Olympiad Test : Algebra - 2 - Class 6 MCQ

3(x + 6) + 2(x + ) = 64
⇒ 3x + 18 + 2x + 6 =64
⇒ 5x + 24 = 64
⇒ 5x = 64 - 24
⇒ 5x = 40

Here, 3(2 – 5p) –2 (1 – 6p) = 1
⇒ 6 - 15p - 2 + 12p =1
⇒ 4 - 3p = 1 ⇒ 3p = 4 -1

Let the number be x.
∴ 3x - 8 = 13 ⇒ 3x = 13 + 8
⇒ 3x = 21

Let the number are x, x + 1, x+ 2.
∴ x + x 1 + x + 2 = 114
⇒ 3x +3 = 114 ⇒ 3x = 114 - 3

Greatest number = 37 + 2 = 39

Let the breadth be x m.
Length = (x + 5)
Perimeter of rectangle = 74
⇒ 2(x + 5 + x) = 74
⇒ 2x + 5 = 37 ⇒ 2x = 37 - 5
⇒ 2x = 32

Length = 16 + 5 = 21m

Let's denote the unknown number as "x." The problem states that if 9 is added to twice the number, the result is 57. We can set up an equation to represent this situation:

2x+9 = 57

Now, solve for x:

Subtract 9 from both sides of the equation:

2x = 48

Divide both sides by 2:

x = 24

So, the unknown number is 24.

Let the number be x.
∴ x - 7 = 37 ⇒ x = 37 + 7 = 44

Let the age of daughter be x years.
∴ Man's age = 3x.
and 5 years ago, daughter's age = x-5
∴ Man's age = 3x —5
⇒ 3x —5= 4x —20 = 4x —3x = — 5 + 20
⇒ x =15 years 

Let the age of karan be x years.
Father’s age = 3x years
After 14 years,
3x +14 = 2(x –14)
⇒ 3x + 14 = 2x + 28
 ⇒ x = 28 - 14
⇒ x = 14 years 

Let the three consecutive even numbers are
x, x + 2, x + 4.
∴ x + x + 2 + x + 4 =78
⇒ 3x = 78 - 6
⇒ 3x = 72

Let the price of the ratio be Rs. x.
5x =170 + 3x
⇒ 2x =170

Let the breadth be x m
Length = 3xm
Perimeter of rectangular park = 168

Let the number be x.
∴ x × 17 + 4 = 225
⇒ 17x = 225 - 4
⇒ 17x = 221

Required result
= 3a –2b + 5c + 2a +5b –7c – a – b + c
= 4a + 2b – c

In the expression 4y²zx³, the coefficient of a variable is the constant factor that multiplies that variable.

The term involving x³ is 4y²zx³.

The coefficient of x³ is everything multiplying x³, which in this case is 4y²z.

Thus, the correct coefficient of x³ is 4y²z.

Required result
= 2a–[3b–{a – (2c + 3b) + 4c –3a + 3b + 6c}]
= 2a –[3b–{–2a +6b +8c}]
= 2a –[3b +2a – 6b – 8c]
= 2a –[2a–3b–8c] = 2a –2a + 3b +8c
= 3b + 8c

xy – [ yz – zx – {yx – (3y – xz) – (xy – zy)}]
=  xy – [ yz – zx – {yx – 3y + xz– xy + zy}]
=  xy – [ yz – zx – yx + 3y – xz + xy – zy]
=  xy + 2xz –3y

Let the number be x.
∴ 3 × x + 7 = 70
⇒ 3x = 70 - 7
⇒ 3x = 63

 Let the breadth be x.
∴ Length = x + 7
Perimeter of wire = 86

∴ Length = x + 7 = 18 + 7 = 25 cm