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# Gauss Contest (NMTC PRIMARY LEVEL- V and VI Grades) - Problems and Solution

###### Problem 1

The value of , when simplified, is

a)
b)
c)
d) 1000

###### Problem 2

When is divided by , the result is . When is divided by , the result is . Then the numerical value of is

a) 38
b) 40
c) 39
d) 48

###### Problem 3

There are 5 cards numbered as shown In the figure. The number of ways in which one can choose 3 or less cards which contain only odd numbers is

a) 8
b) 7
c) 3
d) 21

###### Problem 4

is a triangle. The bisector of meets at . The bisectors of and meet at .
Then the measure of is

a)
b)
c)
d)

###### Problem 5

Samrud secures of the marks but fails by 30 marks. Saket gets marks which is 42 marks more than the minimum pass marks. The maximum marks in the test would be

a) 100
b) 200
c) 300
d) 600

###### Problem 6

The greatest number that divides 25,73 and 97 to leave the same remainder is

a) 19
b) 22
c) 24
d) 37

###### Problem 7

If where are natural numbers, then the numerical value of is

a) 8
b) 13
c) 12
d) 9

###### Problem 8

In the adjoining figure, two equilateral triangles are placed such that is parallel to . If , , the area in of trapezium is

a)
b)
c)
d)

###### Problem 9

Siva found the average of 5 numbers. He got an answer 40 which is wrong because, while listing, instead of writing the number 43 he wrote 48 . The correct average must be

a) 38
b) 39
c) 41
d) 31

###### Problem 10

In the adjoining figure, is a square. Also . Then the value of (in degrees) is

a) 210
b) 220
c) 215
d) 225

###### Problem 11

If the numerator and diameter of a fraction are increased by and respectively, then the fraction becomes . If the original fraction is , where and have no common factors, then is

a) 3
b) 6
c) 7
d) 9

###### Problem 12

Gita divided 360 into 4 parts such that twice the first part, thrice the second part, five times the third part and six times the fourth part are all equal. Then the difference between the third and fourth parts is

a) 20
b) 15
c) 10
d) 7

###### Problem 13

In the adjoining figure, the degree measure of is

a)
b)
c)
d)

###### Problem 14

Consider the following sequence:

The digit in the place is

a) 3
b) 5
c) 7
d) 1

###### Problem 15

In the two figures, there is a pattern of numbers which are same. Then the number in the head of the second figure,

a) 6
b) 13
c) 8
d) 10

###### Problem 16

There are two cars and . The speed of is less than that of . They travel a certain equal distance. The percentage of time does need to travel than is . Then is .

###### Problem 17

Six equal unit squares are arranged in different shapes as shown in the diagram below:

In diagram (1), the perimeter is , which equals 10. Similarly the perimeters of the other shapes also are found out. Let the perimeters be denoted by and .
Then the value of is .

###### Problem 18

In a two digit number, the digit in the tens place is twice the digit in the units place. If we swap the places of these two digits, a new two-digit number is formed. The sum of these two numbers is 132 . The original number is .

###### Problem 19

An ant starts from and wants to go to . It is allowed to go along the lines and pass a line and a point only once. The number of different routes that it can take to go from to is .

###### Problem 20

Three consecutive natural numbers are taken from 1 to 6 . With these three numbers, three digit numbers are formed. The total number of such 3-digit numbers is .

and .
If , then .

###### Problem 22

The number of 5-digit numbers of the form (where are digits), each of which is divisible by 36 is .

###### Problem 23

The units digit of the sum of all 2-digit numbers is .

###### Problem 24

A natural number is taken. One sixth of this number is subtracted from it. From the resulting number, half of the number is taken and from this number one fifth is taken. If the resulting number is 3 , then the original number taken is .

###### Problem 25

The least number that is added to 2716321 to make it exactly divisible by 3456 is .

###### Problem 1

The value of , when simplified, is

a)
b)
c)
d) 1000

###### Problem 2

When is divided by , the result is . When is divided by , the result is . Then the numerical value of is

a) 38
b) 40
c) 39
d) 48

###### Problem 3

There are 5 cards numbered as shown In the figure. The number of ways in which one can choose 3 or less cards which contain only odd numbers is

a) 8
b) 7
c) 3
d) 21

###### Problem 4

is a triangle. The bisector of meets at . The bisectors of and meet at .
Then the measure of is

a)
b)
c)
d)

###### Problem 5

Samrud secures of the marks but fails by 30 marks. Saket gets marks which is 42 marks more than the minimum pass marks. The maximum marks in the test would be

a) 100
b) 200
c) 300
d) 600

###### Problem 6

The greatest number that divides 25,73 and 97 to leave the same remainder is

a) 19
b) 22
c) 24
d) 37

###### Problem 7

If where are natural numbers, then the numerical value of is

a) 8
b) 13
c) 12
d) 9

###### Problem 8

In the adjoining figure, two equilateral triangles are placed such that is parallel to . If , , the area in of trapezium is

a)
b)
c)
d)

###### Problem 9

Siva found the average of 5 numbers. He got an answer 40 which is wrong because, while listing, instead of writing the number 43 he wrote 48 . The correct average must be

a) 38
b) 39
c) 41
d) 31

###### Problem 10

In the adjoining figure, is a square. Also . Then the value of (in degrees) is

a) 210
b) 220
c) 215
d) 225

###### Problem 11

If the numerator and diameter of a fraction are increased by and respectively, then the fraction becomes . If the original fraction is , where and have no common factors, then is

a) 3
b) 6
c) 7
d) 9

###### Problem 12

Gita divided 360 into 4 parts such that twice the first part, thrice the second part, five times the third part and six times the fourth part are all equal. Then the difference between the third and fourth parts is

a) 20
b) 15
c) 10
d) 7

###### Problem 13

In the adjoining figure, the degree measure of is

a)
b)
c)
d)

###### Problem 14

Consider the following sequence:

The digit in the place is

a) 3
b) 5
c) 7
d) 1

###### Problem 15

In the two figures, there is a pattern of numbers which are same. Then the number in the head of the second figure,

a) 6
b) 13
c) 8
d) 10

###### Problem 16

There are two cars and . The speed of is less than that of . They travel a certain equal distance. The percentage of time does need to travel than is . Then is .

###### Problem 17

Six equal unit squares are arranged in different shapes as shown in the diagram below:

In diagram (1), the perimeter is , which equals 10. Similarly the perimeters of the other shapes also are found out. Let the perimeters be denoted by and .
Then the value of is .

###### Problem 18

In a two digit number, the digit in the tens place is twice the digit in the units place. If we swap the places of these two digits, a new two-digit number is formed. The sum of these two numbers is 132 . The original number is .

###### Problem 19

An ant starts from and wants to go to . It is allowed to go along the lines and pass a line and a point only once. The number of different routes that it can take to go from to is .

###### Problem 20

Three consecutive natural numbers are taken from 1 to 6 . With these three numbers, three digit numbers are formed. The total number of such 3-digit numbers is .

and .
If , then .

###### Problem 22

The number of 5-digit numbers of the form (where are digits), each of which is divisible by 36 is .

###### Problem 23

The units digit of the sum of all 2-digit numbers is .

###### Problem 24

A natural number is taken. One sixth of this number is subtracted from it. From the resulting number, half of the number is taken and from this number one fifth is taken. If the resulting number is 3 , then the original number taken is .

###### Problem 25

The least number that is added to 2716321 to make it exactly divisible by 3456 is .

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