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Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1111
Given Kudos: 9
Location: India
Concentration: General Management
Schools: XLRI Jamshedpur, India - Class of 2014
GMAT 1: 700 Q51 V31
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WE:Engineering (Computer Software)
How to Solve: Last Two Digits of Exponents Ending with 5
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24 Jul 2024, 04:10
24 Jul 2024, 04:10
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Attachment:
Last Two Digits of Exponents Ending with 5
Hi All,
I have posted a video on YouTube to discuss Last Two Digits of Exponents Ending with 5
Attached pdf of this Article as SPOILER at the top! Happy learning!
Following is Covered in the Video
Theory of Last Two Digits of Numbers Ending with 5
- ⁍ Find Last two digits of \(735^{637}\) ?
⁍ Find Last two digits of \(785^{989}\) ?
⁍ Find Last two digits of \(15635^{372}\) ?
Theory of Last Two Digits of Numbers Ending with 5
If the exponents is of the format:
- • \((O5)^O\), where O is Odd, then last two digits = 75
• Otherwise, last two digits = 25 (i.e. \((O5)^E\) , \((E5)^O\), \((E5)^E\) , where O is Odd and E is Even)
Q1. Find Last two digits of \(735^{637}\) ?
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Sol: Number before 5 is Odd (735)
Exponent = Odd (637)
=> \((O5)^O\) case
=> Last two digits = 75
Exponent = Odd (637)
=> \((O5)^O\) case
=> Last two digits = 75
Q2. Find Last two digits of \(785^{989}\) ?
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Sol: Number before 5 is Even (785)
Exponent = Odd (989)
=> \((E5)^O\) case
=> Last two digits = 25
Exponent = Odd (989)
=> \((E5)^O\) case
=> Last two digits = 25
Q3. Find Last two digits of \(15635^{372}\) ?
Show: ::
Sol: Number before 5 is Odd(15635)
Exponent = Even (373)
=> \((O5)^E\) case
=> Last two digits = 25
Exponent = Even (373)
=> \((O5)^E\) case
=> Last two digits = 25
Link to Theory for Last Two digits of exponents here.
Link to Theory for Units' digit of exponents here.
Hope it helps!
Re: How to Solve: Last Two Digits of Exponents Ending with 5
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24 Jul 2024, 04:21
24 Jul 2024, 04:21
Expert Reply
gmatclubot
Re: How to Solve: Last Two Digits of Exponents Ending with 5 [#permalink]
24 Jul 2024, 04:21
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