Remainder exponents

GRE Quant Problem Solving
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Now I am stuck in this expression. How come 7^32? Why is it even considered?

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Think about the pattern for 7^x. What do you get?

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7,9,3,1

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Correct. What is the remainder for 7^{32}? Can you use that to find the remainder for 7^{35}?

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Okay I got itā€¦ the remainder is the 7^x & that would be the answer right??

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Indeed - but confirm it for yourself.

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Still I having confusion when I have to use unit digit approach & remainders with exponents approach! Could you please clarify it?

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What do you mean by the two approaches? Clarify your understanding of them.

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When youā€™re dealing with division by 10, 5 or 2 you can instantly tell the remainder just from the unit digit right?

For other numbers you have to do the pattern with the remainder itself.

Check out Question 1, 2 and 3 in this video.

(Iā€™m Overwhelmed) Arithmetic Progress Quiz #7 Solutions

I go through 3 examples, questions 1 and 2 where I use the unit digit (when dividing by 5) and question 3 when I use pattern recognition (when dividing by 3).

Hopefully that clarifies things.

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No division by 5 is also confusing! For 7^28/5 it is said we have to look at ud but for 3^62 we have to do distance type thing. Iā€™m gonna lose my mind. There should be specific rules for each number!

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This is the rule, as I stated right?

When youā€™re dealing with division by 10, 5 or 2 you can instantly tell the remainder just from the unit digit right?

For other numbers you have to do the pattern with the remainder itself.

The ā€œdistanceā€ is just using the unit digit.

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I donā€™t know thereā€™s still confusion, I feel dumb & crying

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Send me an email ganesh@gregmat.com . Iā€™ll help you with a quick call.

2 Likes
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I am also heavily struggling with this concept. I feel similarly to Tishi, I canā€™t figure out the ā€œpatternsā€ or when thereā€™s a rule, when to look at dividing remainder or looking at the unit digit. Is there a longer video I can watch about this topic?

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Please talk to the moderators of the group or make a post , Iā€™m sure they will help you out. There are 3/4videos on unit digits in Prepswift ,you can watch them and after watching,
if you canā€™t understand reach out to the moderators. When I didnā€™t understand the topic even after going through the multiple times of videos, Ganesh decided to give me class on zoom. Now I donā€™t face problems but the topic needs to be practiced over again and again :smiling_face_with_tear: