5 Reasons to make Testing the Answer Choices Plan A

Note: This is article #2 in the multi-article series Are you doing it wrong?

By Brent Hanneson - April 25, 2022

In my last article, I explained that, in order to maximize your quant score, you must be adept at applying both conventional (i.e., high school math) strategies and GMAT-specific strategies. 

In this article, we’ll examine ways in which GMAT-specific strategies are better than conventional strategies. I’ll also explain why GMAT-specific strategies should always be Plan A, and why we should choose an alternate/conventional approach only if we’re certain the alternate approach will be faster. 

Today we’ll examine the most common GMAT-specific strategy, testing the answer choices. 

Ugh! I already know about testing answer choices!

I figured as much, but, if you’re like most GMAT students, you consider testing the answer choices only after conventional strategies have failed. That is, most students make the conventional approach Plan A and don’t consider testing the answer choices until after they’ve wasted a bunch of time with their first approach. 

The truth is your goals are best served when you make testing the answer choices Plan A. There are 5 reasons to follow this advice: 

• Testing the answer choices typically involves easier math. 
• The act of deciding whether to test the answer choices will provide valuable insights if we decide to apply conventional strategies  
• Testing the answer choices is often faster
• In many cases, we can eliminate enough answer choices so that we need only test one answer choice.
• Testing doesn’t suffer from the scourge of clever distractors

Let’s examine each reason, starting with. . . 

Testing the answer choices typically involves easier math. 

Let’s re-examine this question (from the GMAT Official Guide) we reviewed in the last article:

A store currently charges the same price for each towel that it sells. If the current price of each towel were to be increased by $1, 10 fewer towels could be bought for $120, excluding sales tax. What is the current price of each towel?

(A) $ 1

(B) $ 2

(C) $ 3

(D) $ 4

(E) $12

The conventional approach to this question requires us to translate information into a quadratic equation and then solve that equation. The GMAT-specific approach, on the other hand, requires us to divide and subtract. As you can imagine, we’re much less likely to make mistakes while performing elementary school arithmetic than while creating and solving a quadratic equation. If you’re interested, here are both solutions on GMAT Club).  

Here’s a much harder question from the Official Guide: 

At his regular hourly rate, Don had estimated the labor cost of a repair job as $336, and he was paid that amount. However, the job took 4 hours longer than he had estimated and, consequently, he earned $2 per hour less than his regular hourly rate. What was the time Don had estimated for the job, in hours?

(A) 28

(B) 24

(C) 16

(D) 14

(E) 12

On GMAT Club, this question has a 700+ difficulty rating, and students typically spend well over 3 minute solving it. 

Let’s see how we do . . .  

Q: Can we use the answer choices to our advantage? 

A: Yes, we can test each answer choice. 

Q: Is there a conventional approach that’s faster? 

A: It’s hard to tell. So, let’s stick with the approach we know will work. 

Let’s start with choice C, the middle value (you’ll see why shortly). 

(C) 16. This tells us Don originally estimated the job would take 16 hours. 

Hourly rate = (total labor cost)/(number of hours worked) = $336/16 = $21/hour

If the job took 4 extra hours, then Don worked 20 hours, which means his actual hourly rate = $336/20 = 84/5 = $16.80/hour (check out this brief video on dividing numbers by 5 in your head).

The difference in hourly rates = $21/hour - $16.80/hour ≈ $4/hour

So, testing choice C resulted in a rate difference of approximately $4 per hour, but the question tells us the rate difference is only $2 per hour. This bigger-than-needed rate difference tells us that Don’s estimated work time must have been more than 16 hours, since this would reduce the effect of the 4 extra hours (and cause a smaller rate difference). 

Since we need Don's estimated work time to be more than 16 hours, we can eliminate answer choices C, D, and E.

Now let’s test B. 

(B) 24. This tells us Don originally estimated the job would take 24 hours. 

Estimated hourly rate = $336/24 = $14/hour

If the job took 4 extra hours, then Don worked 28 hours, which means his actual hourly rate = $336/28 = $12/hour 

So, the difference in hourly rates = $14/hour - $12/hour = $2/hour. Perfect!!

Answer: B. 

The most common algebraic solution to this question involves creating and solving the quadratic equation t² + 4t – 672 = 0. If we compare this conventional solution to testing answer choices, we see that the calculations involved with the conventional approach are more complex and more prone to errors. 

This question is just another example of the test-makers testing our ability to identify the most efficient approach.  

The act of deciding whether to test the answer choices will provide valuable insights if we decide to apply conventional strategies  

While determining whether testing the answer choices will be more efficient than applying conventional strategies, we gain a better understanding of the relationships between the key values in the question as well as the restrictions placed on those values. Consider this question from the Official Guide:  

Three types of pencils, J, K, and L, cost $0.05, $0.10, and $0.25 each, respectively. If a box of 32 of these pencils costs a total of $3.40, and if there are twice as many K pencils as L pencils in the box, how many J pencils are in the box?

(A) 6

(B) 12

(C) 14

(D) 18

(E) 20

Once again, we’ll ask:

Q: Can we use the answer choices to our advantage? 

To answer this question, our thought process might go something like this: 

A: The answer choices tell us the number of J pencils in the box. The box contains 32 pencils. So, knowing the number of J pencils will let us determine the total number of K- and L- pencils combined. For example, if there are 20 J pencils, then the remaining 12 pencils must consist of K and L pencils. Since there are twice as many K pencils as L pencils in the box, we need to divide those 12 pencils into a 2 to 1 ratio to get 8 K pencils and 4 L pencils. From here, we need calculate the total cost of 20 J pencils, 8 K pencils, and 4 L pencils to see whether it’s $3.40. This seems like a lot of work! So, let’s go with the conventional algebraic solution. 

As you can see, even though we’ve decided to forgo the GMAT-specific strategy of testing the answer choices, we now have a richer understanding of the question’s details, which will make it easier to solve via conventional methods. 

Testing answer choices is often faster

Many students reject the strategy of testing answer choices, because they feel the approach will take too long, especially if they end up testing all 5 values. The truth is that, in many cases, we must test, at most, 2 answer choices, which shouldn’t take long.  

Consider this example from the Official Guide: 

A student responded to all of the 22 questions on a test and received a score of 63.5. If the scores were derived by adding 3.5 points for each correct answer and deducting 1 point for each incorrect answer, how many questions did the student answer incorrectly?

(A) 3

(B) 4

(C) 15

(D) 18

(E) 20

Let’s see how we do . . .  

Q: Can we use the answer choices to our advantage? 

A: Yes, we can test each answer choice. 

Q: Is there a conventional approach that’s faster? 

A: It’s hard to tell whether applying algebraic techniques will be faster. So, let’s stick with the approach we know will work. 

Since the answer choices for most Problem Solving questions are given in ascending or descending order, let’s start by testing choice C, the middle value. 

(C) 15. This tells us the student got 15 of the 22 questions wrong, which also means the student got 7 questions right. 

Total score = (7)(3.5) - (15)(1) = 25.5 - 15 = 10.5

Since we're told the students received a score of 63.5, we know that answer choice C is incorrect.

It's also clear that, in order to increase the score to 63.5, the student must get fewer than 15 questions wrong, which means we can also eliminate answer choices D and E.

At this point, we need only test one more answer choice. For example, if we test choice A and it works, then A is right. Alternatively, if we test choice A and it doesn't work, then B is right.

Let's test choice B: 

(B) 4. This tells us the student got 4 of the 22 questions wrong, which means the student correctly answered 18 questions.

Total score = (18)(3.5) - (4)(1) = 63.5 - 4 = 58.5

Since we're told the student received a score of 63.5, we know that answer choice B is incorrect, and, by the process of elimination, the correct answer must be A.

As you might suspect, there are a lot of questions that can be solved by testing, at most, two answer choices. 

But wait, it gets better. 

In many cases, we can eliminate enough answer choices so that we need to test just one answer choice.

This typically occurs when we can eliminate 2 or more answer choices before we start testing. Consider this question from the GMAT Official Guide:

Each year for 4 years, a farmer increased the number of trees in a certain orchard by 1/4 of the number of trees in the orchard of the preceding year. If all of the trees thrived and there were 6250 trees in the orchard at the end of 4-year period, how many trees were in the orchard at the beginning of the 4-year period?

(A) 1250

(B) 1563

(C) 2250

(D) 2560

(E) 2752

On GMAT Club, this question has a difficulty rating of 650+ largely because students spend, on average, over 2.5 minutes solving it.  

Let’s see how we do . . .  

Q: Can we use the answer choices to our advantage? 

A: Yes, we can test each answer choice BUT, to do so, we must take each answer (the number of trees at the start of the 4-year period) and calculate the number of trees for years 1, 2, 3 and 4 to see if we reach 6250 trees after the fourth year. We wouldn’t want to do this for several answer choices. That said, 3 of the answer choices are automatically disqualified, which means we just need to test one answer choice.  

Q: Is there a conventional approach that’s faster? 

A: I doubt it.  

Here, we’re told the number of trees increases by ¼ each year. Since answer choices A, B, and C aren’t divisible by 4, we can eliminate them immediately. 

To understand why, let’s see what happens when we test choice C: 2250

If there were 2250 trees at the beginning, then the number of trees after 1 year = 2250 + (1/4 of 2250) = 2812.5, which makes no sense, since we can’t have half a tree.  

Useful property: An integer is divisible by 4 if and only if the number created by its last two digits is divisible by 4. 

Since 50 and 63 (the two-digit numbers created by the last two digits of A, B and C) aren’t divisible by 4, we can eliminate A, B and C. 

This leaves us with D and E. From here, we’ll just test one option. If it works, we’re done. If it doesn’t work, the other option must be correct.

I’ll test choice D (2560), since calculating 1/4 of 2560 looks easier than calculating 1/4 of 2752:

Number of trees at beginning = 2560

Number of trees after 1 year = 2560 + (1/4 of 2560) = 2560 + 640 = 3200  

Tip: We can calculate ¼ of k by dividing k by 2 twice

Number of trees after 2 years = 3200 + (1/4 of 3200) = 3200 + 800 = 4000 

Number of trees after 3 years = 4000 + (1/4 of 4000) = 4000 + 1000 = 5000 

Number of trees after 4 years = 5000 + (1/4 of 5000) = 5000 + 1250 = 6250 

Perfect! The correct answer is E. 

Is it a coincidence that 3 of the 5 answer choices are automatically disqualified, leaving us to test just one answer choice? No. This is another way the GMAT test-makers reward number sense and our ability to identify the most efficient solution. 

Here’s another question from the GMAT Official Guide:

The price of lunch for 15 people was $207 including a 15% gratuity for service. What was the average price per person, EXCLUDING the gratuity?

(A) $11.73

(B) $12

(C) $13.80

(D) $14

(E) $15.87

Despite its appearance, this is ranked as a 700+ level question on GMAT Club. Let’s see how we do: 

Q: Can we use the answer choices to our advantage? 

A: Since the answer choices tell us the pre-tip amount per person, we could take an answer choice and calculate the amount each person paid including the tip calculation, and then multiply this per-person cost by 15 to see if we get $207 (the total cost). That seems like a lot of work, so let’s go with the conventional approach.

We’re asked to find the average price per person (excluding the tip). So, let’s first divide $207, the total price, by 15, the total number of people. 

Tip: We can calculate $207 ÷15 by first dividing 207 by 3 and then dividing the result by 5. 

$207 ÷ 3 = $69, and $69 ÷ 5 = $13.80

So, each person paid $13.80, and this amount includes the tip. So, if we exclude the tip, the average cost per person will be less than $13.80, which means we can eliminate C, D and E, since they aren’t less than $13.80

Aha! Now that we’re down to choices A and B, let’s just test one of them to see if it results in a tip-included cost of $13.80 

Which one should we test? 

Let’s test the one that’s easier to work with (unless you enjoy calculating 15% of $11.73!).

Aside: On test day, I’d immediately select B as my response, since I can see that 15% of $11.73 (choice A) will result in each person paying an amount involving fractional pennies (e.g., If we add a 15% to $11.73, we get a per-person cost of $13.4895)

Anyhoo, let’s test B ($12.00) 

If the pre-tip cost was $12.00, the amount including the tip = $12 + (15% of $12) = $12 + $1.80 =$13.80. Perfect!!

Answer: B

There are tons of examples of official questions in which we can eliminate answer choices before testing any values.

For example, in this official GMAT question, we can immediately eliminate choices A and B because the calculations 2/3 of 280 and 2/3 of 400 don’t result in integer values (and the question doesn’t allow for fractional goose eggs!). Here’s my full solution.  

There’s also this question we examined earlier: 

Three types of pencils, J, K, and L, cost $0.05, $0.10, and $0.25 each, respectively. If a box of 32 of these pencils costs a total of $3.40 and if there are twice as many K pencils as L pencils in the box, how many J pencils are in the box?

(A) 6

(B) 12

(C) 14

(D) 18

(E) 20

At the time, I suggested we should use a conventional approach for this question. 

I fibbed. 

We can actually eliminate 3 answer choices and test just one answer choice. Can you see how? To find out, see my solution on GMAT Club, where I solve the question in two different ways.    

You can be certain the test-makers were well aware that 3 answer choices were ineligible to be tested, meaning the correct answer just one test away.

Testing doesn’t suffer from the scourge of clever distractors

Upon solving a difficult math problem, the moment of truth occurs when we search for our answer among the answer choices. If it’s there, we breathe a sigh of relief, knowing our answer is correct. 

But is it? 

When the GMAT test-makers create a Problem Solving question, they typically try to identify incorrect answer choices (aka distractors) that students will think are correct. They do this by predicting the mistakes students typically make. 

Recall this official GMAT question from earlier: 

At his regular hourly rate, Don had estimated the labor cost of a repair job as $336 and he was paid that amount. However, the job took 4 hours longer than he had estimated and, consequently, he earned $2 per hour less than his regular hourly rate. What was the time Don had estimated for the job, in hours?

(A) 28

(B) 24

(C) 16

(D) 14

(E) 12

If we solved this question algebraically, but incorrectly factored x² + 4x – 672 = 0 as (x-28)(x+24) = 0 instead of (x+28)(x-24) = 0, then we’d incorrectly conclude the answer is 28. Upon seeing choice A among the answer choices, we’d conclude we must have done everything right. 

Similarly, in this question from the Official Guide¸ students who incorrectly translate “Jim is 10 years younger than Sam” as J – 10 = S, will incorrectly conclude that Sam is 50 years old and select choice D. Not surprisingly, D happens to be the most popular incorrect answer for this question on GMAT Club. 

This is pretty much a feature of all GMAT Problem Solving questions. So, another great thing about testing the answer choices is that it doesn’t allow for clever distractors to trick us into a false sense of confidence. 

Final words

As you can see, there are several good reasons to add testing the answer choices to your mathematical toolbox. 

In the next article, we’ll examine more GMAT-specific strategies that allow us to identify the correct answer more efficiently than conventional approaches do.

In the meantime, I recommend that you try applying the above GMAT-specific strategies to the following questions from the Official Guide. For an additional challenge, try solving each question by both GMAT-specific strategies and conventional methods to determine which approach is more efficient.  

Sub-600 level questions:

• Question 1 | my solution
• Question 2 | my solution
• Question 3 | my solution
• Question 4 | my solution
• Question 5 | my solution
• Question 6 | my solution
• Question 7 | my solution

600+ Level questions

• Question 1 | my solution
• Question 2 | my solution
• Question 3 | my solution
• Question 4 | my solution
• Question 5 | my solution
• Question 6 | my solution
• Question 7 | my solution 

Click here to read the next article in this strategy series.