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16 Sep 2014, 00:11
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For a given positive integer, \(S\) denotes the sum of its digits, \(T\) denotes the sum of the digits in \(S\), and \(G\) denotes the sum of the digits in \(T\). For instance, for the number 987, we calculate \(S\) as \(9+8+7=24\), \(T\) as \(2+4=6\), and \(G\) as 6. Therefore, the \(G\) value of 987 is 6. Which of the following numbers has the highest \(G\) value?
A. 94123
B. 91964
C. 64678
D. 62355
E. 45689
A. 94123
B. 91964
C. 64678
D. 62355
E. 45689
16 Sep 2014, 00:11
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Official Solution:
For a given positive integer, \(S\) denotes the sum of its digits, \(T\) denotes the sum of the digits in \(S\), and \(G\) denotes the sum of the digits in \(T\). For instance, for the number 987, we calculate \(S\) as \(9+8+7=24\), \(T\) as \(2+4=6\), and \(G\) as 6. Therefore, the \(G\) value of 987 is 6. Which of the following numbers has the highest \(G\) value?
A. 94123
B. 91964
C. 64678
D. 62355
E. 45689
Let's compute the \(G\) value for each option:
A. 94123: \(S = 9+4+1+2+3 = 19\), \(T = 1+9 = 10\), and \(G = 1+0 = 1\).
B. 91964: \(S = 9+1+9+6+4 = 29\), \(T = 2+9 = 11\), and \(G = 1+1 = 2\).
C. 64678: \(S = 6+4+6+7+8 = 31\), \(T = 3+1 = 4\), and \(G = 4\).
D. 62355: \(S = 6+2+3+5+5 = 21\), \(T = 2+1 = 3\), and \(G = 3\).
E. 45689: \(S = 4+5+6+8+9 = 32\), \(T = 3+2 = 5\), and \(G = 5\).
Thus, option E has the highest \(G\) value.
Answer: E
For a given positive integer, \(S\) denotes the sum of its digits, \(T\) denotes the sum of the digits in \(S\), and \(G\) denotes the sum of the digits in \(T\). For instance, for the number 987, we calculate \(S\) as \(9+8+7=24\), \(T\) as \(2+4=6\), and \(G\) as 6. Therefore, the \(G\) value of 987 is 6. Which of the following numbers has the highest \(G\) value?
A. 94123
B. 91964
C. 64678
D. 62355
E. 45689
Let's compute the \(G\) value for each option:
A. 94123: \(S = 9+4+1+2+3 = 19\), \(T = 1+9 = 10\), and \(G = 1+0 = 1\).
B. 91964: \(S = 9+1+9+6+4 = 29\), \(T = 2+9 = 11\), and \(G = 1+1 = 2\).
C. 64678: \(S = 6+4+6+7+8 = 31\), \(T = 3+1 = 4\), and \(G = 4\).
D. 62355: \(S = 6+2+3+5+5 = 21\), \(T = 2+1 = 3\), and \(G = 3\).
E. 45689: \(S = 4+5+6+8+9 = 32\), \(T = 3+2 = 5\), and \(G = 5\).
Thus, option E has the highest \(G\) value.
Answer: E
16 Oct 2017, 03:49
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Bunuel
I did some digging on this and found some interesting properties. You too may find them useful.
Sum of individual sums of a number is called Digit sum or Beejank (in Vedic maths). One shortcut to quickly arrive at the digit sum is to simply ignore 9's. Let me take the first option - 94123. The Digit sum is -
While I was at it, I also discovered that digit-sum/Beejank can be used to quickly check if the addition/multiplications done are correct. There are a lot of links that explain this approach. One such link is - https://www.quickermaths.com/checking-o ... out-nines/
