CDS 2026 (I) Elementary Mathematics, question 79

Topic: HCF and LCM

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Q79

A Question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option.

Question : LCM of three numbers p,qp,q and rr (p>q>r>0)(p>q>r>0) is 3030 and their HCF is 55. What is the product of the three numbers ?

Statement-I : p=15p=15

Statement-II : q=10q=10

Which one of the following is correct in respect of the above Question and the Statements ?

  1. (a) The Question can be answered by using one of the statements alone, but cannot be answered using the other statement aloneCorrect answer
  2. (b) The Question can be answered by using either Statement alone
  3. (c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
  4. (d) The Question can be answered even without using both the Statements

Solution.

Answer: (a) The Question can be answered by using one of the statements alone, but cannot be answered using the other statement alone

  1. Each number must be a multiple of 5 and a divisor of 30, so it belongs to {5, 10, 15, 30}.
  2. I alone fixes p=15p = 15. The strict order forces (q,r)=(10,5)(q,r) = (10,5), whose LCM is 30 and HCF is 5.
  3. The product is uniquely 750.
  4. II alone fixes q=10q = 10 and hence r=5r = 5, but p can be 15 or 30.
  5. The products are 750 and 1500, so II is insufficient.