M31-27

The point is, we are told that x and y are positive integers. For positive integers x and y, where x > 7 and y > 11, it's not possible that x + y = 19.

I had missed that, thanks.

m = xa+7 and x>7
n = yb + 11 and y>11
Eliminate I. and II.
Answer C or E

Ex. for III.
m=15; a=1; x=8
n=23; b=1; y=12
Answer C

I think this is a high-quality question and I agree with explanation.

I think this is a high-quality question and I agree with explanation.

Reminder always < Divisor.
Therefore, 7<X, 11<Y.
Least value of X = 8
Least value of Y = 12
So, lest value of X + Y = 8 + 12 = 20.
Hence, C

Bunuel,

But I thought, diving any positive integers between 1-6 by 7 will lead to a remainder of 7. can you please tell me what I am missing?

Best Regards,

No. When divisor is more than dividend then the reminder equals to the dividend. For example, 1 divided by 7 gives the remainder of 1. 2 divided by 7 gives the remainder of 2...

Check the links below for more:

6. Remainders

• Theory
  REMAINDERS
  Remainders: Tips and hints
  Divisibility and Remainders on the GMAT
  Remainders on the GMAT
  A Remainders Shortcut for the GMAT
  All About Negative Remainders on the GMAT
  A Tricky Question on Negative Remainders
  Compilation of tips and tricks to deal with remainders
  Cyclicity and the remainders on the GMAT
  GMAT Question Patterns: Remainders
  
  • Questions
    Units digits, exponents, remainders problems
    DS Questions
    PS Questions

For other subjects:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread

what is the proof from the equation that the remainder is always less than the divisor?

eq: m/x = q + 7/x

The remainder should always be less than the divisor because that is how we define the remainder in the context of division:

If \(x\) and \(y\) are positive integers, there exist unique integers \(q\) and \(r\), called the quotient and remainder, respectively, such that \(y =divisor*quotient+remainder= xq + r\) and \(0\leq{r}<x\).

When we divide one number (the dividend) by another number (the divisor), we are essentially asking how many times the divisor can fit into the dividend. The quotient is the whole number answer to this question, and the remainder is the amount that is left over after we've taken out as many whole divisors as we can.

For example, if we divide 13 by 3, we get a quotient of 4 and a remainder of 1. This means that 3 times 4 can fit into 13, with 1 left over. The remainder is the "leftover" amount, which must be less than the divisor (in this case, less than 3) because if it were equal to or greater than the divisor, then we could fit another whole divisor into the dividend.

Therefore, the remainder must always be less than the divisor in order for the result of the division to make sense and be consistent with the way we define the operation.

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

I think this is a high-quality question and I agree with explanation.

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.