Exactly 3 deposits have been made in a savings account and the amounts

#1
The amount of one of the deposits is $49.
it can be 42,49,56 = 147
or 35,42,49 = 126
insufficient
#2
The amount of one of the deposits is $63.
only possibility ; 49+56+63 ; 168
sufficient
OPTION B

1. Let the \(3\) investments be \(7x\), \(7x + 7\) and \(7x + 14\)
2. Total investment value \(= 7x + 7x +7 + 7x + 14 = 21x + 21 = 21 * (x + 1)\)
3. \(5 <= x <= 7\) if \(21 * (x + 1)\) has to fall between $120 and $170
4. A statement will be sufficient if it gives us only one value out of \(5\), \(6\) or \(7\)

Statement-I (Insufficient)
1. Here, \(7x = 49\) yields \(7\); \(7x + 7 = 49\) yields \(6\) and \(7x + 14 = 49\) yields \(5\)
2. Since we could not get a single value out of \(5\), \(6\) or \(7\) this statement is not sufficient

Statement-II (Sufficient)
1. Here, \(7x = 63\) yields \(9\); \(7x + 7 = 63\) yields \(8\) and \(7x + 14 = 63\) yields \(7\)
2. Since we could get a single value i.e. 7 this statement is sufficient

Ans. B

The numbers are of the form 7n, 7(n+1), 7(n+2)

Since their sum is between 120 and 170,
120 <= 21n + 21 <= 170
99 <= 21n <= 149

There are 3 possible values n can take
n=5, Sum = 105
n=6, Sum = 126
n=7, Sum = 147

1) One of the numbers is 49
This means that either n or n+1 or n+1 is 7
This means, n can be 5,6,7
Exactly the same info as the basic stem, nothing additional, hence INSUFFICIENT

2) One of the numbers is 63
That means one of n, n+1, n+2 is 9
Since n can only be 5/6/7 therefore, only n+2 can be 9 (with n being 7)
Hence SUFFICIENT

Key to solving this question quickly is recognizing that the second deposit will equal the mean of the 3 deposits, as we are told that the deposits are consecutive multiples. Therefore, sum of the deposits = mean x number of deposits