GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Nov 17Live Online Classes with Top GRE Expert Rich Zwelling
08:00 PM EST
-10:00 PM EST
Get live instruction from a top-scoring, industry-recognized GRE teachers + 6 months of access to TTP Self-Study included! Tues/Thur Sept 7, 2026---Feb. 2, 2027, 1:00pm-3:00pm EST
Dec 14Live Online Classes with Top GRE Expert Michael Butville
08:00 PM EST
-10:00 PM EST
Get live instruction from a top-scoring, industry-recognized GRE teachers + 6 months of access to TTP Self-Study included! Mon/Wed Dec. 14, 2026---Feb. 22, 2027, 8:00pm-10:00pm EST
At a corporate retreat, 120 employees were present. 65
[#permalink]
Updated on: 30 Sep 2026, 23:46
Updated on: 30 Sep 2026, 23:46
1
Expert Reply
1
Bookmarks
00:00
Question Stats:
50% (02:42) correct
50% (02:42) wrong based on 4 sessions
Hide Show timer Statistics
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
Moderators:
