[GMAT math practice question]
If the average (arithmetic mean) price of apples, bananas and oranges is $3.00 per pound, what is their median price?
1) The price of apples is $3.00 per pound.
2) The price of bananas is $2.97 per pound.
If the average (arithmetic mean) price of apples, bananas an
This topic has expert replies
- Max@Math Revolution
- Elite Legendary Member
- Posts: 3991
- Joined: Fri Jul 24, 2015 2:28 am
- Location: Las Vegas, USA
- Thanked: 19 times
- Followed by:37 members
Math Revolution
The World's Most "Complete" GMAT Math Course!
Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
[Course] Starting $79 for on-demand and $60 for tutoring per hour and $390 only for Live Online.
Email to : [email protected]
-
- Legendary Member
- Posts: 2898
- Joined: Thu Sep 07, 2017 2:49 pm
- Thanked: 6 times
- Followed by:5 members
This is how I'd solve it, I don't know if I am wrong.[GMAT math practice question]
If the average (arithmetic mean) price of apples, bananas and oranges is $3.00 per pound, what is their median price?
1) The price of apples is $3.00 per pound.
2) The price of bananas is $2.97 per pound.
"the average (arithmetic mean) price of apples, bananas and oranges is $3.00 per pound" implies that $$\frac{a+b+o}{3}=3\ per\ pound\ \ \ \Rightarrow\ \ a+b+o=9\ per\ pound.\ $$ We need to find the values of a, b and c, to know what is their median price.
1) The price of apples is $3.00 per pound.
This implies that a=3, hence $$3+b+o=9\ per\ pound\ \ \Rightarrow\ \ b+o=6\ per\ pound.$$ Since we don't know anything about b and o, this statement is NOT SUFFICIENT.
2) The price of bananas is $2.97 per pound.
This implies that b=2.97, hence $$a+2.97+o=9\ per\ pound\ \ \Rightarrow\ \ a+o=6.3\ per\ pound.$$ Again, since we don't know anything about a and o, this statement is NOT SUFFICIENT.
Now, Using both statements together
We have that a=3 and b=2.97, hence $$3+2.97+o=9\ per\ pound\ \ \Rightarrow\ \ o=3.3\ per\ pound.$$ This implies that $$b=2.97\ \ <\ \ a=3\ \ \ \ <\ o=3.3.\ \ \ \Rightarrow\ \ The\ median\ price\ is\ 3.$$ Therefore, this case is SUFFICIENT.
Hence, the correct answer is the option C.
Please, let me know if I made a mistake.
- 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
Sum of the 3 prices = (number of prices)(average price) = 3*3 = $9.Max@Math Revolution wrote:[GMAT math practice question]
If the average (arithmetic mean) price of apples, bananas and oranges is $3.00 per pound, what is their median price?
1) The price of apples is $3.00 per pound.
2) The price of bananas is $2.97 per pound.
Statement 1: A=$3, implying that B+C = 9-3 = $6
Case 1: B=$3 and C=$3, with the result that B+C = $6
In this case, the 3 prices are as follows:
$3, $3, $3
Thus, the median price = 3.
Case 2: B<$3 and C>$3 or B>$3 and C<$3, with the result that B+C = 6
In this case, the 3 prices are as follows:
less than $3, exactly $3, more than $3
Thus, the median price = 3.
Since the median price is THE SAME in each case, SUFFICIENT.
Statement 2: A=$2.97, implying that B+C = 9-2.97 = $6.03
Case 1: B=$3 and C=$3.03, with the result that B+C = $6.03
In this case, the 3 prices are as follows:
$2.97, $3, $3.03
Thus, the median price = 3.
Case 2: B=$0.03 and C=$6, with the result that B+C = $6.03
In this case, the 3 prices are as follows:
$0.03, $2.97, $6
Thus, the median price = 2.97.
Since the median price can be different values, INSUFFICIENT.
The correct answer is A.
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
- Max@Math Revolution
- Elite Legendary Member
- Posts: 3991
- Joined: Fri Jul 24, 2015 2:28 am
- Location: Las Vegas, USA
- Thanked: 19 times
- Followed by:37 members
=>
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Since we have 3 variables (a for apples, b for bananas and o for oranges) and 1 equation ( ( a + b + o ) / 3 = 3), C is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.
This question is a new type of GMAT question. The average is provided in the original condition and the question asks for the value of the median. The same average applies for each of the conditions.
Conditions 1) & 2)
If a = 3.00 and b = 2.97, then ( a + b + o ) / 3 = 3.
So,
3.00 + 2.97 + o = 9
and
o = 3.03. Therefore, the median is 3.00.
Thus, both conditions together are sufficient.
Condition 1)
We consider three cases.
Case 1: a = b = c = 3.00
Since all prices are the same, the median is 3.00.
Case 2: b < 3.00
If b < 3.00, then we must have c > 3.00.
Therefore, the median is 3 since b < a < c.
Case 3: b > 3.00
If b > 3.00, then we must have c < 3.00.
Therefore, the median is 3 since c < a < b.
Thus, condition 1) is sufficient on its own.
Condition 2)
If a = 3.00, b = 2.97 and c = 3.03, then the median is 3.00.
If a = 2.00, b = 2.97 and c = 3.00, then the median is 2.97.
Since we don't have a unique solution, condition 2) is not sufficient on its own.
Therefore, A is the answer.
Answer: A
Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Since we have 3 variables (a for apples, b for bananas and o for oranges) and 1 equation ( ( a + b + o ) / 3 = 3), C is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.
This question is a new type of GMAT question. The average is provided in the original condition and the question asks for the value of the median. The same average applies for each of the conditions.
Conditions 1) & 2)
If a = 3.00 and b = 2.97, then ( a + b + o ) / 3 = 3.
So,
3.00 + 2.97 + o = 9
and
o = 3.03. Therefore, the median is 3.00.
Thus, both conditions together are sufficient.
Condition 1)
We consider three cases.
Case 1: a = b = c = 3.00
Since all prices are the same, the median is 3.00.
Case 2: b < 3.00
If b < 3.00, then we must have c > 3.00.
Therefore, the median is 3 since b < a < c.
Case 3: b > 3.00
If b > 3.00, then we must have c < 3.00.
Therefore, the median is 3 since c < a < b.
Thus, condition 1) is sufficient on its own.
Condition 2)
If a = 3.00, b = 2.97 and c = 3.03, then the median is 3.00.
If a = 2.00, b = 2.97 and c = 3.00, then the median is 2.97.
Since we don't have a unique solution, condition 2) is not sufficient on its own.
Therefore, A is the answer.
Answer: A
Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
Math Revolution
The World's Most "Complete" GMAT Math Course!
Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
[Course] Starting $79 for on-demand and $60 for tutoring per hour and $390 only for Live Online.
Email to : [email protected]