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Updated on: 08 Dec 2023, 12:41
Originally posted by XimeSol on 08 Dec 2023, 12:15.
Last edited by gmatophobia on 08 Dec 2023, 12:41, edited 1 time in total.
Last edited by gmatophobia on 08 Dec 2023, 12:41, edited 1 time in total.
Formatted the question
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52% (01:36) correct
48%
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Lea estimated each of the charges on her telephone bill by rounding the charge to the nearest $1. Was the sum of Lea's estimated charges within $8 of the sum of the actual charges on her telephone bill?
(1) Each of the actual charges on Lea's telephone bill was less than $7.75
(2) There were 14 charges on Lea's telephone bill.
(1) Each of the actual charges on Lea's telephone bill was less than $7.75
(2) There were 14 charges on Lea's telephone bill.
A)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D)EACH statement ALONE is sufficient.
E)Statements (1) and (2) TOGETHER are NOT sufficient.
B)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D)EACH statement ALONE is sufficient.
E)Statements (1) and (2) TOGETHER are NOT sufficient.
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25 Sep 2024, 00:10
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Lea estimated each of the charges on her telephone bill by rounding the charge to the nearest $1. Was the sum of Lea's estimated charges within $8 of the sum of the actual charges on her telephone bill?
Lea rounding the charges to the nearest $1 means that if the bill was $10.15, she estimated it as $10, and if it was $2.65, she estimated it as $3. Notice that the maximum difference between the estimated and actual charge for any given call is $0.50. This would occur when the actual charge is something like $7.50, which Lea would round up to $8, creating a difference of $0.50.
(1) Each of the actual charges on Lea's telephone bill was less than $7.75
This statement is clearly insufficient. We don't know the number of charges or their actual values. For example, if there was only one call, the difference between the actual and estimated total would be less than $8. However, if there were 100 calls, each charged at $5.50, the estimated charge for each would be $6, and the total difference would be $100 * 6 - $100 * 5.5 = $50, which is more than $8.
(2) There were 14 charges on Lea's telephone bill.
As we deduced, the maximum difference between the estimated and actual charge for any call is $0.50. Therefore, with 14 calls, the maximum total difference would be 14 * $0.50 = $7, which is less than $8. Sufficient.
Answer: B.
Lea rounding the charges to the nearest $1 means that if the bill was $10.15, she estimated it as $10, and if it was $2.65, she estimated it as $3. Notice that the maximum difference between the estimated and actual charge for any given call is $0.50. This would occur when the actual charge is something like $7.50, which Lea would round up to $8, creating a difference of $0.50.
(1) Each of the actual charges on Lea's telephone bill was less than $7.75
This statement is clearly insufficient. We don't know the number of charges or their actual values. For example, if there was only one call, the difference between the actual and estimated total would be less than $8. However, if there were 100 calls, each charged at $5.50, the estimated charge for each would be $6, and the total difference would be $100 * 6 - $100 * 5.5 = $50, which is more than $8.
(2) There were 14 charges on Lea's telephone bill.
As we deduced, the maximum difference between the estimated and actual charge for any call is $0.50. Therefore, with 14 calls, the maximum total difference would be 14 * $0.50 = $7, which is less than $8. Sufficient.
Answer: B.
General Discussion
08 Dec 2023, 12:54
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XimeSol
Statement 1
(1) Each of the actual charges on Lea's telephone bill was less than $7.75
While we know the actual charge on each of the bills was less than $7.75, we do not know the number of charges that we are looking at.
For example, Lea rounded two charges. The first charge was for $4.45, and the second charge was for $5.90. She rounds the first charge to $4.00, and she rounds the second charge to $6.00. In this case, the actual sum is $(4.45 + 5.90 =) 10.35, while the rounded sum is $10.00
Was the sum of Lea's estimated charges within $8 of the sum of the actual charges on her telephone bill → The answer is Yes.
On the contrary, let's consider that Lea rounded a million charges. Each charge was for $5.90, therefore she rounded each charge to $6.00.
In this case, the actual charge is $5.9M, while the rounded charge is $6M.
Was the sum of Lea's estimated charges within $8 of the sum of the actual charges on her telephone bill → The answer is No.
As we are getting contradicting answers to the question asked, this statement is not sufficient. We can eliminate A and D.
Statement 2
(2) There were 14 charges on Lea's telephone bill.
If there were 14 charges on Lea's telephone bill the maximum difference between the actual sum and the rounded sum can be $7.
To understand this better consider this statement, we need to consider the scenarios when the difference between the actual and the rounded charge is expected to be maximum. The maximum difference between the actual sum and the rounded sum occurs when the actual sum is rounded down from \(x.49\) to \(x-1\) or when the sum is rounded up from \(x.50\) to \(x+1\). In both scenarios, the maximum difference between the actual sum and the rounded sum is $0.50.
If Lea rounded 14 charges, the maximum between the actual sum and the rounded sum can be 14*0.50 = $7
Was the sum of Lea's estimated charges within $8 of the sum of the actual charges on her telephone bill → The answer is Yes.
This statement therefore is sufficient.
Option B
