Problem Solving

Note: I have no issues regarding the solutions to the problems, but only have doubts regarding the language.
Please dont be daunted by the length of the post, if you begin reading you shall find the questions are really regarding simple meaning issues. The questions given here are only to cite examples and not seeking solutions


If a math problem states " there are some boys in the class", then in a such a question we cant take the number of boys=0
The explanation I have received is that, since the question mentions there "are" so we have to take atleast one.


Now consider problem no.38 D.s pg 276 OG 12.
If p1 and p2 are the populations and r1 and r2 are the numbers of representatives of District 1 and District 2, respectively, the ratio of the population to the number of representatives is greater for which of the two districts ?
(1) p1 > p2
(2) r2 > r1
OA=C
note the problem states that r1 and r1 are "numbers" yet the problem does not consider that these "numbers" could be zero in which case the answer would have been E as division by zero is non defined, but this is not considered in the explanation

Consider problem26 of the diagnostic test.
what is the value of the integer p?
(1)Each of the integers 2, 3 and 5 is a factor of p
(2) Each of the integers 2, 5 and 7
OA=E, Explantion says these are factors of but it is NOT clear that these are the ONLY factors of p. (fair enough! )

However, I have encountered various problems where one option might read " the number X has 2 and 3 as factors" in which case the word "only" is not mentioned, yet we are to take that 2 and 3 are the only factors of x.
Another example of this case:
how many 3 digit numbers from numbers 2,3,4,5 are possible in which 2 digits are same? In this problem in order to get the solution we solve only for numbers that have " 2 digits as same". My contention is that since the word "only" was not mentioned "we have to considered the possiblity of all 3 digits are same as well". Other contend that since "atleast" is not mentioned we are to stick to the possiblity when only 2 digits are same.


Last and most surprising.

Question 161
Beginning in January of last year, Carl made deposits of $120 into his account on the 15th of each month for several consecutive months and then made withdrawals of $50 from the account on the 15th of each of the remaining months of last year. There were no other transactions in the account last year. If the closing balance of Carl's account for May of last year was $2,600, what was the range of the monthly closing balances of Carl's account last year?

(1) Last year the closing balance of Carl's account for April was less than $2,625.
(2) Last year the closing balance of Carl's account for June was less than $2,675.
OA=C

To rule out each statement individually,the O.G in the explanation of the quesiton takes the extreme case one in which the depositor has deposited only for one month and withdrawn for several months, and another where he deposits for several months but withdraws only in one month.
My question is, when the question clearly states that deposits have been for "several months"-plural how can the o.g cite the case of only one month-singular?


Your reply would help me take the quantum leap on my test.
Thanks!