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27 Mar 2026, 22:34
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
9% (02:26) correct
91%
(02:05)
wrong
based on 45
sessions
History
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Not Attempted Yet
Professor Blinken scores essays with respect to content, grammar, and spelling. The overall rating she gives each essay is a weighted average of these three scores. Abel’s essay received scores of 8.5 in content, 7.5 in grammar and 6.5 in spelling, and an overall rating of 7.8. What is the overall rating of Hana’s essay, which received scores of 10.0 in content, 10.0 in grammar and 8.0 in spelling?
(1) Mekdes’s essay received scores of 6.0 in content, 9.0 in grammar and 5.0 in spelling, and an overall rating of 6.7.
(2) Dawit’s essay received scores of 7.0 in content, 6.0 in grammar and 5.0 in spelling, and an overall rating of 6.3.
(1) Mekdes’s essay received scores of 6.0 in content, 9.0 in grammar and 5.0 in spelling, and an overall rating of 6.7.
(2) Dawit’s essay received scores of 7.0 in content, 6.0 in grammar and 5.0 in spelling, and an overall rating of 6.3.
26 Apr 2026, 13:54
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Answer is A, and honestly this one is sneakier than it looks. 65% of people pick C here, which makes complete sense instinctively — three unknowns, you want three equations, right? That's the trap.
The stem already gives you one equation from Abel's data. You have three weights (w1, w2, w3) and you know they sum to 1, so that's actually two constraints before any statements even come in.
Let me set it up:
The key move: since w1 + w2 + w3 = 1, write w3 = 1 - w1 - w2.
Abel's data: 8.5w1 + 7.5w2 + 6.5(1 - w1 - w2) = 7.8
Expanding: 2w1 + w2 = 1.3 ... (Equation 1)
That's from the stem alone. Now:
Statement (1): Mekdes scores 6.0, 9.0, 5.0 with overall 6.7
6w1 + 9w2 + 5(1 - w1 - w2) = 6.7
Expanding: w1 + 4w2 = 1.7 ... (Equation 2)
Two equations, two unknowns. You can solve: multiply Equation 2 by 2 and subtract from Equation 1... actually easier to just use substitution. From Eq 1, w2 = 1.3 - 2w1. Plug into Eq 2: w1 + 4(1.3 - 2w1) = 1.7, which gives -7w1 = -3.5, so w1 = 0.5. Then w2 = 0.3, w3 = 0.2.
Hana's rating = 10(0.5) + 10(0.3) + 8(0.2) = 5 + 3 + 1.6 = 9.6. Statement (1) alone gives a definite answer.
Statement (2): 7w1 + 6w2 + 5w3 = 6.3 → combined with Equation 1: 2w1 + w2 = 1.3. That gives us 2 equations again but they solve the same way, so (2) alone also works. Wait — let me check: from Eq 1 we have 2w1 + w2 = 1.3. From statement (2): 7w1 + 6w2 + 5(1 - w1 - w2) = 6.3 → 2w1 + w2 = 1.3. Same equation! So statement (2) gives no new information. Not sufficient alone.
Answer: A
The trap is forgetting that "weights sum to 1" gives you a free constraint. That's what makes the stem's Abel data worth more than it looks — you're not starting with zero constraints, you're starting with one equation already baked in.
I got burned by similar weighted-average DS questions before I internalized this. Every time you see weights in a DS problem, immediately note that they sum to 1 and use it to reduce variables before you even look at the statements.
The stem already gives you one equation from Abel's data. You have three weights (w1, w2, w3) and you know they sum to 1, so that's actually two constraints before any statements even come in.
Let me set it up:
The key move: since w1 + w2 + w3 = 1, write w3 = 1 - w1 - w2.
Abel's data: 8.5w1 + 7.5w2 + 6.5(1 - w1 - w2) = 7.8
Expanding: 2w1 + w2 = 1.3 ... (Equation 1)
That's from the stem alone. Now:
Statement (1): Mekdes scores 6.0, 9.0, 5.0 with overall 6.7
6w1 + 9w2 + 5(1 - w1 - w2) = 6.7
Expanding: w1 + 4w2 = 1.7 ... (Equation 2)
Two equations, two unknowns. You can solve: multiply Equation 2 by 2 and subtract from Equation 1... actually easier to just use substitution. From Eq 1, w2 = 1.3 - 2w1. Plug into Eq 2: w1 + 4(1.3 - 2w1) = 1.7, which gives -7w1 = -3.5, so w1 = 0.5. Then w2 = 0.3, w3 = 0.2.
Hana's rating = 10(0.5) + 10(0.3) + 8(0.2) = 5 + 3 + 1.6 = 9.6. Statement (1) alone gives a definite answer.
Statement (2): 7w1 + 6w2 + 5w3 = 6.3 → combined with Equation 1: 2w1 + w2 = 1.3. That gives us 2 equations again but they solve the same way, so (2) alone also works. Wait — let me check: from Eq 1 we have 2w1 + w2 = 1.3. From statement (2): 7w1 + 6w2 + 5(1 - w1 - w2) = 6.3 → 2w1 + w2 = 1.3. Same equation! So statement (2) gives no new information. Not sufficient alone.
Answer: A
The trap is forgetting that "weights sum to 1" gives you a free constraint. That's what makes the stem's Abel data worth more than it looks — you're not starting with zero constraints, you're starting with one equation already baked in.
I got burned by similar weighted-average DS questions before I internalized this. Every time you see weights in a DS problem, immediately note that they sum to 1 and use it to reduce variables before you even look at the statements.
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