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Data Sufficiency Pack 1, Question 3) If a, b and c are integers...

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Data Sufficiency Pack 1, Question 3) If a, b and c are integers... [#permalink]

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New post Updated on: 30 Oct 2015, 00:14
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Difficulty:

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Question Stats:

55% (02:04) correct 45% (01:44) wrong based on 124 sessions

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QUANT 4-PACK SERIES Data Sufficiency Pack 1 Question 3 If a, b and c are integers...

If a, b and c are integers and abc is an even integer, is b an odd integer?

1) ab + bc + ac is an even integer
2) a + c is an odd integer


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This question is part of the Quant 4-Pack series

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Originally posted by EMPOWERgmatRichC on 27 Oct 2015, 22:03.
Last edited by EMPOWERgmatRichC on 30 Oct 2015, 00:14, edited 2 times in total.
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Re: Data Sufficiency Pack 1, Question 3) If a, b and c are integers... [#permalink]

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New post 28 Oct 2015, 08:53
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EMPOWERgmatRichC wrote:
QUANT 4-PACK SERIES Data Sufficiency Pack 1 Question 3 If a, b and c are integers...

If a, b and c are integers and abc is an even integer, is B an odd integer?

1) ab + bc + ab is an even integer
2) a + c is an odd integer


48 Hour Window Answer & Explanation Window
Earn KUDOS! Post your answer and explanation.
OA, and explanation will be posted after the 48 hour window closes.

This question is part of the Quant 4-Pack series

Scroll Down For Official Explanation


Given a,b,c are integers and abc= even, b = odd?

Per statement 1, 2ab+bc = e ---> b(2a+c) = e ---> 3 cases

Case 1, b=e , 2a+c=o , "Yes"

Case 2, b=o, 2a+c=e, "No"

Cae 3, b=e, 2a+c=e, "Yes"

Thus not sufficient.

Statement 2, a+c=o --> 2 cases

Case 1, a=o and c=e ---> b=even or odd to give abc=even , making this statement clearly not sufficient. You can stop here.

Case 2, not required.

Combining, you get,

a+c=o and abc = even, possible cases

from statement 2,
a b c
o o e
o e e
e o o
e e o

and from statement 1,

a b c
o e e
e e e
o e o
e e o
o o e
e o e


Thus the cases common are:

a b c
o o e
o e e
e e o

Making E the correct answer for "is b =odd"
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Re: Data Sufficiency Pack 1, Question 3) If a, b and c are integers... [#permalink]

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New post 28 Oct 2015, 11:13
1
Quote:
If a, b and c are integers and abc is an even integer, is B an odd integer?

1) ab + bc + ab is an even integer
2) a + c is an odd integer



Given that abc = Even integer. So at least 1 of the 3 integers is Even.
Question asks whether B = ODD ?

Statement 1 says ab + bc + ab is an even integer. So b * (2a+c) = Even. So either b OR (2a+c) is even. NOT sufficient.
Statement 2 says a+c = ODD Integer. i.e. So either a OR c is ODD. So there is no inference of b. NOT sufficient.

Combining Statement 1 & 2, There is no definite answer for b. Both odd & even value of b satisfy the conditions.

So option (E) wins.
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Re: Data Sufficiency Pack 1, Question 3) If a, b and c are integers... [#permalink]

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New post 30 Oct 2015, 00:31
Hi All,

Unfortunately, the original prompt had a typo in it (it's since been 'fixed'); the first two responses to the question were correct for the question that was originally posted. Here is the explanation for the updated question.

We're told that A, B and C are integers and that ABC is EVEN. We're asked if B is EVEN. This is a YES/NO question. The prompt can be solved with a combination of Number Property rules and TESTing VALUES (if needed).

From the prompt, we know that ABC is even, so AT LEAST one of the three variables must be even (since an EVEN multiplied by any other integer(s) is EVEN).

1) AB + BC + AC is an even integer

With this Fact, there is more than one way to end up with an EVEN sum...

IF...
A = Even
B = Even
C = Even
(E)(E) + (E)(E) + (E)(E) = Even
Then the answer to the question is YES.

IF...
A = Even
B = Odd
C = Even
(E)(O) + (E)(E) + (E)(O) = Even
Then the answer to the question is NO.
Fact 1 is INSUFFICIENT

2) A + C is an odd integer

This Fact tells us that ONE of those two variables is EVEN and the other is ODD (since Even + Odd = Odd), but it tells us NOTHING about B.
Fact 2 is INSUFFICIENT.

Combined, we know...
AB + BC + AC = Even
Between A and C, one is Even and the other is Odd

With these limitations, there are only two possibilities...

IF...
A = Even
B = Even
C = Odd
(E)(E) + (E)(O) + (E)(O) = Even
Then the answer to the question is YES.

IF...
A = Odd
B = Even
C = Even
(O)(E) + (E)(E) + (O)(E) = Even
Then the answer to the question is YES.

Combined, SUFFICIENT

Final Answer:

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Rich
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Re: Data Sufficiency Pack 1, Question 3) If a, b and c are integers... [#permalink]

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New post 23 Sep 2016, 04:08
EMPOWERgmatRichC wrote:
Hi All,

Unfortunately, the original prompt had a typo in it (it's since been 'fixed'); the first two responses to the question were correct for the question that was originally posted. Here is the explanation for the updated question.

We're told that A, B and C are integers and that ABC is EVEN. We're asked if B is EVEN. This is a YES/NO question. The prompt can be solved with a combination of Number Property rules and TESTing VALUES (if needed).

From the prompt, we know that ABC is even, so AT LEAST one of the three variables must be even (since an EVEN multiplied by any other integer(s) is EVEN).

1) AB + BC + AC is an even integer

With this Fact, there is more than one way to end up with an EVEN sum...

IF...
A = Even
B = Even
C = Even
(E)(E) + (E)(E) + (E)(E) = Even
Then the answer to the question is YES.

IF...
A = Even
B = Odd
C = Even
(E)(O) + (E)(E) + (E)(O) = Even
Then the answer to the question is NO.
Fact 1 is INSUFFICIENT

2) A + C is an odd integer

This Fact tells us that ONE of those two variables is EVEN and the other is ODD (since Even + Odd = Odd), but it tells us NOTHING about B.
Fact 2 is INSUFFICIENT.

Combined, we know...
AB + BC + AC = Even
Between A and C, one is Even and the other is Odd

With these limitations, there are only two possibilities...

IF...
A = Even
B = Even
C = Odd
(E)(E) + (E)(O) + (E)(O) = Even
Then the answer to the question is YES.

IF...
A = Odd
B = Even
C = Even
(O)(E) + (E)(E) + (O)(E) = Even
Then the answer to the question is YES.

Combined, SUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,
Rich



Hi Rich,

Can you please fix the question to "is B an Even integer"? In your answer, when you combined both facts is always 'Yes', while the old prompt is still 'is B an Odd integer'.

This will help practitioners not to confuse and go back and forth between the original prompt and your answer.


Thanks
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Re: Data Sufficiency Pack 1, Question 3) If a, b and c are integers... [#permalink]

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New post 23 Feb 2017, 06:05
Prompt analysis
abc is even integer, that means either one or two of the integer or all three integers are even.

Superset
The answer will be either yes or no.

Translation
To find the answer, we need:
1# exact value of a,b,c
2# the properties in terms of even/odd for a,b,c
3# three equations and three variables to find a,b,c.

Statement analysis
St 1: ab +bc +ac is even that means each of the term could be even +odd +odd or even +even +even. If a is even, that means ab and ac is even therefore even +odd+odd is ruled out. Hence all the term is even. I.e bc is even as well. But we cannot say is c is even or b is even. INSUFFICIENT

St 2: a +c is odd. Even +odd = odd. That means either a or c is even. Hence abc is even. But cannot say anything about b. INSUFFICIENT.

St 2 & St 1: from statement 2 we can say either a or c is even and the other is odd. Let us take a be even and c be odd. Hence ab and ac is even. From statement 1, we can say that bc is also even. If c is odd, b has to be even. ANSWER. Similarly, you can reverse a and c and you will get the same result.
Option C
Re: Data Sufficiency Pack 1, Question 3) If a, b and c are integers...   [#permalink] 23 Feb 2017, 06:05
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