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Is the average (arithmetic mean) of w, x, y, and z less than 28?

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Intern
Joined: 04 Mar 2017
Posts: 2
Is the average (arithmetic mean) of w, x, y, and z less than 28?  [#permalink]

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26 Jun 2018, 05:13
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Difficulty:

45% (medium)

Question Stats:

56% (01:43) correct 44% (01:39) wrong based on 34 sessions

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Is the average (arithmetic mean) of w, x, y, and z less than 28?

(1) The average (arithmetic mean) of w, x, and y is less than 28.
(2) The average (arithmetic mean) of x, y, and z is less than 28.
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Joined: 25 Feb 2013
Posts: 1217
Location: India
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Is the average (arithmetic mean) of w, x, y, and z less than 28?  [#permalink]

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26 Jun 2018, 07:37
zhouchuzc wrote:
Is the average (arithmetic mean) of w, x, y, and z less than 28?

(1) The average (arithmetic mean) of w, x, and y is less than 28.
(2) The average (arithmetic mean) of x, y, and z is less than 28.

Is $$w+x+y+z<112$$

Statement 1: implies $$w+x+y<84$$. we know nothing about $$z$$. depending upon the value of $$z$$, the sum of four numbers may or may not be less than $$112$$. Insufficient

Statement 2: implies $$x+y+z<84$$. we know nothing about $$w$$. depending upon the value of $$w$$, the sum of four numbers may or may not be less than $$112$$. Insufficient

Combining 1&2: we have four variables and only two inequalities. values cannot be determined. Insufficient

Option E
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Joined: 02 Aug 2009
Posts: 7108
Re: Is the average (arithmetic mean) of w, x, y, and z less than 28?  [#permalink]

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26 Jun 2018, 07:41
zhouchuzc wrote:
Is the average (arithmetic mean) of w, x, y, and z less than 28?

(1) The average (arithmetic mean) of w, x, and y is less than 28.
(2) The average (arithmetic mean) of x, y, and z is less than 28.

Easy to fall for C trap..
Note - the numbers are not in any order...

Each statement alone is not enough as one variable is missing in each..

Combined..
average of w,x,y,x,y,z <28
So if we take w,x,y and z each less than 10, average will be <10..so <28...yes
Say w=70, y=7 and x=6 Avery<28
Also y=7,x=6 and z=70.. average<28
But X+y+w+z=70+7+6+70=153
So average=153/4=38...>28.. so Ans NO
Insufficient

E
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Joined: 07 Feb 2017
Posts: 188
Re: Is the average (arithmetic mean) of w, x, y, and z less than 28?  [#permalink]

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26 Jun 2018, 09:02
w+x+y+z<112 ?
(1) w+x+y<84
(2) x+y+z<84

(1) and (2)

x+y=1; w=82; z=82
No

x+y=1; w=1; z=1
Yes

Re: Is the average (arithmetic mean) of w, x, y, and z less than 28? &nbs [#permalink] 26 Jun 2018, 09:02
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