Oil, vinegar, and water are mixed in a 3 to 2 to 1 ratio to

Expert replies

Previous Topic Next Topic

BTGmoderatorLU: Moderator; Posts: 2558; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Sat Dec 08, 2018 5:07 am

Timer

00:00

Answers

Stats

Difficulty—

Source: Manhattan Prep

Oil, vinegar, and water are mixed in a 3 to 2 to 1 ratio to make salad dressing. If Larry has 8 cups of oil, 7 cups of vinegar, and access to any amount of water, what is the maximum number of cups of salad dressing he can make with the ingredients he has available, if fractional cup measurements are possible?

A. 12
B. 13
C. 14
D. 15
E. 16

The OA is E.

Like this post

Source: Beat The GMAT — Problem Solving | Sat Dec 08, 2018 5:07 am

fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Sat Dec 08, 2018 4:53 pm

BTGmoderatorLU wrote:Source: Manhattan Prep

Oil, vinegar, and water are mixed in a 3 to 2 to 1 ratio to make salad dressing. If Larry has 8 cups of oil, 7 cups of vinegar, and access to any amount of water, what is the maximum number of cups of salad dressing he can make with the ingredients he has available, if fractional cup measurements are possible?

A. 12
B. 13
C. 14
D. 15
E. 16

Excellent opportunity for the k technique!
$$\left\{ \matrix{
\,{\rm{oil}} = 3k\,\,\,\,\,\, \to \,\,\,\,\,\,3k \le 8\,\,\, \Rightarrow \,\,\,k \le 2{2 \over 3} \hfill \cr
\,{\rm{vin}} = 2k\,\,\,\,\,\, \to \,\,\,\,\,\,2k \le 7\,\,\, \Rightarrow \,\,\,k \le 3{1 \over 2} \hfill \cr
\,{\rm{wat}} = k \hfill \cr} \right.$$
$$?\,\,:\,\,\left( {3k + 2k + k} \right)\,\,{\rm{where}}\,\,k = 2{2 \over 3}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = 6\left( {2 + {2 \over 3}} \right) = 12 + 4 = 16$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

Like this post

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Dec 10, 2018 9:56 am

BTGmoderatorLU wrote:Oil, vinegar, and water are mixed in a 3 to 2 to 1 ratio to make salad dressing. If Larry has 8 cups of oil, 7 cups of vinegar, and access to any amount of water, what is the maximum number of cups of salad dressing he can make with the ingredients he has available, if fractional cup measurements are possible?

A. 12
B. 13
C. 14
D. 15
E. 16

GIVEN: oil: vinegar : water = 3 : 2 : 1

Let's first try to use ALL 8 cups of oil
Take 3 : 2 : 1 and multiply all 3 parts by 8/3 to get the EQUIVALENT ratio 8 : 16/3 : 8/3
Simplify to get: 8 : 5 1/3 : 2 2/3
So, in this case, the dressing is comprised of 8 cups of oil, 5 1/3 cups of vinegar, and 2 2/3 cups of water
Notice that we have enough vinegar to make this batch.

8 cups + 5 1/3 cups + 2 2/3 cups = 16 cups
So, the TOTAL volume = 16 cups

IMPORTANT: Notice that 16 is the biggest answer choice.
This means we need not explore what happens when we try to use ALL 7 cups on the vinegar, since the answer choices tell us that we will NOT get a value greater than 16

Answer: E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8157; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Fri Mar 15, 2019 5:37 pm

BTGmoderatorLU wrote:Source: Manhattan Prep

Oil, vinegar, and water are mixed in a 3 to 2 to 1 ratio to make salad dressing. If Larry has 8 cups of oil, 7 cups of vinegar, and access to any amount of water, what is the maximum number of cups of salad dressing he can make with the ingredients he has available, if fractional cup measurements are possible?

A. 12
B. 13
C. 14
D. 15
E. 16

The OA is E.

We can create the ratio of oil : vinegar : water = 3x : 2x : x

Since Larry has 8 cups of oil, we have:

3x = 8

x = 8/3 = 2 â…”

Since Larry has 7 cups of vinegar, we have:

2x = 7

x = 7/2 = 3.5

We see that we must use the smaller of the two values of x since, if we used 3.5 for x, we would need to have 3 x 3.5 = 10.5 cups of oil (but we have only 8 cups of oil).

Since the total number of cups of dressing is 3x + 2x + x = 6x and x = 8/3, the total number of cups of dressing that can be made is 8/3 x 6 = 16 cups.

Answer: E

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

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review