**Q1**. What is the smallest positive integer

(A)

(B)

(C)

(D)

(E)

**Q2**. In the month of August, Pentheus Corporation made

(A)

(B)

(C)

(D)

(E)

**Q3**. Harold needs to buy a ticket to attend a conference for work. His own department contributes

(A)

(B)

(C)

(D)

(E)

**Q4**. Jackson invested

(A)

(B)

(C)

(D)

(E)

**Q5**. Solution

(A)

(B)

(C)

(D)

(E)

Solutions will come at the end of this article.

When all five answers are numerical, that puts us in an excellent position to use backsolving. Backsolving is an alternative to the algebraic method of solution that your wizened Algebra Two teacher would have deemed the only correct way. Backsolving means starting with a numerical answer, and working through with that number to see if it fits the requirements of the scenario.

In a previous post, I recommended the #1 backsolving strategy: start with answer (C). You see, if all five answer are integers, the QUANT always lists them from smallest to largest. Answer choice (C) will always be in the middle. If we plug in (C) and it comes out to the correct value, then we are done. If it is too big, then we can eliminate (C) & (D) & (E); if it is too small, then we can eliminate (A) & (B) & (C). Choice (C) is often the best place to start, because whether it turns out to be too high or too low, there’s more than one answer to eliminate.

Make it easy!

Of course, backsolving is a strategy that should be used to make things easier. Suppose a problem presents a scenario, and then has these answer choices:

(A)

(B)

(C)

(D)

(E)

Well, hmmm. Whatever the calculations in the problem may be, starting with (C) doesn’t seem like it would be a whole lot of fun without a calculator. Also, notice the answers are too close together to estimate. BUT, notice that of the five answer choices, here answer choice (B) is a nice neat round number. In a way, the design of the answer choices presents (B) on a silver platter as the best possible choice for backsolving. If you decide to backsolve, don’t simply go on automatic pilot and choose (C). Scope out the answers, and see if one stands out as a much easier choice for backsolving calculations: if there is such answer choice available, chances are very good that the question-writer placed it for just that purpose.

If you have any questions about what I have said here, or if you would like to add anything, please use our comments section below.

**Q1**. We’ll use backsolving. Start with choice (C). If

That’s just larger than

That’s well below

**Answer = (C)**

**Q2**. First of all,

As we discussed in this post, starting with (C) in this problem would not be fun. Instead, we’ll backsolving starting with the round number, choice (D). Suppose

(a)

(b)

(c) Multiply (a) by

(d) Divide (a) by half:

(e) add (b) & (c) & (d):

That’s a bit shy of the required

**Answer = (E)**

**Q3**. We’ll use backsolving. Start with choice (C). If

department pays

HR pays

Together, they pay

Try (B). If

department pays

HR pays

Together, they pay

**Answer = (B)**

**Q4**. As we discussed in this post, starting with (C) in this problem would not be fun. We’ll backsolving starting with a round number. The answers give us two round numbers, choice (B) and choice (E). Let’s think strategically about this. If we try (E) and it works, then we have the answer, but if it doesn’t work, we would know the amount would have to be less, but we can already see that. Backsolving with (E) does not necessarily give us a lot of information.

Instead, backsolving with (B). Let’s say Jackson puts

In

In

half of that:

Not quite enough interest. To earn that extra

**Answer = (A)**

**Q5**.

We start with

We then add an unknown amount of solution

Combining solution

Now, let's set up a ratio that demonstrates the new solution is

From here, we can cross-multiply and solve for

**Answer = (E)**