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GMAT Diagnostic Test Question 11 Field: special characters, number sets Difficulty: 650

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
_________________

There's a really handy technique called, "casting out 9s," which is good to use whenever a problem comes up that involves "summing up the digits." It's a way to compare all the numbers to each other.

In this problem, instead of laboriously adding up all the digits of every answer choice, you can quickly reduce them by "casting out the nines:"

In general: Step 1: cross out all nines and any two or more digits that add up to nine or multiples of 9 (3,6 or 4,2,3, or 6,4,8, etc). Step 2: add up the digits you have left Step 3: keep adding the digits together until you have a single digit (keep in mind 9=0) Step 4: compare all the single digits of each answer choice and see which is greatest in order to answer this question.

This is really quick:

ex: A. 94123=1 Step 1: cross off 9, and then cross off 4,2,3 b/c they add to 9. Step 2: what's left is 1, so that's your single digit for this number

B. 91964=2 Step 1: cross off 9, and 9 Step 2: add 1+6+4, which equals 11 Step 3: add 1+1, which equals 2, so that's your single digit for this number

C. 64678=4 Step 1: cross off 6,4,8 Step 2: add 6+7, which equals 13 Step 3, add 1+3, which equals 4, so that's your single digit for this number

D. 62355=3 Step 1: cross off 6,3 Step 2: add 2+5+5, which equals 12 Step 4: add 1+2=3, so that's your single digit for this number

E. 45689=5 Step 1: cross of 4,5, and 9 Step 2: add 6+8, which equals 14 Step 3: add 1+4, which equals 5, so this is your single digit for this number, and this is also the greatest one, and thus the answer.

This method is so easy you can do it in your head. Try it!

Explanation Official Answer: E. The explanation follows as under: G of 45689 is 5 where as 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.

LMBO...So I got the right answer and totally did not follow the instructions....disclaimer: was rushing to leave work and looking @ problems. For some reason, I just summed the digits. I omitted 4's and 9's right away and compared what was left: 5, 16, 18, 8, and 19.

Are there any similar problems posted so that I can give it another try and follow instructions? I'm telling myself, "Reading is fundamental."
_________________

Hi, I've checked the latest PDF and here's how this question looks in there:

Quote:

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)?

arturocb86 wrote:

There is an error in the last pdf... it doesn't specify what is g. It says only that g of 786 is 6. In case of a 11 I thought g of 11 would be 11!

For this question I got it wrong because I ruled out answers C-E because the question stem read "and G is the sum of digits in T." I incorrectly regarded this statement to mean that T would have more than one digit (aka digit"s"). Can someone comment on this for me? Am I reading too much into the problem? Thanks in advance.

I added up the numbers and guessed the average . The number with the highest average should have the biggest "G."

A. 94123 = 19/5 B. 91964 = 29/5 C. 64678 = 31/5 D. 62355 = 21/5 E. 45689 = 32/5

You don't even have to workout the average because the denominator for all is the same. The choice with the largest nominator will have the greatest average. In this case, it's E.

if the summation of any two no is 10 and it can be considered as lowest sum. for eg between 94123 and 45689 94123=9+1+423 45689=4+6+589

comparitively the number contains 589 is the biggest, similarily if we do the small calculation for the rest of the numbers. We can easily arrive at option E

gmatclubot

Re: GMAT Diagnostic Test Question 11
[#permalink]
05 May 2014, 01:58