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# If the average (arithmetic mean) of x, y, z, 5, and 7 is 8, which of

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Math Expert
Joined: 02 Sep 2009
Posts: 52911
If the average (arithmetic mean) of x, y, z, 5, and 7 is 8, which of  [#permalink]

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06 Feb 2019, 02:09
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Difficulty:

(N/A)

Question Stats:

67% (02:14) correct 33% (01:48) wrong based on 6 sessions

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If the average (arithmetic mean) of x, y, z, 5, and 7 is 8, which of the following must be true?

I. The median of the five numbers cannot be 5.

II. At least one of x, y, and z is greater than 9.

III. The range of the five numbers is 2 or more.

A. I only
B. II only
C. III only
D. I and III only
E. II and III only

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If the average (arithmetic mean) of x, y, z, 5, and 7 is 8, which of  [#permalink]

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Updated on: 06 Feb 2019, 23:24
Bunuel wrote:
If the average (arithmetic mean) of x, y, z, 5, and 7 is 8, which of the following must be true?

I. The median of the five numbers cannot be 5.

II. At least one of x, y, and z is greater than 9.

III. The range of the five numbers is 2 or more.

A. I only
B. II only
C. III only
D. I and III only
E. II and III only

given
x+y+z+12 = 40
x+y+z= 28
x,y,z have to be atleast be 9
so ii is correct which would make iii also correct
IMO E

chetan2u Bunuel
Hello could you please assist to solve this question .. i am not sure why isnt the answer given as E ...
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If you liked my solution then please give Kudos. Kudos encourage active discussions.

Originally posted by Archit3110 on 06 Feb 2019, 04:51.
Last edited by Archit3110 on 06 Feb 2019, 23:24, edited 1 time in total.
Math Expert
Joined: 02 Aug 2009
Posts: 7334
Re: If the average (arithmetic mean) of x, y, z, 5, and 7 is 8, which of  [#permalink]

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06 Feb 2019, 23:21
Archit3110 wrote:
Bunuel wrote:
If the average (arithmetic mean) of x, y, z, 5, and 7 is 8, which of the following must be true?

I. The median of the five numbers cannot be 5.

II. At least one of x, y, and z is greater than 9.

III. The range of the five numbers is 2 or more.

A. I only
B. II only
C. III only
D. I and III only
E. II and III only

given
x+y+z+12 = 40
x+y+z= 28
x,y,z have to be atleast be 9
so ii is correct which would make iii also correct
IMO E

chetan2u
Hello could you please assist to solve this question .. i am not sure why isnt the answer given as E ...

Even without knowing x,y, z, (iii) will also be correct because the two number 5 and 7 itself tells us that range is atleast 2..
Some typo, Bunuel please look into the typo
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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
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

GMAT Expert

Re: If the average (arithmetic mean) of x, y, z, 5, and 7 is 8, which of   [#permalink] 06 Feb 2019, 23:21
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