Given below are two quantities named A and B. Based on the given information, you have to determine the relation between the two quantities… — Answer & Discussion

Given below are two quantities named A and B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers.
Sum of LCM and HCF of two numbers P and Q are 37.
Quantity A: Product of P and Q.
Quantity B: Sum of P and Q.

AQuantity A > Quantity B
BQuantity A < Quantity B
CQuantity A ≥ Quantity B
DQuantity A ≤ Quantity B

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Discussion 1

CCommunity24 May 2019

We know that LCM is always a multiple of HCF.

Let LCM = k(HCF)

⇒ HCF + k(HCF) = 37

⇒ (k + 1)(HCF) = 37

Possible values of k are 0 and 36.

If k = 0, HCF = 37, which is not possible as LCM will become 0.

If k = 36, HCF = 1, and LCM = 36.

So, P and Q can be 1 and 36, or 4 and 9.

If they are 1 and 36, their sum is 37 and product is 36.

If they are 4 and 9, their sum is 13 and product is 36.

So, sum can be lesser or greater than product.

No relation between A and B can be established.