Data Sufficiency Problem

This topic has expert replies
Newbie | Next Rank: 10 Posts
Posts: 4
Joined: Thu Aug 24, 2017 5:32 am
Location: Alkhobar, Saudi Arabia

Data Sufficiency Problem

by TariqOmar » Wed May 09, 2018 3:26 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Quick Sell Outlet sold a total of 40 televisions, each of which was either a Model P television or a Model Q television, each model P television sold for $p and each Model Q sold for $q. The average (arithmetic mean) selling price of the 40 televisions was $141. How many of the 40 televisions were Model P televisions?

(1) The Model P televisions sold for $30 less than the Model Q televisions.
(2) Either p=120 or q=120.

Correct answer: C.

I was able to solve this problem but it took me a considerable amount of time and certainly not under 2 minutes. I am interested to see how the experts here will solve this problem in the shortest amount of time possible.

Thank you.

User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

P and Q

by GMATGuruNY » Wed May 09, 2018 4:05 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

TariqOmar wrote:Quick Sell Outlet sold a total of 40 televisions, each of which was either a Model P television or a Model Q television, each model P television sold for $p and each Model Q sold for $q. The average (arithmetic mean) selling price of the 40 televisions was $141. How many of the 40 televisions were Model P televisions?

(1) The Model P televisions sold for $30 less than the Model Q televisions.
(2) Either p=120 or q=120.
Since the average price = 141, one price must be LESS than 141, while the other price must be GREATER than 141.

Statement 1: Model P sold for $30 less than Model Q.
Thus, p< 141, while q>141.
Check the ONLY case that also satisfies statement 2:

Case 1: p=120 and q=150.
To evaluate this case, use ALLIGATION -- a very efficient way to handle MIXTURE PROBLEMS.

Step 1: Plot the 3 prices on a number line, with the prices for the two models on the ends and the average price in the middle.
P 120-------------141------------150 Q

Step 2: Calculate the distances between the prices.
P 120-----21------141-----9------150 Q

Step 3: Determine the ratio in the mixture.
The required ratio of Model P televisions to Model Q televisions is equal to the RECIPROCAL of the distances in red.
P:Q = 9:21 = 3:7 = 12:28.
In this case, P=12 and Q=28, for a total of 40 televisions.

Case 2: Reverse the distances from Case 1 and plot the new prices for P and Q on the ends of the number line
P 132-----9------141-----21------162 Q

Here, P:Q = 21:9 = 7:3 = 28:12.
Thus, P=28 and Q=12, for a total of 40 televisions.

Since P can be different values, INSUFFICIENT.

Statement 2: Either p = 120 or q = 120.
Case 1 also satisfies statement 2.

Case 3: If P and Q swap positions on the number line in Case 1 -- so that Q=120 and P=150 -- the alligation will yield the following:
Q : P = 28:12.
Thus, Q=28 and P=12, for a total of 40 televisions.

Since P can be different values, INSUFFICIENT.

Statements combined:
Only Case 1 satisfies both statements.
In Case 1, P=12.
SUFFICIENT.

The correct answer is C.

For two similar problems, check here:

https://www.beatthegmat.com/ratios-fract ... 15365.html
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 7222
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

Re: Data Sufficiency Problem

by Scott@TargetTestPrep » Sat Aug 01, 2020 5:52 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

TariqOmar wrote:
Wed May 09, 2018 3:26 am
Quick Sell Outlet sold a total of 40 televisions, each of which was either a Model P television or a Model Q television, each model P television sold for $p and each Model Q sold for $q. The average (arithmetic mean) selling price of the 40 televisions was $141. How many of the 40 televisions were Model P televisions?

(1) The Model P televisions sold for $30 less than the Model Q televisions.
(2) Either p=120 or q=120.

Correct answer: C.
Solution:

Statement One Alone:

the Model P televisions sold for $30 less than the Model Q televisions

Suppose 20 Model P televisions were sold for $126 each and suppose 20 Model Q televisions were sold for $156 each. Then, the average selling price of 40 televisions is (20*126 + 20*156)/40 = (2,520 + 3,120)/40 = 5,640/40 = $141. In this scenario, 20 of the 40 televisions were Model P.

Suppose, on the other hand, that 28 Model P televisions were sold for $132 and 12 Model Q televisions were sold for $162. Then, the average selling price of the 40 televisions is (28*132 + 12*162)/40 = (3,696 + 1,944)/40 = 5,640/40 = $141. In this scenario, 28 of the 40 televisions were Model P.

Statement one alone is not sufficient. Eliminate answer choices A and D.

Statement Two Alone:

Either p=120 or q=120

Suppose 10 model P televisions were sold for $120 and 30 model Q televisions were sold for $148. Then, the average selling price of a television was (10*120 + 30*148)/40 = (1,200 + 4,440)/40 = 5,640/40 = $141. In this scenario, 10 model P televisions were sold.

Suppose, on the other hand, that 30 model P televisions were sold for $120 and 10 model Q televisions were sold for $204. Then, the average selling price of a television was (30*120 + 10*204)/40 = (3,600 + 2,040)/40 = 5,640/40 = $141. In this scenario, 30 model P televisions were sold.

Statement two alone is not sufficient. Eliminate answer choice B.

Statements One and Two Together:

If Model Q television sells for $120, then a Model P television must sell for 120 - 30 = $90 since statement one tells us that a Model P television sells for $30 less than a Model Q television. Then, the average selling price of a television will be between 90 and 120, which is inconsistent with the given fact that the average selling price of a television is $141. Thus, it must be true that a Model P television sells for $120 and a Model Q television sells for 120 + 30 = $150.

If we let n be the number of Model P televisions sold, then the number of Model Q televisions sold must be 40 - n. We can create the following equation:

(120*n + 150*(40 - n))/40 = 141

120n + 6,000 - 150n = 141*40

-30n = 5,640 - 6,000

-30n = -360

n = 12

So, the number of Model P televisions sold was 12. Statements one and two together are sufficient.

Answer: C


Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

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

ImageImage