Ravi Raja's Classes

Directions for the next four questions :

Mark (a) if the question can be answered using Statement I alone.
Mark (b) if the question can be answered using Statement II alone.
Mark (c) if the question can be answered using either of the statements alone.
Mark (d) if the question can be answered using both the statements together and not by either statement alone.
Mark (e) if the question cannot be answered even after using both statements together.

1. What is the value of n?
I. n is the unit's digit of 4^(2k + 1) × 3^k × 7^(k + 1)
II. n is even

2. Is (p – 1)(p + 5)(p + 1) even?
I. p(p + 2)(p + 6) is even
II. p(p + 1)(p + 4) is even

3. What is the unit's digit of 2^(2p + 1) + 3^(2q + 1)?
I. p and q both are even
II. (p + q) is even

4. What is the remainder when n is divided by 4?
I. n when divided by 5 gives a remainder 4.
II. n when divided by 6 gives a remainder 3.

5. There are 24 students in a class. A student of age 10 years leaves and another student joins and the average of the class increases by 2 months. What is the age of the new student?
(a) 12
(b) 13
(c) 14
(d) 15
(e) 16

6. In a village, there are 100,000 people eligible to vote. Two contestants Zohra and Abir participated and Abir got 40% of the votes polled and lost by 2,560 votes. If each person casts one vote then what percentage of the total voters eligible to vote did not vote?
(a) 87.5
(b) 91.5
(c) 82.5
(d) 88.5
(e) 85.5

7. A company produces two two products A and B. The price of A is 25% less than that of B. By how much percentage more is A produced as compared to B if the sales revenue generated from A is 1.5 times that of B?
(a) 50%
(b) 75%
(c) 100%
(d) 150%
(e) 200%

8. Farah is able to buy 2.5 kg of rice more for Rs. 220 when there is a reduction of 20% in the price per kg. How much more rice can she purchase if the reduction per kg is 25%?
(a) 3 kg
(b) 3.33 kg
(c) 3.5 kg
(d) 4.33 kg
(e) 2 kg

9. What is the discount offered if an article marked at $ 645 is sold for Rs. 516?
(a) 10%
(b) 15%
(c) 20%
(d) 25%
(e) 30%

10. A shopkeeper gives 10% discount on his goods but uses a weight of 800 grams in place of a 1 kg weight. Find his gain or loss percentage.
(a) 10% loss
(b) 15% gain
(c) 12.5% gain
(d) 12.5% loss
(e) 30% gain

11. A and B start a business investing capitals in the ratio 5 : 7. They withdraw respectively 2/3 and 3/4 of their capitals after 4 months. What is B's share if the yearly profit is Rs. 22,600?
(a) Rs. 12,600
(b) Rs. 12,500
(c) Rs. 12,900
(d) Rs. 13,200
(e) Rs. 13,900

12. If a = log 4 to the base 6; b = log 9 to the base 8 and c = log 36 to the base 3, then find the value of a × b × c.
(a) 0
(b) 1
(c) 1/3
(d) 2/3
(e) 3/2

13. Given : log 3 to the base 2 = 1.6, find the value of m if log 9 to the base 4 + log 3 to the base m = log 36 to the base 2.
(a) 3^(1/1.6)
(b) 3^(1/3.2)
(c) 3^(1/3.6)
(d) 3^(1/2.6)
(e) 3^(1/4.8)

14. In a sequence, every term except the first term is 5 less than twice the previous term. If the fifth term is 21, find the first term.
(a) 5
(b) 8
(c) 11
(d) 0
(e) 6

15. In a geometric progression, the sum of the terms is 360 and the number of terms is one more than the common ratio. Then which of the following can be the common ratio of the series?
(a) 2
(b) 3
(c) 4
(d) 5
(e) 6

16. Harish is three times as fast as Lokesh. If Harish takes 60 days less than Lokesh to complete the work, then in how many days will the work be completed if they work together?
(a) 22.5 days
(b) 24.5 days
(c) 27.5 days
(d) 26.5 days
(e) 21.5 days

17. Two numbers whose tens digits are same add up to 57. What is the smaller number?
(a) 26
(b) 27
(c) 28
(d) 29
(e) 25

18. If the L.C.M.(X, Y) = (a^2 – 4a – 21)(a^2 – 3a + 9) and H.C.F.(X, Y) = (a + 3) and if X = (a^3 + 27), then find Y.
(a) (a – 3)^2
(b) (a – 3)
(c) (a + 3)(a – 7)
(d) (a – 3)(a + 7)
(e) (a^2 – 3a + 9)

19. Find the digit in the unit's place of 1^301 + 2^301 + 3^301 + 4^301 + 5^301.
(a) 0
(b) 1
(c) 2
(d) 3
(e) 5

20. What is the remainder when 3^93 is divided by 10?
(a) 3
(b) 9
(c) 7
(d) 1
(e) 2

21. There are digits 0 – 9 and a four digit number with distinct digits is formed. How many such numbers have their sum of digits as 10?
(a) 24
(b) 48
(c) 96
(d) 120
(e) 150

22. A committee of 3 leaders is to be formed from 5 boys and 7 girls. In how many ways can the committee be formed if it has to include at least one boy and at least one girl?
(a) 210
(b) 350
(c) 175
(d) 126
(e) 144

23. Allen, Ben and Charlie take part in an archery competition where each have to shoot only once. The coach predicts that the probabilities of Allen, Ben and Charlie hitting the target are 4/5, 3/4 and 2/3 respectively. What is the probability that exactly two if them hit the target?
(a) 3/5
(b) 11/60
(c) 17/30
(d) 13/60
(e) 13/30

24. In a survey of 100 people, 59 like A, 60 like B and 61 like C. If the number of people liking exactly one is equal to the number of people liking two and number of people liking all three, and everyone likes at least one of these, then find the number of people who like all three.
(a) 20
(b) 25
(c) 30
(d) 35
(e) 40

25. In a survey of 250 people, 100 people liked Tulips only and two – thirds of those who like Lilies also liked Tulips. If 60 people like neither Tulips nor Lilies then how many people like only Tulips?
(a) 20
(b) 25
(c) 30
(d) 35
(e) 40

26. If the difference of the roots of the equation x^2 + 2p = qx is equal to the difference of the roots of the equation x^2 + 2q = px, then find the value of p + q.
(a) 0
(b) 8
(c) 10
(d) – 8
(e) – 10

27. If (AD)^2 = ABC6, and different alphabets represent different digits, then find the value of (A – B).
(a) 5
(b) 6
(c) 7
(d) 4
(e) 3

28. What will be the next number in the series : 3, 16, 45, 96, 175, 288, ?
(a) 441
(b) 336
(c) 312
(d) 400
(e) 480

29. In a certain language, ACTOR is coded as RQVEA. What is the code for MOVIES in that language?
(a) MQXKGS
(b) GKXQMS
(c) SGKXQM
(d) MSGKXQ
(e) SGXXQN

30. In a certain language, PRANAM is coded as 680403. What will be the code of PRAYANAAM in that language?
(a) 680304003
(b) 680404003
(c) 680504003
(d) 680604003
(e) 680704003

31. A puppy walks 10 km east and then walks 10 km southwards. From there he walks 20 Kim northwards and then 10 km to the west and finally 2 km to the south. How far and in which direction is he from the starting point?
(a) 8 km northwards
(b) 8 km southwards
(c) 12 km northwards
(d) 12 km southwards
(e) 2 km northwards

Directions for the next five questions :

Five friends who took up a job in Delhi meet one day and discuss about their starting salaries. Their starting salaries were 6,000 USD, 8,000 USD, 10,000 USD, 12,000 USD and 14,000 USD.
(i) The Engineer earned the highest while the Doctor earned more than Akhil, the Architect.
(ii) Karan, who was not the doctor, earned more than Sunil.
(iii) Rohit, who was a Graphic Designer, started with the least salary.
(iv) Rishabh did not remember much about his amount.
(v) Sunil, who was the lawyer did not start with 10,000 USD nor did Akhil start with that amount.

32. Who was the Doctor?
(a) Akhil
(b) Karan
(c) Rishabh
(d) Rohit
(e) Sunil

33. Who was the Engineer?
(a) Akhil
(b) Rishabh
(c) Rohit
(d) Sunil
(e) Karan

34. Whose salary was the highest?
(a) Akhil
(b) Rishabh
(c) Rohit
(d) Sunil
(e) Karan

35. What was the salary of the Lawyer?
(a) 6,000 USD
(b) 8,000 USD
(c) 10,000 USD
(d) 12,000 USD
(e) 14,000 USD

36. What was the salary of Akhil?
(a) 6,000 USD
(b) 8,000 USD
(c) 10,000 USD
(d) 12,000 USD
(e) 14,000 USD

1. In a class of 20 students, each student was to shake hands with every other student. But half the boys refused to shake hands with one – third of the girls. Which of these could be the total number of handshakes?
(a) 190
(b) 184
(c) 170
(d) 166

2. A shop has three types of candies costing Re. 1, Rs. 2 and Rs. 3. Neha has Rs. 24 and wants to buy exactly 12 candies comprising at least one of each kind. In how many different ways can she buy the candies with all this money?
(a) 3
(b) 11
(c) 5
(d) 9

3. How many powers of 3 divide 270! but don't divide 243!?
(a) 11
(b) 7
(c) 13
(d) 9

4. A dishonest shopkeeper sells sugar at cost price but makes 25% profit by using faulty weights. He decides to give a discount to attract more customers. What percent of discount should he offer to make 12% profit?
(a) 15.2%
(b) 12.5%
(c) 10.4%
(d) 13%

5. Avani bought a yellow saree, a green saree and a red saree at equal costs and sold all the three to Panna at 20% profit, 10% loss and 30% profit, respectively. Panna sold these three sarees to Harsha at 20% profit, 30% profit and 20% loss, respectively. By what percent did the total cost of the three sarees change when Harsha bought them as compared to the cost when Avani bought them?
(a) 47.67%
(b) 30.33%
(c) 39%
(d) 21.67%

6. X can do a piece of work in 20 days working 7 hours a day. The work is started by X and on the second day, one man whose capacity to do the work is twice that of X, joined in. On the third day, another man whose capacity is thrice that of X, joined in and this process continued till the work was completed. In how many days will the work be completed, if everyone works for four hours a day?
(a) 7
(b) 4
(c) 5
(d) 9

7. What is the maximum number of equilateral triangles with side of length 5 cm, that can be cut out of a rectangular sheet of dimensions 10 cm × 15 cm?
(a) 3
(b) 7
(c) 10
(d) 5

8. Two people start their journeys from point A to B with an initial speed of 10 km/hr. The first person then increases his speed by 10 km/hr for every successive 10% of the distance till B, whereas the second person increases his speed by 10 km/hr for every successive 10% of the time of his journey till he reaches B. Who reaches B first?
(a) first person
(b) both reach at the same time
(c) second person
(d) cannot be determined

9. A stick of length 7P is cut into three parts and they form an isosceles triangle. What is the range of 'x' if it is the length of the equal side?
(a) 2.33P < x < 3.5P
(b) 1.75P < x < 3.5P
(c) 1.75P  x  2.33P
(d) None of these

10. Four boys A, B, C, D get either a first class or a second class in their annual exams. The ones who get a first class are to be given two chocolates each, while the others are to be given one chocolate each. What is the probability that 5 chocolates are sufficient?
(a) 11/16
(b) 5/16
(c) 2/5
(d) 3/5

11. Saurabh hosted a party, for which he bought 13 litres Pepsi, 16.4 litres Fanta and 18.8 litres Spirite. With this, he made 4 bottles, one each of Pepsi, Fanta, Sprite and Blossom. Blossom is a mixture of Sprite and Fanta. After filling these 4 bottles (all having the same quantity of drink), Saurabh was left with equal quantities of Pepsi, Fanta and Sprite. Find the quantity of each drink Saurabh was left with.
(a) 3.8 litres
(b) 7.2 litres
(c) 3.4 litres
(d) 9.2 litres

12. Mr. Dutt has lent Rs. 5000 at a rate of 8% p.a. under Simple Interest and Rs. 4000 at a rate of 15% p.a. under Compound Interest (interest compounded annually). For how many years, will the amount accrued under S.I. be more than the amount accrued under C.I.?
(a) 5
(b) 7
(c) 3
(d) 6

13. There are a certain number of children in a class. Each child has a different number of sweets and there is one who has none. No child has exactly 15 sweets and there are more children in the class than there are sweets with any child. Find the maximum possible number of children in the class.
(a) 10
(b) 5
(c) 15
(d) 12

14. A man initially invests Rs. 12000 with a bank at 20% compound interest per annum for 5 years. (interest compounded annually). After 5 years, he uses this money (including the principal and the interest earned) to buy a car which depreciates at 10% per annum. If 2 years after buying the car he sells his car for the amount he initially invested with the bank, then by what percent is the price at which he sold his car greater than or less than its depreciated value?
(a) 30.25% more
(b) 40.46% less
(c) 50.38% less
(d) 80% more

15. Two football players, A and B play together for the same team for 12 matches in a particular year, each scoring 2 goals in the first match. For A, the number of goals increases by 1 every alternate match (starting from the 2nd match) and for the matches in between it remains the same as in the previous match. This pattern of goal scoring, (i.e., which starts from the 2nd match) for A continues till the 12th match. For B, the number of goals increases by 2 in the second match, decreases by 1 in the third match, again increases by 2 in the 4th match, decreases by 1 in the 5th match and this pattern of goal scoring for B continues till the 12th match. From these 12 matches, for how many matches is the number of goals scored by both players for a particular match the same?
(a) 9
(b) 4
(c) 6
(d) 12

13. A certain transport company has two types of trucks – A and B. Type A truck can carry out 20 deliveries per day while Type B can carry out 25 deliveries a day. Fuel cost for a type A truck is Rs.15 per delivery and that for a type B truck is Rs.10 per delivery. Maintenance cost of a Type A truck is Rs.100 per day and that of a Type B truck is Rs.150 per day. If a minimum of 5 and a maximum of 12 Type B trucks can be used, then what is the number of type A trucks to be used so as to carry out 1000 deliveries per day at the minimum cost using only both these type of trucks? (Assume each type of truck makes the exact number of deliveries per day as mentioned above and no less)
(a) 30
(b) 25
(c) 35
(d) 42

14. Mrs. A weaves a cloth in the day and Mrs. B unweaves it in the night. For Mrs. A, work on any day is equal to the total work done by her till the previous day/s. For example, on the 3rd day, work done by Mrs. A is equal to the total work done by her on Day 1 and Day 2. Mrs. A and Mrs. B started the work on Day 1 with the same efficiency. Also, Mrs. B can complete her work in 8 days, working with the same efficiency on all days. In how many days will the weaving of the cloth be completed?
(a) 40/7 days
(b) 32/7 days
(c) 9/2 days
(d) 11/2 days

15. A survey was conducted in a small village among 554 youths for their employment status. There were 377 males. The number of employed graduate males was 15 more than the number of unemployed graduate males. The number of graduate females who were employed was the average of the number of employed graduate males and employed undergraduate females. All the graduate females were employed. The number of unemployed undergraduate females was half the number of employed females. If 350 youths were undergraduate, then find the number of undergraduate males.
(a) 238
(b) 312
(c) 272
(d) 190

16. Which of the following points do not lie in the area enclosed by the lines x – 7 | y | = 35 and x = 50?
(a) (49, 1.5)
(b) (43, 0.67)
(c) (48, 2.5)
(d) (36, 0)

1. The average of 8 positive distinct integers is 456. If the smallest number of the given eight numbers is 56, then what can be the maximum value of the highest number?
(a) 3000
(b) 3875
(c) 2750
(d) 3235

2. If number 448a6b is divisible by 33, which of the following can be the values of a and b?
(a) a = 7, b = 8
(b) a = 9, b = 5
(c) a = 2, b = 1
(d) This situation cannot arise

3. A man can complete a certain job in 8 days. He works for a day and then is replaced by a man who can do the same job in 7 days. Then next day, this man is also replaced by a man who can do this job in 6 days and so on. On which day is the job completed?
(a) Fourth
(b) Seventh
(c) Eighth
(d) Sixth

4. At a party, 40% of the people have only orange juice and snacks, 10% have only food and 80% have snacks. If nobody has all three and everybody has something, how many people have food?
(a) Maximum 70%
(b) Maximum 60%
(c) Minimum 20%
(d) Minimum 15%

5. A number, when written in base 16 notation, contains only three 0s and three 1s and no other digits. Find the maximum number of zeroes in the base 2 notation of that number.
(a) 10
(b) 16
(c) 12
(d) 18

6. How many numbers less than 100000 are such that only the digits 5, 6, 7, 8, 9 are used in the number and the number is divisible by 4?
(a) 672
(b) 558
(c) 700
(d) 781

7. A cross – block is made from a solid cube of side 10 cm by cutting off cubes of side 3 cm at each of the corners. What is the total surface area of the cross – block?
(a) 300
(b) 500
(c) 600
(d) 450

8. A dairy farm owner removes 10 L of milk from a milk can containing 50 L of pure milk, adds in equal quantity of distilled water to it and sells it to the milk wholesaler. The milk wholesaler removes 10 L of mixture, adds an equal quantity of distilled water to it and sells it to the local dairy owner. The local dairy owner pours the contents of the milk can into a dairy container which already contains 40 L mixture of milk and distilled water, costing Rs. 22.5 per litre. If the cost of pure milk is Rs. 25 per litre and that of distilled water is Rs. 15 per litre. What is the quantity of pure milk in the local dairy container at the moment?
(a) 48 L
(b) 62 L
(c) 54 L
(d) 90 L

9. Find the approximate sum of the lengths of all diagonals of a regular hexagon having length of each side as 10 cm.
(a) 144 cm
(b) 182 cm
(c) 192 cm
(d) 164 cm

10. BC is a diameter of circle. Chord AD is perpendicular to BC. If angle DAB = 30 degrees and AD = 12 cm, find the distance of chord AB from centre.
(a) 8 cm
(b) 6 cm
(c) 9 cm
(d) 3 cm

11. S1 is a set consisting of all the natural numbers from 1400 to 2000 (including both numbers). S2 is a set consisting of the numbers of S1 with digits of the same numbers written in the reverse order. (For example 1567 from S1 becomes 7651 in S2). What is the number of 4 – digit numbers in S2?
(a) 460
(b) 400
(c) 540
(d) 330

12. If f is a function defined for natural numbers x, y such that f(x + y) = f(x) × f(y). What is the value of f(11), if f(1) = 2?
(a) 485
(b) 1001
(c) 500
(d) 2048

13. The average price of a share is the arithmetic average of 5 readings taken at regular intervals in a day. The index price is taken by a weighted arithmetic average price of a class A and a class B stock. The respective weights are 1.1 and 0.9 for the two kinds of stocks (i.e., for A and B respectively). If the five readings of a class A stock were 19, 26, 31, 35, 39 and for a class B stock the readings were 7, 8, 17, 20, 23 then what was the index price that day?
(a) 46.5
(b) 25.75
(c) 23.25
(d) 51.50

14. A food processing company received fresh consignment of cherries from a cherry corporation containing 'a' kgs. of cherries. After analysis these cherries were found to contain 99% water. After 15 days, sample of cherries from the same lot found to contain 98% water. What must be the weight of the same (original) lot of cherries at that time?
(a) a/2 kg
(b) 2a/3 kg
(c) 4a/5 kg
(d) a/3 kg

15. Triangle ABC is inscribed in a circle of radius 13 cm. If BC = 10 cm and AC = 26 cm. Find the area of the triangle formed by joining the midpoints of the sides AB, BC and AC.
(a) 30 sq. cm
(b) 45 sq. cm
(c) 25 sq. cm
(d) 40 sq. cm

16. f(xy) = f(x) + f(y) - 2, where xy is the product of x and y. If f(2) = a and f(3) = b, then the value of f(72) is :
(a) a + b – 2
(b) 2a + 2b – 6
(c) 2a + 3b – 8
(d) 3a + 2b – 8

17. 'N' is a natural number between 10 and 1000 (excluding both numbers). P denotes the product of the digits of N. S denotes the sum of the digits of N. If 6P + 4S = 4N, then how many values can N take?
(a) 11
(b) 7
(c) 19
(d) 15

18. A dealer bought rice worth Rs. 1700 and sold 50% of it at the marked price gaining 8% in a particular month. There was an inflation of 4% in the price of rice the following month. What percentage discount (on the inflated M.P.) has to be given to make an overall profit of 9% on the rice bought?
(a) 2.1%
(b) 2.6%
(c) 3%
(d) 3.4%

19. A and B are playing a game of cards. They play n games in all. Each of them gets 1 point for their first win, 2 points for their respective second wins, 4 points for their respective third wins and so on. A wins more games than B does. The sum of the points earned by A and B is 574. How many games does A win?
(a) 6
(b) 8
(c) 9
(d) Cannot be determined

20. How many combinations for the lengths of the sides of a quadrilateral are possible such that the perimeter of the quadrilateral is 10 units and lengths of the sides only have integer values?
(a) 5
(b) 9
(c) 7
(d) 6

21. 'A' represents the area of a square. 'B' represents the area of the square formed by reversing the digits of the length of the side of the first square. It is given that the absolute difference in the areas of the two squares is 495 sq. units. Given that the lengths of the sides of both squares are two digit numbers, what can be the length of the side of one of the squares?
(a) 21 units
(b) 45 units
(c) 34 units
(d) 23 units

1. In how many ways can the digits of the number 9623451 be rearranged to get a number divisible by 12?
(a) 1200
(b) 2800
(c) 900
(d) 2000

2. N^2 has 8 factors less than N^3, where N is a natural number with only one prime factor. The number of factors of N^3 is:
(a) 25
(b) 40
(c) 18
(d) 36

3. A child gets a single note from a 2 – rupee, 20 – rupee or 100 – rupee note each day from his parents to deposit in his piggy bank. For the month of January, his total savings were Rs. 214. How many days in the month of January did he receive 2 – rupee notes? (Assume that he received at least one of each note)
(a) 27
(b) 17
(c) 24
(d) 25

4. If three distinct dice are rolled at random, then what is the probability that at least one of the dice shows 5 given that the sum of the counts on the three dice is equal to 12?
(a) 2/3
(b) 1/3
(c) 3/5
(d) 1/2

5. 'A' represents the area of a square. 'B' represents the area of the square formed by reversing the digits of the length of the side of the first square. It is given that the absolute difference in the areas of the two squares is 495 sq. units. Given that the lengths of the sides of both squares are two digit numbers, what can be the length of the side of one of the squares?
(a) 21 units
(b) 45 units
(c) 34 units
(d) 23 units

6. The speed of a boat is 15 kmph. A stream flows at the rate of 3 kmph. While moving with the stream, the boat travels 90 km. Now, going against the stream how much distance can be covered in the same time?
(a) 75 km
(b) 80 km
(c) 60 km
(d) 40 km

7. S, U, K, H and Y are friends. Their teacher has a box which has a pink toffee, a blue toffee, a green toffee, a yellow toffee and a purple toffee. No one but S, K and H will accept a pink toffee and no one but K and H will accept a green toffee. In how many ways can the toffees be distributed if each one of the five gets one toffee?
(a) 12
(b) 15
(c) 24
(d) 10

8. ABCDE is a regular pentagon inscribed in a circle with centre 'O'. Another pentagon is drawn by joining the midpoints of sides OA, OB, OC, OD and OE. Find the ratio of the area of the smaller pentagon to the larger pentagon.
(a) 1 : 2
(b) 1 : 4
(c) 1 : 5
(d) 1 : 3

9. Ramesh and Suresh are told to select numbers for a game. Ramesh selects integers from 1 to 300 one by one. Suresh always selects a number which is the product of the digits of the number selected by Ramesh. Now Ramesh is told to multiply his number by 20 and divide the result by 9. Suresh is told to add 348 to his number. For how many numbers selected by Ramesh, will the calculations give the same values?
(a) 7
(b) 6
(c) 2
(d) 5

10. Machines A and B together produce 1680 components in 8 hours. Machine A produces one component in 0.66 minutes. In which hour will both the machines finish the assignment of 1000 components, given that machine A works first and both the machines work alternately, each time only for one hour?
(a) 8th hour
(b) 10th hour
(c) 12th hour
(d) 9th hour

11. A and B started running from a common point P on a circular track of radius 7 km, in opposite directions. Initial speeds of A and B were 11 kmph and 22 kmph respectively. After each hour, A increased his speed by 10% and after each half an hour, B decreased his speed by 10%. How much distance did A travel when A and B met for the first time?
(a) 19.2 km
(b) 17.6 km
(c) 15.9 km
(d) 13.3 km

12. 11 is added to a 2 digit number, whose ten's digit is t and units digit is u. The resultant number is also a 2 digit number. Now, in this new number, a digit x is placed before the ten's digit and a digit y is placed after the units digit. The final number after this operation is :
(a) 1000x + 100t + 10y + u + 11
(b) 1000x + 100t + 10u + y + 11
(c) 1000x + 100u + 10t + y + 110
(d) 1000x + 100t + 10u + y + 110

13. If xyz = 8, then what is the minimum value of (1 + x) (1 + y) (1 + z)? (Given x, y, z > 0)
(a) 1
(b) 64
(c) 27
(d) 32

14. A sells an item to B with a profit of 25%. B sells the same item to C. C buys the item for Rs. 3600 with B suffering a loss of 10%. Find the cost price of the item for A.
(a) Rs. 4800
(b) Rs. 3600
(c) Rs. 3200
(d) Rs. 4400

15. Two people A and B start a business investing Rs. 15000 & Rs. 20000 respectively. After some months, B withdrew half of his investment. Two months later, C joins the business investing Rs. 30000. At the end of the year, B and C distribute profits in the ratio 3 : 2. If the total profit is 1.6 lakhs, then what is the share of A (in Rs.)?
(a) 60000
(b) 75000
(c) 48000
(d) 30000

16. James makes perfumes at home. For this, he buys fully concentrated perfume in bottles of 21 litres, removes 9 litres and adds 9 litres of water to it. He again removes 9 litres of the mixture and adds 9 litres of water to it. He repeats this process one more time. Find the percentage of concentrated perfume in the mixture now.
(a) 18%
(b) 32%
(c) 36%
(d) 41%

17. If log 2 = 0.3010 and log 3 = 0.4771, then what is the number of digits in 24^100?
(a) 139
(b) 157
(c) 148
(d) 124

18. Two towns A and B are 180 kms apart. Car 1 and car 2 start travelling from A and B, respectively towards each other. Their speeds are in the ratio 1 : 2 and they start at 7:00 a.m. and 8:00 a.m., respectively. After meeting at C, they return to their starting positions and again start travelling towards each other. In order to meet car 1 for the second time at C, car 2 halts at C. For how much time does it halt?
(a) 2 hours
(b) 1 hour
(c) 5 hours
(d) 4 hours

19. In a geometric progression containing exactly 9 terms, the first term is one and the fourth, sixth and eighth terms of the G.P. are in a arithmetic progression (in that order). Find the sum of all the terms of the geometric progression.
(a) 9
(b) – 1 or 9
(c) 1
(d) 1 or 9

20. A money lender lent a total amount of Rs. 47000 to A, B and C at an interest rate of 5%, 3% and 4% per annum respectively. If the same amount of interest is paid by the three persons A, B and C at the end of 7 years, 10 years and 5 years respectively, then find the amount borrowed by C. (Assume simple interest is charged by the money lender)
(a) Rs. 21000
(b) Rs. 35000
(c) Rs. 40000
(d) Rs. 28000

21. In a certain company there are exactly three departments A, B and C. All the employees are allotted some performance bonus points each day.
1. The average bonus points of employees in departments A, B and C are 100, 150 and 200 respectively for a particular day.
2. The combined average of the bonus points of employees in department A and C is 175 for that same day.
3. The combined average of the bonus points of employees in department B and C is 180 for the same day.
If a total of 10000 bonus points were allotted for that particular day, then what is the total number of employees in the company?
(a) 60
(b) 40
(c) 50
(d) 70

1. If (0, a), (11, 7) and (9, 11) are collinear, then find the value of a.
(a) 17
(b) 19
(c) 23
(d) 29

2. Pipe A can fill a tank in 48 hours and together with Pipe B, it takes 16 hours to fill the tank. How much time does it take for Pipe B to fill the tank?
(a) 12
(b) 18
(c) 24
(d) 36

3. If log37(x^2 - 16x + 56) > 0, then 'x' lies in which range?
(a) 5 < x < 11
(b) -11 < x < -5
(c) (-inf, 5)U(11, inf)
(d) (-inf, -11)U(-5, inf)

4. S1 : 1, 4, 7, 10, 13, ...
S2 : 5, 9, 13, 17, ...
S3 is the product of the corresponding terms of S1 and S2. Find the sum of the first 10 terms of S3.
(a) 3750
(b) 4325
(c) 4375
(d) 5325

5. A train of length 100 metres crosses a milestone in 10 seconds. It crosses another train of the same length in 8 seconds. If the two trains are travelling in opposite directions, then find the distance covered (in Km) by the second train in 3 hours.
(a) 162
(b) 180
(c) 210
(d) 240

6. In how many ways can 4 scholars be selected out of 10 scholars?
(a) 45
(b) 120
(c) 210
(d) 5040

7. On a certain gaming site, 3 games X, Y and Z are available. There are 302 game downloads on a particular day. Seven persons downloaded game Y and Z, 9 persons downloaded games X and Y, 12 persons downloaded games X and Z and 3 people downloaded all three games. Find the number of persons who downloaded only one game.
(a) 230
(b) 250
(c) 280
(d) Cannot be determined

8. A man bought 10 articles all at the same price. He sold the first article at a selling price which was 3 times its cost price. He sold the second article at a price which is 3 times the selling price of the first article and the third at a price which is 3 times the selling price of the second article and so on. Find his profit percentage after he sells 8 articles.
(a) 11230 %
(b) 12230 %
(c) 12290 %
(d) 12930 %

9. A shopkeeper marks up the price of his articles by 20% and by using a faulty balance, gains 12.5%. What will be the actual weight when the weight displayed is 500 gms?
(a) 463.25
(b) 468.75
(c) 472.75
(d) 473.25

10. The ratio of the time periods of investments of A, B and C in a business are 2 : 5 : 7 and the ratio in which the profits were divided is 4 : 10 : 7. Find the ratio of their investments.
(a) 1 : 1 : 2
(b) 2 : 2 : 1
(c) 1 : 2 : 1
(d) Cannot be determined

11. In a factory, 3 fully automatic machines can finish a work in 43 hours whereas 4 semi-automatic machines can do the same work in 43 hours. If 7 fully automatic machines and 5 semi-automatic machines are together working, then in how many hours will the work be completed?
(a) 6
(b) 8
(c) 9
(d) 12

12. If p^x = m, m^y = n and n^z = p, then find the value of (x.y.z)^(m + n + p).
(a) 0
(b) 1
(c) 2
(d) None of these

13. If PANKAJ is coded as 16-1-14-11-1-10, then how is MANGAL coded?
(a) 13-1-14-7-1-10
(b) 13-1-14-9-1-11
(c) 13-1-14-7-1-12
(d) 13-1-12-7-1-13

14. If CARAMEL is coded in one of the four ways
(i) DBSBNFM
(ii) ECTCOGN
(iii) BZQZLDK
(iv) AYPYKCJ
then how is FLOWER coded?
(a) DJMUCQ
(b) EKNUDQ
(c) HNQYGT
(d) ECTDOGN

15. Find the missing number in the following series :
2, 12, 30, 56, _ , 132, 182, 240
(a) 72
(b) 84
(c) 90
(d) 112

16. If k1, k2, k3, ... are the divisors of a number n in increasing order and 11 divides n and n = k5 + k6 + k7, then find the value of n.
(a) 36
(b) 50
(c) 66
(d) 132

17. Two walls are 64 metres apart. A ladder of length 65 metres whose foot is somewhere between the two walls, rests on one wall and its tip touches the wall 60 metres above the foot of the wall. Without moving the ladder, when the same ladder rests on the other wall, its tip touches the wall at a distance 'x' metres above the ground. What is the value of 'x'?
(a) 65
(b) 60
(c) 56
(d) 52

18. Let P # Q represents the number of elements of P
P @ Q represents the number of subsets of Q
If P = {a, b, c}
Q = {p, q, r, s}
Then, find the value of P @ (P x Q).
(a) 512
(b) 1024
(c) 2048
(d) 4096

19. What is the 4th digit from the right hand side in the ternary addition of the decimal numbers 558 and 262?
(a) 3
(b) 2
(c) 1
(d) 0

20. A number when divided by a divisor, the remainder is 25. When 3 times the number is divided by the same divisor, the remainder is 4. Find the divisor.
(a) 79
(b) 29
(c) 71
(d) Cannot be determined

21. The circumference of the rear wheel of a wagon is 137 and the circumference of the front wheel is 173. Find the total distance covered by a wheel if the rear wheel takes 108 revolutions more than the front wheel.
(a) 23701
(b) 47402
(c) 71103
(d) 142206

22. Al, An, At are the children of Mr. and Mrs. Sdg. Mrs. Sdg is the aunt of Sg who is the sister of Bv and Dv. At is the only brother of An. How is Sg related to Al?
(a) Brother-Sister
(b) Sister-Brother
(c) Female Cousins
(d) Cannot be determined

23. Sunita is the mother-in-law of Vanita, who is the sister-in-law of Rahul's only brother Ramesh. How is Sunita related to Ramesh?
(a) Aunt
(b) Mother
(c) Sister-in-law
(d) Sister

24. An amount of Rs. 2,50,000 was distributed between A and B. A invested his amount at Simple Interest for 2 years at 10% per annum while B invested his amount at Compound Interest at 8% per annum for 2 years. If A's amount is Rs. 13390 more than B, find A's share.
(a) 1,12,360
(b) 1,23,720
(c) 1,28,890
(d) 1,32,580

25. Two spheres of radii 1 cm and 2.25 cm are perfectly inscribed in a conical shaped container. Find the height (in cm) of the conical container.
(a) 7
(b) 6.7
(c) 7.5
(d) 8.1

26. Is x + y > 15?
I. x = y^2
II. x = 16

27. What was the compound interest?
I. Amount was invested for 5 years.
II. The rate percent was 10% on the principal amount of Rs. 50,000.

28. If a, b, c are integers whose average is greater than 40, then which among a, b, c is the greatest?
I. a > 30 and a + c < 90
II. a + b + c < 130

Solution to Question 1 :
If (0, a), (11, 7) and (9, 11) are collinear, then the slope of the line joining (0, a) and (11, 7) should be the same as the slope of the line joining (11, 7) and (9, 11).
So, we have :
(7 - a)/(11 - 0) = (11 - 7)/(9 - 11)
or, (7 - a)/(-11) = (-4)/2
or, (7 - a)/11 = -2
or, 7 - a = -22
or, a = 29

Solution to Question Number 2 :
Pipe A can fill the tank in 48 hours.
In hour Pipe A fills 1/48 part of the tank.
Pipe B can fill the tank in 'x' hours.
In hour Pipe B fills 1/x part of the tank.
Together they fill the tank in 16 hours.
In hour they together fill 1/16 part of the tank.
So, we have : 1/48 + 1/x = 1/16
or, 1/x = 1/16 - 1/48
or, 1/x = (3 - 1)/48
or, 1/x = 2/48
or, 1/x = 1/24
or, x = 24 hours

Solution to Question Number 3 :
We know that log 1 to the base 37 = 0 so, if the expression :
log37(x^2 - 16x + 56) > 0, then it implies that x^2 - 16x + 56 > 1
or, x^2 - 16x + 55 > 0
or, (x - 5)(x - 11) > 0
or, x < 5 or x > 11
(-inf, 5)U(11, inf)

Solution to Question Number 4 :
The nth term of 1, 4, 7, 10, ... is (3n - 2).
The nth term of 5, 9, 13, 17, ... is (4n + 1).
The nth term of the product series is (3n - 2)(4n + 1)
tn = 12n^2 - 5n - 2
Sn = Summation (12n^2 - 5n - 2)
= 12n(n + 1)(2n + 1)/6 - 5n(n + 1)/2 - 2n
Now, put n = 10, we get :
= 12x10(10 + 1)(2x10+ 1)/6 - 5x10(10 + 1)/2 - 2x10
= 2x10(11)(21) - 5x5(11) - 2x10
= 4620 - 275 - 20
= 4325

Alternate method is to calculate the 10 terms and add them to arrive at the desired answer.

Solution to Question Number 5 :
Let the speed of the train be 'x' mts/sec.
100/x = 10
or, x = 10 mts/sec
This train crosses another train of the same length in 8 seconds while travelling in opposite directions.
So, we have :
(100 + 100)/(10 + y) = 8
where 'y' is the speed of the second train.
200/(10 + y) = 8
or, 10 + y = 200/8
or, 10 + y = 25
or, y = 15 mts/sec.
In 1 second, it covers 15 metres
In 3600 seconds (1 hour), it will cover 15 x 3600 metres
In 3 hours, it will cover 15 x 3600 x 3 metres = (15 x 3600 x 3)/1000 kms. = 162 kms.

Solution to Question Number 6 :
4 scholars can be selected out of 10 scholars in 10C4 ways
= (10!)/(4!)(6!)
= (10x9x8x7x6!)/(4x3x2x1)(6!)
= (10x9x8x7)/(4x3x2x1)
= 210 ways

Solution to Question Number 7 :
3 people downloaded all three games X, Y and Z.
7 persons downloaded games Y and Z.
Thus, (7 - 3) = 4 persons downloaded only games Y and Z.
Similarly, 6 persons downloaded only games X and Y and 9 persons downloaded only games X and Z.
So the total number of persons who downloaded at least 2 games out if the three = 4 + 6 + 9 + 3 = 22.
So, the total number of persons who downloaded only one game = 302 - 22 = 280.

Solution to Question Number 8 :
Let the cost price of each article be Rs. 10.
So, the total cost price of 10 articles is Rs. 100 and the total cost price of 8 articles is Rs. 80.
Selling price of the first article is 3 times its cost price = Rs. 30.
The selling price of the second article is 3 times the selling price of the first article = Rs. 90 ... and so on.
Total selling price of 8 articles = 30 + 90 + 270 + 810 + ... to 8 terms
= 30(1 + 3 + 9 + 27 + ... to 8 terms)
= 30(3^8 - 1)/(3 - 1)
= 30(6561 - 1)/2
= 15 x 6560
= 98400
Profit % = {(98400 - 80)/80}x100
= 9832000/80
= 122900%

Solution to Question Number 9 :
Let the C.P. of 1 gram be Re. 1.
Marked price = Rs. 1200
If the faulty weight is 'g' gms.
{(1200 - g)/g}x100 = 12.5
or, (1200 - g)/g = 1/8
or, 9600 - 8g = g
or, g = 9600/9
When the actual weight is 9600/9, the weight shown to the customer is 1000.
When the actual weight is 500, the weight shown to the customer is 500x1000x(9/9600) = 468.75.

Solution to Question Number 10 :
Let the investments of A, B and C be 'a', 'b' and 'c' respectively.
Let their respective time periods of investments be 2t, 5t and 7t respectively.
Therefore the profits will be divided in the ratio :
a x 2t : b x 5t : c x 7t
= 2a : 5b : 7c which is in the ratio 4 : 10 : 7 (given)
Comparing each term, we get :
2a = 4k
or, a = 2k
5b = 10k
or, b = 2k
7c = 7k
or, c = k
So, a : b : c = 2k : 2k : k = 2 : 2 : 1

Solution to Question Number 11 :
If 3 fully automatic machines (fam) can do a work in 43 hours and 4 semi-automatic machines (sam) can do the same work in 43 hours, then the efficiency of 3 fam is the same as that of 4 sam.
So, 3 fam = 4 sam
Therefore, 7 fam = 7 x 4/3 sam = 28/3 sam
So, 7 fam + 5 sam = (28/3 + 5) sam = 43/3 sam
4 sam can do a work in 43 hours.
1 sam will do it in 43 x 4 hours.
43/3 sam will do it in 43 x 4 x 3/43 hours = 12 hours.

Solution to Question Number 12 :
Given p^x = m, m^y = n, n^z = p.
Let p = 2, x = 4
Then we have m = 16
Let y = 2, then m^y = n gives n = 256
We have n = 256 and p = 2 so we have z = 1/8
So, the product x.y.z = (2)(4)(1/8) = 1
So, (x.y.z)^(m + n + p) = (1)^(m + n + p) = 1

Solution to Question Number 13 :
Given that PANKAJ is coded as 16-1-14-11-1-10. Note that each number represents the position of the corresponding letter in the alphabetical system.
Thus, the code for MANGAL will be 13-1-14-7-1-12.

Solution to Question Number 14 :
The codes for CARAMEL follows the following pattern :
(i) DBSBNFM : Skip 1 letter forward
(ii) ECTCOGN : Skip 2 letters forward
(iii) BZQZLDK : Skip 1 letter backwards
(iv) AYPYKCJ : Skip 2 letters backwards
Now, going by the options, only one option follows pattern 2 for all the letters of the word FLOWER.
Hence, the code for FLOWER is HNQYGT.

Solution to Question Number 15 :
2, 12, 30, 56, _ , 132, 182, 240
The first differences are
10, 18, 26, __, __, 50, 58
The second differences are
8, 8, __, __, __, 8
So, it is obvious that all second differences has to be 8 to get a definite pattern.
From there we can derive that the first differences are :
10, 18, 26, 34, 42, 50, 58
Thus, the missing term is 56 + 34 = 90.

Solution to Question Number 16 :
Given that n is divisible by 11 and k1, k2, k3, ... are the divisors of n in increasing order.
Here, the best possible method is to go by options and we see that only 66 and 132 are multiples of 11.
If we list the divisors of 66 in increasing order, we get 1, 2, 3, 6, 11, 22, 33, 66 where k1 = 1, k2 = 2, k3 = 3 and so on and we can also check that 66 = 11 + 22 + 33 which satisfies n = k5 + k6 + k7.
Hence, n = 66.

Solution to Question Number 17 :
The tip of the ladder touches the wall 60 metres above the ground and the length of the ladder is 65 metres. So, using Pythagoras Theorem, we can find out that the distance of the foot of the ladder from the foot of the wall is 25 metres.
The distance between the two walls is 64 metres. So, the foot of the ladder is 39 metres from the foot of the second wall and the length of the ladder is 65 metres.
Again, using Pythagoras Theorem, we can find out that the tip of the ladder will touch the second wall 52 metres above the ground.

Solution to Question Number 18 :
If P contains 3 elements and Q contains 4 elements, then the number of elements in P x Q is 12.
If a set contains 'k' elements, then it has 2^k subsets.
Therefore, P x Q contains 2^12 = 4096 elements.

Solution to Question Number 19 :
If we add the decimal numbers 558 and 262, the result is 820 and when we convert 820 into base 3, the result is 1010101.
Thus, the 4th digit from the right is 0.

Solution to Question Number 20 :
Let the number be N and the divisor be 'd', the quotient be 'q' and the remainder is given to be 25. Then, we have :
N = qd + 25
Multiplying both sides by 3, we get :
3N = (3q)d + 75
We know that 3 times the number when divided by the same divisor leaves a remainder 4.
So, the divisor will be the number which will divide 75 to give a remainder 4.
Hence, the divisor is 71.

Solution to Question Number 21 :
The circumference of the rear wheel of a wagon is 137 while that of the front wheel is 173.
So, the two wheels will complete an exact number of revolutions when they have covered a distance of 137 x 173 = 23701.
Difference between the circumference = 173 - 137 = 36.
Difference of 36 revolutions implies distance of 23701.
So, a difference of 108 implies a distance of 23701 x 3 = 71103.

Solution to Question Number 22 :
Given that Al, An, At are the children of Mr. and Mrs. Sdg and Mrs. Sdg is the aunt of Sg who is the sister of Bv and Dv.
So, Sg, Bv and Dv are children of Mrs. Sdg's brother/sister and At being the only brother of An, so Al is a female making Al and Sg Female Cousins.

Solution to Question Number 23 :
Sunita is the mother-in-law of Vanita, so Vanita is Sunita's son's wife.
Also, it is given that Vanita is the sister-in-law of Rahul's only brother Ramesh. So, Rahul becomes Vanita's husband.
Hence, Sunita is Rahul's and Ramesh's mother.