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The average of all consecutive integers from x to y inclusive is 39.

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The average of all consecutive integers from x to y inclusive is 39.  [#permalink]

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New post 08 Oct 2019, 23:05
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

65% (01:23) correct 35% (02:06) wrong based on 75 sessions

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Re: The average of all consecutive integers from x to y inclusive is 39.  [#permalink]

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New post 10 Oct 2019, 06:04
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Top Contributor
Bunuel wrote:
The average of all consecutive integers from x to y inclusive is 39. Which of the following could be x and y?

I. 25 and 53
II. 29 and 61
III. 33 and 45

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


Key Concept: In a set of consecutive integers, the average = (first term + last term)/2

Now test the answers....
I. 25 and 53
(25 + 53)/2 = 39
Perfect.
Statement I is true

II. 29 and 61
(29 + 61)/2 = 45
Statement II is not true

III. 33 and 45
(33 + 45)/2 = 39
Perfect.
Statement III is true

Answer: E

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Brent
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Re: The average of all consecutive integers from x to y inclusive is 39.  [#permalink]

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New post 13 Oct 2019, 18:20
Bunuel wrote:
The average of all consecutive integers from x to y inclusive is 39. Which of the following could be x and y?

I. 25 and 53
II. 29 and 61
III. 33 and 45

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


Any set of consecutive integers constitutes an evenly-spaced set. Recall that the average of any evenly-spaced set’s members is the average of the lowest and highest values of the set. Thus, the average of all consecutive integers from x to y, inclusive, is equal to the average of x and y. Now let’s test each Roman numeral:

(25 + 53)/2 = 78/2 = 39. Yes, I works.

(29 +61)/2 = 90/2 = 45. No, II doesn’t work.

(33 +45)/2 = 78/2 = 39. Yes, III works.

Answer: E
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Re: The average of all consecutive integers from x to y inclusive is 39.  [#permalink]

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New post 13 Oct 2019, 18:49
Bunuel wrote:
The average of all consecutive integers from x to y inclusive is 39. Which of the following could be x and y?

I. 25 and 53
II. 29 and 61
III. 33 and 45

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


x+y must equal 2*average=78
only I and III
E
GMAT Club Bot
Re: The average of all consecutive integers from x to y inclusive is 39.   [#permalink] 13 Oct 2019, 18:49
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