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D01-11

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Math Expert
Joined: 02 Sep 2009
Posts: 41698

Kudos [?]: 124614 [0], given: 12079

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16 Sep 2014, 00:11
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Difficulty:

25% (medium)

Question Stats:

74% (01:15) correct 26% (01:25) wrong based on 150 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
[Reveal] Spoiler: OA

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Kudos [?]: 124614 [0], given: 12079

Math Expert
Joined: 02 Sep 2009
Posts: 41698

Kudos [?]: 124614 [0], given: 12079

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16 Sep 2014, 00:11
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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04 Dec 2014, 11:05
Is there a shortcut to do this? It's not hard to add up all the options manually..

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Senior Manager
Joined: 25 Mar 2013
Posts: 276

Kudos [?]: 33 [0], given: 101

Location: United States
Concentration: Entrepreneurship, Marketing
GPA: 3.5

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05 Dec 2014, 06:41
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!

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

Kudos [?]: 33 [0], given: 101

Intern
Joined: 09 Mar 2013
Posts: 19

Kudos [?]: 19 [0], given: 95

Location: Russian Federation
Concentration: General Management, Entrepreneurship
GMAT 1: 550 Q43 V23
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GMAT 4: 740 Q49 V41

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05 Dec 2014, 15:56
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)

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Intern
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Schools: Haas '20
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20 Feb 2016, 14:39
this requires just the ability to process basic arithmetic quickly in your head.

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Intern
Joined: 26 Jul 2016
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05 Oct 2016, 05:50
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

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Senior Manager
Joined: 18 Jun 2016
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Location: India
Concentration: Strategy, Entrepreneurship
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16 Jul 2017, 12:28
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
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18 Jul 2017, 09:53
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.

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Intern
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21 Aug 2017, 15:28
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.

Cheers!

Kudos [?]: 4 [0], given: 230

Re: D01-11   [#permalink] 21 Aug 2017, 15:28
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