Mathematical Equations for dMAT: Rules and Practice

Mathematical Equations is one of the three dMAT Core Module subtests. It is not engineering mathematics, calculus, or a full quantitative aptitude paper. It is a speed-and-logic task based on small equation systems.

In the official task type, each letter stands for an integer from 1 to 20, and the student must find the value that makes the equations true. The official preparation material gives 20 equation systems in 25 minutes, so your target is about 75 seconds per item.

Read this after the dMAT structure guide and alongside the main dMAT preparation guide.

Last reviewed: 1 August 2026. This article uses the official dMAT preparation material for task format and rule categories. All practice questions below are Think Mile original and are not official dMAT questions.

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Direct Answer

The Mathematical Equations subtest checks whether you can solve short equation systems quickly without notes. The main skills are:

• substitution;
• rearrangement;
• reverse operations;
• integer arithmetic;
• spotting direct values;
• using the 1 to 20 limit;
• avoiding long trial-and-error.

You do not need calculus, trigonometry, logarithms, matrices, or advanced engineering mathematics for this Core Module task.

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Official Evidence

The official dMAT preparation material shows this task structure:

The official examples start with direct substitution and increase toward multi-step systems. The difficulty comes from speed and working memory, not from advanced syllabus breadth.

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Concept Lesson: The Fast Solving Method

Use this sequence in almost every task.

Step 1: Find the direct value

Look first for an equation like:

B = 6

or

C + 2 = 9

These give you a starting point. Do not begin with the longest equation unless it is the only useful one.

Step 2: Substitute immediately

If you know B = 6, put 6 wherever B appears.

Example:

A + 2 = B
B = 6

Then:

A + 2 = 6
A = 4

Step 3: Chain the values

Most systems are chains. One value unlocks another.

Example:

B = 6
A + 2 = B
C = A + B

Solve:

• B = 6
• A = 4
• C = 4 + 6 = 10

Step 4: Use the 1 to 20 range

If the task says every letter is an integer from 1 to 20, use that constraint.

Example:

C = 10 x B

If C must be between 1 and 20, then B cannot be 3, 4, 5, etc. B can only be 1 or 2. This kind of bound can make a hard item much faster.

Step 5: Check the target variable only

If the question asks for A, do not calculate every letter unless necessary. Solve only the chain needed for the asked value.

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Worked Example

This is a Think Mile original example, not an official dMAT question.

Question:

B = 4
A + B = 11
C = 2 x A

What is C?

A. 7
B. 11
C. 14
D. 18

Solution:

1. Start with the direct value: B = 4.
2. Substitute into A + B = 11: A + 4 = 11.
3. Solve: A = 7.
4. Substitute into C = 2 x A: C = 14.

Answer: C. 14

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Common Traps

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Think Mile Original Timed Practice

These questions are original practice, not official dMAT material. Solve without notes if you can.

Easy

A + 5 = 13
B = A + 2

What is B?

A. 6
B. 8
C. 10
D. 13

Solution:
A = 8. B = 8 + 2 = 10.
Answer: C

Medium

C = 3 x B
A + B = 12
A = 2 x B

What is C?

A. 9
B. 12
C. 15
D. 18

Solution:
Since A = 2B, substitute into A + B = 12.
2B + B = 12, so 3B = 12 and B = 4.
C = 3 x 4 = 12.
Answer: B

Difficult

A - B + C = 13
C = 2 x B
A = B + 5
D = A + C

What is D?

A. 15
B. 17
C. 19
D. 21

Solution:
Substitute A and C in terms of B:

(B + 5) - B + (2B) = 13

Simplify:

5 + 2B = 13

So:

2B = 8 and B = 4

Then:

• A = B + 5 = 9
• C = 2 x B = 8
• D = A + C = 17

Answer: B

Difficult: Use the Range

C = 6 x B
A = C - B
D = A + 3
D = 18

What is A?

A. 10
B. 12
C. 15
D. 18

Solution:
Start from the direct equation:

D = 18

Since D = A + 3, A = 15.

You can verify with the other equations:

• A = C - B, so C must be A + B.
• C = 6B.
• Therefore 6B = 15 + B, so 5B = 15 and B = 3.
• C = 18.

All values are integers from 1 to 20.
Answer: C

Difficult: Multi-Step Chain

A - B + C - D = 9
C = 5 x B
A = 4 x B
D = B + 5

What is C?

A. 5
B. 10
C. 15
D. 20

Solution:
Substitute in terms of B:

7B - 5 = 9
7B = 14
B = 2
C = 10

Answer: B. 10

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How to Build Your Own Practice Safely

Because official dMAT material is copyrighted, do not copy or lightly rewrite official questions. To create original Mathematical Equations practice:

1. Pick a target value for one letter, such as B = 3.
2. Build other letters from it, keeping all values between 1 and 20.
3. Write equations that lead back to those values.
4. Check that only one answer option is correct.
5. Solve your own item without notes.

Example design:

• Let B = 3.
• Let A = 2B = 6.
• Let C = A + B = 9.
• Ask for C.

Question:

A = 2 x B
C = A + B
B + 4 = 7

Answer: C = 9.

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Timed Practice Plan

Do not practise algebra only on paper. The dMAT no-note rule makes mental chaining important.

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Free Learning Path

Avoid jumping into advanced books. For this subtest, speed with simple algebra beats broad syllabus study.

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Official vs Think Mile Recommendation

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Frequently Asked Questions

Is this like engineering mathematics?
No. It is closer to mental algebra and short equation systems.

Do I need calculus?
No. The official Mathematical Equations Core task does not require calculus.

Should I use a calculator while practising?
No. The exam does not allow calculators, so practise mental arithmetic.

What is the fastest strategy?
Find the direct value first, substitute immediately, and solve only the variables needed for the answer.

What should I study next?
Continue with Latin Squares, then combine all Core subtests in timed sets.

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Source note: This article was reviewed against the official dMAT preparation material, the official dMAT preparation page, and Khan Academy's systems of equations unit. Think Mile is not affiliated with APS India or g.a.s.t.; all practice items here are original.