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Math Expert V
Joined: 02 Sep 2009
Posts: 58431
If 13,333 – n is divisible by 11, and 0 < n < 11, what is n?  [#permalink]

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Difficulty:   5% (low)

Question Stats: 89% (01:18) correct 11% (01:23) wrong based on 205 sessions

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If 13,333 – n is divisible by 11, and 0 < n < 11, what is n?

(A) 1
(B) 3
(C) 5
(D) 7
(E) 9

Kudos for a correct solution.

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Joined: 05 Apr 2015
Posts: 361
Re: If 13,333 – n is divisible by 11, and 0 < n < 11, what is n?  [#permalink]

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Using divisibility rules on 13,333:

Sum of numbers in odd places(7) - sum of numbers in even places(6) = 1

Hence if we are 1 short of 13,333 the number becomes divisible by 11.

Hence A.

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Dom.
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Manager  Joined: 10 Aug 2015
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Re: If 13,333 – n is divisible by 11, and 0 < n < 11, what is n?  [#permalink]

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Solution : When 13,333 is divided by 11, the remainder is 1. So, n =1.

Option A
Manager  Joined: 13 Apr 2015
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If 13,333 – n is divisible by 11, and 0 < n < 11, what is n?  [#permalink]

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Divisibility Rule for 11.

Add and subtract digits in an alternating pattern (add first digit, subtract second digit, add third digit.... so on). Then the answer must be either 0 or divisible by 11.

Eg - 1364 = + 1 - 3 + 6 - 4 = 0, Therefore this no is divisible by 11.

Eg - 3729 = + 3 - 7 + 2 - 9 = ( - 11 ), Therefore divisible by 11.

In this case 13,333 = 1- 3 + 3 - 3 +3 = 1. If u notice -3 & + 3 will get canceled of, so u need to plug in values in this eq :- 1 - a + b to make it equal to zero. So plug in -3 & +2 .

No will be 13332 which is divisible by 11. And 13332 is 1 less that the original No.

Therefore Ans is A.

Yes it is a bit cummbersome process, but divisibility rule of 11 might help us better in some other question than here.

Alternate way is to check the reminder of 13333 / 11 - which comes out be 1. There fore 1 is to be subtracted to make 13333 divisible by 11.
Intern  Joined: 12 Nov 2013
Posts: 39
Re: If 13,333 – n is divisible by 11, and 0 < n < 11, what is n?  [#permalink]

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Bunuel wrote:
If 13,333 – n is divisible by 11, and 0 < n < 11, what is n?

(A) 1
(B) 3
(C) 5
(D) 7
(E) 9

Kudos for a correct solution.

For a number to be divisible by 11, the absolute difference of the sum of odd place digits - even placed digits = 0 or divisible by 11

Here, sum of odd digits = 7, sum of even digits = 6 difference = 1

So if n = 1, the number is 13,332. Sum of odd placed digits become 6

So difference = 0.
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Re: If 13,333 – n is divisible by 11, and 0 < n < 11, what is n?  [#permalink]

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Divide 13,333 by 11.
Result equals 1212 with a remainder of 1.
Thus if you subtract 1 from 13,333 you will have a multiple of 11.

Looking at our answers, A matches.
Math Expert V
Joined: 02 Sep 2009
Posts: 58431
Re: If 13,333 – n is divisible by 11, and 0 < n < 11, what is n?  [#permalink]

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Bunuel wrote:
If 13,333 – n is divisible by 11, and 0 < n < 11, what is n?

(A) 1
(B) 3
(C) 5
(D) 7
(E) 9

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

Note that this doesn’t look like a remainder problem. It has some algebra to it – we’re solving for n, and what we know about n is based on an inequality presented in fairly abstract form. Your flashcards won’t label this as a remainder problem, but your problem-solving skills should. Before we solve for n, let’s talk about n. What is n in a conceptual sense?

We know that if we subtract n from 13,333, then the resulting number is divisible by 11. Logically, then, we can make the leap that n needs to be taken off of 13,333 in order for it to be divisible by 11. Accordingly, n is the left-over portion of 13,333 when it is divided by 11 – it’s that last remaining portion that makes 13,333 not divisible by 11. So n, conceptually, is the remainder – it’s what’s left over when we try to make this division work.

That logic we just used reverse-engineers the concept of a remainder. We had to create it conceptually, but now that we know that n is just the remainder, this is now a division problem. If we take 13,333 and divide by 11, we end up taking off:

13,333

-11,000

→ 2,333

-2,200

→ 133

-110

→23

-22

→ 1

The remainder is 1, and the correct answer is A (Note: because the problem only asked for the remainder – n – we didn’t need to bother with the quotient, so this problem can be done a little quicker with less hassle).

Keep in mind here that the GMAT isn’t really testing your ability to calculate the remainder in a division problem; that ability is assumed. The GMAT does want to know whether you can take an asset – your ability to perform division problems – and find a way to use it to solve a unique-looking problem. The division is just a vehicle for the GMAT to test your ability to reverse-engineer a concept, to solve a problem using a familiar tool in an unfamiliar way.

To do so, yes, you must have that fundamental math ability, but that’s just the price of admission to showcase your reasoning skills on a problem like this. Your flashcards can’t teach you to do this; reading back through your notes can’t teach you to do this; you need to think analytically: what is the problem? How can I rephrase the question to make it better fit my knowledge base? Were the numbers different and easier to manage, how would I go about solving this, and therefore how can I apply it to this more complex situation? These are the thought processes that business schools want!

If you’re like the student described at the beginning of this article – if you’ve worked hard to build and polish your knowledge base with regard to GMAT content but have hit a plateau with your score – these are the things you need to master. When you study math skills, don’t merely learn them top-down, but ask yourself how the question could be flipped around to test it from another angle. Ask yourself if there are unique cases that might challenge your typical approach to a problem like this (what if there were no remainder? Could n be both 11 and 0?). Challenge yourself to think, and not just to remember.

While many tests you’ve taken could be beaten by what you remembered and what you knew, the GMAT cannot. It’s very nature as a reasoning test is to force you to think in unique ways from odd angles, and if you’ve hit that plateau of frustration with your scores, that’s when you need to challenge yourself not only to follow and remember instructions, but to be able to create them yourself.

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Re: If 13,333 – n is divisible by 11, and 0 < n < 11, what is n?  [#permalink]

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You could even try proces elimination
Let's look at answer A
13332/11 = 1101.

Therefore the answer is A. The other answers are incorrect.
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Re: If 13,333 – n is divisible by 11, and 0 < n < 11, what is n?  [#permalink]

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_________________ Re: If 13,333 – n is divisible by 11, and 0 < n < 11, what is n?   [#permalink] 26 Sep 2018, 11:44
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