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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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gmatt1476 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. DS52402.01 #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 UNC Kenan Flagler Moderator Joined: 18 Jul 2015 Posts: 237 Own Kudos [?]: 254 [1] Given Kudos: 120 GMAT 1: 530 Q43 V20 WE:Analyst (Consumer Products) Re: Exactly 3 deposits have been made in a savings account and the amounts [#permalink] 1 Kudos gmatt1476 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.
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]
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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