Mathematical derivation of log-reduction in microbial thermal destruction:
A log-reduction is defined as $\log_{10}(N_0 / N) = n$.
For a $5\text{-log}$ ($5\text{D}$) reduction:

• Survival fraction: $N / N_0 = 10^{-5} = 0.00001$
• Percentage survival: $0.00001 \times 100\% = 0.001\%$ (Statement B is true).
• Destruction fraction: $1 - (N / N_0) = 1 - 0.00001 = 0.99999$
• Percentage destruction: $0.99999 \times 100\% = 99.999\%$ (Statement A is true).
  Statements (C) and (D) correspond to a 2-log ($99\%$) reduction.

Ultra-pasteurized (UP / Extended Shelf Life or ESL) milk is thermally processed at or above $138^\circ\text{C}$ for at least $2\text{ seconds}$ and packaged under near-aseptic conditions. Unlike commercially sterile aseptic UHT milk which is shelf-stable at room temperature for $6\text{ months}$, ultra-pasteurized milk is not commercially sterile and requires continuous refrigeration at $4\text{ to }5^\circ\text{C}$, yielding an extended refrigerated shelf-life of approximately $60\text{ to }90\text{ days}$.

Option analysis:

• Approx. $90\text{ days}$ at $4\text{ to }5^\circ\text{C}$: Correct. Ultra-pasteurized ESL milk requires refrigeration and stays fresh for up to $90\text{ days}$.
• Approx. $90\text{ days}$ at ambient temperature: Incorrect; ambient storage would spoil non-aseptic UP milk rapidly.
• Approx. $21\text{ days}$ at $4\text{ to }5^\circ\text{C}$: Typical of standard high-temperature short-time (HTST) pasteurized milk.
• Approx. $180\text{ days}$ at ambient temperature: Characteristic of fully aseptic UHT sterilized milk.

According to the National Canners Association (NCA) standards adopted in the dairy and food canning industry, canners' grade granulated sugar must not contain more than a total of $150\text{ thermophilic spores per }10\text{ g}$ of sugar (and an average of not more than $125\text{ spores per }10\text{ g}$ across samples), with flat-sour spores not exceeding $75/10\text{g}$.

Option analysis:

• $450/10\text{g}$: Far exceeds acceptable sanitary limits for canning ingredients.
• $220/10\text{g}$: Exceeds standard specification.
• $150/10\text{g}$: Correct. Maximum permitted total thermophilic spore count in any single sample is $150/10\text{g}$.
• $375/10\text{g}$: Incorrect limit.

Buttons in sweetened condensed milk are firm, reddish-brown button-like colonies of mold growth occurring on the surface of the milk inside the can. They are primarily caused by xerophilic and osmophilic species of molds, especially Aspergillus repens (also Aspergillus glaucus) and Catenularia fuliginea. These molds enter during processing or packing, grow until the available headspace oxygen is exhausted, and form localized gelatinous lumps or buttons.

Option analysis:

• Aspergillus repens: Correct. Aspergillus repens is the classic causative mold responsible for button formation in sweetened condensed milk.
• Proteus vulgaris: Incorrect. Proteus vulgaris is a proteolytic, non-sporeforming Gram-negative rod causing putrefaction, not surface mold buttons.
• Thermobacterium mathiacelle: Incorrect. A thermophilic rod associated with acid development or flat sour defects, not mold buttons.
• Torulopsis globosa: Incorrect. Torulopsis globosa is an osmophilic yeast that causes gaseous fermentation and blowing of cans, rather than button formation.