## On a certain farm the ratio of horses to cows is 7:3. If the farm were to sell 15 horses and buy 15 cows, the ratio of

##### This topic has expert replies
Moderator
Posts: 7183
Joined: Thu Sep 07, 2017 4:43 pm
Followed by:23 members

### On a certain farm the ratio of horses to cows is 7:3. If the farm were to sell 15 horses and buy 15 cows, the ratio of

by BTGmoderatorDC » Fri Feb 24, 2023 8:50 pm

00:00

A

B

C

D

E

## Global Stats

On a certain farm the ratio of horses to cows is 7:3. If the farm were to sell 15 horses and buy 15 cows, the ratio of horses to cows would then be 13:7. After the transaction, how many more horses than cows would the farm own?

A. 30
B. 60
C. 75
D. 90
E. 105

OA D

Source: Princeton Review

### GMAT/MBA Expert

GMAT Instructor
Posts: 6887
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

### Re: On a certain farm the ratio of horses to cows is 7:3. If the farm were to sell 15 horses and buy 15 cows, the ratio

by [email protected] » Thu Mar 02, 2023 6:46 am
BTGmoderatorDC wrote:
Fri Feb 24, 2023 8:50 pm
On a certain farm the ratio of horses to cows is 7:3. If the farm were to sell 15 horses and buy 15 cows, the ratio of horses to cows would then be 13:7. After the transaction, how many more horses than cows would the farm own?

A. 30
B. 60
C. 75
D. 90
E. 105

OA D

Source: Princeton Review
We are given the ratio of horses to cows is 7 to 3, or 7x to 3x. We can create the following equation:

(7x - 15)/(3x + 15) = 13/7

7(7x - 15) = 13(3x + 15)

49x - 105 = 39x + 195

10x = 300

x = 30

Thus, there are 7(30) = 210 horses and 3(30) = 90 cows in the farm before the transaction. After the transaction, there are 210 - 15 = 195 horses and 90 + 15 = 105 cows. So, there are 195 - 105 = 90 more horses than cows after the transaction.

Answer: D

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

### GMAT/MBA Expert

GMAT Instructor
Posts: 16200
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

### Re: On a certain farm the ratio of horses to cows is 7:3. If the farm were to sell 15 horses and buy 15 cows, the ratio

by [email protected] » Sat Mar 11, 2023 7:51 am
BTGmoderatorDC wrote:
Fri Feb 24, 2023 8:50 pm
On a certain farm the ratio of horses to cows is 7:3. If the farm were to sell 15 horses and buy 15 cows, the ratio of horses to cows would then be 13:7. After the transaction, how many more horses than cows would the farm own?

A. 30
B. 60
C. 75
D. 90
E. 105

OA D

Source: Princeton Review
We can also solve this using TWO VARIABLES

Let H = present number of horses
Let C = present number of cows

ratio of horses to cows is 7:3
So, H/C = 7/3
Cross multiply to get 3H = 7C
Rearrange to get: 3H - 7C = 0

If the farm were to sell 15 horses and buy 15 cows, the ratio of horses to cows would then be 13:7
So, (H-15)/(C+15) = 13/7
Cross multiply to get 7(H-15) = 13(C+15)
Expand: 7H - 105 = 13C + 195
Rearrange to get: 7H - 13C = 300

We now have a system of two equations and two variables:
3H - 7C = 0
7H - 13C = 300

Solve to get: H = 210 and C = 90
NOTE: These are the values BEFORE livestock was sold and bought.

After selling 15 horses, there are 195 horses
After buying 15 cows, there are 105 cows

After the transaction, how many more horses than cows would the farm own?
195 - 105 = 90

Answer: D
Brent Hanneson - Creator of GMATPrepNow.com

• Page 1 of 1