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A four digit number divisible by 7 becomes divisible by 3

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vomhorizon
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A four digit number divisible by 7 becomes divisible by 3 [#permalink] New post   Updated on: 01 Oct 2012, 07:23
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A four digit number divisible by 7 becomes divisible by 3 when 10 is added to it. The largest such number is :

A. 9999
B. 9996
C. 9989
D. 9987
E. 9993
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C

Originally posted by vomhorizon on 01 Oct 2012, 07:21.
Last edited by Bunuel on 01 Oct 2012, 07:23, edited 1 time in total.
Renamed the topic.
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Bunuel
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Re: A four digit number divisible by 7 becomes divisible by 3 [#permalink] New post   01 Oct 2012, 07:30
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vomhorizon wrote:
A four digit number divisible by 7 becomes divisible by 3 when 10 is added to it. The largest such number is :

A. 9999
B. 9996
C. 9989
D. 9987
E. 9993


If the four digit number were a multiple of 3, then adding 10 (not a multiple of 3) wouldn't give a number which is divisible by 3. Thus our four digit number is not a multiple of 3. Only answer choices which is not a multiple of 3 is C.

Answer: C.
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sanjoo
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Re: A four digit number divisible by 7 becomes divisible by 3 [#permalink] New post   01 Oct 2012, 10:22
I divided all choices by 7. ..

only two choices were divisble by 7.. choice C and B..

9989..is only divisble by 7..and divisble by 3 when add 10.
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Re: A four digit number divisible by 7 becomes divisible by 3 [#permalink] New post   25 Nov 2013, 10:26
vomhorizon wrote:
A four digit number divisible by 7 becomes divisible by 3 when 10 is added to it. The largest such number is :

A. 9999
B. 9996
C. 9989
D. 9987
E. 9993


Check divisibility by 7: Grab the last number double it and subtract it from the remaining number, if result is divisibie by 7 then so is the number.
First try the largest since that is what you are being asked. You will realize that it is not div by 7. Check the remainder. Then see the answer choices given, you will see that only B,C are left.
Finally, add 10 to each if the numbers add to a multiple of 3 then you're fin/ So C must be the correct answer.

Hope it helps
Cheers
J :)
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Re: A four digit number divisible by 7 becomes divisible by 3 [#permalink] New post   25 Jul 2014, 09:04
This is with respect to the divisibility by 7 rule. As per rule last digit of 9989 which is 9 has to be doubled and subtracted from the original number. If we do that then 9989 -18 = 9971 is not divisible by 7. Can you please explain how is this possible? Am I missing something? Thanks in advance.
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Re: A four digit number divisible by 7 becomes divisible by 3 [#permalink] New post   27 Jul 2014, 13:59
Divisibility by 7 : take the last digit and double it and subtract it from the rest of the number.

9989 ==> 998 - 18 = 980 which is divisible by 7.
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Re: A four digit number divisible by 7 becomes divisible by 3 [#permalink] New post   28 Jul 2014, 09:29
Yeah "rest" of no. My bad. I was subtracting from 9989 itself. Thanks
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Re: A four digit number divisible by 7 becomes divisible by 3 [#permalink] New post   01 Aug 2014, 00:15
vomhorizon wrote:
A four digit number divisible by 7 becomes divisible by 3 when 10 is added to it. The largest such number is :

A. 9999
B. 9996
C. 9989
D. 9987
E. 9993


Out of all the 5 options, only 9989 is NOT divisible by 3. All others are divisible

So Answer = C (No further calculation required)

Explanation

Addition of any two non-divisible numbers by 3 gives the resultant divisible by 3

10 is non-divisible by 3; we are adding a number to that so that the resultant becomes divisible by 3

Applying the above rule, It means that the number which we are going to add should be non-divisible by 3

So comes the answer = 9989
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A four digit number divisible by 7 becomes divisible by 3 [#permalink] New post   12 Sep 2016, 14:29
A four digit number divisible by 7 becomes divisible by 3 when 10 is added to it. The largest such number is :

A. 9999
B. 9996
C. 9989
D. 9987
E. 9993

The set of integers divisible by 7 and, when 10 is added, by 3,
is an AP whose first term is 14 and whose difference is 7*3=21.
Plugging in 14+21x, only 9989 is divisible.
C.
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Re: A four digit number divisible by 7 becomes divisible by 3 [#permalink] New post   12 Sep 2016, 17:01
We just need to check if the number +10 is divisible by 3. Only one option qualifies.
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Re: A four digit number divisible by 7 becomes divisible by 3 [#permalink] New post   06 Dec 2020, 02:36
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Re: A four digit number divisible by 7 becomes divisible by 3 [#permalink]
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