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

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Re: Exactly 3 deposits have been made in a savings account and the amounts [#permalink]
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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. DS52402.01 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
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Re: Exactly 3 deposits have been made in a savings account and the amounts [#permalink]
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
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Re: Exactly 3 deposits have been made in a savings account and the amounts [#permalink]
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
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Re: Exactly 3 deposits have been made in a savings account and the amounts [#permalink]
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
Re: Exactly 3 deposits have been made in a savings account and the amounts [#permalink]
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