Algebraic Expressions Model Questions Set 1 Practice Questions Answers Test with Solutions & More Shortcuts

Algebraic Expressions PRACTICE TEST [1 - EXERCISES]

Algebraic Expressions Model Questions Set 1

Question : 16

Directions :
In each of the following questions, one or two equation(s) is/are given. On their basis you have to determine the relation between x and y and then give answer.

  1. if x < y
  2. if x > y
  3. if x ≤ y
  4. if x ≥ y
  5. if x = y

I.$x^2$ + 3x + 2 = 0
II.$2y^2$ = 5y

a) if x ≥ y

b) if x = y

c) if x < y

d) if x ≤ y

e) if x > y

Answer: (c)

I. $x^2$ + 3x + 2 = 0

or, $x^2$ + 2x + x + 2 = 0

or, (x + 2)(x + 1) = 0

or, x = – 2, – 1

II. $2y^2$ = 5y

or, $2y^2$ – 5y = 0

or, y(2y – 5) = 0

or, y = 0, $5/2$

Hence, y > x

Question : 17

Directions :
In each question below one or more equation(s) is/are provided. On the basis of these, you have to find out relation between p and q.

  1. if p = q
  2. if p > q
  3. if q > p
  4. if p ≥ q
  5. if p ≥ q

I. $6q^2+1/2=7/2a$
II. $12p^2$ + 2 = 10p

a) if p ≥ q and

b) if q ≥ p.

c) if p = q,

d) if q > p,

e) if p > q,

Answer: (a)

I. $6q^2+1/2=7/2q$

or,$12q^2$ - 7q + 1 = 0.

or $(q-{1/4})(q-{1/3})$=0

∴ q = $1/4$ pr $1/3$

II. $12p^2$ + 2 = 10p

or, $6p^2$ – 5p + 1 = 0

or,$(p-{1/3})(p-{1/2})$=0

∴ p=${1/3}$ or $1/2$

Hence, p ≥ q

Question : 18

Directions :
In each question below one or more equation(s) is/are provided. On the basis of these, you have to find out relation between p and q.

  1. if p = q
  2. if p > q
  3. if q > p
  4. if p ≥ q
  5. if p ≥ q

I. $2p^2$ + 40 = 18p
II. $q^2$ = 13q – 42

a) if p ≥ q and

b) if q ≥ p.

c) if p = q,

d) if q > p,

e) if p > q,

Answer: (d)

I. $2p^2$ + 40 = 18p

or, $p^2$ – 9p + 20 = 0

or, (p – 4) (p – 5) = 0

∴ p = 4 or 5

II. $q^2$ = 13q – 42

or, $q^2$ – 13q + 42 = 0

or, (q – 7) (q – 6) = 0

∴ q = 6 or 7

Hence, q > p

Question : 19

Directions :
In each of the following questions two equations I and II are given. You have to solve both the equations and give answer

  1. if a < b
  2. if a ≤ b
  3. if a ≥ b
  4. if a = b
  5. if a > b

I. 2a + 3b = 31
II. 3a = 2b + 1

a) if a = b

b) if a > b

c) if a < b

d) if a ≥ b

e) if a ≤ b

Answer: (c)

2a + 3b = 31 ... (i)

3a – 2b = 1 ..(ii)

Multiply (i) by 2 and (ii) by 3 and then adding

(i) and (ii), we get a = $65/13$ = 5 . Putting the value of 'a'

in any equation, we get b = 7.

Hence, b > a or a < b.

Question : 20

Directions :
In each of the following questions, one or two equation(s) is/are given. On their basis you have to determine the relation between x and y and then give answer.

  1. if x < y
  2. if x > y
  3. if x ≤ y
  4. if x ≥ y
  5. if x = y

I.$ x^2$ – 5x + 6 = 0
II.$y^2$ + y – 6 = 0

a) if x ≥ y

b) if x = y

c) if x < y

d) if x ≤ y

e) if x > y

Answer: (a)

I. $x^2$ – 5x + 6 = 0

or, $x^2$ – 3x – 2x + 6 = 0

or, x(x – 3) – 2(x – 3) = 0

or, (x – 3)(x – 2) = 0

or, x = 2, 3

II. $y^2$ + y – 6 = 0

or, $y^2$ + 3y – 2y – 6 = 0

or, y(y + 3) – 2 (y + 3) = 0

or, (y + 3) (y – 2) = 0

or, y = 2, –3

Hence, x ≥ y

IMPORTANT quantitative aptitude EXERCISES

Algebraic Expressions Model Questions Set 1 Online Quiz

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