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03 Dec 2025, 22:11
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B
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Difficulty:
55%
(hard)
Question Stats:
63% (02:14) correct
37%
(02:15)
wrong
based on 138
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A freelancer charged p dollars per hour for a specific project in January and q dollars per hour for another project in February. If the freelancer's total earnings from the project in February were 25 percent more than her total earnings from the project in January, did the freelancer charge more per hour for the project in February than she did in January?
(1) The freelancer's total earnings from 120 hours of work on the project in February were $6,000.
(2) The freelancer worked 20 percent more hours on the project in February than she did in January.
(1) The freelancer's total earnings from 120 hours of work on the project in February were $6,000.
(2) The freelancer worked 20 percent more hours on the project in February than she did in January.
04 Dec 2025, 04:14
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ExpertsGlobal5
Let:
J = hours worked in January.
F = hours worked in February.
From the stem we get:
\(Fq = 1.25Jp\)
Statement 1: "The freelancer's total earnings from 120 hours of work on the project in February were $6,000."
So F = 120 and \(q*120 = 6000\) Leading to q = 50.
We also get that \(1.25Jp = 6000\), leading to \(Jp = 4800\)
This statement is not sufficient to conclude whether q > p as we can have 2 examples:
If p = 40 , J =120 then q = 50 > p
If p = 80, J = 60 then q=50 < p
Statement 2: " The freelancer worked 20 percent more hours on the project in February than she did in January."
so \(F = 1.2J\)
We can plug this in to the formula we got from the stem:
\(q*1.2J = 1.25Jp\)
1.2q = 1.25p
\(q = \frac{1.25}{1.2}p\)
\(q = \frac{25}{24}p \)
So we know q > p and the second statement is sufficient and the answer is B
28 Dec 2025, 05:17
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ExpertsGlobal5
Explanation:
Let the total number of hours the freelancer worked in January be m.
Let the total number of hours the freelancer worked in February be n.
Since the freelancer charged p dollars per hour in January, total earnings in January = mp.
Since the freelancer charged q dollars per hour in February, total earnings in February = nq.
Since the freelancer's total earnings from the project in February were 25 percent more than her total earnings from the project in January:
nq = 1.25mp (Equation I)
We need to find whether q > p.
Statement (1)
Since n = 120 and nq = 6,000, it follows that q = 6,000 / 120 = 50.
From Equation I,
nq = 1.25mp
6,000 = 1.25mp
mp = 6,000 / 1.25
Since no information is provided regarding the values of m and p, it is NOT possible to determine with certainty whether q > p. Hence, Statement (1) is insufficient.
Statement (2)
n = 1.2m
Substituting the value of n into Equation I:
nq = 1.25mp
(1.2m)q = 1.25mp
Cancelling m from both sides:
1.2q = 1.25p
q = (1.25 / 1.2)p > p
It is possible to determine with certainty that q > p. Hence, Statement (2) is sufficient.
B is the correct answer choice.
