How to Find Remainder When the Divisor Changes on GMAT?

Short Answer

Favorite GMAT remainder question: N leaves remainder 93 when divided by 120; what is N’s remainder when divided by 40? Write N = 120p + 93. Divide each part by 40: 120p leaves 0, 93 leaves 13. Therefore, N’s remainder with 40 is 13.

Overview

In your GMAT prep, one powerful habit is to express numbers cleanly. Remainder questions simplify when you write a number as N = d × q + r and then see how that form behaves when the divisor changes. This article focuses on the GMAT’s favorite pattern: you are told N leaves remainder r on division by d, and you must find the remainder when dividing N by a factor or a multiple of d. We will reduce the large term, cancel what disappears, and track the smaller remainder step by step. The aim is clarity, not heavy arithmetic. The same disciplined thinking strengthens your test approach and carries into MBA admissions, where clear reasoning and careful structure matter.

 

Finding the Remainder When the Divisor Changes

On the GMAT, such remainder questions are often along the lines of: you are told that N leaves remainder r when divided by d, and you are asked for N’s remainder with a different divisor.

Here is the correct approach for solving such questions…

N = the original number

d = the original divisor

k = the whole-number quotient when N is divided by d

r = the remainder when N is divided by d (0 ≤ r < d)

Write N in a standard form

N = d * k + r

If the new divisor is a factor of d

Let the new divisor be f, where f divides d.

Then d * k is divisible by f.

So, the remainder with f depends only on r.

Compute r mod f to get the answer.

Question: N leaves remainder 93 when divided by 120. What remainder will N leave when divided by 40?

Write: N = 120 * k + 93.

New divisor: f = 40

Compute: 120 * k leaves remainder 0 with 40.

Compute: 93 leaves remainder 13 with 40.

Answer: N leaves remainder 13 with 40.

Alternate, simple explanation

N is of the form 120P + 93.

Here, 120P leaves remainder 0 with 40 because 120 is a multiple of 40.

93 leaves remainder 13 with 40.

Adding them together, the overall remainder is 13.

If the new divisor is a multiple of d

Let the new divisor be M = d * t.

Start from N = d * k + r.

When dividing by M, the remainder must be one of:

r, r + d, r + 2d, …, r + (t – 1)d.

Keep only the values that are less than M.

Question: N leaves remainder 87 when divided by 150. What remainder will N leave when divided by 300?

Write: N = 150 * k + 87.

New divisor: M = 300 = 150 * 2 (so t = 2).

Possible remainders: r = 87, and r + d = 87 + 150 = 237.

Both 87 and 237 are less than 300, so both are valid.

If k is even, the remainder is 87.

If k is odd, the remainder is 237.

Answer: there are two possible remainder: 87 and 237

More Complex Cases and Variations: Watch the Video Above

This question type has richer forms that are best learned visually: multiples of the original divisor, layered factors, cancellations that change the denominator, and case splits that create more than one valid remainder. In the video above, a seasoned trainer works through these patterns step by step, starting with small numbers and then moving to full GMAT examples. You will see when to write N = d * k + r, how to handle factor and multiple divisors, and how to track possible remainders like r, r + d, and beyond. Pause, try each case yourself, and then compare with the walkthrough. Watching the method unfold on screen builds clarity faster than dense text. We strongly recommend using the video to master these advanced variations.

The Broader Learning

Remainder questions are not about speed but about clarity of thought. They ask you to see the structure behind the numbers. This clarity builds naturally when you work consistently with GMAT practice tests, which replicate the exact reasoning style tested in the exam. Every problem you solve in this manner is not just practice for the GMAT but training for the kind of logical rigor that will serve you well in your professional journey.

Parting Thought

The beauty of this remainder type is not the arithmetic but the mindset it cultivates. You learn to rewrite a messy number in a clean form, to respect how divisors change the question, and to test cases without bias. Sometimes a single, elegant remainder appears. Sometimes two answers are both valid. In each case the path is the same: slow down, express N as d*q + r, and let the structure lead you. This habit turns pressure into order. Carry it with you beyond the GMAT, wherever clear thinking and small, steady steps resolve what first seemed complicated.