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If the average (arithmetic mean) of six different numbers is 25, how many of the numbers are greater than 25?

(1) None of the six numbers is greater than 50.

(2) Three of the six numbers are 7, 8, and 9, respectively.

I have a question , if the problem statement states that there are six distinct number as in this question, shall we consider positive numbers only or negative numbers too?

If the average (arithmetic mean) of six different numbers is 25, how many of the numbers are greater than 25?

(1) None of the six numbers is greater than 50.

(2) Three of the six numbers are 7, 8, and 9, respectively.

I have a question , if the problem statement states that there are six distinct number as in this question, shall we consider positive numbers only or negative numbers too?

A number can be any real number - positive integer, negative integer, decimal etc

GMAT often uses the terminology of integers to be more specific "positive integer", "non negative integer", "negative integer" etc. Anyway, negative integers don't really have any role to play in this question.

Statement 1: None of the six numbers is greater than 50. It is possible that only 1 number is greater than 25 e.g. 20, 21, 22, 23, 24, 40 It is possible that only 2 numbers are greater than 25 e.g. 21, 22, 23, 24, 29, 31 etc Not sufficient

Statement 2: Three of the six numbers are 7, 8, and 9, respectively. It is possible that only 1 number is greater than 25 e.g. 7, 8, 9, 24, 25, 75 It is possible that only 2 numbers are greater than 25 e.g. 7, 8, 9, 25, 41, 60 etc Not sufficient

Both together, 7, 8 and 9 are 18, 17 and 16 less than 25 respectively. To get the average of 25, the other 3 numbers should together make up this deficit of 18+17+16 = 51. Since no number can be greater than 50, any one number can make up the deficit of at most 25. To make up the deficit of 51, we need at least 3 numbers. Hence, we can say that 3 numbers will be greater than 25. Answer (C) _________________

Both together, 7, 8 and 9 are 18, 17 and 16 less than 25 respectively. To get the average of 25, the other 3 numbers should together make up this deficit of 18+17+16 = 51. Since no number can be greater than 50, any one number can make up the deficit of at most 25. To make up the deficit of 51, we need at least 3 numbers. Hence, we can say that 3 numbers will be greater than 25. Answer (C)

Hi Karishma, I am unable to understand the highlighted part above-Could you please elaborate a little ? Also how do you go about plugging numbers leading up to a specific average(like this question 25) without spending much time ? is there a techinque you could share with us ? This type of sum always gives me a brain freeze ; I'd be happy if any member can share other similar Stats problems.

Both together, 7, 8 and 9 are 18, 17 and 16 less than 25 respectively. To get the average of 25, the other 3 numbers should together make up this deficit of 18+17+16 = 51. Since no number can be greater than 50, any one number can make up the deficit of at most 25. To make up the deficit of 51, we need at least 3 numbers. Hence, we can say that 3 numbers will be greater than 25. Answer (C)

Hi Karishma, I am unable to understand the highlighted part above-Could you please elaborate a little ? Also how do you go about plugging numbers leading up to a specific average(like this question 25) without spending much time ? is there a techinque you could share with us ? This type of sum always gives me a brain freeze ; I'd be happy if any member can share other similar Stats problems.

Say the avg of 6 numbers is 25. The numbers are: 7, 8, 9, 25, 25, m

What is m? When you calculate, you will find that m = 76 i.e. it will be 51 more than 25. Why? Because 7, 8 and 9 give a total deficit of 51.

So the numbers can be 7, 8, 9, 25, 25, 76 (One number is greater than 25) or 7, 8, 9, 25, 50, 51 (Again, 51 is split into 25 and 26 and added to 25 to make two numbers greater than 25) Since no number can be greater than 50, we will need to split 51 into 3 different numbers: e.g. 2, 24, 25 so you get 7, 8, 9, 27, 49, 50 (All 3 numbers are greater than 25) _________________

Both together, 7, 8 and 9 are 18, 17 and 16 less than 25 respectively. To get the average of 25, the other 3 numbers should together make up this deficit of 18+17+16 = 51. Since no number can be greater than 50, any one number can make up the deficit of at most 25. To make up the deficit of 51, we need at least 3 numbers. Hence, we can say that 3 numbers will be greater than 25. Answer (C)

Hi Karishma, I am unable to understand the highlighted part above-Could you please elaborate a little ? Also how do you go about plugging numbers leading up to a specific average(like this question 25) without spending much time ? is there a techinque you could share with us ? This type of sum always gives me a brain freeze ; I'd be happy if any member can share other similar Stats problems.

Thanks

Another way to look at it: the sum of the other three numbers is 6*25-(7+8+9)=150-24=126. If none of the numbers can be greater than 50, and because 50+50+26=126, we can deduce that not even one of those three numbers can be smaller than 25, or in other words, all three must be greater than 25. _________________

PhD in Applied Mathematics Love GMAT Quant questions and running.