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Let x̅1 and x̅2 (where x̅2 > x̅1) be the means of two sets comprising n1 and n2 (where n2 < n1) observations respectively. If x̅ is the mean when they are pooled, then which one of the following is correct?
Consider the following sentences: 1. If a = bc with HCF(b, c) = 1, then HCF(c, bd) = HCF(c, d). 2. If a = bc with HCF(b, c) = 1, then LCM(a, d) = LCM(c, bd). Which of the above statements is/are correct?
HCF of 132, 156 and 192 is x, HCF of 105, 150 and 210 is y, and HCF of 112, 196 and 210 is z. Which is the greatest HCF?
Consider the following statements: 1. The HCF of (p + q) and (p2 – q2) is (p + q). 2. The HCF of (p – q) and (p2 – q2) is (p + q). 3. The HCF of (p + q) and (p3 + q3) is (p + q). 4. The HCF of (p – q) and (p3 – q3)  is (p + q). Which of the above statements is/are correct?
Consider the following in respect of natural numbers a, b and c: 1. LCM(ab, ac) = a × LCM(b, c) 2. HCF(ab, ac) = a × HCF(b, c) 3. HCF (a, b) < LCM(a, b) 4. HCF(a, b) divides LCM(a, b) Where, a ≠ b ≠ c  Which of the above are correct?
Which of the following is/are true? I. HCF of p2-p-6 and p6-93 is 1. II. HCF of x+y and x10-y10 is x+y. III. HCF of x+y and x10+y10 is x+y.
HCF and LCM of two numbers P and Q are 16 and 560 respectively and when 8 is added to P and 20 is added to Q, then HCF and LCM become 20 and 600 respectively, then what is the ratio of the value of P to Q? Assume both P and Q are more than 50.
The Ratio of the value of two numbers P to Q is 5 : 7 and the difference between HCF and LCM of P and Q is 578. If LCM of P and Q is ‘a’, then what is the HCF of ‘a’ and 357?
There are two distinct numbers A and B of which A is larger. If LCM and HCF of A and B are 525 and 15 respectively and their LCM is 7 times that of B, then what is the HCF of A and B when 5 is added to both A and B?
There are two numbers A and B (A > B) of two-digits each and their HCF is 18. If LCM and HCF of B and 45 are 270 and 9 respectively and the difference between digits of A is 5, then what is the LCM of A and B?