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At a corporate retreat, 120 employees were present. 65
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Updated on: 30 Sep 2026, 23:46
Updated on: 30 Sep 2026, 23:46
1
Expert Reply
00:00
Question Stats:
66% (02:42) correct
33% (01:16) wrong based on 3 sessions
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At a corporate retreat, 122 employees were present. 65 of these employees enjoyed hiking, 50 enjoyed kayaking, and 45 enjoyed rock climbing. 15 employees enjoyed all three activities, and 10 employees enjoyed none of the three. If 20 employees enjoyed both hiking and kayaking, and 18 employees enjoyed both kayaking and rock climbing, how many employees enjoyed only hiking?
(A) 30
(B) 35
(C) 38
(D) 42
(E) 45
(A) 30
(B) 35
(C) 38
(D) 42
(E) 45
- Part of the project: GRE Daily Quant Challenge ALL 4 CORE QUANT AREAS
- Also replying to the unanswered questions
At a corporate retreat, 120 employees were present. 65
[#permalink]
30 Sep 2026, 23:48
30 Sep 2026, 23:48
1
Expert Reply
Solution
Since 10 enjoyed none, 122-10=112 employees enjoyed at least one activity.
Inclusion-exclusion gives the hiking-climbing overlap:
\(112=65+50+45-(20+18+x)+15, \text { so } x=25\)
Then:
Only hiking \(=65-20-25+15=\mathbf{3 5}\)
Shortcut: only hiking \( =112-|\mathrm{K} \cup \mathrm{R}|=112-(50+45-18)=35\)
Check with all seven regions
Region & Count
Only hiking & 35
Only kayaking & 50-20-18+15=27
Only rock climbing & 45-25-18+15=17
Hiking & kayaking only & 5
Kayaking & climbing only & 3
Hiking & climbing only & 10
All three & 15
Total & 112 ✓
Since 10 enjoyed none, 122-10=112 employees enjoyed at least one activity.
Inclusion-exclusion gives the hiking-climbing overlap:
\(112=65+50+45-(20+18+x)+15, \text { so } x=25\)
Then:
Only hiking \(=65-20-25+15=\mathbf{3 5}\)
Shortcut: only hiking \( =112-|\mathrm{K} \cup \mathrm{R}|=112-(50+45-18)=35\)
Check with all seven regions
Region & Count
Only hiking & 35
Only kayaking & 50-20-18+15=27
Only rock climbing & 45-25-18+15=17
Hiking & kayaking only & 5
Kayaking & climbing only & 3
Hiking & climbing only & 10
All three & 15
Total & 112 ✓
gmatclubot
At a corporate retreat, 120 employees were present. 65 [#permalink]
30 Sep 2026, 23:48
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