Why Plugging In Beats Pure Algebra
Many GRE algebra questions can be solved faster and with less risk of a sign error by substituting concrete numbers rather than manipulating symbols. Because most GRE Quant questions are multiple choice, you can often work backward from the answer choices just as effectively as working forward from the problem.
অনেক GRE বীজগণিত প্রশ্ন প্রতীকী সমীকরণের বদলে নির্দিষ্ট সংখ্যা বসিয়ে দ্রুত ও কম ঝুঁকিতে সমাধান করা যায়। যেহেতু অধিকাংশ প্রশ্ন multiple choice, উত্তর থেকে পেছনের দিকে কাজ করাও কার্যকর।
The core method: when a question has variables in both the question and the answer choices, "Plug In" simple numbers. When a question describes a scenario and the answer choices are numbers, "Backsolve" by testing an answer choice directly in the scenario.
মূল পদ্ধতি: প্রশ্ন ও উত্তরে চলক থাকলে সংখ্যা বসান; উত্তর সংখ্যা হলে পেছন থেকে পরীক্ষা করুন।
Two Core Techniques
| Technique | When to Use It | How It Works |
|---|---|---|
| Plugging In Numbers (PIN) | Variables appear in the question stem and the answer choices. | Choose simple, "safe" numbers for the variables, compute the target value using those numbers, then find which answer choice produces that same value when the same numbers are substituted. |
| Backsolving | The answer choices are specific numbers and the question describes a scenario (not abstract variables). | Substitute an answer choice (often the middle one) into the scenario; if the result is too high or too low, adjust toward a larger or smaller choice. |
Choosing safe numbers: avoid 0 and 1 (they often make multiple answer choices match by coincidence, since 0 and 1 behave specially in multiplication/exponents), and avoid numbers that already appear elsewhere in the problem.
নিরাপদ সংখ্যা বাছাই: ০ ও ১ এড়িয়ে চলুন, এবং সমস্যায় ইতিমধ্যে থাকা সংখ্যাও এড়িয়ে চলুন।
Worked Examples
"A store increases the price of an item by 20%, then offers a 10% discount on the new price. The final price is what percent of the original price?"
"If 3x + x² = 40, what is the value of x?" Answer choices: (A) 3 (B) 4 (C) 5 (D) 6 (E) 7
Common Mistakes
- Using 0 or 1 as the "safe" number: these can make an answer choice match by coincidence (e.g., anything times 1 stays the same, masking multiplication errors).
- Reusing a number that appears in the problem: this can accidentally make an incorrect answer choice equal the correct one.
- Stopping after only testing one answer choice when backsolving: always confirm the result is exactly right, not just "close," since GRE Quant has no partial credit for near misses.
- Forgetting Plugging In requires checking every answer choice: more than one choice can coincidentally match your chosen numbers — if two choices match, try a second set of numbers to break the tie.
Your Turn
Practice choosing the right technique and applying it. সঠিক কৌশল বেছে প্রয়োগ করুন।
Show the logic
Plug in 100: +50% → 150; −50% of 150 → 75. Result = 75% of the original.
Show the logic
Test C (5): 25 − 10 = 15. Matches — x = 5 (C).
Show the logic
x=4: y = 2(4)+3 = 11. New x = 8: new y = 2(8)+3 = 19. So y increases from 11 to 19, not simply doubling — plugging in reveals the relationship isn't proportional.
Show the logic
Test C (5): 10 + 3(4) = 10+12 = 22. Matches — x = 5 (C).
Show the logic
a=2: 4+2=6 (even). a=3: 9+3=12 (even). Always even — because a² and a always share the same parity, their sum is always even.
Next guide: Geometry Strategies. Apply this skill on Quant Practice Test 3.
পরের গাইড: জ্যামিতি কৌশল।