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Bunuel
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If P is a set of consecutive integers, is there an even number of inte 29 Apr 2019, 08:38
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25% (medium)

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71% (01:15) correct 29% (01:16) wrong based on 110 sessions

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If P is a set of consecutive integers, is there an even number of integers in set P?

(1) The sum of the integers in set P is 0.
(2) The product of the integers in set P is 0.
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A
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If P is a set of consecutive integers, is there an even number of inte Updated on: 29 Apr 2019, 09:22
Originally posted by Archit3110 on 29 Apr 2019, 09:03.
Last edited by Archit3110 on 29 Apr 2019, 09:22, edited 1 time in total.
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Bunuel
If P is a set of consecutive integers, is there an even number of integers in set P?

(1) The sum of the integers in set P is 0.
(2) The product of the integers in set P is 0.
Show more


#1
The sum of the integers in set P is 0.
p= -1,0,1
or = -2,1,0,1,2
sufficent
#2
product is 0 again insufficient

IMO A
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If P is a set of consecutive integers, is there an even number of inte 29 Apr 2019, 09:19
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Archit3110
Bunuel
If P is a set of consecutive integers, is there an even number of integers in set P?

(1) The sum of the integers in set P is 0.
(2) The product of the integers in set P is 0.


#1
The sum of the integers in set P is 0.
p= -1,0,1
or = -2,1,0,1,2
insufficent
#2
product is 0 again insufficient
from 1 & 2
we cannot say whether P has even integer or not
IMO E
Show more

The question asks about the number of integers.

From statement 1 we can see that there are always odd number of elements so we can answer the question as 'NO'

So 1 is sufficient.

Isn't that right?

Posted from my mobile device
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If P is a set of consecutive integers, is there an even number of inte 29 Apr 2019, 09:23
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firas92

yes i misread question.. :| :roll: , edited thanks .

firas92
Archit3110
Bunuel
If P is a set of consecutive integers, is there an even number of integers in set P?

(1) The sum of the integers in set P is 0.
(2) The product of the integers in set P is 0.


#1
The sum of the integers in set P is 0.
p= -1,0,1
or = -2,1,0,1,2
insufficent
#2
product is 0 again insufficient
from 1 & 2
we cannot say whether P has even integer or not
IMO E

The question asks about the number of integers.

From statement 1 we can see that there are always odd number of elements so we can answer the question as 'NO'

So 1 is sufficient.

Isn't that right?

Posted from my mobile device
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If P is a set of consecutive integers, is there an even number of inte 10 Nov 2022, 10:45
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Bunuel
If P is a set of consecutive integers, is there an even number of integers in set P?

(1) The sum of the integers in set P is 0.
(2) The product of the integers in set P is 0.
Show more

Solution:
  • If the idea of -1, 0, 1 or -2, -1, 0, 1, 2 doesn't hit you instantly then this can be solved algebraically too
  • Sum of the integers is 0 which means we can apply the sum of an AP formula and say
    \(\frac{n}{2}[2a+(n-1)d]=0\)
    \(⇒\frac{n}{2}[2a+(n-1)1]=0\)
    \(⇒n(2a+n-1)=0\)
  • n can obviously not be 0
    \(⇒2a+n-1=0\)
    \(⇒n=1-2a\)
    \(⇒n=odd-even\\
    \)
    \(⇒n=odd\)


Hence the right answer is Option A
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