GMAT Quant: How to Find Last 2 Digits of Large Multiplication?

Short Answer

On GMAT Quant, large products do not require full multiplication. To find the last two digits, multiply the last two digits of each factor. Spot friendly pairs like 20 and 25 to lock 00. If a zero appears, track the second last digit using unit digits.

 

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Overview

Last digit problems are some of GMAT’s favorite and you must master these over the course of your GMAT prep. Some GMAT Quant questions are designed to intimidate with sheer size. You may see a product of large numbers and feel it is impossible to compute within the exam’s time limits. But the GMAT does not expect you to multiply everything. Instead, it rewards sharp eyes and logical shortcuts. When asked for the last two digits of a huge product, you need not expand all the numbers. The secret lies in focusing only on the final two digits of each term and spotting patterns. Numbers like 20 and 25, or 42 and 15, can be called “friendly” numbers because together they create an ending that locks the final result. Once such a combination is found, the rest becomes easy.

 

Finding the Last Two Digits of Large Products in GMAT Quant

At first sight, problems that ask for the last two digits of a large product can feel overwhelming. The expression looks too big to handle in the limited time of the GMAT. But these questions are never about brute force. They are about insight.

The Core Concept

To find the last two digits, you only need to multiply the last two digits of each number in the product. This reduces the task into something manageable. The process often reveals a shortcut, because there is usually a “catch” hidden in the sequence.

Example 1: Spotting Friendly Numbers

Question: Find the last two digits of 787 x 625 x 579 x 347 x 520 x 777

Spot 25 and 20 as the last two digits of 625 and 520. If you multiply these two first, the result ends with 00. Once you have 00 at the end, any further multiplication will continue to end with 00, regardless of the other numbers. That is the power of spotting a friendly pair.

In this case, the answer is 00. No full multiplication was needed.

Example 2: Working with a Zero in the Last Digit

Question: Find the last two digits of 989 x 627 x 571 x 342 x 759 x 715

Spot the friendly numbers 342 and 715, with the last two digits as 42 and 15.

Multiply them first: 42 × 15 = 630, which ends with 0.

Once you have a 0 at the end, you know the final digit will remain 0. But you still need the second last digit. To find it, you look at the other remaining numbers and multiply only their last digits step by step:

9 × 7 = 63 → last digit 3

3 × 1 = 3

3 × 9 = 27 → last digit 7

Now, 630 gave us a ‘3’ before ‘0’. Hence, we must multiple ‘7’ and ‘3’.

7 × 3 = 21 → last digit 1

This gives a penultimate digit of 1. With 0 already secured as the last digit, the final answer is 10.

The Deeper Lesson

These questions are not about memory tricks. They are about clarity of thought. You train yourself to notice the right numbers to pair and to trust that logic will take you home faster than calculation. Once you see a factor like 2 and 5 together, or a multiplication that guarantees a trailing 0, the problem is already solved in principle. The test is not checking whether you can multiply large numbers by hand. It is checking whether you can keep your calm, notice patterns, and apply reasoning with confidence. Over time, as you practice, these shortcuts become natural. What once felt intimidating becomes manageable, even enjoyable. For deeper mastery of such number-based strategies, a structured GMAT preparation program with high number of GMAT mock tests will help you practice systematically and build the confidence you need for test day.

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