Real GMAT® Problems Ep. 46: Computation

What This Episode Covers

Three real GMAT® computation problems from the 11th edition of the Official Guide for GMAT® Review, increasing in difficulty. Isaac walks through each one and covers two big ideas: why doing the full math matters even when you think you already know the answer, and how converting decimals to fractions can simplify almost any computation problem.

The third problem adds a third lesson — when to recognize that a question is beyond your current traction, let it go quickly, and redirect your time to problems you can get right.

Problems Covered

0.1 + 0.1² + 0.1³ — A warm-up on decimal exponents. The math is quick, but the real lesson is why you should do it anyway — even when you're 90% sure. Read the worked solution →
(0.045 × 1.9) / (0.03 × 0.005 × 0.1) — A medium-difficulty decimal fraction problem. Convert every decimal to a fraction, flip and multiply, cancel. One approach that works on almost every problem like this. Read the worked solution →
x = 1/(2² × 3² × 4² × 5²), distinct non-zero digits — Only about 40% of test takers get this one right. Consolidate 2² × 5² = 100 first (no new digits). Then long-divide 1 ÷ 144 to reveal 0.00694̄. Three distinct non-zero digits: 6, 9, 4. Read the worked solution →

Key Takeaways

Missing easy questions hurts more than missing hard ones. The GMAT® scoring algorithm is adaptive. Dropping a question you know how to do has an outsized negative effect on your score. If there's any doubt — even 10% — do the full computation.

Convert decimals to fractions when computation gets messy. Flip the denominators, multiply across, cancel zeros. This one approach works on roughly 99% of decimal computation problems. You don't need to memorize a dozen specific decimal tricks.

2² × 5² = 100 is a move worth knowing. Multiplying by powers of 10 only shifts the decimal point — it doesn't add new non-zero digits. Spotting that on Problem 3 reduces the problem to 1 ÷ 144.

Sometimes brute force is the right answer. There is no elegant shortcut for 1 ÷ 144. Set up the long division. Work through it. Some problems reward the student who is willing to sit down and do the math.

Letting go is also a skill. On the GMAT®, recognizing when you don't have traction on a problem — and moving on quickly — is a form of resource management. The time you save can go toward questions you can get right. That's the trade worth making.

The scoring algorithm rewards execution, not just knowledge. A lot of people study hard, know the material, and still underperform. The gap is usually execution: rushing through familiar problems and making careless errors. Slowing down on the questions you know is one of the highest-leverage habits you can build.

Episodes Referenced

Transcript

Read the full transcript

Welcome to the GMAT® Strategy Podcast. You're here because you believe there's a better way to study for the GMAT®, and so do we.

We created the GMAT® Strategy to maximize your results and minimize your efforts so you can get to the fun parts about business school and life as quickly as possible.

My name is Isaac Puglia and I've been teaching GMAT® classes and tutoring privately for over a decade. I've achieved a 99th percentile GMAT® score and helped thousands of students get into the business schools of their choice.

If this show is bringing you value, please share it with your friends and family who are studying so that together we can make this process as easy and painless as it can possibly be.

Let's go.

Problem 1: 0.1 + 0.1² + 0.1³

Welcome to Real GMAT® Problems Episode 46. Doing Real GMAT® problems is one of the most tried and true ways to make test day go well. The problems we'll go through are from the 11th edition of the Official Guide for GMAT® Review. You can web search them if you'd like to follow along visually, and a link to the YouTube video is below if you'd like to see the scratch work.

Just so you know, the 11th edition is out of print — that's partly why we're using it. If you purchased this year's Official Guide, there shouldn't be any overlap.

The Official Guide contains retired problems that have appeared on past GMAT® exams, so these are extremely similar to what you'll see on your official test. We recommend pausing after each problem and trying to solve it before reading on. Even if you can't execute every step in your head, just think through the approach.

We're going to focus on computation questions today. It's a big pain point for a lot of people.

Problem 1: 0.1 + 0.1² + 0.1³ = ?

(A) 0.1 (B) 0.111 (C) 0.1221 (D) 0.2341 (E) 0.3

This is a great warm-up. There aren't too many steps, and it's one of those problems where if your skills are solid, you'll get it right. If they're a little shaky, it'll help reveal that.

Now, some of you can look at this and instantly know the answer with complete confidence. If that's you, great. But if there's even a small amount of doubt — even 10% — it's worth doing the full computation all the way through.

Here's the philosophy behind that. In our previous episode, "How to Break Through a GMAT® Score Plateau," we went into depth on the scoring algorithm. The short version: missing easy questions hurts your score more than missing hard questions. So that extra 10% certainty you get from doing the full math is more valuable than the time you'd save by skipping it.

Most of us are wired to speed up on questions we know. The GMAT® rewards the opposite habit — slowing down on familiar territory and making sure you get credit for what you already know.

Working through it. For 0.1², write 0.1 × 0.1. Ignore the decimal places. Do 1 × 1 = 1. Then count the decimal places in the original numbers — one decimal place each, so two total. Shift the decimal two places left: 0.01.

For 0.1³, we already know 0.1² = 0.01. Multiply 0.01 × 0.1. Do 1 × 1 = 1. Count decimal places — two from 0.01, one from 0.1, three total. Shift three places left: 0.001.

Now add:

0.100 0.010 0.001

Each column sums to 1. The result is 0.111.

The answer is (B).

The shortcut is just having done this enough times that you can see the pattern intuitively. If you're not there yet, the long multiplication approach is more than good enough. Practice builds the intuition.

Problem 2: (0.045 × 1.9) / (0.03 × 0.005 × 0.1)

This one is about four times harder than Problem 1 by the accuracy numbers.

Problem 2: (0.045 × 1.9) / (0.03 × 0.005 × 0.1) = ?

(A) 5,700 (B) 570 (C) 57 (D) 5.7 (E) 0.57

Recommend pausing here.

The cleanest approach is to convert every decimal into a fraction, then flip and multiply.

0.045 = 45/1,000 1.9 = 19/10 0.03 = 3/100 0.005 = 5/1,000 0.1 = 1/10

The original expression becomes:

(45/1,000 × 19/10) ÷ (3/100 × 5/1,000 × 1/10)

Dividing by a fraction is the same as multiplying by its reciprocal. Flip the denominator fractions and multiply everything across:

45/1,000 × 19/10 × 100/3 × 1,000/5 × 10/1

Cancel the zeros from top and bottom. You'll wind up with:

45 × 19 × 100 / (3 × 5)

Cancel the 45 with 3 × 5 = 15. 15 × 3 = 45, so we cancel and get:

3 × 19 × 100 = 5,700

The answer is (A).

The big takeaway: one approach works for almost every decimal computation problem you'll see. Convert to fractions, flip, multiply, cancel. You don't need to memorize a dozen decimal tricks. You need one approach that's reliable.

If you're a few days from test day and not feeling great with decimal computation, switching everything to fraction form is a defensible strategy. If you have more time, building your decimal skills gives you more flexibility. Either way, the fraction approach is your fallback.

Problem 3: x = 1/(2² × 3² × 4² × 5²), Distinct Non-Zero Digits

This one is significantly harder — about 60% harder than Problem 2 by the accuracy numbers.

Problem 3: If x = 1/(2² × 3² × 4² × 5²) is expressed as a decimal, how many distinct non-zero digits will x have?

(A) 1 (B) 2 (C) 3 (D) 7 (E) 10

There's a lot going on here. Complicated fraction, exponents, decimals, and a question about distinct digits. Take your time with it.

This problem is also a good occasion to talk about letting go. If you reach a point during a problem where your confidence is dropping — you started at 80% and now you're at 30% — that's valuable information. Letting go of hard questions quickly and redirecting your time to questions you can get right is a form of resource management. It's a leadership skill. The GMAT® is partly testing that.

Working through it. The first useful move is to pull out the 2² and 5² from the denominator and multiply them together. Order of multiplication doesn't matter here.

2² = 4. 5² = 25. 4 × 25 = 100.

So we can rewrite the denominator as 100 × 3² × 4². Separating out the 1/100, we have:

x = (1/100) × (1/(3² × 4²))

Why does this help? Dividing by 100 just moves the decimal point two places — it doesn't add any new non-zero digits. So we can set aside the 1/100 and focus on 1/(3² × 4²).

3² = 9. 4² = 16. 9 × 16 = 144.

We need to figure out 1 ÷ 144.

Set up the long division: 144 goes into 1,000 about 6 times. 6 × 144 = 864. Remainder 136.

Bring down a zero: 144 goes into 1,360 about 9 times. 9 × 144 = 1,296. Remainder 64.

Bring down a zero: 144 goes into 640 about 4 times. 4 × 144 = 576. Remainder 64.

The remainder repeats. So 1/144 = 0.006944444...

The non-zero digits are 6, 9, and 4. Three distinct non-zero digits.

Combined with the 1/100 factor (which just shifts the decimal), x = 0.0000694444...

The distinct non-zero digits are still 6, 9, and 4.

The answer is (C).

There's no elegant shortcut here. Some problems reward the student who is willing to sit down and do the math. That's also a skill worth building.

If you have questions about anything from this episode, reach us anytime at the GMAT® Strategy on current social channels, or email us at contact@TheGMATStrategy.com.

As always, our greatest hope is that this material makes your studies as easy and painless as they can possibly be. For more tips and strategies, visit TheGMATStrategy.com.

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