What is the last digit of the number 537^1279089028?
(A) 1
(B) 3
(C) 6
(D) 7
Hi guys i tried the method where u follow the 7^2 n get the series of 7,9,3,1,7... N then tried to divide it! somehow i get 7 but that is the wrong answer!!
[spoiler]OA = 1[/spoiler]
Exponents again?
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537^1279089028
Consider 1279089028
Perform divisibility test by "4" .. as we know that for "4" we check last 2 digits.. so 28/4 = 0
When the result is "0".. then the power is "4"
So, (7)^4 = xxx1
Answer {A}
Consider 1279089028
Perform divisibility test by "4" .. as we know that for "4" we check last 2 digits.. so 28/4 = 0
When the result is "0".. then the power is "4"
So, (7)^4 = xxx1
Answer {A}
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General Steps to such question:
- Consider the power and divide it by "4"
if remainder is "1" -> Take Unit digit of the base number to power "1"
if remainder is "2" -> Take Unit digit of the base number to power "2"
if remainder is "3" -> Take Unit digit of the base number to power "3"
if remainder is "0" -> Take Unit digit of the base number to power "4"
- Consider the power and divide it by "4"
if remainder is "1" -> Take Unit digit of the base number to power "1"
if remainder is "2" -> Take Unit digit of the base number to power "2"
if remainder is "3" -> Take Unit digit of the base number to power "3"
if remainder is "0" -> Take Unit digit of the base number to power "4"
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To simplify and speed up the process use the property of cyclicity on these problems:AIM TO CRACK GMAT wrote:What is the last digit of the number 537^1279089028?
(A) 1
(B) 3
(C) 6
(D) 7
Consider the last digit of 537
This number raised to any power would yield a number having the units digit as per the above table.
thus we need to find : 7^1279089028
Now, notice that the last two digits are 28.
there is a neat divisibility property for the numbers divisible by 4.
"If the last two digits of a number are divisible by four then the complete number is divisible by 4"
Using this property we know that our very weird looking number "1279089028" is a multiple of 4.
Thus considering the cyclicity for 7 we know that 7(raised to multiples of 4) would yield a unit digits 1
[spoiler]
Answer : (A) 1[/spoiler]
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Take it as 7^8 (We have to take only the last digits, rest doesn't mattter)
Last digit for exponents are:-
7^1 = 7
7^2 = 9
7^3 = 3
7^4 = 1...
So, 7^8 = 1
So, the correct answer is A
Last digit for exponents are:-
7^1 = 7
7^2 = 9
7^3 = 3
7^4 = 1...
So, 7^8 = 1
So, the correct answer is A
Sahil Chaudhary
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Hi Sahil,sahilchaudhary wrote:Take it as 7^8 (We have to take only the last digits, rest doesn't mattter)
Unfortunately this approach cannot be generalized.
Consider this case
7^18
Now if you just consider the last digit "8" the units digit of the answer would be 1
but actually 7^18 = 1628413597910449 (used the calculator to explain the point )
So basically you have to consider the complete number (in our example its 18, and in the original question it is 1279089028)
Applying our shortcut to 7^18 --> 18 is a multiple of 9 --> check the cyclicity table --> according to the table the units digit should be 9
Hope it helps.
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7^1 = 7AIM TO CRACK GMAT wrote:What is the last digit of the number 537^1279089028?
(A) 1
(B) 3
(C) 6
(D) 7
Hi guys i tried the method where u follow the 7^2 n get the series of 7,9,3,1,7... N then tried to divide it! somehow i get 7 but that is the wrong answer!!
[spoiler]OA = 1[/spoiler]
7^2 = 49
7^3 = 343
7^4 = ...1
7^5 = ...7
and so on.
Clearly, there's a pattern here: 7,9,3,1,7,9,3,1,...
This pattern has a cyclicity of 4.
Now, divisibility rule of 4 is that the number formed by the last 2 digits of the given number should be divisible by 4.
In this case: 1279089028 => 28 should be divisible by 4 (and it is)
So the units digit is 1.
Choose A
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If anyone is interested, we have a free video on this topic: https://www.gmatprepnow.com/module/gmat- ... ts?id=1031
I also wrote an article for BTG called "The Units Digits of Big Powers": https://www.beatthegmat.com/mba/2012/10/ ... big-powers
Cheers,
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I also wrote an article for BTG called "The Units Digits of Big Powers": https://www.beatthegmat.com/mba/2012/10/ ... big-powers
Cheers,
Brent
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Thanks mevicks for telling me.mevicks wrote:Hi Sahil,sahilchaudhary wrote:Take it as 7^8 (We have to take only the last digits, rest doesn't mattter)
Unfortunately this approach cannot be generalized.
Consider this case
7^18
Now if you just consider the last digit "8" the units digit of the answer would be 1
but actually 7^18 = 1628413597910449 (used the calculator to explain the point )
So basically you have to consider the complete number (in our example its 18, and in the original question it is 1279089028)
Applying our shortcut to 7^18 --> 18 is a multiple of 9 --> check the cyclicity table --> according to the table the units digit should be 9
Hope it helps.
Does using the last 2 digits works all the time ?
Sahil Chaudhary
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Yes, since the procedure requires divisibility by "4" and to check any number's divisibility by "4" we consider last two digits.sahilchaudhary wrote: Thanks mevicks for telling me.
Does using the last 2 digits works all the time ?
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