Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

The prompt asks us for what MUST be a factor of X+Y...

Using your example (36 and 63), we would have a total of 99. In this case, TWO of the answers 'fit' - both 9 and 11 are factors of 99. So one of these MUST be the solution, but we won't know which one until we find another example that is NOT divisible by one of the two options.

Re: The positive two-digit integers x and y have the same digits, but in [#permalink]

Show Tags

28 Oct 2015, 12:52

1

This post was BOOKMARKED

Bunuel wrote:

The positive two-digit integers x and y have the same digits, but in reverse order. Which of the following must be a factor of x + y?

(A) 6 (B) 9 (C) 10 (D) 11 (E) 14

Kudos for a correct solution.

Remember: When you take the difference between the two, it will always be 9. e.g 23-32=9, 89-98=9 and when you add both integers, the sum will always be a multiple of 11 e.g 23+32=55, 89+98= 187

Re: The positive two-digit integers x and y have the same digits, but in [#permalink]

Show Tags

16 Mar 2016, 01:22

Bunuel wrote:

The positive two-digit integers x and y have the same digits, but in reverse order. Which of the following must be a factor of x + y?

(A) 6 (B) 9 (C) 10 (D) 11 (E) 14

Kudos for a correct solution.

Supposing that the numbers are ab and ba, then ab can be written as 10a+b and ba can be written as 10b+a Adding we get 11a+11b=11*(a+b) Therefore, the sum is divisible by 11 as well as by sum of the digits.

The positive two-digit integers x and y have the same digits, but in reverse order. Which of the following must be a factor of x + y?

(A) 6 (B) 9 (C) 10 (D) 11 (E) 14

Kudos for a correct solution.

We can solve this question using the natural relationships that all two-digit numbers have. As an example, we can express 37 as (10 x 3) + 7. We multiply the digit in the tens position by 10 and then add the digit in the ones position.

If we let a = the tens digit of x and b = the ones digit of x, we know:

x = 10a + b

Since the digits of y are the reverse of those of x, we can express y as:

y = 10b + a

When we sum x and y we obtain:

x + y = 10a + b + 10b + a = 11a + 11b

x + y = 11(a + b)

The final expression 11(a + b) is a multiple of 11, and therefore 11 divides evenly into it.

We see, therefore, that 11 must be a factor of x + y.

Answer: D
_________________

Scott Woodbury-Stewart Founder and CEO

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

Re: The positive two-digit integers x and y have the same digits, but in [#permalink]

Show Tags

23 Jun 2016, 10:09

bimalr9 wrote:

I thought same digits were 11, 22, 33, 44, 55, 66..... 99. I am confused now.

Ok Let me try once -

X = 14 , Y = 41

X + Y = 14 + 41 =>55

55 = 11 * 5

Check again -

X = 12 , Y = 21

X + Y = 12 + 21 =>33

33 = 11 * 3

Check again -

X = 16 , Y = 61

X + Y = 16 + 61 =>77

77 = 11 * 7

Check in each case the common factor is 11 , hence the answer must be 11......

Feel free to revert in case of the slightest doubt, I will love to explain it again... PS: IMHO the best method for this problem will be (10a + b ) + (10b + a ) => 11(a+b) as posted earlier... _________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS