Question: At College X, the faculty-to-student ratio is 1:9. If two-thirds of the students are female and one-quarter of the faculty is female, what fraction of the combined students and faculty are female?
(A) 11/24
(B) 5/8
(C) 25/56
(D) 11/12
(E) It cannot be determined from the information given.
Correct Answer: B
Solution and Explanation
Approach Solution 1:
There's a trick to solve this question
A 1:9 ratio has a total of ten parts,
we're taking thirds of the faculty, and quarters of the students.
So we need a number divisible by 10, 3, and 4;
multiply them out and we get
10 x 3 x 4 = 120
Lets Start there,
12 faculty, 3 female faculty, 108 students, 72 female students,
Total females = 72 + 3 = 75
Total student and faculty = 12 + 108 = 120
Which will gives us
\(=\frac{75}{120}\)
\(=\frac{15}{24}\)
\(=\frac{5}{8}\)
The answer is B , \(\frac{5}{8}th\) of the combined students and faculty are female.
Approach Solution 2:
Let's try to solve this with arithmetic process
Let us take the Total number of people be 400
The faculty-to-student ratio is 1:9.
Total number of faculty will be 40
Total number of students will be 360
Female faculty members are 10
Female students are 240
So,total females= 250
The fraction of females will be
\(\frac{total female}{total people}\)
\(=\frac{250}{400}\)
\(=\frac{25}{40}\)
\(=\frac{5}{8}\)
The answer is B , \(\frac{5}{8}th\) of the combined students and faculty are female.
Approach Solution 3:
Using sample numbers:
Faculty to Student is 1:9
2/3 of students are female and 1/4 of faculty is female, so we need to pick a number that is easy to divide by those fractions
Suppose there are 4 faculty memebers, then there are 36 students
1/4 of 4 = 1
2/3 of 36 = 24
Total of 25 females out of 40 (4 faculty and 36 students) = 25/40=> 5/8
“At College X, the faculty-to-student ratio is 1:9.”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT 800". To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.
Suggested GMAT Problem Solving Questions
- I Travel The First Part Of My Journey At 40 Miles Per Hour GMAT Problem Solving
- Profit Earned By Selling An Article At 1060 Is 20 % More Than The Loss GMAT Problem Solving
- A Perfect Square is a Number that Becomes an Integer when Square GMAT Problem Solving
- If x + y = 2 and x^2 + y^2 = 2, What is the Value of xy? GMAT Problem Solving
- If x^2 − 2 < 0, which of the following specifies all the possible GMAT Problem Solving
- A Train Approaches A Tunnel AB. Inside The Tunnel Is A Cat Located GMAT Problem Solving
- A Dairyman Pays Rs. 6.40 Per Liter Of Milk GMAT Problem Solving
- John is 20 years older than Brian. 12 years ago, John was twice as old GMAT Problem Solving
- A Train Overtakes Two Persons Who Are Walking In The Same Direction GMAT Problem Solving
- If 1/x − 1/x+1= 1/x+4, Then x could be GMAT Problem Solving
- (x^2 + 2x - 8)/(x^2 - 6x + 8) = ? GMAT Problem Solving
- Which Of The Following Is Equal To The Average (Arithmetic Mean) GMAT Problem Solving
- A Trader Has 400 kg Of Rice, A Part Of Which He Sells At 36% GMAT Problem Solving
- A Number, x is Chosen at Random from the Set of Positive Integers Less GMAT Problem Solving
- Which of the Following Could be the Area of an Isosceles Triangle GMAT Problem Solving
- After M Students Took a Test, There was a Total of 64% GMAT Problem Solving
- Perimeter of a Triangle with Integer Sides is Equal to 15 GMAT Problem Solving
- PQRS is a Quadrilateral Whose Diagonals are Perpendicular to Each Other GMAT Problem Solving
- Which of the following is closest to (10.001)^2 ? GMAT Problem Solving
- A Train of Length L is Traveling at a Constant Velocity and Passes a Pole GMAT Problem Solving
- In United States Currency, a Nickel is Worth 5 Cents GMAT Problem Solving
- After 200 Grams of Water were Added to the 24%- Solution of Alcohol GMAT Problem Solving
- Which of The Following Numbers is A Perfect Square? GMAT Problem Solving
- What is 1/(1*2) + 1/(2*3) + 1/(3*4) + 1/(4*5) + 1/(5*6) + 1/(6*7) GMAT Problem Solving
- What is the Remainder When\( 2^{99}\) is Divided by 99? GMAT Problem Solving
- The First Five Numbers in a Regular Sequence are 4, 10, 22, 46, and 94 GMAT Problem Solving
- A Bar is Creating a New Signature Drink. There are Five possible Alcohol GMAT Problem Solving
- A Can Complete a Certain Job in 12 Days. B is 60% More Efficient than GMAT Problem Solving
- An Alloy of Gold,Silver and Bronze Contain 90% Bronze, 7% Gold and GMAT Problem Solving
- When Positive Integer n is Divided by 5, the Remainder is 1 GMAT Problem Solving
- A is Thrice as Efficient as B and Hence Takes 12 Days Less to Complete GMAT Problem Solving
- A Tank is Filled by Three Pipes with Uniform Flow. The First Two Pipes GMAT Problem Solving
- Each Person in a Group of 110 Investors Has Investments in Either GMAT Problem Solving
- Jim Travels the First 3 Hours of His Journey at 60 mph Speed GMAT Problem Solving
- A Committee Of 7 Members Is To Be Formed To Put Up The Christmas GMAT Problem Solving
- In A Class Of 60 Students, 23 Play Hockey, 15 Play Basketball GMAT Problem Solving
- The Area Of An Equilateral Triangle With Side Length X Is The Same GMAT Problem Solving
- Which Of The Following Has A Decimal Equivalent That Is A GMAT Problem Solving
- A Number when Divided by a Divisor Leaves a Remainder of 24 GMAT Problem Solving
- How many Integers Less than 1000 have no Factors (other than 1) GMAT Problem Solving
- How Many Prime Numbers are there Between 50 and 70? GMAT Problem Solving
- If a Circle Passes through Points (1, 2) (2, 5), and (5, 4) GMAT Problem Solving
- If the Perimeter of Square Region S and the Perimeter of Rectangular GMAT Problem Solving
- If x^9= 9^9^9, What is the Value of x? GMAT Problem Solving
- In a Competition, a School Awarded Medals in Different Categories GMAT Problem Solving
- In How Many Ways can 5 Apples (Identical) be Distributed Among 4 Children? GMAT Problem Solving
- What is Greatest Positive Integer n such that 2^n is a Factor of 12^10? GMAT Problem Solving
- All The Five Digit Numbers In Which Each Successive Digit Exceeds Its GMAT Problem Solving
- A Box Contains Two White Balls, Three Black Balls And Four Red Balls GMAT Problem Solving
- Consider An Obtuse-Angled Triangles With Sides 8 Cm, 15 Cm GMAT Problem Solving
Comments