The arithemetic mean and the geometric mean of two distinct 2-digit numbers x and y are two integers one of which can be obtained by reserving the dig

Question

The arithemetic mean and the geometric mean of two distinct 2-digit numbers x and y are two integers one of which can be obtained by reserving the dig

The arithemetic mean and the geometric mean of two distinct 2-digit numbers x and y are two integers one of which can be obtained by reserving the digits of the other (in base 10 representation). Then x + y equals
A. 82
B. 116
C. 130
D. 148

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - C
`(x+y)/(2)=10 a+b, sqrt(xy)=10 b+a" "(a, b in N)`
`xy=(10b+a)^(2)`
`(x-y)^(2)=4(11a+11b)(9a-9b)`
`=4.11 . (a+b). 9(a-b)`
`rArr a+b=11, a-b=1`
`a=6, b=5`
`((x-y)^(2)" is perfect square of an integer")`
`x+y=130`

4 views Answered 2023-02-05 15:29