At a fruit stand, apples can be purchased for $0.15 each and pears for $0.20 each. At these rates a bag of apples and pears was purchased for $3.80. If the bag contained exactly 21 pieces of fruit how many were pears?
I tried to use alligation method for solving this problem.
First, I divide the prices of apples and fruits to find the ratio of prices. The ratio of prices of peach to apples is 4:3.So,
apple------------peach
3 ----3.8------- 4
or 1:4
Therefore, p:p+a is 4:5=p:21.Therefore p is 84/5. My solution leads to the wrong answer. Would you please explain the reason?
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
alligation
This topic has expert replies
-
talaangoshtari
- Master | Next Rank: 500 Posts
- Posts: 154
- Joined: Wed May 21, 2014 4:29 am
- Thanked: 8 times
- Followed by:1 members
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
Here's an algebraic solution:talaangoshtari wrote:At a fruit stand, apples can be purchased for $0.15 each and pears for $0.20 each. At these rates a bag of apples and pears was purchased for $3.80. If the bag contained exactly 21 pieces of fruit how many were pears?
Let A = the number of apples purchased
Let P = the number of pears purchased
A bag of apples and pears was purchased for $3.80
So, we get: 0.15A + 0.2B = 3.80
The bag contained exactly 21 pieces of fruit
So, A + P = 21
We now have a system of two equations:
0.15A + 0.2B = 3.80
A + P = 21
For the top equation, multiply both sides by 100.
For the bottom equation, multiply both sides by 15.
We get:
15A + 20P = 380
15A + 15P = 315
Subtract the bottom equation from the top equation to get:
5P = 65
Solve: P = 13
Answer: 13 pears
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
-
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
The GMAT would include answer choices:
When the correct answer choice is plugged in, the total price will be 380 cents.
Answer choice D: 12 pears, implying 9 apples
Total price for 12 pears and 9 apples = 12(20) + 9(15) = 375 cents.
Too small.
Eliminate D.
For the total price to increase, more PEARS must be purchased, since pears are more expensive than apples.
The correct answer is E.
We can PLUG IN THE ANSWERS, which represent the number of pears.At a fruit stand, apples can be purchased for $0.15 each and pears for $0.20 each. At these rates a bag of apples and pears was purchased for $3.80. If the bag contained exactly 21 pieces of fruit how many were pears?
8
10
11
12
13
When the correct answer choice is plugged in, the total price will be 380 cents.
Answer choice D: 12 pears, implying 9 apples
Total price for 12 pears and 9 apples = 12(20) + 9(15) = 375 cents.
Too small.
Eliminate D.
For the total price to increase, more PEARS must be purchased, since pears are more expensive than apples.
The correct answer is E.
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
-
DavidG@VeritasPrep
- Legendary Member
- Posts: 2663
- Joined: Wed Jan 14, 2015 8:25 am
- Location: Boston, MA
- Thanked: 1153 times
- Followed by:128 members
- GMAT Score:770
talaangoshtari,
If you wanted to use the approach you outlined, you'd have to find the overall average price for the fruit purchased. In this case that number ends up being a decidedly unfriendly: 3.80/21 = .18 (rounded to the nearest hundredths)
Now you'd have
apples--------- pears
.15-----.18----.20
Giving you, approximately, a 2:3 ratio in favor of pears.
Apples: 2x
Pears: 3x
Total: 21
2x + 3x = 21
5x = 21. x = a little more than 4.
Pears: 3 * (a little more than 4) = a little more than 12. Round up to 13.
If you wanted to use the approach you outlined, you'd have to find the overall average price for the fruit purchased. In this case that number ends up being a decidedly unfriendly: 3.80/21 = .18 (rounded to the nearest hundredths)
Now you'd have
apples--------- pears
.15-----.18----.20
Giving you, approximately, a 2:3 ratio in favor of pears.
Apples: 2x
Pears: 3x
Total: 21
2x + 3x = 21
5x = 21. x = a little more than 4.
Pears: 3 * (a little more than 4) = a little more than 12. Round up to 13.
Last edited by DavidG@VeritasPrep on Mon May 18, 2015 6:42 am, edited 1 time in total.
-
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
Alternate approach:
Price for each apple = 15.
Price for each pear = 20.
Average price for the MIXTURE of apples and pears = 380/21.
The following approach is called ALLIGATION -- a very efficient way to handle MIXTURE PROBLEMS.
Step 1: Put the prices over a COMMON DENOMINATOR
Price for each apple = (15*21)/21 = 315/21.
Price for each pear = (20*21)/21 = 420/21.
Average price for the MIXTURE of apples and pears = 380/21.
Step 2: Plot the 3 numerators on a number line, with the numerators for A and P on the ends and the numerator for the mixture in the middle.
A 315-----------380-----------420 W
Step 3: Calculate the distances between the numerators.
A 315----65-----380----40-----420 P
Step 4: Determine the ratio in the mixture.
The required ratio of A to P is equal to the RECIPROCAL of the distances in red.
A : P = 40:65 = 8:13.
Thus, A=8 and P=13, for a total of 21 pieces of fruit.
For two similar problems, check here:
https://www.beatthegmat.com/ratios-fract ... 15365.html
Price for each apple = 15.
Price for each pear = 20.
Average price for the MIXTURE of apples and pears = 380/21.
The following approach is called ALLIGATION -- a very efficient way to handle MIXTURE PROBLEMS.
Step 1: Put the prices over a COMMON DENOMINATOR
Price for each apple = (15*21)/21 = 315/21.
Price for each pear = (20*21)/21 = 420/21.
Average price for the MIXTURE of apples and pears = 380/21.
Step 2: Plot the 3 numerators on a number line, with the numerators for A and P on the ends and the numerator for the mixture in the middle.
A 315-----------380-----------420 W
Step 3: Calculate the distances between the numerators.
A 315----65-----380----40-----420 P
Step 4: Determine the ratio in the mixture.
The required ratio of A to P is equal to the RECIPROCAL of the distances in red.
A : P = 40:65 = 8:13.
Thus, A=8 and P=13, for a total of 21 pieces of fruit.
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
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
-
Mo2men
- Legendary Member
- Posts: 712
- Joined: Fri Sep 25, 2015 4:39 am
- Thanked: 14 times
- Followed by:5 members
GMATGuruNY wrote:The GMAT would include answer choices:
Alternative way to think about questionAt a fruit stand, apples can be purchased for $0.15 each and pears for $0.20 each. At these rates a bag of apples and pears was purchased for $3.80. If the bag contained exactly 21 pieces of fruit how many were pears?
8
10
11
12
13
Price/apple(A)=15 cent
Price/Pear (P)= 20 cent
Total = 380 cent
15A+ 20P =380
(15A) must be multiple of 10 as (20P) is multiple of 10 and total is multiple of 10.
so (15A) could be multiple of 10 when multiplied by even number. It implied that pear is odd number (21-even=odd) So Eliminate choices A,B and D.
Check C....15*10 + 20*11=375 does nt equal to 380. Eliminate C
Only answer: E
Is my reasoning correct?
Last edited by Mo2men on Sat May 13, 2017 4:18 pm, edited 1 time in total.
-
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
Nice work!Mo2men wrote:Alternative way to think about questionAt a fruit stand, apples can be purchased for $0.15 each and pears for $0.20 each. At these rates a bag of apples and pears was purchased for $3.80. If the bag contained exactly 21 pieces of fruit how many were pears?
8
10
11
12
13
Price/apple(A)=15 cent
Price/Pear (P)= 20 cent
Total = 380 cent
15A+ 20P =380
(15A) must be multiple of 10 as (20P) is multiple of 10 and total is multiple of 10.
so (15A) could be multiple of 10 when multiplied by even number. It implied that pear is odd number (21-even=odd) So Eliminate choices A,B and D.
Check D....15*10 + 20*11=375 does nt equal to 380. Eliminate C
Only answer: E
Is my reasoning correct?
One typo: the letter in red should be not D but 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
