If you push your muscles as hard as you can until you can't do any more reps, that's what really makes them grow bigger. It doesn't matter how many reps you do, as long as you're giving your absolute best effort.
Evidence from Studies
Supporting (4)
Community contributions welcome
Neither load nor systemic hormones determine resistance training-mediated hypertrophy or strength gains in resistance-trained young men
Resistance Training Load Effects on Muscle Hypertrophy and Strength Gain: Systematic Review and Network Meta-analysis
The Effects of Low-Load Vs. High-Load Resistance Training on Muscle Fiber Hypertrophy: A Meta-Analysis
Low-Load Resistance Training to Volitional Failure Induces Muscle Hypertrophy Similar to Volume-Matched, Velocity Fatigue
Contradicting (2)
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Effects of Resistance Training Performed to Failure or Not to Failure on Muscle Strength, Hypertrophy, and Power Output: A Systematic Review With Meta-Analysis.
Gold Standard Evidence Needed
According to GRADE and EBM methodology, here is what ideal scientific evidence would look like to definitively prove or disprove this specific claim, ordered from strongest to weakest evidence.