Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: The units digit of 35^87 + 93^46 is: [#permalink]
17 Jul 2013, 09:55

1

This post received KUDOS

Step 1: (35)^(87) can be broken up into (5)^87 x (7)^87. Each power of 7 ends in a units digit of either a 7,9,3 or 1. Each power of 5 ends in a 5. When you multiply 5 by any odd number you will end up with a units digit of 5.

Step 2: (93)^(46) can be broken up into (3)^46 x (31)^46. Each power of 31 ends in a units digit of 1. Each power of 3 ends in a units digit of either 3,9,7 and 1. Since there is a pattern here where every 4th power of 3 ends in a units digit of 3, the 46th power of 3 would end in a units digit of 9. When you multiply 1 by 9 you end up with a units digit of 9.

Therefore, the units digit we are looking for is 5 + 9 = 14. Units digit will be 4. Answer B.

It is quite intuitive to go for a basic two step approach for this problem.

When dealing with 35^87, we can apply a simple concept here. 5 raised to any power > 0 must have 5 as its units digit. When dealing with 93^46, we can apply the concept of cyclicity. Since the cyclicity of 3 is 4, so units digit of 93^46 is equivalent to teh units digit of 3^2 i.e. 9. On adding these 2 digits i.e. 9 and 5, we get 14 of which the units digit is 4. Will be curious to know how others deal with such questions. _________________

It is quite intuitive to go for a basic two step approach for this problem.

When dealing with 35^87, we can apply a simple concept here. 5 raised to any power > 0 must have 5 as its units digit. When dealing with 93^46, we can apply the concept of cyclicity. Since the cyclicity of 3 is 4, so units digit of 93^46 is equivalent to teh units digit of 3^2 i.e. 9. On adding these 2 digits i.e. 9 and 5, we get 14 of which the units digit is 4. Will be curious to know how others deal with such questions.

Good question, I have the same question in my mind.