Algebra Quantitative Reasoning

Algebra Quantitative Reasoning refers to the Quantitative portion of the National Aptitude Test (NAT), a standardised test for admissions in Pakistan.

1 / 50

Expand:

2x+4

x + 8

2 x + 8

2x+6

2 / 50

For what value of will the system and have infinitely many solutions?

3 / 50

Solve the inequality: $- 4$

x ≤ − 4

x ≤ 4

x ≥ 4

x ≥ − 4

4 / 50

Expand:

2 y − 15

6 y − 5

5 y − 15

6 y − 15

5 / 50

A two-digit number is such that the sum of its digits is 10. When the digits are reversed, the number increases by 36. Find the original number.

6 / 50

Which of the following is a binomial?

2x+5y

4x−2x+1

7 / 50

Solve for : $63$

8 / 50

The width of a rectangle is $w$ . The length is 5 meters more than twice the width. If the perimeter is 40 meters, find the width.

4 m

7 m

5 m

6 m

9 / 50

If $= 14$ and $7$ , find the value of $p$ .

10 / 50

The sum of two numbers is 24. Their difference is 6. What is the product of the two numbers?

125

135

120

130

11 / 50

Solve the system: $= 10$ and $8$

x = 4 , y = − 0.5

x = 1 , y = 2 x

x = 3 , y = 0.25

x = 2 , y = 1

12 / 50

If and $- 2$ , what is the value of $s$ ?

-13

-14

-12

-11

13 / 50

If $8$ and $= 40$ , what is the value of ?

14 / 50

Solve for $m$ :

15 / 50

The product of two consecutive even integers is 168. What is the smaller integer?

16 / 50

Solve for : $81$

17 / 50

Solve for $x$ :

18 / 50

If $15$ and $4$ , what is the value of ?

-1

19 / 50

Expand:

x^2 − 25

x^2 +10x+25

x^2 + 25

x^2 − 10 x + 25

20 / 50

Expand:

x 2 + 25

x 2 − 25

x 2 + 10 x + 25

x 2 − 10 x + 25

21 / 50

Factorize completely: $2x^2$

2 ( x^2 − 4 )

2(x−2) (x+2)

2 ( x − 2 ) ^2

2(x−4)(x+2)

22 / 50

Twice a number subtracted from 15 gives the same result as the number added to 3. What is the number?

23 / 50

Solve for :

24 / 50

The product of two consecutive odd integers is 143. What is the larger integer?

25 / 50

Solve for $p$ : $27$

26 / 50

Identify the constant term in the expression $4x^2−2x$ .

-2

27 / 50

Find if the system $10$ and $5$ has no solution.

28 / 50

What is the coefficient of $x$ in the expression $2 x^2$ ?

-3

-5

29 / 50

What is the value of $a^2+b$ if $3$ and $5$ ?

30 / 50

The sum of the digits of a two-digit number is 9. If the digits are reversed, the new number is 27 less than the original number. What is the original number?

31 / 50

The length of a rectangle is 3 cm more than its width. If the perimeter is 26 cm, what is the width?

4 cm

6 cm

7 cm

5 cm

32 / 50

Solve for : $2 y + 15$

33 / 50

If $= 4$ and $3$ , what is the value of $a^2−b^2?$

34 / 50

The sum of three consecutive even integers is 72. What is the largest integer?

35 / 50

Simplify:

3m−4n

7m−2n

3m+4n

7m−4n

36 / 50

The area of a trapezium with bases 10 cm and 6 cm and height 5 cm is _______.

20 cm²

30 cm²

40 cm²

50 cm²

37 / 50

The sum of three consecutive integers is 78. What is the smallest integer?

38 / 50

If $3$ , what is the value of $5$ ?

39 / 50

For what value of will the system $= 7$ and $14$ have infinitely many solutions?

40 / 50

If $= 5$ and $2$ , what is the value of $n 2$ ?

41 / 50

The sum of two numbers is 15 and their difference is 5. What are the numbers?

5 and 10

7 and 8

6 and 9

8 and 7

42 / 50

Simplify:

4 a + 7 b

4 a + 3b

2a+7b

3 a + 7 b

43 / 50

Factorize: $+ 14$

7p (1 + 2)

7 ( p + 14)

p ( 7 + 14)

7 ( p + 2 )

44 / 50

A number is doubled and then increased by 5. The result is 7 less than triple the original number. What is the number?

45 / 50

Solve the system: $13$ and $5$

x = 4 , y = 1

x = 2 , y = 3

x = 1 , y = 4

x = 3 , y = 2

46 / 50

If and $= 4$ , what is the value of ?

47 / 50

If $= 4 x - 3$ and $2$ , what is the value of $y$ ?

48 / 50

Which of the following is a linear equation in one variable?

xy=10

y=2x+3

2x+5=11

x 2 +2x+1=0

49 / 50

What are the roots of the equation $0$ ?

1, 10

-1, -10

2, 5

-2, -5

50 / 50

Solve for : $= 21$

Your score is

The average score is 52%

Expand: 2(x+4)

For what value of k will the system 2x+3y=7 and kx+6y=14 have infinitely many solutions?

Solve the inequality: 8−3x≤−4

Expand: 3(2y−5)

A two-digit number is such that the sum of its digits is 10. When the digits are reversed, the number increases by 36. Find the original number.

Which of the following is a binomial?

Solve for k: 7k=63

The width of a rectangle is ww. The length is 5 meters more than twice the width. If the perimeter is 40 meters, find the width.

If 5p−2q=14 and p+q=7, find the value of p.

The sum of two numbers is 24. Their difference is 6. What is the product of the two numbers?

Solve the system: 3x+4y=10 and 5x−2y=8

If s=3t−5 and t=−2, what is the value of s?

If x+y=8 and x2+y2=40, what is the value of xy?

Solve for mm: 2m+5=17.

The product of two consecutive even integers is 168. What is the smaller integer?

Solve for x: 32x=81

Solve for x: x+12=25

If 4a−b=15 and a=4, what is the value of b?

Expand: (x+5)(x−5)

Expand: (x+5)(x−5)

Factorize completely: 2x^2 −8

Twice a number subtracted from 15 gives the same result as the number added to 3. What is the number?

Solve for x: 5(x+2)=3(x+8)

The product of two consecutive odd integers is 143. What is the larger integer?

Solve for p: 3p=27

Identify the constant term in the expression 4x^2−2x+9.

Find k if the system 4x+6y=10 and 2x+ky=5 has no solution.

What is the coefficient of x in the expression 5−3x+2x^2?

What is the value of a^2+b if a=3 and b=5?

The sum of the digits of a two-digit number is 9. If the digits are reversed, the new number is 27 less than the original number. What is the original number?

The length of a rectangle is 3 cm more than its width. If the perimeter is 26 cm, what is the width?

Solve for y: 5y+3=2y+15

If a=4 and b=3, what is the value of a^2−b^2?

The sum of three consecutive even integers is 72. What is the largest integer?

Simplify: 5m−3n+2m+n

The area of a trapezium with bases 10 cm and 6 cm and height 5 cm is _______.

The sum of three consecutive integers is 78. What is the smallest integer?

If x=3, what is the value of 2x+5?

For what value of k will the system 2x+3y=7 and kx+6y=14 have infinitely many solutions?

If m=5 and n=2, what is the value of 2m2−n2?

The sum of two numbers is 15 and their difference is 5. What are the numbers?

Simplify: 3a+2b−a+5b

Factorize: 7p+14

A number is doubled and then increased by 5. The result is 7 less than triple the original number. What is the number?

Solve the system: 2x+3y=13 and 4x−y=5

If y=2x−1 and x=4, what is the value of y?

If y=4x−3 and x=2, what is the value of y?

Which of the following is a linear equation in one variable?

What are the roots of the equation x2−7x+10=0?

Solve for z: 4z−7=21

Expand:

For what value of will the system and have infinitely many solutions?

Solve the inequality: $- 4$

Expand:

Solve for : $63$

The width of a rectangle is $w$ . The length is 5 meters more than twice the width. If the perimeter is 40 meters, find the width.

If $= 14$ and $7$ , find the value of $p$ .

Solve the system: $= 10$ and $8$

If and $- 2$ , what is the value of $s$ ?

If $8$ and $= 40$ , what is the value of ?

Solve for $m$ :

Solve for : $81$

Solve for $x$ :

If $15$ and $4$ , what is the value of ?

Expand:

Expand:

Factorize completely: $2x^2$

Solve for :

Solve for $p$ : $27$

Identify the constant term in the expression $4x^2−2x$ .

Find if the system $10$ and $5$ has no solution.

What is the coefficient of $x$ in the expression $2 x^2$ ?

What is the value of $a^2+b$ if $3$ and $5$ ?

Solve for : $2 y + 15$

If $= 4$ and $3$ , what is the value of $a^2−b^2?$

Simplify:

If $3$ , what is the value of $5$ ?

For what value of will the system $= 7$ and $14$ have infinitely many solutions?

If $= 5$ and $2$ , what is the value of $n 2$ ?

Simplify:

Factorize: $+ 14$

Solve the system: $13$ and $5$

If and $= 4$ , what is the value of ?

If $= 4 x - 3$ and $2$ , what is the value of $y$ ?

What are the roots of the equation $0$ ?

Solve for : $= 21$