Forgive my stupidity. But I am not getting this correct at all.
My answer is is 120, and the answer choices don't have it.
I got this question in LBS practice test:
The ratio of boarders to day scholars at a school is 7 to 16. However, after a few new students join the initial 560 boarders, the ratio changed to 1 to 2, respectively. If no boarders became day scholars and vice versa, and no students left the school, how many boarders joined the school?
A)44
B)64
C)70
D)80 (Correct Answer as per practice test)
E)84
Change in Ratio - Boarders:Day Scholars
This topic has expert replies
- Testtrainer
- Junior | Next Rank: 30 Posts
- Posts: 18
- Joined: Thu Dec 31, 2009 10:24 am
- Location: San Francisco,CA
- Thanked: 2 times
- GMAT Score:760
B/A = 7/16 = 560/(16 * 80)
New B/A = (560 + x)/(16 * 80) = 1/2
x = 80
New B/A = (560 + x)/(16 * 80) = 1/2
x = 80
I can't make you smarter, just a whole lot faster
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Let b = borders and d = day scholars.The ratio of boarders to day scholars at a school is 7 to 16. However, after a few new students join the initial 560 boarders, the ratio changed to 1 to 2, respectively. If no boarders became day scholars and vice versa, and no students left the school, how many boarders joined the school?
A) 48
B) 64
C) 70
D) 80
E) 84
Original ratio:
Here, b/d = 7/16.
Since the actual value of b is 560, and 7*80 = 560, the multiplier for the ratio is 80:
b/d = (80*7)/(80*16) = 560/1280.
Thus:
b=560, d=1280, total number of students = 560+1280 = 1840.
New ratio:
Here, b/d = 1/2.
Thus, of every 3 students, 1 is a boarder and 2 are day scholars, implying that the 1280 day scholars must be equal to 2/3 of the new total:
1280 = (2/3)x
x = 1920.
Thus, after the new boarders join the school, the new total number of students = 1920.
Thus:
New boarders = (new total) - (old total) = 1920 - 1840 = 80.
The correct answer is D.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
-
- GMAT Instructor
- Posts: 2630
- Joined: Wed Sep 12, 2012 3:32 pm
- Location: East Bay all the way
- Thanked: 625 times
- Followed by:119 members
- GMAT Score:780
I'd think of it as
(7x + y)/(16x) = 1/2
and
7x = 560
Then you can solve it algebraically without too much fuss: the numbers are more manageable.
(7x + y)/(16x) = 1/2
and
7x = 560
Then you can solve it algebraically without too much fuss: the numbers are more manageable.