Methylene-blue stained fecal smear reveled numerous neutrophils (but not any organisms). Shigella is colorless when stained with methylene blue; E coli stains blue with methylene blue because it ferments lactose.
Apart from the line in FA referencing PMN infiltrate in Shigella, there is no way to differentiate here between it and E. Coli. Cheap shot.
I think Shigella is the most appropriate, as it is actually regarded as highly inflammatory. Yes, E. coli can be of the EHEC/STEC variety, but E. coli could also be of the ETEC variety or whatever other strains it has. Ergo, E. coli may be plausible, but it is not the 'most likely.' Bleh to these kinds of questions.
Shigella causes an inflammatory diarrhea; it produces a toxin and can invade tissue directly. In addition, it is resistant to acid, so it has a characteristically low infective dose (~10 organisms), which facilitates its fecal-oral (person-to-person) spread especially in settings where hygiene may be compromised, such as in daycare or institutional housing. It can be differentiated from E. Coli (EHEC) because E Coli doesn't have as much person-to-person spread and only causes GI damage by the shiga-like toxin, not direct invasion. Therefore, EHEC wouldn't facilitate as strong of a neutrophilic response.
sOn EMB Agar, isolated colonies of lactose-fermenting bacteria appear brown to blue-black in color. Escherichia coli appears as large, blue-black colonies, often with a green metallic sheen. Enterobacter spp. present as brown to blue-black, mucoid colonies with no sheen. Non-lactose-fermenting colonies, such as Shigella spp. and Salmonella spp., appear transparent and colorless.
We basically needed to correlate that → no organisms seen but only neutrophils to being a lactose non-fermentor organism. Therefore the answer is Shigella and not E coli