If Thomas divides half of his comic books in a 1:2 ratio between Alex

Question

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

gmatophobia · Answer

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

Kinshook · Answer

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

HarshaBujji · Answer

Assume Thomas currently owns 6t comic books. (Because he will divide them in 1:2 ration later).

We want to avoid fractions. So after the shuffle 
 
  Thomas will have  3t 
 Alex will have 2 + t  → Because Alex currently owns 2 comic books and gets x comic books from Thomas. 
 Jordan will have 4(2+t)→ As Alex will have one-fourth as many comic books as Jordan.

Jordan will in turn have twice as many comic books as Thomas

8 + 4t = 2*3t

t = 4

Hence IMO A

saynchalk · Answer

Can someone please explain the part after we get x=4, and why Thomas has 8 more books than Jordan currently

Bunuel · Answer

The number of books Thomas has is 6x = 24. Out of which he would give 2x = 8 books to Jordan.

The number of books Jordan would have after division is 4(2+x) = 24. Hence, before division, Jordan had 24 - 2x = 16 books, resulting in a difference of 8 books.

saynchalk · Answer

Hi Bunuel, thanks!! I get it now

bumpbot · Answer

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If Thomas divides half of his comic books in a 1:2 ratio between Alex

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