Events & Promotions
|
|
GMAT 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.
Apr 2610:00 AM EDT
-11:00 AM EDT
The Target Test Prep course represents a quantum leap forward in GMAT preparation, a radical reinterpretation of the way that students should study. Try before you buy with a 5-day, full-access trial of the course for FREE!
Apr 2711:00 AM EDT
-12:00 PM EDT
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
18 Feb 2026, 11:33
Kudos
Bookmarks
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:
57% (03:03) correct
43%
(03:24)
wrong
based on 51
sessions
History
Date
Time
Result
Not Attempted Yet
Regulations mandate that at least 2/3 but no more than 4/5 of the students at a certain school be girls, that the ratio of students to teachers be less than 18 to 1, and that the ratio of the number of teachers to the number of support staff employees be no greater than 3 to 2. If the school has 5 support staff employees, what is the greatest possible number of boys that would be consistent with these regulations?
(A) 25
(B) 40
(C) 41
(D) 44
(E) 45
(A) 25
(B) 40
(C) 41
(D) 44
(E) 45
19 Feb 2026, 02:41
Kudos
Bookmarks
kevincan
Given that:
(2/3)* Students <= Girls < (4/5)* Students.
Student / Teachers < (18/1)
Teacher / Support staff < = (3/2)
If support staff = 5
Then, teacher <= (3/2)*5
Teacher <= 7.5
Possible integer value for teacher = 7
If teacher is 7, student < 18*7
Student < 126 .
So, student can be 125.
Student includes boys and girls.
Greatest boy means minimum girls.
Boys <= (1/3)* 125
Boys < = 41.66
Closest answer choice 41.
OR (2/3)*125 <= Girls < (4/5)*125
83.33 <= Girls < 100
So, girls can be any value from 84 to 99 (Both inclusive).
125-84 = 41 (max boys)
125 - 99 = 26 (min boys)
Option C
19 Feb 2026, 04:26
Kudos
Bookmarks
To maximize boys, we need to maximize total students first, then find what fraction can be boys.
Let's work through this step by step:
Step 1: Find Maximum Teachers
We're told: Teachers/Support Staff ≤ 3/2
Since support staff = 5:
Teachers/5 ≤ 3/2
Teachers ≤ 7.5
Maximum teachers = 7 (must be a whole person!)
Step 2: Find Maximum Students
We're told: Students/Teachers < 18 (notice: strictly less than, not "at most")
Students/7 < 18
Students < 126
Maximum students = 125 (since we need strictly LESS than 126)
Common trap: Using ≤ instead of < would give 126 students — but that violates the "less than" condition!
Step 3: Find Maximum Boys
We're told: At least 2/3 of students must be girls, but no more than 4/5
If at least 2/3 are girls → at most 1/3 can be boys
Maximum boys = (1/3) × 125 = 41.67
Maximum boys = 41 (must be a whole person!)
Quick Verification:
• Boys = 41, Total students = 125 → Girls = 84
• Girls/Students = 84/125 = 67.2%
• Is 67.2% between 66.67% (2/3) and 80% (4/5)? Yes!
Answer: C (41)
Principle for similar problems: When you see multiple constraints, chain them together starting from what you know. And always watch out for "less than" vs "at most" - one gives you the boundary value, the other doesn't!
Let's work through this step by step:
Step 1: Find Maximum Teachers
We're told: Teachers/Support Staff ≤ 3/2
Since support staff = 5:
Teachers/5 ≤ 3/2
Teachers ≤ 7.5
Maximum teachers = 7 (must be a whole person!)
Step 2: Find Maximum Students
We're told: Students/Teachers < 18 (notice: strictly less than, not "at most")
Students/7 < 18
Students < 126
Maximum students = 125 (since we need strictly LESS than 126)
Common trap: Using ≤ instead of < would give 126 students — but that violates the "less than" condition!
Step 3: Find Maximum Boys
We're told: At least 2/3 of students must be girls, but no more than 4/5
If at least 2/3 are girls → at most 1/3 can be boys
Maximum boys = (1/3) × 125 = 41.67
Maximum boys = 41 (must be a whole person!)
Quick Verification:
• Boys = 41, Total students = 125 → Girls = 84
• Girls/Students = 84/125 = 67.2%
• Is 67.2% between 66.67% (2/3) and 80% (4/5)? Yes!
Answer: C (41)
Principle for similar problems: When you see multiple constraints, chain them together starting from what you know. And always watch out for "less than" vs "at most" - one gives you the boundary value, the other doesn't!
