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# Gauss Contest (NMTC PRIMARY 2018 - V and VI Grades) - Stage I- Problems and Solution

## Part A

###### Problem 1

Observe the following sequence. What is the 100th term?

(A) 1
(B) 0
(C) 2
(D) 3

###### Problem 2

A number is multiplied by 2 then by , then by 4 , then by then by 6 and finally by . The answer is 16 . Then the number is
(A) odd
(B) even
(C) Square
(D) a cube

###### Problem 3

Samrud bought a t- shirt for Rs.250. His friend Shlok wanted by buy it. Samrud wants to have a profit on that. The selling price is (in rupees)
(A) 280
(B) 278
(C) 276
(D) 275

The value of is
(A) -50
(B) 50
(C) 100
(D) -100

###### Problem 5

In the adjoining figure what portion of the figure is shaded ?

(A)
(B)
(C)
(D)

###### Problem 6

The sum of the numbers in the three brackets ( ) is

(A) 60
(B) 55
(C) 50
(D) 45

###### Problem 7

A is the smallest three digit number which leaves a remainder 2 when divided by is the smallest three digit number which leaves remainder 7 . When divided by 12 . Then is
(A) 205
(B) 312
(C) 215
(D) 207

###### Problem 8

A square of side 3 cm in cut into 9 equal squares. Another square of side 4 cm is cut into 16 equal squares. Saket made a bigger square using all the smaller square bits. The length of the side of the bigger square is (in cm)

(A) 7
(B) 6
(C) 5
(D) 8

###### Problem 9

A contractor constructed a big hall, rectangular in shape, with length 32 meters and breadth 18 meters. He wanted to buy 1 meter by 1 meter tiles. But in the shop 3 meter by 2 meter tiles only were available. How many tiles he has to buy for tilting the floor?

(A) 48
(B) 96
(C) 120
(D) 126

###### Problem 10

The fraction to be added to to get the fraction is
(A)
(B)
(C)
(D)

#### Part B

###### Problem 11

In the adjoining figure . GE is parallel to , and . If , the measure of is .

###### Problem 12

is a triangle in which the angles are in the ratio . PQR is a triangle in which the angles are in the ratio . The difference between the least angle of and the least angle of PQR is . Then .

###### Problem 13

Samrud had to multiply a number by 35 . By mistake he multiplied by 53 and got a result 720 more. The new product is .

###### Problem 14

Vishva plays football every 4 th day. He played on a Tuesday. He plays football on a Tuesday again in is days.

###### Problem 15

In an elementary school of the students are girls. If there are 240 less girls than boys, then the strength of the school is .

###### Problem 16

There are three concentric circles as shown in the figure. The radii of them are and 6 . The ratio of the area of the shaded region to the area of the dotted region is where are integers and have no common factor other than 1. Then .

###### Problem 17

The value of is .

###### Problem 18

When a two digit number divides 265 , the remainder is 5 . The number of such two digit numbers is .

###### Problem 19

If , the value of is .

###### Problem 20

When water becomes ice, its volume increases by . When ice melts into water its volume decreases by . Then .

## Part A

###### Problem 1

Observe the following sequence. What is the 100th term?

(A) 1
(B) 0
(C) 2
(D) 3

###### Problem 2

A number is multiplied by 2 then by , then by 4 , then by then by 6 and finally by . The answer is 16 . Then the number is
(A) odd
(B) even
(C) Square
(D) a cube

###### Problem 3

Samrud bought a t- shirt for Rs.250. His friend Shlok wanted by buy it. Samrud wants to have a profit on that. The selling price is (in rupees)
(A) 280
(B) 278
(C) 276
(D) 275

The value of is
(A) -50
(B) 50
(C) 100
(D) -100

###### Problem 5

In the adjoining figure what portion of the figure is shaded ?

(A)
(B)
(C)
(D)

###### Problem 6

The sum of the numbers in the three brackets ( ) is

(A) 60
(B) 55
(C) 50
(D) 45

###### Problem 7

A is the smallest three digit number which leaves a remainder 2 when divided by is the smallest three digit number which leaves remainder 7 . When divided by 12 . Then is
(A) 205
(B) 312
(C) 215
(D) 207

###### Problem 8

A square of side 3 cm in cut into 9 equal squares. Another square of side 4 cm is cut into 16 equal squares. Saket made a bigger square using all the smaller square bits. The length of the side of the bigger square is (in cm)

(A) 7
(B) 6
(C) 5
(D) 8

###### Problem 9

A contractor constructed a big hall, rectangular in shape, with length 32 meters and breadth 18 meters. He wanted to buy 1 meter by 1 meter tiles. But in the shop 3 meter by 2 meter tiles only were available. How many tiles he has to buy for tilting the floor?

(A) 48
(B) 96
(C) 120
(D) 126

###### Problem 10

The fraction to be added to to get the fraction is
(A)
(B)
(C)
(D)

#### Part B

###### Problem 11

In the adjoining figure . GE is parallel to , and . If , the measure of is .

###### Problem 12

is a triangle in which the angles are in the ratio . PQR is a triangle in which the angles are in the ratio . The difference between the least angle of and the least angle of PQR is . Then .

###### Problem 13

Samrud had to multiply a number by 35 . By mistake he multiplied by 53 and got a result 720 more. The new product is .

###### Problem 14

Vishva plays football every 4 th day. He played on a Tuesday. He plays football on a Tuesday again in is days.

###### Problem 15

In an elementary school of the students are girls. If there are 240 less girls than boys, then the strength of the school is .

###### Problem 16

There are three concentric circles as shown in the figure. The radii of them are and 6 . The ratio of the area of the shaded region to the area of the dotted region is where are integers and have no common factor other than 1. Then .

###### Problem 17

The value of is .

###### Problem 18

When a two digit number divides 265 , the remainder is 5 . The number of such two digit numbers is .

###### Problem 19

If , the value of is .

###### Problem 20

When water becomes ice, its volume increases by . When ice melts into water its volume decreases by . Then .

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