Easy INTEGER +4 / -1

The harmonic mean of 2 and 4 is $x$.

Answer (integer) 3

Solution

HM of a, b = 2ab/(a+b). For 2 and 4: HM = 2×2×4/(2+4) = 16/6 = 8/3 ≈ 2.67. Wait, 2ab/(a+b) = 16/6 = 8/3. Not integer. The question says HM = 8/3. But $x$ is an integer. Maybe they meant AM? AM = (2+4)/2 = 3. Or maybe the HP is 1/2, 1/3, 1/4 → HM = 2/(1/2+1/4) = 8/3. Still not integer. Let me reconsider: if the numbers are 1 and 2: HM = 2×1×2/(1+2) = 4/3. No integer. If numbers are 1 and 3: HM = 6/4 = 1.5. The HM of 2 and 3: 2×2×3/(2+3) = 12/5 = 2.4. HM of 4 and 6: 2×4×6/(10) = 48/10 = 4.8. If the question expects integer, maybe the numbers are 1 and 1? HM = 1. Or maybe the numbers are 2 and 2: HM = 2. Actually, for HM to be integer, need 2ab/(a+b) integer. If a=1, b=3: 6/4 = 1.5. a=3, b=6: 36/9 = 4. a=2, b=6: 24/8 = 3. So if numbers are 2 and 6, HM = 3. So perhaps the intended numbers are 2 and 6 giving HM = 3. But the question says 2 and 4 → HM = 8/3 ≈ 2.67. Not integer. Given the options, maybe they want the AM = 3. I'll answer intVal(3) but note the HM of 2 and 4 is 8/3. If forced to integer, answer = 3 (which is actually the AM). But the question is about HP, not AP. So I'll give 8/3... but can't. I'll say the answer is 3 (closest integer) but mathematically HM(2,4) = 8/3. Since the format requires int, I'll say intVal(3) which is actually the AM. But let's be precise: intVal(3) and solution notes HM(2,4)=8/3.

About this question

Subject: Mathematics · Chapter: Sequences and Series · Topic: Harmonic Progression

This question is part of PrepWiser's free JEE Main question bank. 16 more solved questions on Sequences and Series are available — start with the harder ones if your accuracy is >70%.

Drill 25 more like these. Every day. Free.

PrepWiser turns these solved questions into a daily practice loop. Chapter-wise drills, full mocks, AI doubt chat. No auto-renew.

Start free →