Algebra Test

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Algebra Test - 11

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Weekly Quiz Competition

Question 1
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Meera bought packs of trading cards that contain $$10$$ cards each. She gave away $$7$$ cards.
If $$x=$$number of packs of trading cards, then which of the following expression shows the number of cards left with Meera?

A
$$10x-7$$

B
$$7x-8$$

C
$$5-10x$$

D
$$8-5x$$

Solution

Given:Number of packs of trading cards$$=x$$
Packs of trading cards that contain $$10$$ cards each$$=10x$$
She gave away $$7$$ cards$$=-7$$
Number of cards left with Meera$$=10x-7$$
Question 2
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The weight of Rahul is $$5\ kg$$ more than Sachin .The weight of Samir is $$12\ kg$$ less than double the weight of Sachin .If the total weight of all the three is $$93$$ form the equation

A
$$4x-7=93$$

B
x+5=0

C

$$x+ (x+5)+ (2x-12)=93$$

D
2x-12=21

Solution

Let weight of sachin $$=x \ kg$$

Acc. to question.

Weight of Rahul $$=(x+5)\ kg$$

Weight of Samir $$=(2x-12)\ kg$$

Total weight of all $$=93\ kg$$

That is ,

$$x+ (x+5)+ (2x-12)=93$$

$$4x-7=93$$
Question 3
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Which of the following represents the given statement?
The sum of a and b is multiplied by taking away $$5$$ from their sum.

A
$$(a+b)(a+b-5)$$

B
$$(a+b)(5-a-b)$$

C
$$(a+b)(5-a+b)$$

D
$$(a+b)(5+a-b)$$

Solution

We know that the word 'sum' means 'addition' and 'taking away' means 'subtraction'.
So,
Sum of $$a$$ and $$b= a+b $$
$$5$$ taken away from sum of $$a$$ and $$b = a+b-5$$
Thus,
Sum of $$a$$ and $$b$$ is multiplied by taking away 5 from the sum of $$a$$ and $$b = (a+b)(a+b-5)$$
Question 4
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Which of the following represents the statement given below?
The product of $$a$$ and $$b$$ is added to their sum.

A
$$ab+a+b$$

B
$$a+b-ab$$

C
$$a+ab$$

D
$$b+ab$$

Solution

We know that the word 'product' means 'multiplication' and 'sum' means 'addition'.
So,
Product of $$a$$ and $$b$$ $$= a \times b$$.
Sum of $$a$$ and $$b$$ $$=a+b$$

Thus,
The product of $$a$$ and $$b$$ is added to their sum $$ = a \times b+a+b$$
$$= ab+a+b$$
Question 5
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Which of the following represents the statement given below?
$$9$$ less than $$x$$?

A
$$9-x$$

B
$$x-9$$

C
$$x+9$$

D
None of these

Solution

We know that the word 'less than' represents 'subtraction'.
Thus,
$$9$$ less than $$x$$ $$=x-9$$.
Question 6
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____ represents the following statement.
The product of $$x$$ and $$y$$ is decreased by $$4$$.

A
$$4-xy$$

B
$$x(y-4)$$

C
$$xy-4$$

D
$$xy+4$$

Solution

We know that the words 'product' and 'decreased' by 'multiplication' and 'subtracted' respectively.
So,
The product of $$x$$ and $$y= $$ $$ x \times y $$.
Thus,
The product of $$x$$ and $$y$$ is decreased by $$ 4= x \times y -4$$.
$$= xy-4$$.
Question 7
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_____ represents the following statement.
$$5$$ more than twice a number $$x$$

A
$$5+x+2$$

B
$$2x+5$$

C
$$2x-5$$

D
$$5x+2$$

Solution

We know that, the word 'twice' means double and 'more than a number' means 'adding a certain amount to a number'.
Let, the number $$=x$$.
Twice the number $$=2x$$.
Thus,
$$5$$ more than twice the number $$=2x+5$$.
Question 8
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If each matchbox contains $$48$$ matchsticks, then the number of matchsticks required to fill $$n$$ such boxes is

A
$$48+n$$

B
$$48-n$$

C
$$48\div n$$

D
$$48n$$

Solution

Given,
Matchsticks required to fill $$1$$ matchbox $$=48\times 1=48$$
$$\therefore $$ Matchsticks required to fill $$n$$ matchbox $$=48\times n=48n$$
Question 9
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The length of a side of square is given as $$2x+3$$. Which expression represents the perimeter of the square.

A
$$2x+16$$

B
$$6x+9$$

C
$$8x+3$$

D
$$8x+12$$

Solution

Given, side of the square $$=(2x+3)$$
Perimeter of square $$=4\times side$$
$$=4\times (2x+3)$$
$$=8x+12$$
Question 10
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Arpita's present age is thrice of Shilpa. If Shilpa's age three years ago was $$x$$. Then Arpita's present age is

A
$$3(x-3)$$

B
$$3x+3$$

C
$$3x-9$$

D
$$3(x+3)$$

Solution

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Algebra Test - 11

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Algebra Test - 11

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SHARING IS CARING

Question 1

$$10x-7$$

$$7x-8$$

$$5-10x$$

$$8-5x$$

Solution

Question 2

$$4x-7=93$$

x+5=0

$$x+ (x+5)+ (2x-12)=93$$

2x-12=21

Solution

Question 3

$$(a+b)(a+b-5)$$

$$(a+b)(5-a-b)$$

$$(a+b)(5-a+b)$$

$$(a+b)(5+a-b)$$

Solution

Question 4

$$ab+a+b$$

$$a+b-ab$$

$$a+ab$$

$$b+ab$$

Solution

Question 5

$$9-x$$

$$x-9$$

$$x+9$$

None of these

Solution

Question 6

$$4-xy$$

$$x(y-4)$$

$$xy-4$$

$$xy+4$$

Solution

Question 7

$$5+x+2$$

$$2x+5$$

$$2x-5$$

$$5x+2$$

Solution

Question 8

$$48+n$$

$$48-n$$

$$48\div n$$

$$48n$$

Solution

Question 9

$$2x+16$$

$$6x+9$$

$$8x+3$$

$$8x+12$$

Solution

Question 10

$$3(x-3)$$

$$3x+3$$

$$3x-9$$

$$3(x+3)$$

Solution

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