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21 Sep 2019, 19:33
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B
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Difficulty:
35%
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Question Stats:
74% (02:31) correct
26%
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wrong
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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) The amount of one of the deposits is $49.
(2) The amount of one of the deposits is $63.
DS52402.01
16 Apr 2022, 07:40
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gmatt1476
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.
(2) The amount of one of the deposits is $63.
DS52402.01
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)
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
General Discussion
22 Sep 2019, 01:19
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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
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
