CDS 2026 · PYQ · Data Sufficiency / LCM and HCF · medium
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, q and r (p > q > r > 0) is 30 and their HCF is 5. What is the product of the three numbers?
Statement-I: p = 15
Statement-II: q = 10
Which one of the following is correct in respect of the above Question and the Statements?
A.The Question can be answered by using one of the statements alone, but cannot be answered using the other statement alone
B.The Question can be answered by using either Statement alone
C.The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
D.The Question can be answered even without using both the Statements✓ Correct
Explanation
Since HCF is 5, all three numbers are multiples of 5. Since LCM is 30 = 2·3·5, the numbers must be divisors of 30 that are multiples of 5, i.e., from {5, 10, 15, 30}. Since HCF = 5 (not 10 or 15), and LCM = 30, with p > q > r > 0 all positive multiples of 5 dividing 30: the only triple satisfying both LCM = 30 and HCF = 5 with three distinct values is p = 30, q = 15, r = 10 (HCF of 30,15,10 = 5; LCM = 30) or considering all options carefully, p=30, q=15, r=10 works. Product = 30 × 15 × 10 = 4500. The triple is uniquely determined just from the LCM, HCF and ordering conditions without needing either statement.
💡 Practice unlimited CDS PYQs + AI-tracked progress on each topic. Sign up free →
Want more CDS practice?
Free daily 10-Q quiz · adaptive mocks · 4,000+ verified PYQs · AI doubt solver in Hindi + English