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## Difficult Math Question #44 - Ratios

This topic has 1 expert reply and 4 member replies
800guy Master | Next Rank: 500 Posts
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#### Difficult Math Question #44 - Ratios

Wed Nov 01, 2006 11:00 am
There 3 kinds of books in the library fiction, non-fiction and biology. Ratio of fiction to non-fiction is 3 to 2; ratio of non-fiction to biology is 4 to 3, and the total of the books is more than 1000?which one of following can be the total of the book?

A 1001 B. 1009 C.1008 D.1007 E.1006

Thanked by: abfromcs
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800guy Master | Next Rank: 500 Posts
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Fri Nov 03, 2006 1:10 pm
OA:

fiction : non-fiction = 3 : 2 = 6 : 4
non-fiction : biology = 4 : 3

fiction : non-fiction : biology = 6 : 4 : 3

6x + 4x + 3x = 1000
x = 76 12/13
if we add 1, 13 will divide evenly (1001/13 = 77)
1000 + 1 = 1001

### GMAT/MBA Expert

Scott@TargetTestPrep GMAT Instructor
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Fri Dec 15, 2017 6:15 am
800guy wrote:
There 3 kinds of books in the library fiction, non-fiction and biology. Ratio of fiction to non-fiction is 3 to 2; ratio of non-fiction to biology is 4 to 3, and the total of the books is more than 1000?which one of following can be the total of the book?

A 1001
B. 1009
C.1008
D.1007
E.1006
Solution:

We are given:

Ratio of fiction to nonfiction = 3 : 2

Ratio of nonfiction to biology = 4 : 3

We can multiply the first ratio by 2 and we have:

fiction to nonfiction = 6 : 4

Thus, we now have a three-part ratio (which we can express using an x multiplier):

fiction to nonfiction to biology = 6x : 4x : 3x

We see that the total books must be a multiple of 6x + 4x + 3x = 13x, or a multiple of 13.

Of the answer choices, only 1001 is a multiple of 13.

_________________

Scott Woodbury Stewart Founder & CEO
GMAT Quant Self-Study Course - 500+ lessons 3000+ practice problems 800+ HD solutions
5-Day Free Trial 5-DAY FREE, FULL-ACCESS TRIAL TTP QUANT

800guy Master | Next Rank: 500 Posts
Joined
27 Jun 2006
Posted:
354 messages
Followed by:
5 members
11
Fri Nov 03, 2006 1:10 pm
OA:

fiction : non-fiction = 3 : 2 = 6 : 4
non-fiction : biology = 4 : 3

fiction : non-fiction : biology = 6 : 4 : 3

6x + 4x + 3x = 1000
x = 76 12/13
if we add 1, 13 will divide evenly (1001/13 = 77)
1000 + 1 = 1001

### GMAT/MBA Expert

Scott@TargetTestPrep GMAT Instructor
Joined
25 Apr 2015
Posted:
548 messages
Followed by:
3 members
43
Fri Dec 15, 2017 6:15 am
800guy wrote:
There 3 kinds of books in the library fiction, non-fiction and biology. Ratio of fiction to non-fiction is 3 to 2; ratio of non-fiction to biology is 4 to 3, and the total of the books is more than 1000?which one of following can be the total of the book?

A 1001
B. 1009
C.1008
D.1007
E.1006
Solution:

We are given:

Ratio of fiction to nonfiction = 3 : 2

Ratio of nonfiction to biology = 4 : 3

We can multiply the first ratio by 2 and we have:

fiction to nonfiction = 6 : 4

Thus, we now have a three-part ratio (which we can express using an x multiplier):

fiction to nonfiction to biology = 6x : 4x : 3x

We see that the total books must be a multiple of 6x + 4x + 3x = 13x, or a multiple of 13.

Of the answer choices, only 1001 is a multiple of 13.

_________________

Scott Woodbury Stewart Founder & CEO
GMAT Quant Self-Study Course - 500+ lessons 3000+ practice problems 800+ HD solutions
5-Day Free Trial 5-DAY FREE, FULL-ACCESS TRIAL TTP QUANT

rajs.kumar Senior | Next Rank: 100 Posts
Joined
09 Jun 2006
Posted:
87 messages
2
Thu Nov 02, 2006 3:50 am

F:NF = 3:2
NF:B = 4:3

F:NF:B = 6:4:3

the number of books should be divisable by the total => 1001

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