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MahmoudFawzy
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Set S is a set of consecutive integers beginning with x and ending wit 13 Sep 2019, 08:06
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

55% (hard)

Question Stats:

62% (02:21) correct 38% (02:07) wrong based on 332 sessions

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Set S is a set of consecutive integers beginning with x and ending with y. If the sum of all the integers in set S is odd, which of the following must be true?

(I) x and y are even
(II) Set S contains an even number of integers
(III) The average (arithmetic mean) of x and y is even

(A) None

(B) II only

(C) III only

(D) I and II

(E) I and III
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A
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Set S is a set of consecutive integers beginning with x and ending wit 13 Sep 2019, 08:15
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Mahmoudfawzy83
Set S is a set of consecutive integers beginning with x and ending with y. If the sum of all the integers in set S is odd, which of the following must be true?

(I) x and y are even
(II) Set S contains an even number of integers
(III) The average (arithmetic mean) of x and y is even

(A) None

(B) II only

(C) III only

(D) I and II

(E) I and III
Show more


For example..
1) E, O, E
2) E, O,
3) O, E, O, E, O, E, O, E, O
4) O, E, O, E, O

(I) x and y are even
In case (1) x and y are even, but in case (3) and (4) they are odd...False

(II) Set S contains an even number of integers
In case (2) numbers are even, but in case of (1), (3) and (4) they are odd...False

(III) The average (arithmetic mean) of x and y is even
In consecutive integers, middle value is the average...
In case (2) average is a fraction, but in case (1), (3) and (4) they are odd...False

ALL false.. A
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Set S is a set of consecutive integers beginning with x and ending wit 13 Sep 2019, 08:37
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solve using set of different arrangements : ( 1,2,3,4,5) we get answer as none and (1,2,3,4,5,6) yes
IMO A; is valid answer


Mahmoudfawzy83
Set S is a set of consecutive integers beginning with x and ending with y. If the sum of all the integers in set S is odd, which of the following must be true?

(I) x and y are even
(II) Set S contains an even number of integers
(III) The average (arithmetic mean) of x and y is even

(A) None

(B) II only

(C) III only

(D) I and II

(E) I and III
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Set S is a set of consecutive integers beginning with x and ending wit 13 Sep 2019, 08:41
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hi chetan2u if the number of integers is just 2, and if it starts with 1, then the sum( 1+2=3) is odd but the number of integers are even right..

where i am going wrong? do correct me

i solved something like this

if the x is odd, then the total sum gives = o,o,e, e,o,o, e,e so if y can be odd or even

i cant get any 3 to be true, so marked none

where i am wrong do correct me?



chetan2u
Mahmoudfawzy83
Set S is a set of consecutive integers beginning with x and ending with y. If the sum of all the integers in set S is odd, which of the following must be true?

(I) x and y are even
(II) Set S contains an even number of integers
(III) The average (arithmetic mean) of x and y is even

(A) None

(B) II only

(C) III only

(D) I and II

(E) I and III

The SUM of consecutive integers is ODD only when the number of integers is ODD..
For example..
1) E, O, E
2) E, O, E, O, E
3) O, E, O
4) O, E, O, E, O

(I) x and y are even
In case (1) and (2) x and y are even, but in case (3) and (4) they are odd...False

(II) Set S contains an even number of integers
The SUM of consecutive integers is ODD only when the number of integers is ODD....False

(III) The average (arithmetic mean) of x and y is even
In consective integers, middle value is the average...
In case (3) and (2) x and y are even, but in case (1) and (4) they are odd...False

ALL false.. A
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chetan2u
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Set S is a set of consecutive integers beginning with x and ending wit 13 Sep 2019, 08:46
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ccheryn
hi chetan2u if the number of integers is just 2, and if it starts with 1, then the sum( 1+2=3) is odd but the number of integers are even right..

where i am going wrong? do correct me

i solved something like this

if the x is odd, then the total sum gives = o,o,e, e,o,o, e,e so if y can be odd or even

i cant get any 3 to be true, so marked none

where i am wrong do correct me?



chetan2u
Mahmoudfawzy83
Set S is a set of consecutive integers beginning with x and ending with y. If the sum of all the integers in set S is odd, which of the following must be true?

(I) x and y are even
(II) Set S contains an even number of integers
(III) The average (arithmetic mean) of x and y is even

(A) None

(B) II only

(C) III only

(D) I and II

(E) I and III

The SUM of consecutive integers is ODD only when the number of integers is ODD..
For example..
1) E, O, E
2) E, O, E, O, E
3) O, E, O
4) O, E, O, E, O

(I) x and y are even
In case (1) and (2) x and y are even, but in case (3) and (4) they are odd...False

(II) Set S contains an even number of integers
The SUM of consecutive integers is ODD only when the number of integers is ODD....False

(III) The average (arithmetic mean) of x and y is even
In consective integers, middle value is the average...
In case (3) and (2) x and y are even, but in case (1) and (4) they are odd...False

ALL false.. A
Show more

That is a perfectly valid value and can be taken that way..
You are correct, I require to edit my examples and add this value too..
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Set S is a set of consecutive integers beginning with x and ending wit 13 Sep 2024, 21:11
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