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If Thomas divides half of his comic books in a 1:2 ratio between Alex
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24 Feb 2024, 14:42
24 Feb 2024, 14:42
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If Thomas divides half of his comic books in a 1:2 ratio between Alex and Jordan, respectively, then Alex will have one fourth as many comic books as Jordan, who will in turn have twice as many comic books as Thomas. If Alex currently owns 2 comic books, then how many more comic books does Thomas currently own than Jordan?
A. 8
B. 7
C. 6
D. 9
E. 3
A. 8
B. 7
C. 6
D. 9
E. 3
Quant Chat Moderator
Joined: 22 Dec 2016
Posts: 3128
Given Kudos: 1859
Location: India
Concentration: Strategy, Leadership
If Thomas divides half of his comic books in a 1:2 ratio between Alex
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24 Feb 2024, 15:26
24 Feb 2024, 15:26
1
Kudos
iwantroca wrote:
If Thomas divides half of his comic books in a 1:2 ratio between Alex and Jordan, respectively, then Alex will have one fourth as many comic books as Jordan, who will in turn have twice as many comic books as Thomas. If Alex currently owns 2 comic books, then how many more comic books does Thomas currently own than Jordan?
A. 8
B. 7
C. 6
D. 9
E. 3
A. 8
B. 7
C. 6
D. 9
E. 3
Let's assume Thomas currently owns 6x comic books
After Thomas divides, the number of comic books owned by
- Thomas = 3x
- Alex = 2 + x → Because Alex currently owns 2 comic books and gets x comic books from Thomas.
- Jordan = 4(2+x) = 8 + 4x → Because Alex will have one-fourth as many comic books as Jordan.
Given: Post-division, Jordan will in turn have twice as many comic books as Thomas
8 + 4x = 2*3x
2x = 8
x = 4
In the process of division, Thomas gives 2x books to Jordan. Hence, Thomas currently owns 2*4 = 8 more books than Jordan does.
Option A
Re: If Thomas divides half of his comic books in a 1:2 ratio between Alex
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25 Feb 2024, 02:38
25 Feb 2024, 02:38
1
Kudos
iwantroca
Given: If Thomas divides half of his comic books in a 1:2 ratio between Alex and Jordan, respectively, then Alex will have one fourth as many comic books as Jordan, who will in turn have twice as many comic books as Thomas.
Asked: If Alex currently owns 2 comic books, then how many more comic books does Thomas currently own than Jordan?
Let Thomas own x books.
Thomas divides half of his comic books in a 1:2 ratio between Alex and Jordan
Books Alex gets = x/6
Books Jordan gets = 2x/6 = x/3
Books left with Thomas = x/2
Books Alex have after gift from Thomas = 2 + x/6
Let Jordan curently have y books.
Books Jordan have after gift from Thomas = y + x/3
2 + x/6 = (y + x/3)/4 = y/4 + x/12
y + x/3 = 2*x/2 = x
2x/3 = y
2 + x/12 = y/4 = x/6
x = 24; y = 2x/3 = 16
Number of books Thomas currently own more than Jordan = x - y = 24 - 16 = 8
IMO A
Given: If Thomas divides half of his comic books in a 1:2 ratio between Alex and Jordan, respectively, then Alex will have one fourth as many comic books as Jordan, who will in turn have twice as many comic books as Thomas.
Asked: If Alex currently owns 2 comic books, then how many more comic books does Thomas currently own than Jordan?
Let Thomas own x books.
Thomas divides half of his comic books in a 1:2 ratio between Alex and Jordan
Books Alex gets = x/6
Books Jordan gets = 2x/6 = x/3
Books left with Thomas = x/2
Books Alex have after gift from Thomas = 2 + x/6
Let Jordan curently have y books.
Books Jordan have after gift from Thomas = y + x/3
2 + x/6 = (y + x/3)/4 = y/4 + x/12
y + x/3 = 2*x/2 = x
2x/3 = y
2 + x/12 = y/4 = x/6
x = 24; y = 2x/3 = 16
Number of books Thomas currently own more than Jordan = x - y = 24 - 16 = 8
IMO A
