SOLUTIONA certain high school with a total enrollment of 900 students held a science fair for three days last week. How many of the students enrolled in the high school attended the science fair on all three days?The trick here is that we don't know whether all of 900 students attended on
at least one day. Meaning that there can be # of students which didn't take part in the fair.
So we have the following groups:
A. Attended on
only one day
B. Attended on
two days exactlyC. Attended on
all three daysD. Not attended.
And the sum of these groups is A+B+C+D=900. We want to determine the value of C.
(1) Of the students enrolled in the school, 30 percent attended the science fair on two or more days. So, 900*0.3=270 attended 2 or more days --> B+C=270. Not sufficient.
(2) Of the students enrolled in the school, 10 percent
of those that attended the science fair on at least one day attended on all three days --> 10%*(A+B+C)=C --> A+B=9C. Not sufficient.
(1)+(2) B+C=270, A+B=9C and A+B+C+D=900. Three equations four unknowns. Not sufficient.
Answer: E.
Kudos points given to everyone with correct
solution. Let me know if I missed someone.
_________________
NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!
PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders
COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!! ,11 Mixed Questions NEW!!!, 12 Fresh Meat NEW!!!
DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!, 11 New DS set. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
close
65% (02:18) correct
