very tough ds question from OG 12

Here in this question to determine the range of the monthly closing balances for last year..
that means u should know the closing balance of each month.
Now, take statement 1,
it says that closing balance of april was less than 2625.. and by question u can either add 120 or subtract 50. also from the question u have may balance. i.e. 2600
ok, now to keep the balance of may to be 2600 u have to add 120 in the previous balance i.e. 2600-120 = 2480..
now we don't have any info regarding the no. of months for which we need to add the money to this account.. hence 1 is insufficient..

take statement 2,
it says that balance for june is 2675.. and we know that may balance is 2600. so here u have to subtract 50 from may balance to get the june balance coz u cannot add 120 to may balance to get june balance..
ok by this we don't know whether july balance will me more or less..
hence insuff.

take both the statements,
u know that in april we added 120 to get may balance.. and to get june balance we subtracted 50 from may balance..
and as per the question we know that adding is for consecutive months only.. so that means from june onwards, withdrawal takes place ever months.. that means june is the month where the type of transaction changes i.e. subtraction takes place..
hence by this we can calculate all the balances and hence can find the range..
hence sufficient..

I got the question.
But what do they mean by range.
DOes it mean highest closing balance - lowest closing balance?

Thank you

Yes! Range = max in the set - min in the set

Good question.. IMO C and the explanation is

We know that 2600 is the balance at the end of may.
from (1) we know that closing balance for april < 2625. This simply implies that may was not the month of withdrawal because if it was then april's closing balance would have been 2650. So may was a month of deposit. And we know for certain than none of the previous months were months of withdrawal because deposits are supposed to be consecutive as per the question!!!. This gives us what the initial balance could have been at the beginning of jan (2000 in this case)
But this doesnt tell us that june will be month of withdrawal or deposit because anything could follow so we can never tell the final balance at the end of the year so range cannot be determined hence insuff!!

From (2) we apply similar logic and find out that may is a month of withdrawal. But we cannot tell which month the sequence of withdrawal has started before june so we cannot tell the initial balance at the beginning of the year although we can tell the final balance. So range cannot be determined hence insuff

So from (1) we can tell the initial balance and (2) we can tell the final balance and only combining we can tell both and hence the range so C