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

let the three numbers be 7(x-1), 7x, 7(x+1)
as the sum is between 120 and 170, so 5.something < x < 8.something
x can be 6,7,8, and the middle number can be 42,49,56 respectively.

from statement (1), one of the numbers is 49,
it can be the middle number itself
or it can be the largest number assuming that the middle is 42
or it can be the smallest number assuming that the middle is 56 --> insufficient

from statement (2), one of the numbers is 63,
the only possibility is that 63 is the largest number for the middle number 56 --> sufficient

#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

Given: Exactly 3 deposits have been made in a savings account and the amounts of the deposits are 3 consecutive integer multiples of $7. The sum of the deposits is between $120 and $170
STRATEGY: For questions like this in which we have a limited number of possible cases, I like to invest a little bit of time up front to list of all of those possible cases. This will typically make things much easier when analyzing the two statements.
Also, when I scan the answer choices, I see that two of the three deposits are $49 and $63. This will help me list the various cases

Since the sum of the deposits is between $120 and $170, the possible cases are:
case i: $49, $56, and $63 (sum = $168) [ since $168 is very close to the upper limit of $170, I can see that the remaining cases must start with smaller values than $49]
case ii: $42, $49, and $56 (sum = $147)
case iii: $35, $42, and $49 (sum = $126)
case iv: $28, $35 and $42 (sum = $105) TOO small

Target question: What is the amount of each of the deposits?

Statement 1: The amount of one of the deposits is $49.
Check the three possible cases . . . i, ii and iii all apply, which means we can't answer the target question with certainty
Statement 1 is NOT SUFFICIENT

Statement 2: The amount of one of the deposits is $63.
Check the three possible cases . . . case i is the only one that satisfies statement 2, which means the three deposits are $49, $56, and $63
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent
_________________