Common Entrance Quantitative Reasoning
Past Questions

AI Explanation

**The reasoning** Look at how each number relates to the one before it: - 2 × 2 = 4 - 4 × 2 = 8 - 8 × 2 = 16 - 16 × 2 = **32** This is a **geometric sequence** where each term is found by multiplying the previous term by a constant ratio (in this case, 2). You're literally doubling each time. It's also powers of 2: 2¹, 2², 2³, 2⁴, 2⁵ = 32. **Why the wrong options tempt you** **A) 20** tricks you if you mistakenly added 4 to 16 (thinking it's addition). **B) 24** catches you if you added 8 to 16 (noticing the differences but applying them wrongly). **D) 48** looks appealing if you tripled 16 instead of doubled, or got confused about the pattern midway. **Quick takeaway** In number series, always check: "Am I adding, multiplying, or using powers?" — here, each number is **double** the last, not a fixed addition.

AI Explanation

**The reasoning** Look at the pattern carefully: 1, 4, 9, 16, ? These are **perfect squares**: - 1 = 1² - 4 = 2² - 9 = 3² - 16 = 4² So the next number must be **5² = 25**. The sequence follows the rule: (position number)². You're simply squaring consecutive whole numbers: 1, 2, 3, 4, 5... **Why the wrong options tempt you** - **20**: If you thought "just add 4 each time" (because 4-1=3, 9-4=5 looks irregular, you might guess randomly) - **30**: Adds 14 to 16, which has no pattern basis — pure guessing - **36**: This is actually 6², so you skipped a step! The sequence goes in order, don't jump ahead. **Quick takeaway** When you see 1, 4, 9, 16... always check: "Are these perfect squares?" Most JAMB number patterns test squares (n²), cubes (n³), or simple addition/multiplication rules. Spot the squares, and you'll never miss this again! 💪

AI Explanation

**The reasoning** This question tests your understanding of **even and odd numbers**. An **even number** is any whole number that can be divided by 2 without a remainder (like 2, 4, 6, 8, 10...). An **odd number** cannot be divided evenly by 2 (like 1, 3, 5, 7, 9...). Let's check each: - 2 ÷ 2 = 1 (no remainder) → **even** - 4 ÷ 2 = 2 (no remainder) → **even** - 7 ÷ 2 = 3 remainder 1 → **odd** ✓ - 8 ÷ 2 = 4 (no remainder) → **even** So **7** is the only odd number in the group. **Why the wrong options tempt you** If you rushed, you might pick 2 because it's the smallest, or 8 because it's the largest. But the question isn't asking about size — it's asking which number is *mathematically different* (odd vs. even). **Quick takeaway** Even numbers end in 0, 2, 4, 6, or 8; odd numbers end in 1, 3, 5, 7, or 9 — just check the last digit!

AI Explanation

**The reasoning** Look at how each number relates to the one before it: - 6 ÷ 3 = 2 - 12 ÷ 6 = 2 - 24 ÷ 12 = 2 This is a **geometric sequence** where each term is multiplied by a constant ratio (called the common ratio, r = 2). So the pattern is simply "multiply by 2 each time." Following this pattern: 24 × 2 = **48** **Why the wrong options tempt you** **A) 30** — This comes from adding 6 (24 + 6). You might think the differences are increasing, but that's not the pattern here. **B) 36** — You get this by adding 12 (24 + 12), maybe thinking we're adding the previous difference doubled. Close thinking, but wrong pattern! **D) 60** — This might come from overthinking or adding random increments. **Quick takeaway** In number sequences, always check the **ratio** (division) first, then the difference (addition) — geometric patterns multiply or divide; arithmetic patterns add or subtract. Once you spot "each divided by the last gives the same number," you've cracked it!

AI Explanation

**The reasoning** This is a **number pattern** (also called a sequence). Look at what's happening between the numbers: - From 3 to 6: we add 3 - From 6 to 9: we add 3 again The pattern is clear: **add 3 each time** (or count in multiples of 3). So: 3, 6, 9, **12** You can also think of it as the **3 times table**: 3×1, 3×2, 3×3, 3×4 = 12. **Why the wrong options tempt you** - **10 & 11**: These come from just counting forward (9, 10, 11...), ignoring the actual pattern. That's the trap — you're rushing and not checking *how* the numbers increase. - **15**: This jumps too far. You might pick it if you saw "multiples of 3" but skipped counting properly (3, 6, 9, 15 misses the 12). **Quick takeaway** Always find the **difference between consecutive terms** first — that difference is your key to unlocking any number pattern!

AI Explanation

**The reasoning** This is a simple **multiplication problem** about equal groups. If 1 box holds 4 pens, then 3 boxes hold: 3 boxes × 4 pens per box = **12 pens** Think of it this way: You're just adding the same amount three times: - Box 1: 4 pens - Box 2: 4 pens - Box 3: 4 pens - Total: 4 + 4 + 4 = 12 pens Or use multiplication (which is faster): 3 × 4 = 12 **Why the wrong options tempt you** **A) 7** — You added 4 + 3 instead of multiplying. That's mixing the number of boxes with the number of pens! **B) 10** — Maybe you added wrong or got confused with a different calculation. **D) 16** — You multiplied 4 × 4 instead of 3 × 4. You used the wrong number! **Quick takeaway** When dealing with equal groups, **multiply** the number of groups by what each group contains—don't just add the two numbers together!