Hi silviao,Great question — here's the fast way to crack this.
First, set up the key relationship. Let Larry's rate = L.
- Barry's rate =
3L (three times Larry's)
- Barry's rate = G/
2 (half of Garry's), so G =
2 ×
3L =
6L
This gives you the
golden ratio: Garry's rate is always [b]6 times Larry's rate.[/b]Now, since Larry picks for
5 hours, Larry's total =
5L, which means Larry's rate = Larry's total ÷
5.
Substitute that into the golden ratio:
Garry's rate = 6 × (Larry's total ÷ 5) = (6/5) × Larry's totalSo the quick test is: Garry's rate must be exactly
6/5 of Larry's total. That's the only thing you need to check.
Now scan the answer choices —
6,
13,
52,
65,
78,
390 — and ask: which pair has a
6-to-
5 ratio?
-
78 and
65 →
78 ÷
65 =
6/5 ✓No other pair works. Try a few to confirm:
-
390 and
65 →
390/
65 =
6 (
too big)
-
78 and
52 →
78/
52 =
3/2 (
wrong ratio)
-
52 and
13 →
52/
13 =
4 (
nope)
Only
78 and
65 have that
6-to-
5 relationship.
So Garry's rate =
78 apples per hour, and Larry's total =
65 apples.
To verify: Larry's rate =
65 ÷
5 =
13. Barry's rate =
3 ×
13 =
39. Garry's rate =
2 ×
39 =
78.
Everything checks out.Speed trick: derive the ratio between the two columns (here, 6/5), then scan for the pair of numbers with that ratio. That way you avoid testing every combination.Answer: 5A, 4B