If x and y are positive integers and $(5^x)-(5^y)=(2^{y-1})*(5^{x-1})$ , what is the value of xy?

Answer Choices

Correct answer marked below

Correct

See the full step-by-step explanation

You can see the correct answer above. Sign in for free to unlock the complete worked solution.

Track your performance and improve

Get detailed analytics, unlock full explanations, and move up difficulty tiers as you practice.

Start for free Sign in

Explanation

Preview

Official Explanation

Official

A little bit of observation can help you solve this question within a minute.

x and y are positive integers which means we will have clean numbers.

On the right hand side, you have a 2 as a factor while it is not there on the left hand side. Can a 2 be generated on the left hand side by the subtraction?

Here I am thinking that if we take

5^y

common on the left hand side, I might be able to get a 2:

5^y (5^{x-y} - 1) = 2^{y-1}*5^{x-1}

Now I want only 2s and 5s on the left hand side. If x-y is 1, then

(5^{x-y} - 1)

becomes 4 which is

2^2

.…

Read the full explanation

Create free account Sign in

Comments

No comments yet

Be the first to share your thoughts and help others understand it better.

What this question tests

What it tests

Your understanding of divisibility rules, least common multiples, and greatest common factors.

Common trap

Forgetting that 1 is not prime and that every integer divides 0.

If x and y are positive integers and (5x)−(5y)=(2y−1)∗(5x−1)(5^x)-(5^y)=(2^{y-1})*(5^{x-1})(5x)−(5y)=(2y−1)∗(5x−1), what is the value of xy?