This set of Aptitude Questions and Answers (MCQs) focuses on “Algebraic Variables”.

1. Find the HCF of polynomials (x+1)^{2}(x-2)(x+3) and (x+1)(x+2)(x+3)^{2}.

a) (x+1)(x+2)(x+3)^{2}

b) (x+1)(x-2)(x+3)^{2}

c) (x+1)(x-3)

d) (x+1)(x+3)

View Answer

Explanation: The common factors between (x+1)

^{2}(x-2)(x+3) and (x+1)(x+2)(x+3)

^{2}is (x+1)(x+3).

Hence, HCF is (x+1)(x+3).

2. Find the HCF of 16(x^{5}+x^{4}-6x^{3}) and 40(x^{4}+4x^{3}+3x^{2}).

a) 8(x+3)

b) 8x(x+3)

c) 8x(x+3)^{2}

d) 8x^{2}(x+3)

View Answer

Explanation: Let p(x) = 16(x

^{5}+x

^{4}-6x

^{3}) = 16x

^{3}(x-2)(x+3) and q(x) = 40(x

^{4}+4x

^{3}+3x

^{2}) = 40x

^{2}(x+1)(x+3).

The common factors are 8x

^{2}(x+3).

Therefore, HCF is 8x

^{2}(x+3).

3. Find the HCF of 48x^{5}y^{7}z^{3}, 18x^{6}y^{4}z^{5} and 54x^{7}y^{2}z^{7}.

a) 6x^{5}y^{2}z^{3}

b) 6x^{5}y^{3}z^{3}

c) 8x^{5}y^{2}z^{3}

d) 6x^{5}y^{4}z^{3}

View Answer

Explanation: The common factors between 48x

^{5}y

^{7}z

^{3}, 18x

^{6}y

^{4}z

^{5}and 54x

^{7}y

^{2}z

^{7}is 6x

^{5}y

^{2}z

^{3}.

Therefore, HCF is 6x

^{5}y

^{2}z

^{3}.

4. Find the LCM of 8a^{4}b^{5}c^{6}, 10a^{6}b^{2}c^{3} and 15a^{5}b^{6}c^{4}.

a) 240a^{6}b^{6}c^{6}

b) 120a^{6}b^{6}c^{6}

c) 120a^{5}b^{6}c^{6}

d) 120a^{6}b^{7}c^{6}

View Answer

Explanation: LCM of 8, 10 and 15 is 120.

We have to choose the highest power of a, b and c to find its LCM.

Therefore, the LCM of 8a

^{4}b

^{5}c

^{6}, 10a

^{6}b

^{2}c

^{3}and 15a

^{5}b

^{6}c

^{4}is 120a

^{6}b

^{6}c

^{6}.

5. Find the LCM of (x+4)(x^{2}-4x+4), (x-2)(x^{2}-16) and (x-4)(x+3).

a) (x-2)(x^{2}-16) (x+3)

b) (x+2)(x^{2}-16) (x+3)

c) (x-2)^{2}(x^{2}-16) (x+3)

d) (x-2)^{2}(x^{2}-16) (x-3)

View Answer

Explanation: Let p(x) = (x+4)(x

^{2}-4x+4) = (x+4)(x-2)

^{2}, q(x) = (x-2)(x

^{2}-16) = (x-2)(x+4)(x-4) and r(x) = (x-4)(x+3).

Therefore, LCM is (x-2)

^{2}(x

^{2}-16) (x+3).

6. Find the LCM of 40(2x^{6}+3x^{5}-2x^{4}) and 60(2x^{5}+x^{4}-x^{3}).

a) 120(2x-1)(x^{2}+3x+2)

b) 120(2x-1)(x^{2}-3x+2)

c) 120(2x-1)^{2}(x^{2}+3x+2)

d) 120(2x-1)(x-1)(x+2)

View Answer

Explanation: Let p(x) = 40(2x

^{6}+3x

^{5}-2x

^{4}) = 2

^{3}*5x

^{4}(x+2)(2x-1) and q(x) = 60(2x

^{5}+x

^{4}-x

^{3})

= 2

^{2}*3*5x

^{3}(x+1)(2x-1).

Therefore, LCM is 120(2x-1)(x+1)(x+2) = 120(2x-1)(x

^{2}+3x+2).

7. The HCF and LCM of two polynomials is (x+2) and (x+1)(x+2)(x-4). If one of the polynomial is (x+2)(x-4), find the other.

a) (x+1)

b) (x+1)(x+2)

c) (x+1)(x+2)(x-4)

d) (x+1)(x-2)

View Answer

Explanation: We know that, product of two polynomials = HCF * LCM.

Other polynomial = \(\frac{(x+2)*(x+1)(x+2)(x-4)}{(x+2)(x-4)}\)=(x+1)(x+2).

8. If LCM of two variables is p^{2}q^{3}, then which of the following could not be its HCF?

a) p^{2}

b) p^{2}q^{2}

c) p^{3}q^{3}

d) q^{2}

View Answer

Explanation: LCM is a multiple of HCF.

p

^{2}q

^{3}is not a multiple of p

^{3}q

^{3}.

Hence, p

^{3}q

^{3}could not be its HCF.

9. What is the LCM of x^{3}y-xy^{3}, x^{3}y^{2}+x^{2}y^{3} and x^{2}y+xy^{2}?

a) x^{2}y(x^{2}-y^{2})

b) x^{2}y^{2}(x^{2}-y^{2})

c) xy(x^{2}-y^{2})

d) x^{2}y^{2}(x^{2}+y^{2})

View Answer

Explanation: p(x) = x

^{3}y-xy

^{3}= xy(x

^{2}-y

^{2}), q(x) = x

^{3}y

^{2}+x

^{2}y

^{3}= x

^{2}y

^{2}(x+y) and r(x) = x

^{2}y+xy

^{2}= xy(x+y).

Therefore, LCM is x

^{2}y

^{2}(x

^{2}-y

^{2}).

10. Find the HCF of p^{6}-q^{6} and p^{8}-q^{8}.

a) p-q

b) p+q

c) p^{2}+q^{2}

d) p^{2}-q^{2}

View Answer

Explanation: Let p(x) = p

^{6}-q

^{6}= (p

^{2}-q

^{2})(p

^{4}+q

^{4}+p

^{2}q

^{2}) and q(x) = p

^{8}-q

^{8}= (p

^{4}+q

^{4})(p

^{2}+q

^{2})(p

^{2}-q

^{2}).

Therefore, HCF is p

^{2}-q

^{2}.

To practice all aptitude questions, please visit “1000+ Quantitative Aptitude Questions”, “1000+ Logical Reasoning Questions”, and “Data Interpretation Questions”.