#### September 21, 2019

### Welcome!

#### Total Questions: 80

#### Total Points: 200

#### Timer Set: 90 Minutes

#### All items carry equal marks. For each correct answer you GET 2.5 points. For each wrong attempt you LOSE 1/3rd of the points assigned i.e. 0.833. No penalty if an item left blank. All the best!

1. **The number of times the digit 5 will appear while writing the integers from 1 to 1000 is**

2. **A solid cube is painted yellow, blue and black such that opposite faces are of same colour. The cube is then cut into 36 cubes of two different sizes such that 32 cubes are small and the other four cubes are Big. None of the faces of the bigger cubes is painted blue. How many cubes have only one face painted?**

3. **A and B are two heavy steel blocks. If B is placed on the top of A, the weight increases by 60%. How much weight will reduce with respect to the total weight of A and B, if B is removed from the top of A?**

4. **Mr 'X' has three children. The birthday of the first child falls on the 5th Monday of April, that of the second one falls on the 5th Thursday of November. On which day is the birthday of his third child, which falls on 20th December?**

5. **Consider the following Statements and Conclusions:**

*Statements:*

1. Some rats are cats.

2. Some cats are dogs.

3. No dog is a cow.

*Conclusions:*

I. No cow is a cat.

II. No dog is a rat.

III. Some cats are rats.

**Which of the above conclusions is/are drawn from the statements?**

6. **The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of four parallel lines, is**

7. ** In a school every student is assigned a unique identification number. A student is a football player if and only if the identification number is divisible by 4, whereas a student is a cricketer if and only if the identification number is divisible by 6. If every number from 1 to 100 is assigned to a student, then how many of them play cricket as well as football?**

8. **When a runner was crossing the 12 km mark, she was informed that she had completed only 80% of the race. How many kilometres was the runner supposed to run in this event?**

9. **Raju has Rs. 9000 with him and he wants to buy a mobile handset; but he finds that he has only 75% of the amount required to buy the handset. Therefore, he borrows 2000 from a friend. Then**
10. **In 2002, Meenu's age was one-third of the age of Meera, whereas in 2010, Meenu's age was half the age of Meera. What is Meenu's year of birth?**

11. **Rakesh and Rajesh together bought 10 balls and 10 rackets. Rakesh spent 1300 and Rajesh spent 1500. If each racket costs three times a ball does, then what is the price of a racket?**

12. ** In a conference, out of a total 100 participants, 70 are Indians. If 60 of the total participants are vegetarian, then which of the following statements is/are correct?**

1. At least 30 Indian participants are vegetarian.

2. At least 10 Indian participants are non-vegetarian.

**Select the correct answer using the codes given below:**

20. **A five-storeyed building with floors from I to V is painted using four different colours and only one colour is used to paint a floor.**

**Consider the following statements:**

1. The middle three floors are painted in different colours.

2. The second (II) and the fourth (IV) floors are painted in different colours.

3. The first (I) and the fifth (V) floors are painted red.

**To ensure that any two consecutive floors have different colours**

21. **P, Q and R are three towns. The distance between P and Q is 60 km, whereas the distance between P and R is 80 km. Q is in the West of P and R is in the South of P. What is the distance between Q and R?**
22. **All members of a club went to Mumbai and stayed in a hotel. On the first day, 80% went for shopping and 50% went for sightseeing, whereas 10% took rest in the hotel. Which of the following conclusion(s) can be drawn from the above data?**

1. 40% members went for shopping as well as sightseeing.

2. 20% members went for only shopping.

**Select the correct answer using the code given below:**

23. **In a school, 60% students play cricket. A student who does not play cricket, plays football. Every football player has got a two-wheeler. Which of the following conclusions cannot be drawn from the above data?**

1. 60% of the students do not have two-wheelers.

2. No cricketer has a two-wheeler.

3. Cricket players do not play football.

**Select the correct answer using the code given below:**

24. **The ratio of a two-digit natural number to a number formed by reversing its digits is 4: 7. The number of such pairs is**

25. **In an examination, A has scored 20 marks more than B. If B has scored 5% less marks than A, how much has B scored?**

26. **Seeta and Geeta go for a swim after a gap of every 2 days and every 3 days respectively. If on 1st January both of them went for a swim together, when will they go together next?**

27. **X, Y and Z are three contestants in a race of 1000 m. Assume that all run with different uniform speeds. X gives Y a start of 40 m and X gives Z a start of 64 m. If Y and Z were to compete in a race of 1000 m, how many metres start will Y give to Z?**

28. **If x is greater than or equal to 25 and y is less than or equal to 40, then which one of the following is always correct?**
29. **Ena was born 4 years after her parents' marriage. Her mother is three years younger than her father and 24 years older than Ena, who is 13 years old. At what age did Ena's father get married?**

30. **Rakesh had money to buy 8 mobile handsets of a specific company. But the retailer offered very good discount on that particular handset. Rakesh could buy 10 mobile handsets with the amount he had. What was the discount the retailer offered?**

31. **The average marks of 100 students are given to be 40. It was found later that marks of one student were 53 which were misread as 83. The corrected mean marks are**

40. **If every alternative letter of the English alphabet from B onwards (including B) is written in lower case (small letters) and the remaining letters are capitalized, then how is the first month of the second half of the year written?**
41. **Sunita cuts a sheet of paper into three pieces. Length of first piece is equal to the average of the three single digit odd prime numbers. Length of the second piece is equal to that of the first plus one-third the length of the third. The third piece is as long as the other two pieces together. The length of the original sheet of paper is**
42. **In the sequence 1, 5, 7, 3, 5, 7, 4, 3, 5, 7, how many such 5s are there which are not immediately preceded by 3 but are immediately followed by 7?**

43. **A joint family consists of seven members A, B, C, D, E, F and G with three females. G is a widow and sister-in-law of D's father F. B and D are siblings and A is daughter of B. C is cousin of B. Who is E?**

1. Wife of F

2. Grandmother of A

3. Aunt of C

**Select the correct answer using the code given below:**

44. **Each face of a cube can be painted in black or white colours. In how many different ways can the cube be painted?**

45. **How many triplets (x, y, z) satisfy the equation x + y + z = 6, where x, y and z are natural numbers?**
46. **If $ means 'divided by'; @ means 'multiplied by'; # means 'minus', then the value of 10#5@1$5 is**
47. **An 8-digit number 4252746B leaves remainder 0 when divided by 3. How many values of B are possible?**