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

Simplify:

3 a + 7 b

4 a + 7 b

2a+7b

4 a + 3b

2 / 50

Solve for : $2 y + 15$

3 / 50

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

-5

-3

4 / 50

Solve the inequality: $- 4$

x ≥ 4

x ≤ − 4

x ≥ − 4

x ≤ 4

5 / 50

Expand:

x^2 − 25

x^2 +10x+25

x^2 + 25

x^2 − 10 x + 25

6 / 50

Solve for : $63$

7 / 50

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

-2

8 / 50

Solve the system: $13$ and $5$

x = 2 , y = 3

x = 1 , y = 4

x = 3 , y = 2

x = 4 , y = 1

9 / 50

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

10 / 50

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

x = 1 , y = 2 x

x = 4 , y = − 0.5

x = 2 , y = 1

x = 3 , y = 0.25

11 / 50

Factorize: $+ 14$

7p (1 + 2)

7 ( p + 14)

p ( 7 + 14)

7 ( p + 2 )

12 / 50

Solve for : $81$

13 / 50

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

14 / 50

Solve for $x$ :

15 / 50

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

30 cm²

50 cm²

20 cm²

40 cm²

16 / 50

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

17 / 50

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

-12

-11

-13

-14

18 / 50

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

19 / 50

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

20 / 50

Solve for $p$ : $27$

21 / 50

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

6 cm

4 cm

7 cm

5 cm

22 / 50

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

23 / 50

What are the roots of the equation $0$ ?

2, 5

1, 10

-1, -10

-2, -5

24 / 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?

25 / 50

Simplify:

7m−4n

3m+4n

7m−2n

3m−4n

26 / 50

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

27 / 50

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

28 / 50

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

-1

29 / 50

Expand:

x 2 − 25

x 2 + 25

x 2 + 10 x + 25

x 2 − 10 x + 25

30 / 50

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

31 / 50

Expand:

2x+4

x + 8

2 x + 8

2x+6

32 / 50

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

33 / 50

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

7 and 8

6 and 9

8 and 7

5 and 10

34 / 50

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

35 / 50

Solve for :

36 / 50

Factorize completely: $2x^2$

2 ( x^2 − 4 )

2(x−2) (x+2)

2(x−4)(x+2)

2 ( x − 2 ) ^2

37 / 50

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

38 / 50

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

39 / 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.

40 / 50

Expand:

5 y − 15

2 y − 15

6 y − 5

6 y − 15

41 / 50

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

42 / 50

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

43 / 50

Solve for : $= 21$

44 / 50

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

45 / 50

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

46 / 50

Which of the following is a binomial?

2x+5y

4x−2x+1

47 / 50

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

135

120

125

130

48 / 50

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

y=2x+3

2x+5=11

xy=10

x 2 +2x+1=0

49 / 50

Solve for $m$ :

50 / 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.

5 m

7 m

4 m

6 m

Your score is

The average score is 52%

Simplify: 3a+2b−a+5b

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

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

Solve the inequality: 8−3x≤−4

Expand: (x+5)(x−5)

Solve for k: 7k=63

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

Solve the system: 2x+3y=13 and 4x−y=5

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

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

Factorize: 7p+14

Solve for x: 32x=81

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

Solve for x: x+12=25

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

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

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

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

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

Solve for p: 3p=27

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

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

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

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?

Simplify: 5m−3n+2m+n

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

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

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

Expand: (x+5)(x−5)

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

Expand: 2(x+4)

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

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

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

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

Factorize completely: 2x^2 −8

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

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

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.

Expand: 3(2y−5)

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

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

Solve for z: 4z−7=21

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

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

Which of the following is a binomial?

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

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

Solve for mm: 2m+5=17.

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.

Simplify:

Solve for : $2 y + 15$

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

Solve the inequality: $- 4$

Expand:

Solve for : $63$

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

Solve the system: $13$ and $5$

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

Factorize: $+ 14$

Solve for : $81$

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

Solve for $x$ :

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

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

Solve for $p$ : $27$

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

What are the roots of the equation $0$ ?

Simplify:

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

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

Expand:

Expand:

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

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

Solve for :

Factorize completely: $2x^2$

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

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

Expand:

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

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

Solve for : $= 21$

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

Solve for $m$ :

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.