Number/Numbers

Onell wrote:1.Having more than the usual number of fingers or toes on the hands or feet is termed polydactyly. --MGMT
2.New Jersey has one of the five highest numbers of reported cases of Lyme disease in the United States. -TEST PAPERS
3A Labor Department study states that the number of women employed outside the home increased by more than thirty-five percent in the past decade and accounted for more than sixty-two percent of the total growth in the civilian work force. --OG
4.The gryfalcon, an Arctic bird of prey, has survived a close brush with extinction; its numbers are now five times greater than when the use of DDT was sharply restricted in the early 1970's. --OG

It has to co-exist with the verb

All above are the correct sentences either from OG or some other reputed sources.In first and 3rd sentences NUMBERS is used whereas in 2 nd and 4th "NUMBER " is used. Can someone highlight the important differences between Number vs Numbers? when to choose one over another?

Thank you

Hey guys

So, technically "THE numbers of" or "A numbers of" is wrong - that whole thing, including the article in front, not just "numbers of." You can have "numbers of" without those articles, as in the example at the top of the thread.

(You can also, technically, have "the numbers of" if you are literally talking about multiple numbers - eg, two players have the numbers 7 and 13 on their jerseys, and I say "the numbers of the jerseys are 7 and 13." But that kind of set-up would be very unusual on this test.)

Also, remember that there's almost always an obscure exception to any rule you can think of. Annoying, but true. ("Being" is not always wrong either - it's just almost always wrong on the GMAT.) Because of the frequent, obscure exceptions, we should mostly just worry about the most likely / primary rules. Otherwise, we'll drive ourselves crazy. - from Stacey Instructor