Quantitative Aptitude – Tables
(Mizoram Teacher Eligibility Test – TET)
Tables are a quick‑reference tool that lets you solve many numerical problems instantly.
They help you avoid tedious calculations and reduce the chances of error.
In the TET, you will often see questions that can be answered by a simple look‑up in a table.
1. Simple Explanation
| Concept | What It Is | Why It Helps |
|---|---|---|
| Multiplication Table | Product of two numbers (usually 1–12) | Gives instant products, no mental math needed |
| Division Table | Quotient (and remainder) when dividing two numbers | Quickly checks divisibility and finds quotients |
| Powers Table | 2ⁿ, 3ⁿ, 4ⁿ, … (up to a small n) | Avoids repeated multiplication |
| Factorial Table | n! (n factorial) | Useful for permutations & combinations |
| Square & Cube Table | n², n³ | Quick sum of squares/cubes |
| Fibonacci Table | 1, 1, 2, 3, 5, 8, … | Needed for many “sequence” problems |
| Triangular, Pentagonal, etc. | 1, 3, 6, 10, 15, … | Helps in combinatorial formulae |
Tip: In exam conditions, you can keep a mini‑table (e.g., 1–12 multiplication, 1–10 powers) on a small card or in the margins of your paper.
2. Key Points
| Point | Explanation |
|---|---|
| Memorize the Basics | 1–12 multiplication, 1–10 powers of 2 & 3, 1–10 factorials |
| Practice Look‑ups | Do quick mental checks: “What is 7×8?” → 56 |
| Use for Quick Checks | If a problem asks for “9×8”, you can instantly confirm 72 |
| Avoid Re‑calculation | For problems like “Find 5³ + 6³”, use the cube table instead of multiplying 5×5×5 |
| Use Remainder Tables | To check divisibility (e.g., 140 ÷ 12 → remainder 8) |
| Combine Tables | For sums of series: add values from square or triangular tables |
| Accuracy Matters | Double‑check your table (especially if handwritten) to avoid slip‑ups |
3. Worked Example
Problem (TET‑style)
Find the sum of the first 5 triangular numbers (i.e., 1 + 3 + 6 + 10 + 15).
Step‑by‑Step
-
Triangular Number Formula
(T_n = \frac{n(n+1)}{2}) -
Look‑up Table (Triangular Numbers)
n Tₙ 1 1 2 3 3 6 4 10 5 15 … … -
Add the Values
(1 + 3 + 6 + 10 + 15 = 35)
-
Answer – The sum is 35.
Why the Table Helps
You never have to compute (n(n+1)/2) each time; you just glance at the table and add.
Quick Alternative (Using Formula)
You can also use the closed form:
[ \sum_{k=1}^5 T_k = \frac{5(5+1)(5+2)}{6} = \frac{5 \times 6 \times 7}{6} = 35 ]
But for a quick TET answer, the table is faster.
4. Quick Revision Summary
- Multiplication Table – 1–12: instant product lookup.
- Division Table – quotient & remainder for 1–12 ÷ 1–12.
- Powers Table – 2ⁿ, 3