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On Tuesday, after market close, tech giant Apple (AAPL -1.22%) reported better-than-expected third fiscal quarter results. Shares climbed as high as 7% in after-hours trading as investors digested the implications of the news.

Apple reported earnings per share of $1.42. While this figure was down 23% compared with Apple's EPS in the year-ago quarter, it was higher than the consensus analyst estimate for EPS of $1.38. Total revenue was $42.4 billion, down 14.5% from its revenue of $49.6 billion in the year-ago quarter. Analysts were expecting Apple to report third-quarter revenue of $42 billion.

"We are pleased to report third quarter results that reflect stronger customer demand and business performance than we anticipated at the start of the quarter," said Apple CEO Tim Cook in the company's earnings release.

The late-March-introduced iPhone SE was a highlight during the quarter. Q3 was its first full quarter of availability, and Cook said the launch of the lower-priced iPhone was "very successful."

It's worth emphasizing that the iPhone SE was supply constrained for much of Apple's third quarter, so the lower-cost iPhone's start despite its constraints highlights a promising opportunity for the tech giant.

Apple's guidance for its fourth quarter importantly included expectations for a narrower year-over-year decline in revenue than in the current quarter. Apple guided for fourth-quarter revenue of $45.5 billion to $47.5 billion. The midpoint of this guidance range represents a 9.7% year-over-year decline for Q4 -- better than the Apple's second-quarter revenue decline of 14.5%.

Does it matter?

The quarter marks an important milestone for investors for several reasons. First, it shows the company is moderating its revenue decline by reporting better-than-expected results and by guiding for a smaller decline in Q4. Second -- and perhaps more importantly -- it previews what could become a key market for Apple: lower-priced iPhones.

Stay tuned to The Motley Fool for some deeper analysis of Apple's third-quarter results.