GATE CSE
First time here? Checkout the FAQ!
x
+2 votes
168 views

If (65)x = (52)y, then what is the minimum value of x+y ?

asked in Digital Logic by Boss (6.5k points) 3 14 34 | 168 views

3 Answers

+2 votes
Best answer

Converting both sides to decimal,

6x+5 = 5y+2

We get, 5y - 6x = 3

Now, the first number has 5 and 6 as its digits. So x is definitely greater than 6. The second number has 5 and 2 as its digits. So, y is definitely greater than 5.

So, x can be 7,8,9,10..... and y can be 6,7,8,9.....

By inspection, if we take y as 9 and x as 7, then the equation is satisfied.

So, minimum value of (x+y) should be 16.

answered by Veteran (10.2k points) 6 43 108
selected by
why  y as "9" not "6"?
Give it a try..
oh okay we are comparing x and y with (65)x =(52)y , I thought that we are just trying to find min value of (x + y).  thanks
Yes bro!!
0 votes

Minimum value of  x+y is 16

answered by Junior (697 points) 1 5
0 votes
we know that x>6 and y>5

     6x+5=5y+2

=>   6x+3=5y

=>   3(2x+1)=5y

=>  2x+1 is divisible by 5 and is odd at the same time x>6

so minimum value possible for 2x+1 is 15

which gives x=7

=>from solving above equation we get y=9.

So minimum value of x+y is 7+9=16
answered by (105 points) 1

Related questions

+11 votes
3 answers
1
0 votes
0 answers
3
asked by chaser (493 points) 8 20 | 86 views


Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
Top Users Oct 2017
  1. Arjun

    23210 Points

  2. Bikram

    17018 Points

  3. Habibkhan

    6652 Points

  4. srestha

    5864 Points

  5. Debashish Deka

    5430 Points

  6. jothee

    4908 Points

  7. Sachin Mittal 1

    4762 Points

  8. joshi_nitish

    4274 Points

  9. sushmita

    3954 Points

  10. Silpa

    3698 Points


Recent Badges

Regular Juhi Sehgal
Popular Question vineet.ildm
Nice Comment Arjun
100 Club vipul verma
Notable Question jothee
Popular Question jothee
Nice Question shivangi5
Regular rinks5
Notable Question shipra tressa
Regular sasi
27,247 questions
35,056 answers
83,703 comments
33,183 users