Tom, Jane, and Sue each purchased a new house. The average

We have three prices: a, b and c. (a+b+c)/3=120
The median price would be: the second biggest.
a<=b<=c --> median price b.

(1) One of the prices is 110, less than average of 120. It's possible 110 to be a or b price, so insufficient.

(2) One of the prices is 120 equals to average. It must be the b price, as it's not possible this price to be lowest or highest because it's equals to the average, only 2 cases a<120<c or a=b=c=120

Answer B.
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By defintion, Median divides the distribution of values such that exactly half lie below the median and half above the median. example, given 2,5,9,50 (notice that to calculate median, the values must first be arranged in ascending order), the median is (5+9)/2=7. meaning below 7 like two values and above 7 lie two values.

By contrast, Mean or average doesn't necessarily do that. It is affected by the magnitude of each value. if one value is extreme, the mean or average shifts towards that extremity. In the above example, the average is about 16. half of the numbers aren't less than this 16, there are three numbers less than 16. similarly, half aren't above 16, only one i.e. 50 is above 16.

When you are told that there are only three values and one of them is actually the mean or the average, what's that really saying? if all three numbers are different, you know that the average has to fall somewhere between the smallest and the biggest number. and we are given that this middle number is 120,000 and also happens to be the mean. it doesn't matter now what the other two numbers are. this becomes an evenly spaced set of three numbers. the smaller the smallest number, the larger the largest number has to be to keep the average 120,000 constant.

So as a rule, you can remember that for any evenly spaced set, the mean is always equal to the median. example, 2,4,6 or 10,20,30,40.

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Did not you get B?
If one of the house is equal to mean, then it is the median because other 2 houses (both) cannot be > 120,000 or < 120,000. The wrost case, is one is < 120,000 and the other is >120,000.

So B is suff....

Mean and one of the values out of 3 values are same, hence median has to be equal to mean.

Ans. is B.

if one of the price is 110, aka not avg 120, wouldn't it be "a"? Since there are 3 numbers, average is 120, anything less than average will be "a"? How can 110 possibly be b?

Try to construct different scenarios, you'll see that it's not that hard:

Sum is 120*3=360.
110+120+130=360;
100+110+150=360.
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You have no idea how long I've been looking for a more well explained answer, thank you so much!!! Everyone else justs calculates the 360-250 and shows examples, this Issa much more intuitive when you pair it with a bell curve, thank you thank you thank uou

Is the above a rule general to all sets?

Could someone answer this please

Tom, Jane, and Sue each purchased a new house. The average (arithmetic mean) price of the three houses was $120,000. What was the median price of the three houses?

(1) The price of Tom’s house was $110,000.
(2) The price of Jane’s house was $120,000.

They are asking us for the median house price, out of the group of three houses.

Given information:
(T+J+S)/3= 120,000.

Statement 1 is telling us that T = 110,000. This means that the other two houses has to have a mean of 130,000. This could be any two prices that deviate with the same amount from 130,000.

Statement one is therefore insufficient. We're looking for the house with the median price and that could be 110,000 ->130,000. We're not sure which one it is currently.

Statement 2 gives us that Jane's house is 120,000. This is the same as the mean and even though we might think that we need info on another house, we're actually already done.

Together with the information given in the question stem we've got the following:

(T +120,000+ S)/3=120,000.

(T+S)/2 = 120,000.

If T is above 120,000 then S has to be equally far from 120,000 in the negative direction. This means that either all of the houses has the mean price of 120,000 or:

T=120,000+x
J=120,000
S=120,000-x

Whatever x is(zero included) we still know that the median will be 120,000.

Hence the answer is B.

Don't fall for the trap here. This question is not about the math. Many explanations of Quantitative questions focus blindly on the math, but remember: the GMAT is a critical-thinking test. For those of you studying for the GMAT, you will want to internalize strategies that actually minimize the amount of math that needs to be done, making it easier to manage your time. The tactics I will show you here will be useful for numerous questions, not just this one. My solution is going to walk through not just what the answer is, but how to strategically think about it. Ready? Here is the full “GMAT Jujitsu” for this question:

Many people spend too much time on Data Sufficiency questions because they think they need to solve to the bitter end. The question asks “What was the median price of the three houses?” This is a "Specific Value" question – a very common structure for Data Sufficiency problems. If you can think of two situations (or two variable inputs) that are consistent with all of the problem’s constraints but come up with different answers to the question, you know a statement is insufficient. In my classes, I call this strategy “Play Both Sides.”

Let’s analyze each statement, and you will see what I mean. Statement #1 tells us that Tom’s house cost \($110,000\). Trying to “mathematize” this into a formula is unnecessary. We just need to think of two situations that would give us different answers to question. The price of Tom’s house is below the average of \($120,000\), but we don’t know the values of the other two houses, including the value of the home in the middle. Remember, median is the middle value of a set of numbers when arranged in ascending order. Now, we go through the headache of inventing specific numbers here (for example, if the three homes were valued at \($110,000\), \($120,000\), and \($130,000\), the average would be \($120,000\) – but so would three homes valued at \($1\), \($110,000\), and \($249,999\). The median values of these two sets are clearly different.) However, coming up with concrete values here is is more work than we need to do. We don’t need to do all the math to show that there are multiple possible solutions. We just need to know that multiple possible solutions COULD exist. Statement #1 is insufficient.

Statement #2 tells us that Jane’s house cost \($120,000\). The primary bait behind this statement is to trick you into turning your brain off. Statement #2 is very similar in appearance to Statement #1. The two statements sound like they are "playing the same game." But when you see similar statements in Data Sufficiency questions, you should start by looking at how the statements are different, and see if those differences are meaningful. You see, if Jane’s house is equal in value to the average, then it must be the median value in a set of three homes. We don’t know what the other two homes are valued at, but we don’t need to know. If they were all the same value, the median value would be \($120,000\). If the other two homes had different prices, then the only way to get an “average” would be to have one home be lower than \($120,000\) and one home higher. Either way, the median home stays the same. Statement #2 is totally sufficient.

The answer is “B”.

Now, let’s look back at this problem through the lens of strategy. This question can teach us patterns seen throughout the GMAT. First, notice that this problem is much more about logic and critical-thinking than it is about math. This is especially true with problems involving statistics. Such problems trap you into thinking that you need all the information. But you only need enough information to prove or disprove sufficiency. If you can think of two situations (or two variable inputs) that are consistent with all of the problem’s constraints but come up with different answers to the question, you know a statement is insufficient. Second, similar-looking statements in Data Sufficiency questions often bait you into thinking that you must treat each statement in the exact same way. Rather than thinking linearly and assuming because they sound the same that they play the same game, the trick is to leverage the differences between the statements. That is how you think like the GMAT.

Tom, Jane, and Sue each purchased a new house. The average (arithmetic mean) price of the three houses was $120,000. What was the median price of the three houses?
Given: t+j+s = 3*120k

(1) The price of Tom’s house was $110,000. --> insufficient: j +s = 3*120k - 110k = 250k, if j=s, j=s=125k, median =125k, but if s>j i.e. s =4j, j=50k, s = 200k, median=110k
(2) The price of Jane’s house was $120,000. --> sufficient: t+s = 3*120k-120k = 240k, if j=s, j=s=120k, median =120k, but if s>j i.e. s =2j, j=80k, s =160k, median=120k --> so the median is always 120k

So answer: B

Solution:

Question Stem Analysis:

We are given that the average price of 3 houses is $120,000, which means that the sum of the 3 house prices is $360,000. We are to determine the median price of the 3 houses. Recall that the median of a set of 3 values is the middle value.

Statement One Alone:

If Tom paid $110,000 and Jane paid $90,000 and Sue paid $160,000, then the average would still be 360,000/3 = $120,000. In this case, the median price would be $110,000.

If Tom paid $110,000 and Jane paid $130,000 and Sue paid $120,000, the average would still be 360,000/3 = $120,000. In this case, however, the median price would be $120,000.

Statement one is not sufficient.

Statement Two Alone:

Jane paid $120,000 for her house. This means that the other two individuals could not both have paid more than $120,000 OR that they both paid less than $120,000 because, in either of these cases, the average house price could not equal $120,000. Therefore, we see that either of two situations could apply:

1. The first case is that all 3 paid $120,000. This would keep the average price at $120,000, and the median price would be $120,000.

2. The second case is that one paid less than $120,000, and the other paid more than $120,000. We know that Jane paid $120,000. Thus, no matter what the other two paid for their houses, Jane’s purchase of $120,000 would be the median price.

Statement two is sufficient.

Answer: B
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Answer: Option B

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Given: The average (arithmetic mean) price of the three houses was $120,000.
This means (sum of the three house values)/3 = 120,000
Multiply both sides by 3 to get: sum of the three house values = 360,000

Target question: What was the median price of the three houses?

Statement 1: The price of Tom’s house was $110,000.
There are several scenarios that satisfy statement 1. Here are two:
Case a: The 3 house values are $110,000, $120,000 and $130,000. In this case, the answer to the target question is the median house price is $120,000
Case b: The 3 house values are $110,000, $110,000 and $140,000. In this case, the answer to the target question is the median house price is $110,000
Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The price of Jane’s house was $120,000
Important: $120,000 is the average price of the 3 houses.
Since one house is valued at $120,000, there are two possible cases:
Case a: All three house prices are the same: $120,000, $120,000 and $120,000. In this case, the answer to the target question is the median house price is $120,000
Case b: All three house prices are the NOT same. In order for the sum of the 3 values to be 360,000, one value must be less than $120,000, and the other value must be greater than $120,000. So, the three house prices are: less than $120,000, $120,000, and greater than $120,000. In this case, the answer to the target question is the median house price is $120,000
In both possible cases, the answer to the target question is the same: the median house price is $120,000
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent

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