If 13,333 n is divisible by 11, and 0

Question

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

dominicraj · Accepted Answer

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.

Regards,
Dom.

anudeep133 · Answer

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

Option A

goldfinchmonster · Answer

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

Eg - 3 7 2 9  = + 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.

harishbiyani8888 · Answer

Answer is A

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.

BASSLJ · Answer

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.

Bunuel · Answer

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.

matthewsmith_89 · Answer

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.

Jawad001 · Answer

13,333/11 = 1212 *11 +1 
Remainder = 1, that is, if 1 is deducted from 13,333, the resulting figure is divisible by 11
Answer:1

hvelas93 · Answer

I thought I came across this somewhere but when a number is divisible by 11 its hundreds digit and ones digit add up to the tens digit?

In this case, 13,333-3=13,330. ---> 3+0=3 which would make this divisible by 11.

It's obviously not right but can someone tell me what rule I may be confused with? (I know I saw it somewhere)
I know the alternating odd-even rule for divisibility by 11 so no need to explain that.

CrackverbalGMAT · Answer

Hello hvelas93,

If you knew the alternating odd-even rule, you SHOULD have applied that rule to solve this question. Because, that IS THE divisibility test for 11.

Whatever you have mentioned in your first sentence is essentially a corollary of this rule and NOT the rule itself. It works ONLY in the case of 3-digit numbers. 
Think about it, will you generalize a divisibility test based on a certain number of digits? Not really, right?

Think about the number 1001. The sum of the ones and the hundreds digit here is 1 and the tens digit is 0. Both are not equal. Does that mean that 1001 is not divisible by 11? A resounding NO. 1001 IS divisible by 11.

So my advice to you would be to learn a rule in its entirety. Do not try to extrapolate specific cases and expect it to work under all conditions. This is essentially the reason why you got 3, which is the wrong answer. Also, do not attempt to make a short-cut out of a short-cut; divisibility tests are short-cuts themselves. They help you ascertain whether a number is divisible without you having to actually divide it.

Apply the divisibility test for 11 (the alternating odd-even rule), which you said you know, and you will see that n has to be 1 so that the difference between the respective sums is ZERO. 
 The correct answer option is A .

Hope that helps!

MyNameisFritz · Answer

Divisibility rule of 11: This particular rule states that the given number can only be completely divided by 11 if the difference of the sum of digits at odd position and sum of digits at even position in a number is 0 or 11

Right now 1+3+3=7; 3+3=6
7-6=1 (but we need 0, not 1)

Hence, answer A = 1

Right now 1+3+3=7; 3+3=6
7-6=1 (but we need 0, not 1)

Hence, answer A = 1

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

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

GMAT Problem Solving (PS) Questions