Number S is obtained by squaring the sum of digits of a two digit numb

Letting t = the tens digit of D and u = the units digit of D, we have D = 10t + u and S = (t + u)^2. Since S - D = 27, we can create the equation:

(t + u)^2 - (10t + u) = 27

Since 10t + u is positive, we see that t + u should be at least 6.

If t + u = 6, then (t + u)^2 = 36 and 10t + u (or D) should be 9. However, D is a two-digit number, so t + u actually should be at least 7.

If t + u = 7, then (t + u)^2 = 49 and 10t + u (or D) should be 22. However, 22 is not one of the given choices.

If t + u = 8, then (t + u)^2 = 64 and 10t + u (or D) should be 37. However, 37 is not one of the given choices.

If t + u = 9, then (t + u)^2 = 81 and 10t + u (or D) should be 54. We see that E is the correct answer.

(Note: If you don’t know how to analyze the problem algebraically, you can just check each given answer. For example, take 24, the first given choice. If D = 24, then S = (2 + 4)^2 = 36 and S - D would be 36 - 24 = 12. However, that is not 27. So you can move on to the next given choice and so on, and when you arrive at the last choice, you will see that if D = 54, then S = (5 + 4)^2 = 81 and S - D = 81 - 54 = 27.)

Answer: E

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.