A software developer is optimizing a mobile app’s data usage. The app sends a 4.8 MB diagnostic packet every 15 minutes. After enabling compression, the packet size reduces by 42.5%. If the device has a daily data cap of 120 MB, how many compressed packets can it send without exceeding the limit?

How Data Compression Boosts Mobile App Efficiency: A Case Study

In today’s interconnected world, mobile apps must balance performance with data efficiency—especially for users on limited data plans. A key challenge for many apps is managing network usage, particularly for diagnostic features that transmit data regularly.

Consider a mobile app that sends diagnostic packets of 4.8 MB every 15 minutes. Without compression, these packets add up quickly, quickly approaching daily data caps and potentially triggering overages or throttled connections.

Understanding the Context

After implementing data compression, the packet size is reduced by 42.5%. This significant reduction makes a tangible difference in overall data consumption.

Step-by-Step: Calculate Compressed Packet Size

First, determine the size of the compressed packet:

A software developer is optimizing a mobile app’s data usage. The app sends a 4.8 MB diagnostic packet every 15 minutes. After enabling compression, the packet size reduces by 42.5%. If the device has a daily data cap of 120 MB, how many compressed packets can it send without exceeding the limit?

Key Insights

Original size:
4.8 MB

Compression reduces size by 42.5%, meaning the packet retains:
100% − 42.5% = 57.5% of the original
Compressed size = 4.8 MB × 0.575 = 2.76 MB per packet

Calculate Daily Packet Transmissions Within a 120 MB Data Cap

The app transmits packets every 15 minutes, so in one hour:
60 ÷ 15 = 4 packets per hour
In a full day (24 hours):
4 × 24 = 96 packets/day

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📰 We are to compute the probability that in 4 independent choices among 4 options (say labeled A, B, C, D, with equal likelihood), exactly one option appears twice, and two other distinct options appear once each, with the fourth position filled by a fourth distinct option — but wait: this would require 4 distinct options total, and one repeated. Since only 4 positions exist, and we want exactly one option repeated, and the other two being different, the only valid pattern is: one option appears twice, two others appear once, and the fourth option appears zero times — but that’s only 4 choices total. So the pattern is: one option repeated twice, and two other distinct options appearing once each — that uses up 2 + 1 + 1 = 4 choices, with one option appearing twice and two others once each, and one option not used at all. So the multiset of choices is of the form {A, A, B, C}, where A, B, C are distinct, and D is unused. 📰 We compute the probability of such a multiplicity pattern. 📰 Total number of possible outcome sequences: $4^4 = 256$, since each of the 4 decisions has 4 choices.

Final Thoughts

Now, calculate total daily data usage after compression:
96 packets × 2.76 MB = 265.92 MB

But wait—this exceeds the 120 MB daily data cap. That means only a subset of compressed packets can be sent daily.

Determine Maximum Allowable Packets Without Exceeding the Data Cap

Divide the total daily data cap by the compressed packet size:
120 MB ÷ 2.76 MB per packet ≈ 43.48 packets

Since apps cannot send a fraction of a packet, the maximum number of compressed packets that can be transmitted daily is:
43 packets

Final Insight

By compressing diagnostic packets from 4.8 MB to 2.76 MB, developers significantly reduce mobile data usage. For an app sending 96 packets per day, compression ensures total usage stays under a 120 MB daily cap, empowering users to run critical diagnostics without exceeding data limits.

Optimizing data packets is more than performance—it’s about delivering reliability, control, and cost efficiency in mobile app design.