BTGmoderatorDC wrote:Exactly 3 deposits have been made in a savings account and the amounts of the deposits are 3 consecutive integer multiples of $7. If the sum of the deposits is between $120 and $170, what is the amount of each of the deposits?
(1) The amount of one of the deposits is $49.
(2) The amount of one of the deposits is $63.
OA B
Source: Official Guide
Say the three deposits are 7n, 7(n + 1), and 7(n + 2). Thus, their sum = 7n + 7(n + 1) + 7(n + 2) = 21n + 21
=> 120 > (21n + 21) > 170
=> 7... > n > 4...
=> n can be one among 7/6/5.
Question rephrased: What's the value of n?
Let's take each statement one by one.
(1) The amount of one of the deposits is $49.
Case 1: Say 49 is the greatest multiple of 7: 49 = 7(n + 2) => n = 5, a possible value.
Case 2: Say 49 is the middle-most multiple of 7: 49 = 7(n + 1) => n = 6, a possible value.
Case 3: Say 49 is the smallest multiple of 7: 49 = 7n => n = 7, a possible value.
No unique answer. Insufficient.
(2) The amount of one of the deposits is $63.
Case 1: Say 63 is the greatest multiple of 7: 63 = 7(n + 2) => n = 7, a possible value.
Case 2: Say 63 is the middle-most multiple of 7: 63 = 7(n + 1) => n = 8, not a possible value.
There's no need to try for the smallest multiple of 7 as 63 as the middle-most multiple of 7 does not return a valid value of n.
Thus, n = 7. Sufficient.
The correct answer:
B
Hope this helps!
-Jay
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