Here’s How to Crack It
Let’s go through the steps.
1. Know the question. “What is the value of the larger of the two integers?” The key word here is
larger. The numbers in the answer choices will be possibilities for this larger value. Notice this is
asking for a specific value, which means we can PITA.
2. Let the answers help. We’ve got a list of non-variable answers in ascending order. Each one
offers a possible answer to the specific question posed in the problem. Let’s PITA, and use the
answers to work backwards through the problem.
3. Break the problem into bite-sized pieces. Even though this is a short problem, there’s a lot of
information here, so we should use columns to help us keep all the information straight. The
problem says that the sum of the two integers is 28, so let’s start there. Begin with (C) to help with
Process of Elimination.
- The product of two distinct integers is 192. If the sum of those same two integers is 28, what is the value of the
larger of the two integers?
Larger integer Smaller integer (Larger × Smaller) = 192?
F. 18
G. 16
H. 12 16 CAN’T WORK
J. 10
K. 8
We can eliminate (H) right off the bat. Just from what we’ve found, 12 can’t be the larger integer if 16 is
the smaller integer. We will therefore need a number larger than 12, so we can eliminate (J) and (K) as
well. Let’s try (G).
- The product of two distinct integers is 192. If the sum of those same two integers is 28, what is the value of the
larger of the two integers?
Larger integer Smaller integer (Larger × Smaller) = 192?
F. 18
G. 16 12 16 × 12 = 192 Yes!
H. 12 16 CAN’T WORK
J. 10
K. 8
Choice (G) works, so we can stop there. Notice how PITA and Plugging In have enabled us to do these
problems quickly and accurately without getting bogged down in generating difficult algebraic formulas.
A NOTE ON PLUGGING IN AND PITA
Plugging In and PITA are not the only ways to solve these problems, and it may feel weird using these
methods instead of trying to do these problems “the real way.” You may have even found that you knew
