If the average (arithmetic mean) of four numbers is 10, how many of

Question

If the average (arithmetic mean) of four numbers is 10, how many of the numbers are greater than 10?

(1) Precisely two numbers are equal to 10

(2) The largest of the 4 numbers is 10 greater than the smallest of the 4 numbers.

EMPOWERgmatRichC · Answer

Hi AverageGuy123,

This question has some very specific 'restrictions' to it, but if you take the proper notes and TEST VALUES, you can answer this question without too much trouble.

We're told that the average of 4 numbers is 10. We're asked how many (of those 4) are greater than 10.

From the first sentence, we can create an equation:

(W + X + Y + Z)/4 = 10
W + X + Y + Z = 40

Fact 1: Precisely 2 of the numbers equal 10

I'm going to "lock in" the W and the X as 10s....

10 + 10 + Y + Z = 40
Y + Z = 20

Since Fact 1 states that PRECISELY 2 of the numbers equal 10, neither Y nor Z can now be 10s. That means we need 2 numbers that add up to 20 and NEITHER can be a 10...

9 and 11
8 and 12
0 and 20
-1 and 21
Etc.
In EVERY possible example, one number is LESS than 10 and ONE number is GREATER than 10. Thus, the answer to the question is ALWAYS ONE number.
Fact 1 is SUFFICIENT

Fact 2: The largest of the numbers is 10 greater than the smallest of the numbers

IF... the numbers are....
5, 10, 10 and 15.... then the answer to the question is ONE.
4, 10, 12 and 14.... then the answer to the question is TWO.
Fact 2 is INSUFFICIENT.

Final Answer:  A

GMAT assassins aren't born, they're made,
Rich

mvictor · Answer

now this one is a very tricky one...precisely 2..so other 2 cannot be 10...A for sure...

sandeep211986 · Answer

I dont agree with this no where it is written that the other two numbers can't be 10 and 10.

mvictor · Answer

it clearly says that only 2 are 10:

1)  Precisely two numbers are equal to 10

MathRevolution · Answer

Assume that  a ,  b ,  c  and  d  are four numbers, where  a \leq b \leq c \leq d .
Then we have 1 equation that  a + b + c + d = 40 .

Let's translate the conditions to mathematical expressions.

1)  b = c = 10 ,  a < 10 ,  d > 10 
2)  d = a + 10

For the first condition, only  d  is greater than 10 form the above mathematical expression.
Hence the condition 1) is sufficient.

For the second condition, we have following examples.
Let  a = 5  and  d = 15 .
Then we have two kinds of cases as follows.
5, 10, 10, 15 : They have just 1 number of elements greater than 10, which is just 15.
5, 9, 11, 15 : They have 2 numbers of elements greater than 10, which are 11 and 15.
Hence, we don't have a unique solution about the question how many numbers are greater than 10.
Therefore, the second condition is not sufficient.

Please remind that we should forget everything about the condition 1), when we consider the second condition only.

mohd_int · Answer

I just made the same mistake.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If the average (arithmetic mean) of four numbers is 10, how many of

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

If the average (arithmetic mean) of four numbers is 10, how many of

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards