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Gauss Contest (NMTC PRIMARY LEVEL- V and VI Grades) 2022 - Problems and Solution

Problem 1

If $\left(8^* 4\right)+6-(10 \div 5)=8$, then * stands for the operation.

a) $+$
b) $\times$
c) $\div$
d) $-$

Problem 2

$20 \%$ of a number is equal to $30 \%$ of another number. Six times the bigger of these numbers added to the smaller number is 2000 . Then $10 \%$ of the smallest number is

a) 10
b) 20
c) 30
d) 25

Problem 3

Samrud chooses a two-digit number. He subtracts it from 200 and doubles the result. The largest number he can get is

a) 390
b) 380
c) 400
d) 370

Problem 4

The least number which leaves 2 as remainder when divided by $5,6,8,9$ and 12 is

a) 362
b) 342
c) 332
d) 322

Problem 5

Saket takes the number 2021. There are two $2 \mathrm{~s}$, one 0 and one 1.
Using these numbers, he makes 3 -digit numbers, the sum of all these number is

a) 1488
b) 150
c) 1409
d) 1610

Problem 6

In the net of the adjoining figure numbers 1 to 6 are marked. The net is folded to form a cube The number that appears on the opposite face of 6 is

a) 4
b) 3
c) 2
d) 1

Problem 7

$10^{2021}-1$ is written as an integer in the usual decimal form. The sum of all digits of this written number is

a) 18189
b) 18187
c) 18199
d) 19189

Problem 8

August $15^{\text {th }} 1992$ was a Saturday. What day was $15^{\text {th }}$ August 1991 ?

a) Monday
b) Wednesday
c) Thursday
d) Sunday

Problem 9

Two thirds of the students in a class room are seated in three fourths of the chairs. The rest of the students are punished for not submitting the homework and hence asked to stand. There are 6 empty chairs. The number of persons (that is the number of students including the teacher) in the classroom.

a) 27
b) 28
c) 31
d) 32

Problem 10

Three are 24 four digit numbers with different digits, formed by $2,4,5$ and 7 . One of these four-digit number is a multiple of another.
Which one of the following is it?

a) 7245
b) 7542
c) 7254
d) 7425

Problem 11

Twelve friends went to a restaurant to have lunch. They ordered for 12 meals. When they were served, they found that the food was too much which can be shared by 18 people. The number of meals they would order to cater to only 12 is $\rule{2cm}{0.5mm}$

Problem 12

The least multiple of 23 which when divided by 18,21 and 24 leaves the remainders 7,10 and 13 respectively is $\rule{2cm}{0.5mm}$

Problem 13

The value of $\sqrt{\frac{(0.1)^2+(0.01)^2+(0.008)^2}{(0.01)^2+(0.001)^2+(0.0008)^2}}$ is $\rule{2cm}{0.5mm}$

Problem 14

Two numbers are respectively $20 \%$ and $50 \%$ of a third number. The percentage of the first number to the second is $\rule{2cm}{0.5mm}$.

Problem 15

Water flows through a rectangular opening $3 \mathrm{~m} \times 2 \mathrm{~m}$ with a speed of $1.5 \mathrm{~km} / \mathrm{hr}$. The amount of water that passes through the opening in 5 minutes is $\mathrm{x}^3$. Then the value of $\mathrm{x}$ is $\rule{2cm}{0.5mm}$

Problem 16

If $A=\frac{1111+3333+5555}{222+333+444}, B=\frac{555+222}{1111+2222+4444}$, then $A \times B=$ is $$\rule{1cm}{0.15mm}$$ .

Problem 17

In the adjoining figure of a cat, each small square is $1 \mathrm{~cm}^2$. The area of the cat (in $\mathrm{cm}^2$ ) is $$\rule{1cm}{0.15mm}$$ .

Problem 18

The sum of the digits of the number given by the product $\frac{666 \ldots \ldots \ldots . .666}{2021 \text { digits }} \times \frac{999 \ldots \ldots \ldots \ldots . .999}{2021 \text { digits }}$ is $$\rule{1cm}{0.15mm}$$ .

Problem 19

Two buses $X, Y$ started from two different places $P_1$ and $P_2$ respectively, moving towards each other. The ratio of the speed of bus $X$ to that of bus $Y$ was $5: 4$ after they meet, the speed of bus $X$ was reduced by $20 \%$ and the speed of $Y$ was increased by $20 \%$. When bus $X$ arrived at $P_2$, bus $Y$ was still $10 \mathrm{~km}$ away from $P_1$ The distance between the places $P_1$ and $P_2$ (in kilometers) is $$\rule{1cm}{0.15mm}$$ .

Problem 20

In the adjoining diagram, $A B C D$ is a square $P, Q, R, S$ are the mid points of sides $A B, B C, C D$ and DA respectively. PQ and SR are quadrants of circles with $B, D$ as centres and $B P$ as radius. PS and $R Q$ are part of the circle passing through $P, Q, R$ and $S$. If $A B=20 \mathrm{~cm}$, the area of the shaded region $\left(\right.$ in $\left.\mathrm{cm}^2\right)$ is $\rule{1cm}{0.15mm}$ .

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