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22 Jun 2020, 02:45
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C
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Difficulty:
35%
(medium)
Question Stats:
63% (01:18) correct
37%
(00:58)
wrong
based on 107
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Q is a set of integers If Q contains more than 2 numbers, are all the numbers in Q even?
(1) The sum of any two numbers in Q is even.
(2) The product of any two numbers in Q is even.
Are You Up For the Challenge: 700 Level Questions
(1) The sum of any two numbers in Q is even.
(2) The product of any two numbers in Q is even.
Are You Up For the Challenge: 700 Level Questions
22 Jun 2020, 03:11
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Hi all,
First let's revise some baisc rules regarding addition, subtraction, division and multiplication of odd and even numbers :
Odd + Odd = Even
Even + Even = Even
Even + Odd = Odd
Odd - Odd = Even
Even - Even = Even
Even x Even = Even
Odd x Even = Even
Odd x Odd = Odd
Even/Odd = Even
Odd/Odd = Odd
Even/Even = Odd or Even
Now, coming back to the question,
We know that set Q contains more than 2 numbers
Statement 1:
As per the rules discussed above we can see that the sum of two odd numbers will be even and the sum of two even numbers will also be even.
There is no way to find out if the numbers are odd or even, thus statement 1 alone is not sufficient.
Statemnet 2:
As we can see in the above mentioned rules that if one out of the two numbers is even then the product is also even
There is no way to find out if the second number is odd or even, thus, statemnet 2 alone is also not sufficient
Statement 1 and 2 together:
In this case we know that the sum as well as product of any two numbers from the set is even:
If one number is odd and the other is even, then the product will be even but the sum will be odd, thus this can't be the case
If both numbers are odd, then the sum will be even but the product will be odd, thus this can't be the case either
If both numbers are even then the product as well as the sum will be even, as this is the only case that gives us a definate answer of all the numbers in set Q being even, we can safely conclude that the correct answer to this question is:
Option C) BOTH statements TOGETHER are SUFFICIENT.
Hope this helped!
Posted from my mobile device
First let's revise some baisc rules regarding addition, subtraction, division and multiplication of odd and even numbers :
Odd + Odd = Even
Even + Even = Even
Even + Odd = Odd
Odd - Odd = Even
Even - Even = Even
Even x Even = Even
Odd x Even = Even
Odd x Odd = Odd
Even/Odd = Even
Odd/Odd = Odd
Even/Even = Odd or Even
Now, coming back to the question,
We know that set Q contains more than 2 numbers
Statement 1:
As per the rules discussed above we can see that the sum of two odd numbers will be even and the sum of two even numbers will also be even.
There is no way to find out if the numbers are odd or even, thus statement 1 alone is not sufficient.
Statemnet 2:
As we can see in the above mentioned rules that if one out of the two numbers is even then the product is also even
There is no way to find out if the second number is odd or even, thus, statemnet 2 alone is also not sufficient
Statement 1 and 2 together:
In this case we know that the sum as well as product of any two numbers from the set is even:
If one number is odd and the other is even, then the product will be even but the sum will be odd, thus this can't be the case
If both numbers are odd, then the sum will be even but the product will be odd, thus this can't be the case either
If both numbers are even then the product as well as the sum will be even, as this is the only case that gives us a definate answer of all the numbers in set Q being even, we can safely conclude that the correct answer to this question is:
Option C) BOTH statements TOGETHER are SUFFICIENT.
Hope this helped!
Posted from my mobile device
firas92
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22 Jun 2020, 03:26
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Bunuel
(1) The sum of any two numbers in Q is even.
This means that the integers in Q are either all even or all odd
1 is not sufficient
(2) The product of any two numbers in Q is even.
This means that Q can have at most 1 odd integers and rest are even integers, that is 0 odd integers or 1 odd integer with the rest being even integers
2 is not sufficient
(1)+(2)
Q cannot have 1 odd integer and rest even
So Q must be all even integers
(1)+(2) is sufficient
Answer is (C)
