number properties....

Question

Recently a very wealthy individual died and left a large amount of money to be distributed to two individuals. The problem was that this person did not tell anybody who these two people were. This rather cryptic message was left to help someone solve the mystery.
Social security numbers have nine digits. Assuming there is a unique social security number for each person, find the number that contains no 0's and the first number from the left is divisible by 1, the first two numbers from the left are divisible by 2, the first three numbers from the left are divisble by three and so on. No number is used twice. What is the number??
A.147258963
B.741258963
C.183654729
D.381654729
E.981654729

Let the 9-digit integer M be represented by
abcdefghi where each letter represents a unique digit from the set of {1, 2, ...9}. Since abcde must be divisible by 5, e can only be 5 or 0. However the digits are non-zero, so e = 5. b, d, f, and h are even numbers since they are the last digits of numbers that are divisible by 2, 4, 6, and 8. When examining combinations of cd and fgh, where cd will be divisible by 4 and fgh will be divisible by 8, one can conclude that d is 2 or 6, and h is 2 or 6, since c and g cannot be even. The possible values for cd are 12, 16, 32, 36, 52, 56, 72, 76, 92, and 96.
The possible values for fgh are 416, 432, 472, 496, 816, 832, 872, 896. a+b+c must be divisible by 3 and d+e+f must be divisible by 3. The only possibilities of a, b, c, d, e, and f left are
147258963
741258963
183654729
381654729
981654729

Among the five possibilities, only 3816547 is divisible by 7
so,381654729
is the ans...
Its an instresting problem...(logical explanation)...thought of sharing with fellow members.... if it already in the forum..im sorry...

Archived Topic

Hi there,

This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.

Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum

Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.

Thank you for understanding, and happy exploring!

Show Answer

Official Answer

D

AswinKrishnan · Answer

is there no other short cut to this question ? it took me 3 min to solve

feellikequitting · Answer

Took me 12 seconds to get it right.

MHIKER · Answer

Please explain your technique.

harithakishore · Answer

laythesmack23,
can you please let us know the procedure you have followed(12 seconds..)
thankyou in advance....

mission2009 · Answer

hey haritha, a very good logical question indeed, keep posting such questions..

@laythesmack23: can you post ur technique..

IanStewart · Answer

It would be impressive if someone could read the question in 12 seconds, let alone solve it that quickly. I suspect the post above was facetiously mocking the complexity of the question - justifiably, since it's not a realistic GMAT question.

I saw this question a while ago, and it didn't have answer choices. I think in that version, it's an interesting logic/number theory puzzle. As a GMAT question, though, it's a lot less interesting, because the fastest strategy is almost certainly backsolving. We have dead quick divisibility tests for 2, 3, 4, 5, 6, 8, and 9, so we can quite quickly see that each answer choice passes those tests. So all we need to do is figure out for which answer choice the first seven digits form a number divisible by 7. You could do long division, but we don't care what the quotient is - we only need a yes/no answer - so you can save time by not tracking the quotient at all. That is, when you see a number like 1472589, you can start from the left and take out multiples of 7 to get down to a smaller number; you can drop the 147 right away to get to 2589, then take away 21 from the 25 to get to 489, and since this is 1 less than 490, a multiple of 7, we can see that 1472589 is not a multiple of 7. Doing the same thing for the other answer choices lets you find the right answer reasonably quickly, though certainly it takes longer than 12 seconds

Archived Topic

Hi there,

This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.

Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum

Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.

Thank you for understanding, and happy exploring!

number properties....

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards