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19 Feb 2026, 00:09
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
54% (02:21) correct
46%
(02:37)
wrong
based on 59
sessions
History
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Time
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Not Attempted Yet
Fabio bought several pairs of socks, some woolen and the others cotton. The price of the each pair of woolen socks was $3 higher than the price of each pair of cotton socks. What was the average price of the pairs of socks that Fabio bought?
(1) He bought three times as many pairs of cotton socks as woolen socks.
(2) He spent twice as much money on cotton socks as he did on woolen socks.
(1) He bought three times as many pairs of cotton socks as woolen socks.
(2) He spent twice as much money on cotton socks as he did on woolen socks.
19 Feb 2026, 02:12
Kudos
Bookmarks
Key concept: Data Sufficiency — testing whether variables cancel
The common trap here is assuming Statement (1) is sufficient because "we know the ratio of quantities." But the average price depends on both the quantity ratio AND the actual price of cotton socks, which is unknown. Let's be precise.
Setup: Let cotton price = c, woolen price = c + 3, woolen pairs = w, cotton pairs = k.
Average price = [w(c+3) + kc] / (w + k)
Step 1 — Statement (1): k = 3w
Substitute: [w(c+3) + 3wc] / 4w = [wc + 3w + 3wc] / 4w = c + 3/4
Average price = c + 0.75 — still depends on c.
INSUFFICIENT
Step 2 — Statement (2): Money spent on cotton = 2 × money spent on woolen
kc = 2w(c+3) → k = 2w(c+3)/c
Plugging into the average expression, after simplifying:
Average = c(c+3)/(c+2) — still depends on c.
INSUFFICIENT
Step 3 — Both together:
From (1): k = 3w
From (2): kc = 2w(c+3) → 3wc = 2w(c+3) → 3c = 2c + 6 → c = 6
So cotton = $6, woolen = $9, cotton pairs = 3w, woolen pairs = w.
Average = (w×9 + 3w×6) / (w + 3w) = (9w + 18w) / 4w = 27/4 = $6.75
SUFFICIENT
Answer: C
Takeaway: In DS word problems with a price difference between two items, a quantity ratio alone won't fix the average — you need a second equation that pins down the actual price.
The common trap here is assuming Statement (1) is sufficient because "we know the ratio of quantities." But the average price depends on both the quantity ratio AND the actual price of cotton socks, which is unknown. Let's be precise.
Setup: Let cotton price = c, woolen price = c + 3, woolen pairs = w, cotton pairs = k.
Average price = [w(c+3) + kc] / (w + k)
Step 1 — Statement (1): k = 3w
Substitute: [w(c+3) + 3wc] / 4w = [wc + 3w + 3wc] / 4w = c + 3/4
Average price = c + 0.75 — still depends on c.
INSUFFICIENT
Step 2 — Statement (2): Money spent on cotton = 2 × money spent on woolen
kc = 2w(c+3) → k = 2w(c+3)/c
Plugging into the average expression, after simplifying:
Average = c(c+3)/(c+2) — still depends on c.
INSUFFICIENT
Step 3 — Both together:
From (1): k = 3w
From (2): kc = 2w(c+3) → 3wc = 2w(c+3) → 3c = 2c + 6 → c = 6
So cotton = $6, woolen = $9, cotton pairs = 3w, woolen pairs = w.
Average = (w×9 + 3w×6) / (w + 3w) = (9w + 18w) / 4w = 27/4 = $6.75
SUFFICIENT
Answer: C
Takeaway: In DS word problems with a price difference between two items, a quantity ratio alone won't fix the average — you need a second equation that pins down the actual price.
19 Feb 2026, 06:29
Kudos
Bookmarks
Setup:
Let cotton socks cost $c per pair, so woolen socks cost $(c+3) per pair.
Let Fabio buy n cotton pairs and m woolen pairs.
Average price = Total money spent ÷ Total pairs bought
Statement 1: He bought 3 times as many cotton as woolen socks.
→ n = 3m
Average = (3m·c + m·(c+3)) / 4m = c + 0.75
Problem: We don't know what c is!
• If c = $5 → Average = $5.75
• If c = $10 → Average = $10.75
Not Sufficient
Statement 2: He spent twice as much on cotton as on woolen socks.
→ n·c = 2·m·(c+3)
This gives us a relationship, but we still have 3 unknowns (n, m, c).
Problem: Multiple scenarios work:
• If woolen = $9, cotton = $6, buy 3 cotton and 1 woolen → Average = $6.75
• If woolen = $6, cotton = $3, buy 4 cotton and 1 woolen → Average = $3.60
Not Sufficient
Combining Both Statements:
From S1: n = 3m
From S2: n·c = 2m(c+3)
Substitute n = 3m into the second equation:
3m·c = 2m(c+3)
3c = 2c + 6
c = 6
Now we know: Cotton = $6, Woolen = $9
Average = (3m × $6 + m × $9) / 4m = $27m / 4m = $6.75
Answer: C
Let cotton socks cost $c per pair, so woolen socks cost $(c+3) per pair.
Let Fabio buy n cotton pairs and m woolen pairs.
Average price = Total money spent ÷ Total pairs bought
Statement 1: He bought 3 times as many cotton as woolen socks.
→ n = 3m
Average = (3m·c + m·(c+3)) / 4m = c + 0.75
Problem: We don't know what c is!
• If c = $5 → Average = $5.75
• If c = $10 → Average = $10.75
Not Sufficient
Statement 2: He spent twice as much on cotton as on woolen socks.
→ n·c = 2·m·(c+3)
This gives us a relationship, but we still have 3 unknowns (n, m, c).
Problem: Multiple scenarios work:
• If woolen = $9, cotton = $6, buy 3 cotton and 1 woolen → Average = $6.75
• If woolen = $6, cotton = $3, buy 4 cotton and 1 woolen → Average = $3.60
Not Sufficient
Combining Both Statements:
From S1: n = 3m
From S2: n·c = 2m(c+3)
Substitute n = 3m into the second equation:
3m·c = 2m(c+3)
3c = 2c + 6
c = 6
Now we know: Cotton = $6, Woolen = $9
Average = (3m × $6 + m × $9) / 4m = $27m / 4m = $6.75
Answer: C
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