Question

2. 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?​

Answer 1

Answer:

Step-by-step explanation:Product of these two numbers = 2160.

HCF of these two numbers = 12.

Therefore, LCM of these two numbers = (2160 / 12) = 180.

So, none of these two numbers is smaller than 12 and larger than 180.

Moreover, both these numbers will be divisible by 12; and 180 should be divisible by both of them.

Now, 180 / 12 = 15 = (3*5) = (1*15)

Therefore, the eligible pairs are:

(12*1) & (180 / 1) = 12 & 180

(12*3) & (180 / 3) = 36 & 60

(12*5) & (180 / 5) = 60 & 36

(12*15) & (180 / 15) = 180 & 12

So, the pairs are:

12 & 180

36 & 60.