dMAT mock testsCore · 02

dMAT Mathematical Equations

Mathematical Equations is the second subtest of the dMAT Core Module: 20 items in 25 minutes. Each item gives you a small system of equations in which letters stand for whole numbers, with exactly one solution, and asks for the value of one letter. The mathematics never goes beyond school arithmetic — there is no calculus, no trigonometry and no advanced algebra. What is being tested is whether you can spot the shortest route to a single unknown under time pressure, without a calculator and without writing anything down.

Items: 20
Time: 25 min
Per item: 75 sec

Format last checked against g.a.s.t. on 2 August 2026

How to approach mathematical equations

There is no syllabus to revise for this subtest, so preparation means having a routine you can run without thinking. This is the order that wastes the least time at 75 seconds an item.

1
Read what is actually being asked first
You are asked for one letter, not for the full solution. Solving the whole system when you only need C is the single biggest time leak in this subtest.
2
Try adding every equation together
When each letter appears the same number of times across the system, summing all equations collapses it to a multiple of (A + B + C). Subtract the equation containing the two letters you do not want, and the one you do want falls out in a single step.
3
Otherwise substitute from the smallest equation
Take the equation with the fewest terms, express one letter in terms of another, and push it into the equation that contains your target. Two substitutions is usually the ceiling on these items.
4
Use the whole-number constraint
Every letter is a whole number, which rules out most candidates fast. If a substitution leaves you needing 7B = 20, you have made an arithmetic slip — no whole number satisfies it.
5
Check by back-substitution, not by re-solving
Drop your answer into an equation you have not used yet. It catches a sign error in about five seconds; re-solving from scratch costs you the next item.

Mathematical Equations practice questions

Worked examples in the documented dMAT format, with the full reasoning underneath each one. Time yourself: 75 seconds per item is the pace the real clock allows.

These are practice questions written by AdmitVerse to the format g.a.s.t. publishes. They are not official or past dMAT papers — no past papers exist for this exam, since the first sitting is on 26 September 2026.

Q1 · Mathematical Equations
Each letter stands for a whole number. What is the value of C?
```
A + B  =  9
B + C  = 11
A + C  = 10
```
A4
B5
C6
D7
Solution: Add all three equations: 2(A + B + C) = 30, so A + B + C = 15. Subtract the first equation (A + B = 9) to get C = 6. Checking: B = 11 − 6 = 5, A = 9 − 5 = 4, and A + C = 10. ✓ No calculator is allowed, so the trick is spotting the "add everything" shortcut rather than solving step by step.
Q2 · Mathematical Equations
Each letter stands for a whole number. What is the value of X?
```
X + 2Y = 16
    3Y =  12
```
A4
B6
C8
D10
Solution: The second equation gives Y = 4 immediately. Substituting: X + 8 = 16, so X = 8. When one equation contains a single letter, always start there — the system is built to be entered at that point, and hunting for a cleverer route wastes the time the shortcut just saved you.
Q3 · Mathematical Equations
Each letter stands for a whole number. What is the value of P?
```
P + Q + R = 20
Q + R      = 13
P + Q      = 12
```
A5
B6
C7
D8
Solution: Subtract the second equation from the first: P = 20 − 13 = 7. Done in one step, and the third equation is never needed — it is there to tempt you into a fuller solution. Scan for the pair of equations that differ by exactly your target letter before doing anything else.

What costs people marks here

Solving for all three letters when the question asks for one.
Missing the "add everything" shortcut and grinding through substitution instead.
Sign errors when subtracting one equation from another — the most common wrong answer is usually the right magnitude with the wrong sign.
Reaching for a calculator habit you cannot use. No calculator is allowed, so practise the arithmetic mentally from the start rather than discovering the gap on exam day.
Forgetting you cannot take notes. Practise holding a two-step substitution in your head, because that is the exam condition.

Know your pace before 26 September.

One exam date, one attempt, and no past papers. A timed mock is the only way to find out whether you are inside 75 seconds an item — free during early access.

Take a free Mathematical Equations mock