IPMAT Quant Tricks: Faster Ways to Solve QA Questions

Quick Answer

The best IPMAT Quant tricks are not magic formulas. They are reliable decision tools that reduce unnecessary work.

Useful techniques include:

Translating words into mathematical statements
Assuming a convenient value such as 100
Working backwards from the options
Factorising before expanding
Keeping quantities in ratio units
Using remainder and unit-digit cycles
Approximating when the options allow it
Drawing simple diagrams
Testing boundary values
Stopping once the answer is determined

Shortcuts become useful only after you understand the underlying concept. If you cannot explain why a method works, it is not yet safe to use under exam pressure.

First Rule: A Shortcut Must Be Reliable

A shortcut should do at least one of these things:

Reduce the number of calculations
Replace large numbers with simpler values
Use the answer options intelligently
Eliminate impossible cases
Make the information easier to represent
Help you decide quickly whether to solve or skip

A method that saves ten seconds in practice but causes frequent mistakes is not a useful shortcut.

Use the sequence:

Correct method → stable accuracy → shorter method → timed application

Build your basic calculation speed before relying heavily on faster methods. You can use the IPMAT calculation-speed routine for this foundation.

1. Translate the Question Before Solving

Do not begin calculating immediately after reading a word problem.

First identify:

What is given?
What must be found?
What relationship connects the values?
Are there any restrictions or hidden conditions?

Convert important phrases into mathematical language.

Phrase	Mathematical Meaning
20% more than $x$	$1.2x$
20% less than $x$	$0.8x$
At least $x$	Greater than or equal to $x$
At most $x$	Less than or equal to $x$
Directly proportional	Both quantities change in the same ratio
Inversely proportional	Their product remains constant

Many difficult-looking questions become manageable once the correct equation is formed.

2. Assume 100 in Percentage Questions

When the original value is not required, assume it to be 100.

Example

A population increases by 20% and then decreases by 20%. Find the overall percentage change.

Assume the original population is 100.

After the increase:

$100 \times 1.20 = 120$

After the decrease:

$120 \times 0.80 = 96$

The final value is 96 instead of 100.

Therefore, the overall change is a 4% decrease.

A 20% increase followed by a 20% decrease does not cancel because the second percentage is calculated on a different base.

Use this technique for:

Successive percentage changes
Profit and loss
Population questions
Income and expenditure
Election and survey questions
Percentage-based Data Interpretation

Do not assume 100 when the question specifically requires the original absolute value.

3. Work Backwards From the Options

In an MCQ, the answer options are part of the question.

If direct algebra is lengthy, substitute the options into the given condition.

When the options are arranged in increasing order, begin with a middle option. Its result may show whether the required answer should be larger or smaller.

Option substitution works best when:

The answer is a single numerical value
The condition is easy to test
The options are widely separated
Direct calculation requires lengthy algebra
The relationship changes consistently as the value increases

Avoid it when:

Every option requires a long calculation
Multiple options can satisfy an incomplete condition
The question asks for a proof or general expression
Direct algebra is already shorter

Option-based methods are mainly useful in MCQs. Short Answer questions still require you to reach the final numerical value without options.

4. Factor Before Expanding

Expanding an expression immediately can create larger numbers and additional steps.

Check for:

Common factors
Algebraic identities
Difference of squares
Cancellation
Symmetry around a convenient number

Example

$49 \times 51$

Instead of multiplying directly:

$(50-1)(50+1)$

Using:

$(a-b)(a+b)=a^2-b^2$

We get:

$50^2-1^2=2500-1=2499$

Factorisation is especially useful in Algebra, Number System and calculation-heavy Arithmetic questions.

5. Keep Values in Ratio Units

Do not calculate every actual quantity at the beginning of a ratio question.

Example

The ratio of boys to girls is 3:5, and the total number of students is 64.

Total ratio units:

$3+5=8$

One ratio unit:

$64 \div 8=8$

Therefore:

$\text{Boys}=3 \times 8=24$

$\text{Girls}=5 \times 8=40$

If the question asks only for the fraction of girls, you may not need to calculate 24 and 40 at all. The required fraction is directly:

$\frac{5}{8}$

Keep quantities in ratio units until actual values become necessary.

6. Use Remainder and Unit-Digit Cycles

If a question asks only for the last digit, divisibility or remainder, calculating the entire power is wasteful.

Example

Find the unit digit of:

$7^{103}$

The unit digits of powers of 7 repeat in a cycle:

$7,\ 9,\ 3,\ 1$

The cycle length is four.

$103 \div 4$

The remainder is three, so select the third value in the cycle.

Therefore, the unit digit is:

$3$

Before calculating a large power, check whether the question requires only:

The unit digit
The last two digits
Divisibility
A remainder
An odd-even conclusion

Calculate only what the question asks for.

7. Approximate Only When the Options Allow It

Approximation is a decision based on the gap between the answer options.

Suppose your rough calculation gives approximately 66.

If the options are:

The approximate result is enough to identify 68.

However, if the options are:

65.8
66.1
66.4
66.7

You need a more accurate calculation.

Before approximating, check:

How far apart are the options?
Could the approximation error change the answer?
Is the question asking for an exact value?
Can some options be eliminated immediately?

Approximation is particularly useful in Data Interpretation, averages, percentages and questions containing inconvenient decimals.

8. Draw a Simple Diagram

A rough diagram can save repeated reading.

Use diagrams for:

Geometry
Time, speed and distance
Directions
Arrangement-based Quant
Work and pipeline questions
Sets and Venn diagrams
Coordinate Geometry

The diagram does not need to look attractive. It only needs to show the relevant relationships.

For a time-speed-distance question, mark the locations, direction of travel, speeds and meeting point.

For Geometry, redraw the figure and label all known angles, lengths and conditions. Do not depend entirely on the diagram supplied in the question because it may not be drawn to scale.

9. Test Simple and Boundary Values

This technique is useful in:

Inequalities
Functions
Number properties
Statement-based questions
Modulus
Algebraic identities

If a statement claims to be true for every allowed value, one valid counterexample is enough to eliminate it.

For an interval, test:

A value inside the interval
The lower boundary
The upper boundary
A value outside the interval, where relevant

Be careful with zero, negative numbers, fractions and one. These values frequently reveal conditions that appear valid for positive integers but fail more generally.

10. Stop When the Answer Is Determined

Students sometimes continue solving even after one option has been uniquely identified.

Once the answer is clear:

Recheck the important condition
Confirm the sign or unit
Select the answer
Move to the next question

Do not calculate extra values that the question never requested.

For example, if a question asks only for the ratio of two quantities, calculating both absolute quantities may be unnecessary.

Which Technique Should You Try First?

Question Type	Technique to Consider
Successive percentages	Assume a base of 100
Complicated numerical MCQ	Option substitution
Large algebraic expression	Factor before expanding
Ratio distribution	Work in ratio units
Large powers	Unit-digit or remainder cycle
Widely separated options	Approximation
Geometry or TSD	Draw a diagram
Inequality or function statement	Test simple and boundary values
Long word problem	Translate words into equations
Answer already uniquely identified	Stop calculating

This table is a starting point, not a fixed law. The direct method may still be faster in a particular question.

When Not to Use an IPMAT Quant Shortcut

Avoid a shortcut when:

You cannot explain why it works
You do not remember its conditions
It applies only to a special case
The direct method is shorter
The answer options are too close for approximation
Substituting every option would take too long
You discovered the method through a short video but never practised it
The technique produces different answers on similar-looking questions

A shortcut should reduce work without reducing reliability.

How to Practise These Techniques on Setwise

Do not maintain a long list of disconnected tricks.

Use this four-step process:

Step 1: Solve Normally

Attempt the question using the standard concept-based method.

Step 2: Review the Shorter Method

Compare your approach with the solution and identify exactly which step was avoided.

Step 3: Solve a Similar Question

Apply the shorter method to a new question without looking at the previous solution.

Step 4: Reattempt After a Gap

Bookmark the question and solve it again after three to seven days.

While reviewing a Setwise solution, ask:

Did I use the shortest reliable approach?
Could the answer options have helped?
Did I calculate something the question never asked for?
Could I have simplified before multiplying?
Is the method reusable or limited to one question?

Methods are remembered through application—not by copying them into a large shortcut notebook.

Short Answer and MCQ Tricks Are Different

For QA Short Answer

Prioritise:

Clean equations
Complete numerical calculation
Factorisation
Unit-digit and remainder patterns
Convenient assumptions
Checking the final entry

You cannot depend on answer options.

For QA MCQ

You can additionally use:

Option substitution
Elimination
Approximation
Back-solving
Comparing option gaps
Testing counterexamples

Learn the complete QA Short Answer vs MCQ attempt strategy before applying the same approach to both formats.

Mistakes to Avoid

Collecting hundreds of tricks without practising them
Using approximation when the options are close
Substituting all four options when direct calculation is easier
Expanding expressions before checking for factorisation
Ignoring restrictions such as positive integers or non-zero values
Assuming a diagram is drawn to scale
Continuing calculations after the answer is established
Treating a lucky guess as a successful shortcut
Sacrificing accuracy to increase attempts

Frequently Asked Questions

Are shortcuts necessary to score well in IPMAT Quant?

No.

Concept clarity, calculation accuracy and question selection matter more. Shortcuts become valuable after you can already solve the question correctly.

Can I use answer options in every MCQ?

No.

Option substitution works best when the condition is easy to test and direct algebra would take longer.

Can option substitution be used in Short Answer questions?

No answer options are provided in the Short Answer section.

However, other methods such as factorisation, assuming convenient values, remainder cycles and boundary-value testing may still reduce the calculation.

How do I remember IPMAT Quant tricks?

Save one model question for each useful technique and reattempt it after a gap.

Do not try to memorise a long list without application.

Should I learn tricks before completing the syllabus?

Learn small efficiency improvements while practising each topic, but do not make shortcuts a substitute for concept learning.

What if the shortcut and standard method give different answers?

Recheck the conditions and use the standard method.

A method you cannot apply reliably should not be used in the examination.