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 : 11

Directions :
In each of these questions two equations are given. You have to solve these equations and Give answer

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

I. $x^2$ – 6x = 7
II. $2y^2$ + 13y + 15 = 0

a) if x ≥ y

b) if x ≤ y

c) if x < y

d) if x = y

e) if x > y

Answer: (e)

I. $x^2$ – 6x = 7

or, $x^2$ – 6x – 7 = 0

or, (x – 7) (x + 1) = 0

or, x = 7, – 1

II. $2y^2$ + 13y + 15 = 0

or, $2y^2$ + 3y + 10y + 15 = 0

or, (2y + 3) (y + 5) = 0 or, y =${-3}/2,$-5

Hence, x > y

Question : 12

Directions :
For the two given equations I and II give answer

  1. if p is greater than q
  2. if p is smaller than q
  3. if p is equal to q
  4. if p is either equal to or greater than q
  5. if p is either equal to or smaller than q.

I.$3p^2$ + 15p = –18
II. $q^2$ + 7q + 12 =0

a) if p is either equal to or greater than q

b) if p is either equal to or smaller than q.

c) if p is greater than q

d) if p is equal to q.

e) if p is smaller than q

Answer: (a)

I. $3p^2$ + 15p + 18 = 0

or,$3p^2$ + 9p + 6p + 18 = 0

or, 3p (p + 3) + 6(p + 3) = 0

or, (3p + 6)( p + 3) = 0

or, p = ${-6}/3,-3$= – 2, – 3

II.$q^2$ + 7q + 12 = 0

or, $q^2$ + 4q + 3q + 12 = 0

or, q(q + 4) + 3(q + 4) = 0

or, (q + 3)(q + 4) = 0

or, q = – 3, –4

Therefore, p ≥ q

Question : 13

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. $2a^2$ + 5a + 3 = 0
II. $2b^2$ – 5b + 3 = 0

a) if a = b

b) if a > b

c) if a < b

d) if a ≥ b

e) if a ≤ b

Answer: (c)

a = –3/2 & –1; b = $3/2$ & 1

Question : 14

Directions :
In each question one or more equation(s) is (are) provided. On the basis of these you have

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

(i) $4p^2$ – 5p + 1 = 0 (ii) $q^2$ – 2q + 1 = 0

a) if p ≥ q and

b) if q ≥ p

c) if p = q

d) if q > p

e) if p > q

Answer: (b)

(i) $4p^2$ – 5p + 1 = 0 or, $4p^2$ – 4p – p + i = 0

or, 4p(p – 1) – 1(p – 1) = 0

or, (4p – 1)(p – 1) = 0

or, p = 1 and p = $1/4$

(ii) $q^2$–2q +1 = 0

⇒(q – 1) (q –1) = 0

or, q = 1

∴q ≥ p

Question : 15

Directions :
In each of these questions two equations are given. You have to solve these equations and Give answer

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

I. $10x^2$ – 7x + 1 = 0
II. $35y^2$ – 12y + 1 = 0

a) if x ≥ y

b) if x ≤ y

c) if x < y

d) if x = y

e) if x > y

Answer: (a)

I. $10x^2$ – 7x + 1 = 0

or, $10x^2$ – 5x – 2x + 1 = 0

or, (2x – 1) (5x – 1) = 0

or, x = 1/2, 1/5

II. $35y^2$ – 12y + 1= 0

or, $35y^2$ – 7y – 5y + 1 = 0

or, (5y – 1) (7y – 1) = 0

or, y = $1/5 , 1/7$

Hence, x ≥ y

IMPORTANT quantitative aptitude EXERCISES

Algebraic Expressions Model Questions Set 1 Online Quiz

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