Average Question!

[Strongt]

If x is a prime number, and x-1 is the median of the set {x-1, 3x +3, 2x-4}, then what is the average (arithmetic mean) of the set?

Answer is [spoiler] 10/3 [/spoiler]

would anyone please explain to me the logic in simple terms?


Thank you,

[therealtomrose]

I'll write an answer, but first: This is not a real GMAT question, beware. You also did not supply answer choices, so I'm conjecturing it's PS?

The game here is to find the prime numbers that satisfy the given constraints.

The main constraint supplied is that there are three numbers in a set, each defined by a given expression, and one of them (x-1) must be the median.

There are in fact two prime numbers that satisfy the constraint: 2 and 3. Just try plugging them in and you'll see. Only for the numbers 2 and 3, does (x-1) become the median term. For all other primes, (x-1) will be the smallest term with no repeating terms.

There are two solutions to this problem:
When you plug in 2, the arithmetic mean of the terms becomes 10/3
When you plug in 3, the arithmetic mean of the terms becomes 16/3

[Anurag@Gurome]

If x is a prime number, and x-1 is the median of the set {x-1, 3x +3, 2x-4}, then what is the average (arithmetic mean) of the set?

Answer is [spoiler] 10/3 [/spoiler]

would anyone please explain to me the logic in simple terms?


Thank you,

Average of the given set {x-1, 3x +3, 2x-4} = {(x - 1) + (3x + 3) + (2x - 4)}/3 = (6x - 2)/3
Now if you know the answer choices, one by one you can put them equal to (6x - 2)/3 and see which of them gives you a prime number.
Since you have the answer is 10/3, you can check this: (6x - 2)/3 = 10/3 implies 6x - 2 = 10 or x = 2, which is a prime number.

[force5]

yes correct i think these are approach questions. but i would really suggest posters to check and mention the source and write complete questions. This helps other members to think clearly. As in this question there could be two answers.

[Strongt]

I'll write an answer, but first: This is not a real GMAT question, beware. You also did not supply answer choices, so I'm conjecturing it's PS?

The game here is to find the prime numbers that satisfy the given constraints.

The main constraint supplied is that there are three numbers in a set, each defined by a given expression, and one of them (x-1) must be the median.

There are in fact two prime numbers that satisfy the constraint: 2 and 3. Just try plugging them in and you'll see. Only for the numbers 2 and 3, does (x-1) become the median term. For all other primes, (x-1) will be the smallest term with no repeating terms.

There are two solutions to this problem:
When you plug in 2, the arithmetic mean of the terms becomes 10/3
When you plug in 3, the arithmetic mean of the terms becomes 16/3

First of all, I appreciate your well explained answer.
as far as the question, I got it from the Beat the GMAT Practice Questions.

I thought they were the closest to the real GMAT. I was looking for GMAT practice questions with video explainations.

Do you suggest any other source for practice questions with video tutorials


Thank you,

[therealtomrose]

Practice questions with video tutorials is a TALL order. BTG is the first time I have ever seen this broken down by question. MGMAT has recordings of questions solved as part of the online course content. That's basically what the online course content is. Of course, you're paying for a course (several hundred) vs. a q-bank. Also, the MGMAT videos are not broken down by question like the BTG q-bank is.

The single greatest source of questions is, of course, the OG. I don't think that there is really a compelling need for questions beyond the OG unless those questions are presented in a unique format.

Adaptive tests are obviously a compelling format: GMAT Prep, and MGMAT are great sources of questions in that format.
Video explanations are amazing, and as far as I know, BTG is the only source of those currently.