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Math Expert V
Joined: 02 Sep 2009
Posts: 53709

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1 00:00

Difficulty:   25% (medium)

Question Stats: 75% (01:19) correct 25% (01:16) wrong based on 167 sessions

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If $$S$$ is the sum of the digits of a given number, $$T$$ is the sum of the digit of $$S$$, and $$G$$ is the sum of digits in $$T$$. For example $$S$$ of 987 is $$9+8+7 = 24$$, $$T$$ of $$S$$ is $$2+4 = 6$$ and $$G$$ of 6 is 6. Therefore $$G$$ of 987 is 6. Which of the following has the greatest $$G$$?

A. 94123
B. 91964
C. 64678
D. 62355
E. 45689

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Math Expert V
Joined: 02 Sep 2009
Posts: 53709

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Official Solution:

If $$S$$ is the sum of the digits of a given number, $$T$$ is the sum of the digit of $$S$$, and $$G$$ is the sum of digits in $$T$$. For example $$S$$ of 987 is $$9+8+7 = 24$$, $$T$$ of $$S$$ is $$2+4 = 6$$ and $$G$$ of 6 is 6. Therefore $$G$$ of 987 is 6. Which of the following has the greatest $$G$$?

A. 94123
B. 91964
C. 64678
D. 62355
E. 45689

The explanation follows as under: $$G$$ of 45689 is 5 whereas the rest have $$G$$ smaller than 5.

A. $$S = 9+4+1+2+3 = 19$$, $$T = 1+9 = 10$$ and $$G = 1+0 = 1$$.

B. $$S = 29$$, $$T = 11$$ and $$G = 2$$.

C. $$S = 31$$, $$T = 4$$, and $$G = 4$$.

D. $$S = 21$$, $$T = 3$$, and $$G = 3$$.

E. $$S = 32$$, $$T = 5$$, and $$G = 5$$.

Therefore E is the highest.

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Intern  Joined: 13 Sep 2013
Posts: 1

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Is there a shortcut to do this? It's not hard to add up all the options manually..
Manager  S
Joined: 25 Mar 2013
Posts: 238
Location: United States
Concentration: Entrepreneurship, Marketing
GPA: 3.5

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E
But took 2.15sec
Solved by adding each Digits in mind and noted down
Finding Out just S is Enough
Greater S value >>Mean Greater T >> Greater G! _________________

I welcome analysis on my posts and kudo +1 if helpful. It helps me to improve my craft.Thank you

Intern  Joined: 09 Mar 2013
Posts: 14
Location: Russian Federation
Concentration: General Management, Entrepreneurship
GMAT 1: 550 Q43 V23 GMAT 2: 590 Q49 V22 GMAT 3: 690 Q49 V34 GMAT 4: 740 Q49 V41 ### Show Tags

kanusha wrote:
E
Greater S value >>Mean Greater T >> Greater G! it doesn't work
look
S in B) is greater than S in D), however T is greater in D) than in B)
Manager  S
Joined: 12 Mar 2015
Posts: 54
Location: United States
GMAT 1: 670 Q45 V38 GPA: 2.99
WE: Corporate Finance (Aerospace and Defense)

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this requires just the ability to process basic arithmetic quickly in your head.
Intern  Joined: 26 Jul 2016
Posts: 28
Location: India
Concentration: Operations, Entrepreneurship
Schools: Tepper '19
GPA: 3.69
WE: Analyst (Manufacturing)

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another way is to cancel out the number in your head first cut 9 then 5 etc.. then u will be left with e last value with maximum weightage
Senior Manager  G
Joined: 18 Jun 2016
Posts: 262
Location: India
GMAT 1: 720 Q50 V38 GMAT 2: 750 Q49 V42 GPA: 4
WE: General Management (Other)

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I think this is a poor-quality question and I agree with explanation. Because there is no shorter way to solve this question.
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Manager  B
Joined: 02 Nov 2015
Posts: 163
GMAT 1: 640 Q49 V29 ### Show Tags

seeing the question stem I understand that its simply adding the individual digits of each number. so option E yields 32 which is the highest.
Intern  B
Joined: 21 May 2015
Posts: 15

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rayzha wrote:
Is there a shortcut to do this? It's not hard to add up all the options manually..

Yes, these type of problems are called digit sum. The shortest way is to find out the remainder when divided by 9.
This should give the answer.

Cheers!
Manager  G
Joined: 12 Jun 2016
Posts: 214
Location: India
WE: Sales (Telecommunications)

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1
Hello umg,

I too had the same concern. 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 - 9 + 4 + 1 + 2 + 3 = 1 (Simply strike out the digit 9 or the numbers that add up to 9. You can try it on others options and find that this holds true.

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 - http://www.quickermaths.com/checking-of ... out-nines/

umg wrote:
I think this is a poor-quality question and I agree with explanation. Because there is no shorter way to solve this question.

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Manager  B
Joined: 15 Sep 2016
Posts: 72
Location: Pakistan
Concentration: Finance, Technology
Schools: CBS '20
GMAT 1: 640 Q43 V35 ### Show Tags

I solved the question using simple addition. I don't know the probability of this question showing up on the GMAT exam. but thanks to susheelh and his method:

susheelh wrote:

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 - http://www.quickermaths.com/checking-of ... -out-nines

I could solve the question in a minute or a few seconds less.
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Director  P
Joined: 04 Sep 2015
Posts: 556
Location: India
WE: Information Technology (Computer Software)

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A. 94123
B. 91964
C. 64678
D. 62355
E. 45689

Hi,Only way to solve is to add up? D01-11   [#permalink] 21 Aug 2018, 10:45
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