A soda machine sells both bottles and cans, and no other items. Bottles cost $1.50 each, while cans cost $0.75 each. If on one day, the soda machine sold 250 total beverages and yielded $315, how many more bottles than cans were sold?
A) 60
B) 80
C) 90
D) 115
E) 170
The OA is the option C .
What is the best approach for solving this PS question? Could someone give me an explanation here? Thanks.
A soda machine sells both bottles and cans, and no other
This topic has expert replies
- GMATGuruNY
- 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
Price per bottle = 150 cents.VJesus12 wrote:A soda machine sells both bottles and cans, and no other items. Bottles cost $1.50 each, while cans cost $0.75 each. If on one day, the soda machine sold 250 total beverages and yielded $315, how many more bottles than cans were sold?
A) 60
B) 80
C) 90
D) 115
E) 170
Price per can = 75 cents.
Average price for the MIXTURE of bottles and cans = (total revenue)/(total number of beverages) = (315 dollars)/(250 beverages) = 63/50 dollars = 126/100 dollars = 126 cents.
To determine the ratio of bottles to cans, we can use ALLIGATION.
Step 1: Plot the 3 prices on a number line, with the prices for bottles and canes on the ends and the price for the mixture in the middle.
B 150---------------------126----------------------75 C
Step 2: Calculate the distances between the averages.
B 150---------51---------126---------24---------75 C
Step 3: Determine the ratio in the mixture.
The ratio of bottles to cans is equal to the RECIPROCAL of the distances in red.
B:C = 24:51 = 8:17 = 80:170.
The ratio in blue implies that B=80 and C=170, for a total of 250 beverages.
Thus:
C-B = 170-80 = 90.
The correct answer is C.
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
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
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Let B = # of bottles soldVJesus12 wrote:A soda machine sells both bottles and cans, and no other items. Bottles cost $1.50 each, while cans cost $0.75 each. If on one day, the soda machine sold 250 total beverages and yielded $315, how many more bottles than cans were sold?
A) 60
B) 80
C) 90
D) 115
E) 170
Let C = # of cans sold
If on one day, the soda machine sold 250 total beverages...
We can write: B + C = 250
...and yielded $315.
So: 1.5B + 0.75C = 315
We can eliminate the decimals by multiplying both sides by 4 to get: 6B + 3C = 1260
How many more bottles than cans were sold?
So, we must determine the value of B - C.
We have the system:
B + C = 250
6B + 3C = 1260
When we solve this system for B and C , we get: B = 170 and C = 80
So, B - C = 170 - 80 = 90
Answer: C
Cheers,
Brent
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Hi VJesus12,
We're told that a soda machine sells both bottles and cans, and no other items. Bottles cost $1.50 each, while cans cost $0.75 each and in one day, the soda machine sold 250 total beverages and yielded $315. We're asked how many MORE bottles than cans were sold. This question can be approached in a number of different ways; here's how you can use a 'comparison' to get to the correct answer.
While we know that some bottles and some cans were sold, IF all 250 items sold were bottles, then THAT revenue would be (250)($1.50) = (125)($3) = $375.
For each bottle that we 'trade' for a can, we 'lose' $0.75 from the total revenue. To get $375 down to $315, we have to 'lose' $60 (in $0.75 increments). That would be...
60/.75 =
120/1.5 =
240/3 =
80 cans
With 250 items sold, there would be 80 cans and 170 bottles - and that would be 170 - 80 = 90 MORE bottles than cans.
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
We're told that a soda machine sells both bottles and cans, and no other items. Bottles cost $1.50 each, while cans cost $0.75 each and in one day, the soda machine sold 250 total beverages and yielded $315. We're asked how many MORE bottles than cans were sold. This question can be approached in a number of different ways; here's how you can use a 'comparison' to get to the correct answer.
While we know that some bottles and some cans were sold, IF all 250 items sold were bottles, then THAT revenue would be (250)($1.50) = (125)($3) = $375.
For each bottle that we 'trade' for a can, we 'lose' $0.75 from the total revenue. To get $375 down to $315, we have to 'lose' $60 (in $0.75 increments). That would be...
60/.75 =
120/1.5 =
240/3 =
80 cans
With 250 items sold, there would be 80 cans and 170 bottles - and that would be 170 - 80 = 90 MORE bottles than cans.
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
GMAT/MBA Expert
- Jeff@TargetTestPrep
- GMAT Instructor
- Posts: 1462
- Joined: Thu Apr 09, 2015 9:34 am
- Location: New York, NY
- Thanked: 39 times
- Followed by:22 members
We can let b = the number of bottles of soda sold and c = the number of cans of soda sold, and create the equations:VJesus12 wrote:A soda machine sells both bottles and cans, and no other items. Bottles cost $1.50 each, while cans cost $0.75 each. If on one day, the soda machine sold 250 total beverages and yielded $315, how many more bottles than cans were sold?
A) 60
B) 80
C) 90
D) 115
E) 170
b + c = 250
and
1.5b + 0.75c = 315
Multiplying the first equation by 3, we have 3b + 3c = 750.......[Eq. 1]
Multiplying the second equation by 4, we have 6b + 3c = 1260...... [Eq. 2]
Subtracting Eq. 1 from Eq. 2, we have 3b = 510. So b = 510/3 = 170.
Since b + c = 250, so c = 250 - 170 = 80.
Therefore, the number of bottles sold is 170 - 80 = 90 more than the number of cans sold.
Answer: C
Jeffrey Miller
Head of GMAT Instruction
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews