Is it more typical to say that there are a large amount of calories or a high amount of calories?
Chocolate cake contains a high/large amount of calories.
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Actually the most common phrasing I've personally seen is:
It is high in calories.
The number of calories can be thought of as either a number (number of) or aggregate (amount of). Other answers/comments have indicated that there's debate over which is more common/appropriate, but what one you use influences which adjective you pick.
Per this NGram:
large number of --> Most Common
large amount of --> Common
high number of --> Uncommon
high amount of --> Almost Unheard Of
Bill Franke's comment suggests that this question asks for “a proper distinction between count and non-count nouns”, then reasons that because uncountable substances take “amount” ie “total number or quantity : aggregate” while countable substances take “number” the answer is like “Chocolate cake contains a large number of calories”, calories being countable. I suppose his comment is intended to rule out either of the alternatives mentioned in the question.
However, the question actually asks which of two forms is more typical. That question can be answered by reviewing corpuses of English text. For example, the English 2009 ngrams corpus shows no usage¹ of high amount of calories, and shows that in recent decades, large number of calories appears at least twice as frequently as large amount of calories. As another example, COCA (Corpus of Contemporary American English) includes one instance of “large amount of calories” and no instances of the other two phrases. (But as Barrie England notes in a comment, the shorter phrases “amount of calories” and “number of calories” appear 51 times and 137 times, respectively.)
¹ In google ngrams, phrases that appear in fewer than 40 books are not treated, ie show as zero. (See FAQ question “Why are you showing a 0% flatline when I know the phrase in my query occurred in at least one book?”)
Here the bone of contention is a question asked for the English Grammar part of the Kerala Public Service Commission Examination conducted on the 5th of January, 2013.
The question runs:
Chocolate cake contains a __ amount of calorie.
The options given are: high; numerous; large; big
What the Public Service Commission expects is:
Chocolate cake contains a large amount (high amount) of calorie.
But here the problem is: the very question is wrongly constructed.
Cake is a common noun and so the question should have been:
Chocolate cakes contain....
Again, the noun calorie should have been in the plural. So, the question should have been:
Chocolate cakes contain ... calories.
The most accurate answer, of course, is:
Chocolate cakes contain a large amount of calories.
The question can be challenged in a court of law, whatever be the answer given by the PUBLIC SERVICE COMMISSION.