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25 Aug 2023, 08:00
Kudos
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
79% (01:15) correct
21%
(01:51)
wrong
based on 191
sessions
History
Date
Time
Result
Not Attempted Yet
\(F(n)\) denotes the units digit of a positive integer \(n\). What is the value of \(F(3^8+7^{15})\)?
A. \(3\)
B. \(4\)
C. \(7\)
D. \(8\)
E. \(9\)
A. \(3\)
B. \(4\)
C. \(7\)
D. \(8\)
E. \(9\)
25 Aug 2023, 11:44
Kudos
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F(3^8+7^15)
3^8=(3^4)^2 =(81)^2 i.e. Unit digit 1
7^15=[(7^4)^3](7^3) = [(2401)^3](343) i.e Unit digit 3
Now, F(3^8+7^15) = F(Unit digit 1 + Unit digit 3) = F(Unit digit 4) = 4
Hence B
3^8=(3^4)^2 =(81)^2 i.e. Unit digit 1
7^15=[(7^4)^3](7^3) = [(2401)^3](343) i.e Unit digit 3
Now, F(3^8+7^15) = F(Unit digit 1 + Unit digit 3) = F(Unit digit 4) = 4
Hence B
Prk1410
Joined: 01 Aug 2023
Last visit: 20 Jun 2024
Posts: 9
Location: India
Concentration: Marketing, Strategy
Schools: LBS MiM "26 (II) INSEAD MiM "26 (D) Duke Fuqua (S) McDonough Kellogg MiM "26 Booth (Chicago)
GMAT 1: 710 Q50 V34
GPA: 3.88
Schools: LBS MiM "26 (II) INSEAD MiM "26 (D) Duke Fuqua (S) McDonough Kellogg MiM "26 Booth (Chicago)
GMAT 1: 710 Q50 V34
Posts: 9
25 Aug 2023, 12:11
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Bunuel
Lets take an example to understand this concept and trick associated with these type of questions.
Suppose we are asked to find the units digit of 7^100
First step is to divide the power by 4 and write its remainder. Here 100/4 --> Remainder is 0
Now the base is 7, we write the units digit of first 4 powers i.e. 7,7^2,7^3,7^4 which are 7,9,3,1 respectively.
Now if the remainder had been 1 we chose the first power digit (in the case of 7 its 7)
If the remainder is 2 we chose the 2nd digit (in the case of 7 its 9)
And similarly for remainder as 3 we take the 3rd digit and for remainder as 0 we consider the 4th digit
Coming back to the question
Ans == Units place of 3^8 + Units place of 7^15
For Units place of 3^8, we divide the power i.e. 8 by 4 giving 0 as the remainder. Hence we consider the units digit of the 4th power of the base i.e. units digit of 3^4 which is 1
Now for Units place of 7^15, lets divide the power i.e. 15 by 4 giving us 3 as the remainder. Hence we now consider the units digit of the 3rd power of the base i.e. units digit of 7^3 which is 3
Ans = 1+3 = 4
