Average

[paresh_patil]

Is the average(arithmetic mean) of 5 different integer atleast 30?
1) Each integer is a multiple of 10
2) The sum of 5 integer is 160

Statement 2 is sufficient(a+b+c+d+e>=30*5-->150)

I need explanation for statement 1.

[Zarrolou]

a+b+c+d+e>=150

If a,b,c,d,e each is multiple of 10; the least sum of 5 different integers, multiples of 10, is:

0+10+20+30+40=100

Statement 1 is not sufficient.

(check this https://www.beatthegmat.com/is-zero-to-b ... t4268.html)

[Anju@Gurome]

Is the average(arithmetic mean) of 5 different integer atleast 30?
1) Each integer is a multiple of 10
2) The sum of 5 integer is 160

Statement 1: As the integers can be positive or negative, the mean also can be positive or negative. Hence, from this statement we can only conclude that the mean is a multiple of 10 also.
For example, consider the following two cases,

• {-20, -10, 0, 10, 20} ---> Mean = 0 < 30
  {100, 200, 300, 400, 500} ---> Mean = 300 > 30

Not sufficient

Statement 2: Mean of the integers = 160/5

Sufficient

The correct answer is B.

[GMATGuruNY]

Is the average (arithmetic mean) of 5 different positive integers at least 30?

1. Each of the integers is a multiple of 10

2. The sum of the five integers is 160

This question is from GMATPrep.
Please note the word in red, which was omitted from the OP: the actual question stem requires that the all of the integers be POSITIVE.

Statement 1: Each integer is a multiple of 10
Least possible values: 10, 20, 30, 40, 50.
When values are EVENLY SPACED, the average = the median.
Thus, the average here is 30.
Since the least possible average is 30, the average of the 5 integers must be at least 30.
SUFFICIENT.

Statement 2: Sum = 160.
Since average = sum/number, the average of the 5 integers can be determined.
SUFFICIENT.

The correct answer is D.

Please note the following:
When a GMAT problem asks about multiples, the problem is invariably restricted to POSITIVE INTEGERS.
Thus, we don't have to consider 0 (which is a multiple of every integer) or negative values.

[freyesinsb]

When the GMAT asks "at least 30," does that mean greater than OR equal to 30? In the solution proposed by Mitch, the least possible answer for the mean was equal to 30.