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

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Manager
Joined: 24 Jun 2014
Posts: 51
Concentration: Social Entrepreneurship, Nonprofit
If the average(arithmetic mean) of four numbers is 10 ,how many of the  [#permalink]

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27 Feb 2015, 21:22
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50% (01:19) correct 50% (01:33) wrong based on 148 sessions

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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.
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Re: If the average(arithmetic mean) of four numbers is 10 ,how many of the  [#permalink]

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27 Feb 2015, 23:53
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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.

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# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Board of Directors Joined: 17 Jul 2014 Posts: 2723 Location: United States (IL) Concentration: Finance, Economics GMAT 1: 650 Q49 V30 GPA: 3.92 WE: General Management (Transportation) Re: If the average(arithmetic mean) of four numbers is 10 ,how many of the [#permalink] ### Show Tags 23 Feb 2016, 19:16 now this one is a very tricky one...precisely 2..so other 2 cannot be 10...A for sure... Intern Joined: 04 Nov 2015 Posts: 33 Re: If the average(arithmetic mean) of four numbers is 10 ,how many of the [#permalink] ### Show Tags 09 Mar 2017, 15:41 mvictor wrote: now this one is a very tricky one...precisely 2..so other 2 cannot be 10...A for sure... I dont agree with this no where it is written that the other two numbers can't be 10 and 10. Board of Directors Joined: 17 Jul 2014 Posts: 2723 Location: United States (IL) Concentration: Finance, Economics GMAT 1: 650 Q49 V30 GPA: 3.92 WE: General Management (Transportation) Re: If the average(arithmetic mean) of four numbers is 10 ,how many of the [#permalink] ### Show Tags 09 Mar 2017, 15:46 1 sandeep211986 wrote: mvictor wrote: now this one is a very tricky one...precisely 2..so other 2 cannot be 10...A for sure... I dont agree with this no where it is written that the other two numbers can't be 10 and 10. it clearly says that only 2 are 10: 1) Precisely two numbers are equal to 10 Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5878 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If the average(arithmetic mean) of four numbers is 10 ,how many of the [#permalink] ### Show Tags 09 Mar 2017, 16:31 AverageGuy123 wrote: 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. 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. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Re: If the average(arithmetic mean) of four numbers is 10 ,how many of the  [#permalink]

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25 Sep 2017, 22:44
sandeep211986 wrote:
mvictor wrote:
now this one is a very tricky one...precisely 2..so other 2 cannot be 10...A for sure...

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

I just made the same mistake.
Re: If the average(arithmetic mean) of four numbers is 10 ,how many of the &nbs [#permalink] 25 Sep 2017, 22:44
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