Multiplying Near 100: Fast Mental Math Trick (Case Interviews)
Multiplying Numbers Near 100
What is the near-100 multiplication method? The close-together method is a mental math shortcut for multiplying numbers within 10-15 units of 100. Instead of traditional multiplication, you use cross-subtraction and multiply small differences. For example, 96 × 102 becomes (96 + 2) × 100 + (−4 × 2) = 9,800 + (−8) = 9,792. This technique transforms difficult two-digit multiplication into simple arithmetic you can do in seconds.
What Is the Near-100 Method?
The near-100 multiplication method (also called the close-together method) is a mental math technique specifically designed for multiplying numbers close to 100. This technique is incredibly powerful in consulting case interviews because many business calculations involve percentages, growth rates, and market shares that cluster around 100.
Why this matters: Traditional multiplication of numbers like 94 × 107 requires complex mental calculations or paper. The near-100 method reduces this to two simple steps: a basic addition or subtraction, followed by multiplying small numbers.
The sweet spot: This technique works best when both numbers are within 10-15 units of 100—meaning numbers from roughly 85-115. Beyond this range, the traditional methods or other shortcuts become more efficient.
Real interview context: When a case interviewer asks you to calculate "If the market grew 103% and last year's revenue was $94 million, what's this year's revenue?"—this method lets you compute 103 × 94 = 9,682 mentally in under 5 seconds.
How the Method Works
The Mathematical Foundation
The near-100 method works because of an algebraic identity that simplifies multiplication around benchmark numbers like 100.
The formula:
When multiplying two numbers near 100, you can express them as:
- First number: 100 + a (where a can be positive or negative)
- Second number: 100 + b (where b can be positive or negative)
(100 + a) × (100 + b) = 100 × (100 + a + b) + (a × b)
In practice, this means:
- Add the differences cross-wise: (100 + a + b) gives you the first digits
- Multiply the differences: (a × b) gives you the last two digits
Example breakdown: 97 × 95
• 97 = 100 − 3, so a = −3
• 95 = 100 − 5, so b = −5
• Cross-addition: 97 + (−5) = 92 OR 95 + (−3) = 92
• Multiply differences: (−3) × (−5) = 15
• Result: 9,215
Step-by-Step Process
The 3-Step Near-100 Method
Find the Differences from 100
For each number, calculate how far it is from 100. If the number is below 100, the difference is negative. If above 100, it's positive.
Example: 94 is −6 from 100
Example: 106 is +6 from 100
Cross-Add the Differences
Take either number and add the other number's difference to it. You can do this in either direction—both will give the same answer. This gives you the first part of your result (the hundreds and thousands).
Example: 94 + 6 = 100 OR 106 + (−6) = 100
Multiply the Differences
Multiply the two differences together. This gives you the last two digits of your answer. If the product is a single digit, add a leading zero.
Example: (−6) × 6 = −36
Since we got 100 from step 2 and −36 from step 3:
100 − 0.36 = 99.64 (in hundreds) = 9,964
Important note: When multiplying differences where both numbers are below 100 (both differences negative), the product is positive. When one is above and one below, watch the sign carefully.
Worked Examples
Real Calculations Step-by-Step
EXAMPLE 1: Both Numbers Below 100
Problem: 93 × 96
Step 1: Find differences
93 → difference is −7
96 → difference is −4
Step 2: Cross-add
93 + (−4) = 89 OR 96 + (−7) = 89
Step 3: Multiply differences
(−7) × (−4) = 28
Result: 89 | 28 = 8,928
EXAMPLE 2: Both Numbers Above 100
Problem: 104 × 108
Step 1: Find differences
104 → difference is +4
108 → difference is +8
Step 2: Cross-add
104 + 8 = 112 OR 108 + 4 = 112
Step 3: Multiply differences
4 × 8 = 32
Result: 112 | 32 = 11,232
EXAMPLE 3: One Above, One Below 100
Problem: 91 × 105
Step 1: Find differences
91 → difference is −9
105 → difference is +5
Step 2: Cross-add
91 + 5 = 96 OR 105 + (−9) = 96
Step 3: Multiply differences
(−9) × 5 = −45
Result: 96 | (−45) = 9,600 − 45 = 9,555
💡 Pro Tip: When the product of differences is negative (one number above 100, one below), you're actually subtracting from your cross-sum. Think of it as 96 "hundred" minus 45 = 9,555.
Where You'll Use This in Real Cases
The near-100 method appears constantly in case interviews because business metrics naturally cluster around 100: growth percentages, capacity utilization rates, market penetration, and year-over-year comparisons.
Common Case Scenarios:
Market Sizing & Growth Calculations
"If the market is growing at 107% annually and the current size is $96 million..." → 107 × 96 = 10,272 million. Using the method: 107 + (−4) = 103, then (7 × −4) = −28, giving 103|−28 = 10,300 − 28 = 10,272.
Capacity & Utilization
"The factory is running at 92% capacity with a theoretical maximum of 105,000 units..." → 92 × 105 = 9,660. Method: 92 + 5 = 97, (−8 × 5) = −40, so 97|−40 = 9,660.
Revenue Projections
"If we achieve 98% of our target and the target is $103 million..." → 98 × 103 = 10,094. Method: 98 + 3 = 101, (−2 × 3) = −6, so 101|−6 = 10,094.
Percentage-Based Pricing
"A client wants to offer a 95% discount structure on a $108 base price..." → 95 × 108 = 10,260. Method: 95 + 8 = 103, (−5 × 8) = −40, so 103|−40 = 10,260.
Year-Over-Year Analysis
"Revenue was 89% of forecast, and forecast was $112 million..." → 89 × 112. Method: 89 + 12 = 101, (−11 × 12) = −132, so 101|−132 = 10,100 − 132 = 9,968.
Interview Insight: Interviewers specifically test whether you can handle numbers near 100 because these scenarios appear in nearly every profitability, market entry, and operations case. Candidates who can compute these instantly demonstrate quantitative fluency that distinguishes them from those who struggle with mental math.
Build Speed and Accuracy with Focused Drills
Reading about the near-100 method is valuable, but mastery requires repetition under realistic conditions. You need to internalize the three-step process so it becomes automatic when you're managing interview pressure.
Our drills adapt to your skill level: begin with numbers very close to 100 (like 98-102), then expand to the full range (85-115) as you build confidence. Track your improvement over time and identify patterns where you need more practice.
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