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Question

Given that a, b, c, d, p and q are natural numbers such that a < b and d < c. It is also given that the following result holds true:

ab×dc=qp

Choose the correct option(s):


A

ab>qp and dc>qp

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B

ab<qp and dc<qp

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C

q>p

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D

q<p

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Solution

The correct options are
A

ab>qp and dc>qp


D

q<p


Given that,
ab×dc=qp
here, ab>qp and dc>qp and q<p
For eg,
ab×dc=qp
Let a = 2, b= 3 and c = 6, d = 5,
23×56=1018
here, 23>1018(as 2×63×6=1218>1018)
and 56>1018(as 5×36×3=1518>1018)
Here, q = 10 and p = 18.
Hence, q<p (as 10<18).

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