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Kaprekar Contest Screening Test

Total questions: 30

Worksheet time: 2hrs 6mins

Name
Class
Date
1.

If 4921 × D = ABBBD, then the sum of the digits of ABBBD × D is _________

a)

19

b)

20

c)

25

d)

26

2.

What is the 2019th digit to the right of the decimal point, in the decimal representation of 28^5?

a)

2

b)

4

c)

8

d)

7

3.

If X is a 1000 digit number, Y is the sum of its digits, Z the sum of the digits of Y and W the sum of the digits of Z, then the maximum possible value of W is

a)

10

b)

11

c)

12

d)

22

4.

Let x be the number 0.000.......001 which has 2019 zeroes after the decimal point. Then which of the following numbers is the greatest?

a)

10000 + x

b)

10000 · x

c)

x/10000

d)

2x

5.

If DDED + ABC = CBA, then the number of possible values for A, B, C, D, E satisfying this equation where A, B, C, D and E are distinct digits is

a)

6

b)

5

c)

4

d)

3

6.

In a 5 × 5 grid having 25 cells, Janani has to enter 0 or 1 in each cell such that each sub square grid of size 2 × 2 has exactly three equal numbers. What is the maximum possible sum of the numbers in all the 25 cells put together?

a)

23

b)

21

c)

19

d)

18

7.

ABCD is a square. E is one fourth of the way from A to B and F is one fourth of the way from B to C. X is the centre of the square. Side of the square is 8 cm. Then the area of the shaded region in the figure in cm^2 is

a)

14

b)

16

c)

18

d)

20

8.

ABCD is a rectangle with E and F are midpoints of CD and AB respectively and G is the mid-point of AF. The ratio of the area of ABCD to area of AECG is

a)

4 : 3

b)

3 : 2

c)

6 : 5

d)

8 : 3

9.

If R A T + M A T + V A T + F L A T and each alphabet represents a different digit, what is the maximum possible value of FLAT?

a)

2450

b)

2405

c)

2305

d)

2350

10.

How many positive integers smaller than 400 can you get as a sum of eleven consecutive positive integers?

a)

37

b)

35

c)

33

d)

31

11.

Let x, y and z be positive real numbers and let x ≥ y ≥ z so that x + y + z = 20.1. Which of the following statements is true?

a)

Always xy < 99

b)

Always xy > 1

c)

Always xy ≠ 75

d)

Always yz ≠ 49

12.

A sequence [a_n] is generated by the rule, a_n = a_n – 1 – a_n – 2 for n ≥ 3. Given a_1 = 2 and a_2 = 4, then sum of the first 2019 terms of the sequence is given by

a)

8

b)

2692

c)

-2692

d)

-8

13.

There are exactly 5 prime numbers between 2000 and 2030. The difference between the largest and the smallest among these is

a)

16

b)

20

c)

24

d)

26

14.

Which of the following geometric figures is possible to construct?

a)

A pentagon with 4 right angled vertices

b)

An octagon with all 8 sides equal and 4 angles each of measure 60° and other four angles of measure 210°

c)

A parallelogram with 3 vertices of obtuse angle measures.

d)

A hexagon with 4 reflex angles.

15.

If y^10 = 2019, then

a)

2 < y < 3

b)

1 < y < 2

c)

4 < y < 5

d)

3 < y < 4

16.

The 100th term of the sequence of all natural numbers whose second digit (from left to right) is 1, is written in strictly increasing order without repetition.

4 lines
17.

In ΔABC, AB = 6 cm, AC = 8 cm, median AD = 5 cm. Then, the area of ΔABC in cm² is ________.

4 lines
18.

Given a, b, c are real numbers such that 9a + b + 8c = 12 and 8a - 12b - 9c = 1. Then a^2 - b^2 + c^2 = _________.

4 lines
19.

In the given figure, ΔABC is a right angled triangle with ∠ABC = 90°. D, E, F are points on AB, AC, BC respectively such that AD = AE and CE = CF. Then, ∠DEF = ______ (in degree).

a)

45

b)

90

c)

60

d)

30

20.

Numbers of 5-digit multiples of 13 is ___________.

4 lines
21.

The area of a sector and the length of the arc of the sector are equal in numerical value. Then the radius of the circle is __________.

4 lines
22.

If a, b, c, d are positive integers such that 30/(1/a + 1/b + 1/c + 1/d), then d is __________.

4 lines
23.

A teacher asks 10 of her students to guess her age. They guessed it as 34, 38, 40, 42, 46, 48, 51, 54, 57 and 59. Teacher said "At least half of you guessed it too low and two of you are off by one. Also my age is a prime number". The teacher's age is __________.

4 lines
24.

The sum of 8 positive integers is 22 and their LCM is 9. The number of integers among these that are less than 4 is __________.

4 lines
25.

The number of natural numbers n ≤ 2019 such that 3^n * 48 is an integer is __________.

4 lines
26.

Anita is riding her bicycle at the rate of 18 km/h. When Anita is riding her bicycle on a straight road, she sees Basker skating at the rate of 12 km/h in the same direction, 1/2 km in front of her. Anita overtakes him and can see him in her rear view mirror until he is 1/2 km behind her. The total time in seconds that Anita can see Baskar is ____________.

4 lines
27.

In a room, 50% of the people are wearing gloves, and 80% of the people are wearing hats. The minimum percentage of people in the room wearing both a hat and a glove is __________.

4 lines
28.

In ΔABC, AB = BC = 29 and AC = 42 cm. The area of ΔABC = ________ cm^2.

4 lines
29.

The smallest integer larger than the perimeter of any triangle with two sides of length 10 and 20 units is ____________.

4 lines
30.

The number of perfect cubes that lie between 2^9 + 1 and 2^18 + 1 is __________.

4 lines