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18 Jul 2016, 04:25
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
29% (01:38) correct
71%
(01:31)
wrong
based on 91
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Is a+b+c=even?
1) abc=even
2) ac=odd
*An answer will be posted in 2 days
1) abc=even
2) ac=odd
*An answer will be posted in 2 days
Updated on: 18 Jul 2016, 08:07
Originally posted by DAllison2016 on 18 Jul 2016, 04:40.
Last edited by DAllison2016 on 18 Jul 2016, 08:07, edited 1 time in total.
Last edited by DAllison2016 on 18 Jul 2016, 08:07, edited 1 time in total.
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Note: My working, does not give the OA and can't see where I went wrong.
Is a+b+c=even?
----
Each addition of a number can transform it from odd to even, or vice versa.
Therefore, to know the answer, we must determine whether each of {a,b,c} is odd or even.
1) abc = even
If at least one factor of a product is even, then the product is even.
(1) informs us that at least one of the three variables is even.
This is not sufficient as we do not know which variables this applies to.
2) ac = odd
If the result of two variables multiplied together is odd, then both variables are odd. From this, we know:
a = odd
c = odd
We do not know whether b is odd, so this is not sufficient.
Both statements
We know that both a and c are odd, and that there is at least one even variable. From this, we can conclude that:
b = even
We now know whether all variables are odd or even. Therefore:
Is a+b+c=even?
----
Each addition of a number can transform it from odd to even, or vice versa.
Therefore, to know the answer, we must determine whether each of {a,b,c} is odd or even.
1) abc = even
If at least one factor of a product is even, then the product is even.
(1) informs us that at least one of the three variables is even.
This is not sufficient as we do not know which variables this applies to.
2) ac = odd
If the result of two variables multiplied together is odd, then both variables are odd. From this, we know:
a = odd
c = odd
We do not know whether b is odd, so this is not sufficient.
Both statements
We know that both a and c are odd, and that there is at least one even variable. From this, we can conclude that:
b = even
We now know whether all variables are odd or even. Therefore:
(C) both statements taken together are sufficient to answer the question, but neither statement alone is sufficient
18 Jul 2016, 07:34
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I have a feeling that you meant to specify that a, b and c are INTEGERS. So, I have worded the question accordingly.
----------------------------------------------------------------------
If a, b and c are INTEGERS, is the sum a+b+c even?
1) abc is even
2) ac is odd
-----------------------------------------------------------------------
Some important rules for intgers:
1. ODD +/- ODD = EVEN
2. ODD +/- EVEN = ODD
3. EVEN +/- EVEN = EVEN
4. (ODD)(ODD) = ODD
5. (ODD)(EVEN) = EVEN
6. (EVEN)(EVEN) = EVEN
ADDITIONAL RULE: In ANY product of integers, if there is 1 or more EVEN numbers, the entire product will be EVEN. So, the if a product of integers is ODD, we can conclude that all of the numbers are ODD.
----------------------------
Target question: Is the sum a+b+c even?
Statement 1: abc is even
From this, we can conclude that 1 or more of the numbers is EVEN
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of a, b and c that satisfy statement 1. Here are two:
Case a: a = 1, b = 2 and c = 2, in which case a+b+c = 5. So, the sum a+b+c is ODD
Case b: a = 1, b = 1 and c = 2, in which case a+b+c = 4. So, the sum a+b+c is EVEN[/color]
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values
Statement 2: ac is odd
This means that a and c are ODD. However, we have no info about b.
There are several values of a, b and c that satisfy statement 1. Here are two:
Case a: a = 1, b = 1 and c = 1, in which case a+b+c = 3. So, the sum a+b+c is ODD
Case b: a = 1, b = 2 and c = 1, in which case a+b+c = 4. So, the sum a+b+c is EVEN[/color]
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 2 tells us that a and c are ODD
Statement 1 tells us that at least one of the numbers is EVEN. Since a and c are ODD, it must be the case that b is EVEN.
This means that a+b+c = ODD+EVEN+ODD = EVEN
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer =
Cheers,
Brent
----------------------------------------------------------------------
If a, b and c are INTEGERS, is the sum a+b+c even?
1) abc is even
2) ac is odd
-----------------------------------------------------------------------
Some important rules for intgers:
1. ODD +/- ODD = EVEN
2. ODD +/- EVEN = ODD
3. EVEN +/- EVEN = EVEN
4. (ODD)(ODD) = ODD
5. (ODD)(EVEN) = EVEN
6. (EVEN)(EVEN) = EVEN
ADDITIONAL RULE: In ANY product of integers, if there is 1 or more EVEN numbers, the entire product will be EVEN. So, the if a product of integers is ODD, we can conclude that all of the numbers are ODD.
----------------------------
Target question: Is the sum a+b+c even?
Statement 1: abc is even
From this, we can conclude that 1 or more of the numbers is EVEN
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of a, b and c that satisfy statement 1. Here are two:
Case a: a = 1, b = 2 and c = 2, in which case a+b+c = 5. So, the sum a+b+c is ODD
Case b: a = 1, b = 1 and c = 2, in which case a+b+c = 4. So, the sum a+b+c is EVEN[/color]
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values
Statement 2: ac is odd
This means that a and c are ODD. However, we have no info about b.
There are several values of a, b and c that satisfy statement 1. Here are two:
Case a: a = 1, b = 1 and c = 1, in which case a+b+c = 3. So, the sum a+b+c is ODD
Case b: a = 1, b = 2 and c = 1, in which case a+b+c = 4. So, the sum a+b+c is EVEN[/color]
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 2 tells us that a and c are ODD
Statement 1 tells us that at least one of the numbers is EVEN. Since a and c are ODD, it must be the case that b is EVEN.
This means that a+b+c = ODD+EVEN+ODD = EVEN
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer =
Cheers,
Brent
