SAT Math Questions Forum + Help

Test Preparation
1

Hey guys!
I have a grid - in math question that I forgot how to do. I know there’s a certain way to do it without having to go through every single possibility.
Here’s the question:

What is the greatest four-digit integer that meets the following three restrictions?

  1. All of the digits are different.
  2. The greatest digit is the sum of the other digits.
  3. The product of the four digits is divisible by 10 and not equal to zero.

Does anyone know an efficient way to do this grid-in?
Thanks in advance and feel free to post any other math questions you may have!

2

There is a consolidated “SAT Math Questions” thread under the sub-topic “SAT Preparation.”

For your question, it is a good idea to pick the digits first. The product of the digits is a positive multiple of 10, so we have the following conditions:

  • The # contains 5
  • The # contains an even nonzero digit, and the # does not contain 0

Greedily assign 9 as the largest digit. The remaining digits must be 40 or 31 or 22 (since 9 = 5 + two other digits). 40 doesn’t work since 0 cannot be a digit, 22 doesn’t work since the digits are distinct, and 31 doesn’t work since the product of the digits is divisible by 10.

Next try 8 as the largest digit. Now the remaining two digits are 30 or 21. Again, 30 doesn’t work but 21 does.

The best case scenario uses the digits 8, 5, 2, 1 and 8521 is the largest such number.

3

Thanks! I’ll make sure to post on that thread next time