Question

LCM of two numbers A & B is 72 and HCF is 12. What is the number B?

I. A is not a factor of B.
II. B is greater than A.

• A. if the question can be answered by using any of the statements alone but not by using the other statement alone.
• B. if the question can be answered by using either of the statements alone
• C. if the question can be answered only by using both the statements together.
• D. if the question cannot be answered.

Answer 1

The correct option is C if the question can be answered only by using both the statements together.

Option c
LCM & HCF of A & B are 72 & 12 respectively.
LCM $\times$ HCF = A $\times$ B(product of the two numbers) $\Rightarrow$ 72 $\times$ 12 = A $\times$ B
Values (A, B) can take so that HCF will be 12 & LCM 72 are (12, 72) and (24, 36)
I. A is not a factor of B, which means A and B can take24 and 36 as values but not necessarily in the same order i.e.,
A = 36 and B = 24 OR
A = 24 and B = 36
II. B is greater than A. This means B can be 36.
Hence II alone is not sufficient. Combining, I & II, we get A = 24 & B = 36. Hence, the answer is (c).