Bissoy.com
Doctors Medicines MCQs Q&A

Two unequal pairs of numbers satisfy the following conditions: (i) The product of the two numbers in each pair is 2160 (ii) The HCF of the two numbers in each pair is 12. If x is the mean of the numbers in the first pair and y is the mean of the numbers in the second pair, then what is the mean of x and y?

Two unequal pairs of numbers satisfy the following conditions: (i) The product of the two numbers in each pair is 2160 (ii) The HCF of the two numbers in each pair is 12. If x is the mean of the numbers in the first pair and y is the mean of the numbers in the second pair, then what is the mean of x and y? Correct Answer 72

Given: 

HCF of the numbers in a pair = 12

Concept Used:
Mean = (First term + last term)/2

Calculation:

Let, the numbers be ‘12p’ and ‘12q’

Product of numbers = 2160

⇒ 12p × 12q = 2160

⇒ pq = 15

This is only possible when the values of p and q are either 1 and 15 or 3 and 5

Hence, the two pairs of numbers are (12, 180) and (36, 60)

⇒ Mean of first pair = x = (12 + 180)/2 = 96

⇒ Mean of second pair = y = (36 + 60)/2 = 48

Mean of x and y = (96 + 48)/2 = 72

∴ Mean of x and y is 72. 

Related Questions

The HCF of two numbers is 8 and the product of the two numbers is 6400. How many pairs of numbers exist, which satisfy the above conditions?
Product of two numbers is 16184 and their HCF is 17, then how many possible pairs of numbers are there which will satisfy the given conditions.
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?
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?
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?
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?
Two stores A and B bought the same product from the company at the same price. Store A marked the price of the product 50% above its cost price and offered two successive discounts of 15% and 10% on the marked price of the product, while store B marked the price of the product 60% above its cost price and offered two successive discounts of 15% and 12% on the marked price of the product. If a customer buys the product from store B, he has to pay Rs. 986 more than that at store A. At what price the two stores bought the product from the company?
The sum of two numbers is 552 and their HCF is 23. What is the minimum number of pairs that satisfy these conditions?
A container of 425 liters was filled with chemicals through two pipes. The first pipe was kept open for 5 hours more than the second pipe. If the first pipe remains open for as long as the second pipe remains open, and the second pipe remains open for as long as the first pipe remains open, then the quantity of chemical filled by the first pipe was half the quantity of chemical filled by the second pipe. If both the pipes are opened simultaneously, the tank will be filled in 17 hours. For how long was the second pipe open?
Which of the following statement (s) is/are true about the following eliminations? (1) Hoffmann product is major product in I (2) Saytzeff product is major product in I (3) Hoffmann product is major product in II (4) Saytzeffproduct is major product in II