself.   Hence the primer numbers are 2,3,5,7,11,13,17,... Answer : Option 2
Answer: D
Working alone at its constant rate, machine A produces x boxes in 10 minutes and working alone at its constant rate, machine B produces 2x boxes in 5 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce 10x boxes?  Choose the correct choice from the following choices.
A) 13 minutes	B) 14 minutes	C) 15 minutes	D) 16 minutes	E) 20 minutes

Solution: Rate = Work / Time   Given Rate of Machine A = X / 10 min   Machine B Produces 2x boxes in 5 min hence , Machine B produces 4x boxes in 10 min .   Rate of Machine B = 4x / 10   we need tofind the combined time that machines A and B, working simultaneouslytakeat their respective constant rates   let's first find the combined Rate of Machine A and B   Rate of Machine A = X / 10 min + Rate of Machine B = 4x / 10 = 5X/10   Now combine Time = combine work needs to be done / Combine Rate = 10x/5x * 10 = 6 Min   Ans: 20 minutes
Answer: E
The average weight of 29 students is 28 kg. By the admission of a new student, the average weight is reduced to 27.5 kg. The weight of the new student is
Options:
A) 22 kg B) 21.6 kg C) 22.4 kg D) 13 kg E) None of these

Solution: Exp . The total weight of 29 students = 29* 28   The total weight of 30 students = 30* 27.5   Weight of the new student = ( 30*27.5 – 29*28)   = 825 - 812= 
825 - 812 = 13
13   Answer:13 kg
Answer: D
A pump can fill a tank with water in 3 hours. Because of a leak, it took 6 hours to fill the tank. The leak can drain all the water in ?
Choose the correct answer:
A) 2hr
B) 1hr
C) 3hr
D) 4hr
E) 6hr

Solution: Work done by the leak in 1 hour = 1/3 - 1/6 = 1/6   Leak will empty the tank in 6 hours   Answer is 6hr
Answer: E
How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm? Choose the correct choice from the following
A) 5600
B) 6000
C) 6400
D) 7200
E) None

Solution: Solution   Number of bricks = Volume of the wall/Volume of 1 brick   =(800x600x22.5 /25x11.25x6)   = 6400.   Answer 6400
Answer: C
Ayesha's father was 42 years of age when she was born while her mother was 30 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?  Pick one
A) 12 years B) 14 years C) 16 years D) 17 years E) 6 years

Solution: Explanation:   Mother's age when Ayesha's brother was born = 30 years.   Father's age when Ayesha's brother was born = (42 + 4)= 
(42 + 4) = 46
46 years.   Required difference= (46 - 30)= 
(46 - 30) = 16
16 years.   Answer: Option 16 years
Answer: C
If a trader sold two cars each at Rs. 325475 and gains 13% on the first and loses 13% on the second, then his profit or loss percent on the whole is? Pick.
A) 1.69% B) 1.74% C) 1.84% D) 1.47% E) 1.24%

Solution: SP of each car is Rs. 325475, he gains 13% on first car and losses 13% on second car.   In this case, there will be loss and percentage of loss is given by   = [(profit%)(loss%)]/100   = (13)(13)/100 % = 1.69%   1.69%nswer:1.69%
Answer: A
The average weight of 48 students in a class is 52 kg. 5 of them whose average weight is 48 kg leave the class and other 5 students whose average weight is 54 kg join the class. What is the new average weight (in kg) of the class ?  Pick one:  A) 51 1⁄3  B) 52 5/8  C) 52 1⁄8  D) 43.42  E) None of these

Solution: Total weight of 48 students   = 48 × 52 = 2496 kg   Total weight of 5 students who leave   = 5 × 48 = 240 kg   Total weight of 5 students who join   = 5 × 54 = 270 kg   Therefore, new total weight of 48 students   = 2496 – 240 + 270 = 2526   ⇒ New average weight = 2526⁄48 = 52 5/8 kg   Answer 52 5/8
Answer: B
Mike took 5 mock tests before appearing for the GMAT. In each mock test he scored 8 points more than the previous mock test. If he scored 760 on the GMAT and his average score for the mocks and the GMAT was 726.67, what was the difference in the score of his last mock and his GMAT score? Select:
A) 24  B) 30  C) 40  D) 50  E) 60

Solution: One way to do this would be weighted average method..   1) let the average of 5 mocks be x...   so take it as a mix of5 quantitites of xand1 quantity of 760resulting in an average of 726.67...   By alligation/weighted average..   the difference in 760 and 726.67 is 5/6 of difference of 760 and x..   760-726.67 = 5/6 * (760-x)   760-x= 33.33*6/5=40...   so x = 720..   the last of mock test will be 720+8+8=736...   so ans = 760-736= 
760-736 = 24
24   24
Answer: A
If the sides of a triangle are 26 cm, 24 cm and 10 cm, what is its area?  Choose the correct choice from the following choices:	A) 120 cm2	B) 187 cm2	C) 178 cm2	D) 189 cm2	E) 176 cm2

Solution: The triangle with sides 26 cm, 24 cm and 10 cm is right angled, where the hypotenuse is 26 cm.   120 cm2rea of the triangle   = 1/2 * 24 * 10= 
1/2 * 24 * 10 = 120
120 cm2   120 cm2nswer: 120 cm2
Answer: A
In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when a boy gets any no. of prizes? Options:
A) 58	B) 60	C) 64 ways	D) 68	E) 90

Solution: Ans.(C)   Sol. In this case, repetitions are allowed, so all the three prizes can be given in 4 ways, i.e. (4 x 4 x 4) ways = 43 ways = 64 ways Or nr ways = 43 ways = 64 ways
Answer: C
The average time of Izzy's past 3 100-meter sprints is 15 seconds. If the average falls 1 second after Izzy finishes another sprint, how many seconds did it take Izzy to run the most recent sprint?
Choices.
A) 16  B) 11  C) 15  D) 14  E) 10

Solution: Total time to run 3 sprints = 3*15= 
3*15 = 45
45   Total time to run 4 sprints= 4*14= 
4*14 = 56
56   Time to run most recent sprint= 56-45= 
56-45 = 11
11 seconds   Answer is 11
Answer: B
From a Group of 10 People, Including George and Nina, 3 people are to be selected at random to work on a certain project. What is the probability that 3 people selected will include George but not Nina	Choices:
A) 5/56	B) 9/56	C) 28/120	D) 21/56	E) 25/56

Solution: Number of ways of selecting 3 people out of 10 people = 10C3   In the three members George will always be there in the team. At this step we have vacancy for 2 more members and 9 members are available. Lina cannot be there in the team. So 2 members have to be selected and the number of available members = 9 - Nina = 8   Number of ways to form a 3 member team that includes George and excludes Nina = 828/1202   Probability = 828/1202/1028/1203 = 28/120   Answer: 28/120
Answer: C
If a coin is tossed twice, what is the probability that on the first toss the coin lands heads and on the second toss the coin lands heads?
Choose the correct choice from the following options.
A) 1/2	B) 1/8	C) 3/8	D) 3/4	E) 1/4

Solution: Since there are two options for how a coin can land (heads or tails), that means there is a 1/2 chance to land on heads and a 1/2 chance to land tails. To solve this problem you multiply each probability for each flip together. (1/2) chance to land heads the first time * (1/2) chance to land heads the second time = (1/4) chance to land heads both times.   Answer: 1/4
Answer: E
What would be the missing number in the series: 1, 20, 266, 675,?	Choices:  A) 76  B) 78  C) 80  D) 82  E) 84

Solution: 1,20,x,266,675   > 20-1,x-20,266-x,675-266.   >again doing the same upto   >325-3x, -143+3x.   >we get 6x-486 equate it with zero.   > 6x-486 = 0   >x = 78.   ANSWER:78
Answer: B
If one of the followings is the product of the two 3-digit integers 8K7 and 6L7 (K and L denote the tens digit of the respective integers), then that product must be Choose the correct option.
A) 478,823	B) 511,913	C) 531,875	D) 538,424	E) 569,119

Solution: To know the unit digit you can multiply both digit number: 7 x 7 = 49   This eliminates A,B,C and D because the number must end with a 9   So the answer is 569,119
Answer: E
What is difference between biggest and smallest fraction among 2/3, 3/4, 4/5 and 5/7 Choose the correct answer:
A) 2/15 B) 3/5 C) 1/6 D) 1/7 E) None of these

Solution: Explanation:   2/3 = .66, 3/4 = .75, 4/5 = .8 and 5/7 = .71   So biggest is 4/5 and smallest is 2/3   Their difference is 4/5 - 2/3 = 2/15   Option 2/15
Answer: A
R = {2, 3, 4, 5}
B = {4, 5, 6, 7, 8}
Two integers will be randomly selected from the sets above, one integer from set R and one integer from set B. What is the probability that the sum of the two integers will equal 9 ?
Pick:	A) 0.15	B) 0.20	C) 0.25	D) 0.30	E) 0.33

Solution: The total number of pairs R,B possible is   4*5= 
  4*5 = 20
20. Out of these 20 pairs only 4 sum up to 9: (2, 7); (3, 6), (4, 5) and (5, 4). The probability thus is 4/20=0.2.   Answer: 0.20.
Answer: B
An article is bought for Rs.705 and sold for Rs.900, find the gain percent? Answers:
A) 27.65%	B) 33 1/2%	C) 33 1/3%	D) 33 5/3%	E) 35 1/3%

Solution: 705 ---- 195   100 ---- ? => 27.65%   27.65%nswer:27.65%
Answer: A
Car A runs at the speed of 50 km/hr and reaches its destination in 8 hours. Car B runs at the speed of 65 km/h and reaches its destination in 4 hours. What is the ratio of distances covered by Car A and Car B? Pick one:  A) 3 : 7  B) 4 : 9  C) 20 : 13  D) 5 : 7  E) 6 : 11

Solution: 20 : 13ar A travels 50 × 8 = 400 km   20 : 13ar B travels 65 × 4 = 260 km   The ratio is 400 : 260 = 40 : 26 = 20 : 13   The answer is 20 : 13.
Answer: C
What is the 10th digit to the right of the decimal point in the decimal equivalent of 124/22?  Choose the correct choice from the following answers
A) 2
B) 3
C) 4
D) 7
E) 6

Solution: 124/22 = 5.6363....   63 is non-terminating repeating decimal.   The 10th digit to the right of decimal point will be 3.   Answer 3
Answer: B
Find a two digit number, given that the sum of the digits is 12 and the difference of the digits is 2.?	Options.
A) 66
B) 87
C) 75
D) 88
E) 90

Solution: Using elimination method find which of the options fit the description of the number   ... from the option only 75 meets this description   sum of digits---7+5 = 12   difference of digits ---7-5 = 2   Answer 75.
Answer: C
The probability that event M will not occur is 0.8 and the probability that event R will not occur is 0.7. If events M and R cannot both occur, which of the following is the probability that either event M or event R will occur?  Pick.
A) 1/2 B) 2/5 C) 3/5 D) 4/5 E) 12/25

Solution: p(m) =0.2   p(r) =0.3   p(m intersection r) = 0 (If events M and R cannot both occur)   p(m or r) = 0.2+0.3= 
0.2+0.3 = 0.5
0.5   Corrected !!   1/2nswer 1/2
Answer: A
In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?
Choose the correct choice from the following.
A) 360  B) 480  C) 720  D) 5040  E) 1020

Solution: 5!*3!=720   ANSWER:720
Answer: C
In how many different ways can the letters of the word 'RETAIL' be arranged such that the vowels must occupy only the odd positions?	Answers.
A) None of these	B) 64	C) 120	D) 360	E) 36

Solution: OEOEOE   3 vowels EAI can be arranged on odd places in 3!=6 ways. Similarly 3 consonants can be arranged on even places in 3!=6 ways.   Total = 6*6= 
6*6 = 36
36.   Answer: 36.
Answer: E
How many digits are required to number a book containing 220 pages?
Choose the correct choice from the following.
A) 674	B) 604	C) 552	D) 372	E) 250

Solution: 9 pages from 1 to 9 will require 9 digits.   90 pages from 10 to 99 will require   90*2= 
  90*2 = 180
180 digits.   220-(90+9)= 
220-(90+9) = 121
121 pages will require   121*3= 
  121*3 = 363
363 digits.   The total number of digits is 9+180+363= 
9+180+363 = 552
552.   The answer is 552.
Answer: C
The total marks obtained by a student in Mathematics and Physics is 60 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together. Choose the correct choice from the following:  A) 40  B) 30  C) 25  D) Data inadequate  E) None of these.

Solution: Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively.   Given , M + C = 60 and C - P = 20 M + C / 2 = [(M + P) + (C - P)] / 2 = (60 + 20) / 2= 
(60 + 20) / 2 = 40
40.   40NSWER:40
Answer: A