GRE Quantitative Reasoning
Past Questions

AI Explanation

**The reasoning** This is a **simple linear equation**. To find x, we need to isolate it on one side: 2x + 3 = 11 First, subtract 3 from both sides: 2x = 11 − 3 2x = 8 Then divide both sides by 2: x = 8 ÷ 2 **x = 4** Let's verify: 2(4) + 3 = 8 + 3 = 11 ✓ **Why the wrong options tempt you** - **Option A (2)**: You might have divided 11 by 3, ignoring the +3 entirely - **Option B (3)**: You subtracted 2x from 11, confusing the operations - **Option D (5)**: You might have done 11 − 3 = 8, then mistakenly thought 8 − 3 = 5, or subtracted instead of dividing These traps catch students who rush or forget to **undo operations in reverse order** (BODMAS backwards!) **Quick takeaway** When solving equations, think "What's being done to x?" then do the opposite: addition becomes subtraction, multiplication becomes division — always work backwards to free x!

AI Explanation

**The reasoning** The **mean** (or average) is the sum of all values divided by how many values you have. Here's the calculation: - Sum = 4 + 8 + 12 = 24 - Count = 3 numbers - Mean = 24 ÷ 3 = **8** Think of it like sharing money equally: if you have ₦24 to share among 3 people, each gets ₦8. **Why the wrong options tempt you** **A) 6** – You might subtract instead of adding, or divide by the wrong number (24 ÷ 4 = 6). The trap is using 4 (the first number) as your divisor instead of 3 (the count). **C) 10** – This looks like the "middle" between 4 and 12, but that's just finding the midpoint of two numbers, not the mean of all three. **D) 12** – You might pick the largest number by mistake, forgetting that mean requires actual calculation. **Quick takeaway** Mean = Add everything up, then divide by how many numbers you counted—always verify your "how many" is correct!

AI Explanation

**The reasoning** To find a percentage of a number, convert the percentage to a decimal (or fraction) and multiply: 30% = 30/100 = 0.3 So: 30% of 200 = 0.3 × 200 = **60** Think of it this way: "percent" means "per hundred" (from Latin). So 30% literally means "30 out of every 100." If you have 200, that's *two* sets of 100, so you'd have 30 + 30 = **60**. **Why the wrong options tempt you** - **A (30)**: You might just write down the percentage itself, forgetting to actually calculate it *of* 200. - **C (90)**: This comes from incorrectly adding 30 to 60, or confusing your steps. - **D (120)**: This would be 60% of 200, not 30% — you doubled the percentage somewhere. **Quick takeaway** When you see "X% of Y," always multiply: (X ÷ 100) × Y — and remember, percentages are usually *smaller* than the original number unless they exceed 100%.

AI Explanation

**The reasoning** Start by solving for x: - If 3x = 27, we need to find what power of 3 gives us 27 - Write 27 as a power of 3: 27 = 3³ (since 3 × 3 × 3 = 27) - So 3x = 3³, which means x = 3 Now find x²: - x² = 3² = 3 × 3 = **9** Wait... the answer says 81? Let me recalculate. If x = 3, then x² = 9, not 81. **Actually, there's an error here.** If the correct answer is truly 81, then either: - The question should be "3^x = 27" (3 to the power x), OR - The correct answer should be A) 9, not C) 81 Assuming the question meant **3^x = 27**: Then x = 3, and x² = 9. ✓ **Why the wrong options tempt you** Students confuse x with x², or mix up the original value (27) with the final answer. **Quick takeaway** Always solve for x FIRST, then square that result separately — don't skip steps or you'll square the wrong number!

AI Explanation

## The reasoning The equation x² = 49 asks: "What number, when multiplied by itself, gives 49?" Two numbers work: 7 × 7 = 49 **and** (−7) × (−7) = 49. (Remember: negative times negative equals positive!) But here's the key — the question adds a **condition**: x < 0, meaning x must be negative. So even though both 7 and −7 satisfy x² = 49, only **−7** meets the requirement that x < 0. ## Why the wrong options tempt you **A) 7** — This is the "automatic" answer when you see √49. You forgot to check the condition x < 0. **C) 49** — Basic confusion. If x² = 49, then x ≠ 49. Test it: 49² = 2401, not 49. **D) −49** — You might think "negative answer needed" and just slap a minus sign on 49. But (−49)² = 2401, not 49. ## Quick takeaway Always read the full question — conditions like x < 0 or x > 0 tell you **which** solution to pick when there are multiple possibilities.

AI Explanation

**The reasoning** Start by solving for x in the equation 2x = 18. Divide both sides by 2: x = 18 ÷ 2 = 9 Now the question asks for x + 5, not just x: x + 5 = 9 + 5 = **14** This tests **two-step problem solving** — first find the variable, then use it to answer what's actually being asked. **Why the wrong options tempt you** - **Option A (9)** — This is the trap! You stopped after finding x = 9 and forgot to add 5. The question didn't ask for x; it asked for x + 5. Always read what the question is *actually* asking for. - **Options C (13) and D (23)** — These come from calculation errors, like adding incorrectly (9 + 4 = 13) or misreading the original equation as 2x = 28. **Quick takeaway** Finding x is only half the battle — always check what the question is asking you to calculate with that x!

AI Explanation

3x = 15 → x = 5.

AI Explanation

9 + 16 = 25; √25 = 5.

AI Explanation

Average × count = sum: 12 × 5 = 60.

AI Explanation

x² = 16 → x = ±4.

AI Explanation

0.30 × 250 = 75.

AI Explanation

a/b = 3/4 → a = (3/4) × 12 = 9.

AI Explanation

√((4−1)² + (5−1)²) = √(9+16) = √25 = 5.