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M27-13

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M27-13 [#permalink]

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Official Solution:


In order for the product of the integers to be even, at least one of them must be even.

(1) \(b\) is halfway between \(a\) and \(c\). On the GMAT we often see such statement and it can ALWAYS be expressed algebraically as \(b=\frac{a+c}{2}\). Now, does that mean that at least one of them is even? Not necessarily: \(a=1\), \(b=3\) and \(c=5\), of course it's also possible that for example \(b= 4 = even\), for \(a=1\) and \(c=7\). Not sufficient.

(2) \(a = b - c\). Re-arrange: \(a+c=b\). Since it's not possible the sum of two odd integers to be odd, then the case of 3 odd numbers is ruled out, hence at least one of them must be even. Sufficient.


Answer: B
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Re M27-13 [#permalink]

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New post 22 Sep 2016, 09:26
I think this is a high-quality question and I agree with explanation.

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Re: M27-13 [#permalink]

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Bunuel wrote:
Official Solution:


In order for the product of the integers to be even, at least one of them must be even.

(1) \(b\) is halfway between \(a\) and \(c\). On the GMAT we often see such statement and it can ALWAYS be expressed algebraically as \(b=\frac{a+c}{2}\). Now, does that mean that at least one of them is even? Not necessarily: \(a=1\), \(b=3\) and \(c=5\), of course it's also possible that for example \(b= 4 = even\), for \(a=1\) and \(c=7\). Not sufficient.

(2) \(a = b - c\). Re-arrange: \(a+c=b\). Since it's not possible the sum of two odd integers to be odd, then the case of 3 odd numbers is ruled out, hence at least one of them must be even. Sufficient.


Answer: B



Bunuel please try putting in number 121 !! 1=2-1 but 121 is an odd number

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New post 31 Oct 2016, 02:19
yashrakhiani wrote:
Bunuel wrote:
Official Solution:


In order for the product of the integers to be even, at least one of them must be even.

(1) \(b\) is halfway between \(a\) and \(c\). On the GMAT we often see such statement and it can ALWAYS be expressed algebraically as \(b=\frac{a+c}{2}\). Now, does that mean that at least one of them is even? Not necessarily: \(a=1\), \(b=3\) and \(c=5\), of course it's also possible that for example \(b= 4 = even\), for \(a=1\) and \(c=7\). Not sufficient.

(2) \(a = b - c\). Re-arrange: \(a+c=b\). Since it's not possible the sum of two odd integers to be odd, then the case of 3 odd numbers is ruled out, hence at least one of them must be even. Sufficient.


Answer: B



Bunuel please try putting in number 121 !! 1=2-1 but 121 is an odd number


I tried to decipher your post but could not. Please elaborate. Thank you.
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M27-13 [#permalink]

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New post 31 Oct 2016, 03:11
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Bunuel wrote:
yashrakhiani wrote:
Bunuel wrote:
Official Solution:


In order for the product of the integers to be even, at least one of them must be even.

(1) \(b\) is halfway between \(a\) and \(c\). On the GMAT we often see such statement and it can ALWAYS be expressed algebraically as \(b=\frac{a+c}{2}\). Now, does that mean that at least one of them is even? Not necessarily: \(a=1\), \(b=3\) and \(c=5\), of course it's also possible that for example \(b= 4 = even\), for \(a=1\) and \(c=7\). Not sufficient.

(2) \(a = b - c\). Re-arrange: \(a+c=b\). Since it's not possible the sum of two odd integers to be odd, then the case of 3 odd numbers is ruled out, hence at least one of them must be even. Sufficient.


Answer: B



Bunuel please try putting in number 121 !! 1=2-1 but 121 is an odd number


I tried to decipher your post but could not. Please elaborate. Thank you.


Bunuel ' 'abc' an even integer this means that abc is a 3 digit even integer , statement 2 says a=b-c , 1=2-1 & 121 is an odd number . Bunuel Please check if the question is indeed asking for condition if abc is an even number or if the question intends to ask the condition for A * B * C is an even number.


According to the provided answer clearly the question is asking for value of abc and not a*b*c .

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New post 31 Oct 2016, 03:25
yashrakhiani wrote:
Bunuel ' 'abc' an even integer this means that abc is a 3 digit even integer , statement 2 says a=b-c , 1=2-1 & 121 is an odd number . Bunuel Please check if the question is indeed asking for condition if abc is an even number or if the question intends to ask the condition for A * B * C is an even number.


According to the provided answer clearly the question is asking for value of abc and not a*b*c .


abc is a*b*c. If it were 3-digit number it would have been explicitly mentioned.
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Re: M27-13 [#permalink]

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New post 21 Nov 2016, 07:47
Brilliant Question this one.
Here we need to check if abc is even or not
As all of a,b,c are integers (very important piece of information )=> If anyone of a or b or c is even, we can say with assurance that abc will be even
Lets look at statements now
Statement 1
b=a+c/2
2,3,4 => abc=even
7,9,11=> abc is odd
hence not sufficient

Statement 2
Here a=b-c
making cases for b,c=>
even,even
even,odd
odd,even
odd,odd

So corresponding to the above cases a will be=>
even
odd
odd
even

Hence clearly one out of a,b,c is always even
Conversely => as a=b-c and is b and c are both odd => a will be even
hence abc is always even
Hence B
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Re: M27-13 [#permalink]

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New post 24 Nov 2017, 08:23
Bunuel wrote:
Official Solution:


In order for the product of the integers to be even, at least one of them must be even.

(1) \(b\) is halfway between \(a\) and \(c\). On the GMAT we often see such statement and it can ALWAYS be expressed algebraically as \(b=\frac{a+c}{2}\). Now, does that mean that at least one of them is even? Not necessarily: \(a=1\), \(b=3\) and \(c=5\), of course it's also possible that for example \(b= 4 = even\), for \(a=1\) and \(c=7\). Not sufficient.

(2) \(a = b - c\). Re-arrange: \(a+c=b\). Since it's not possible the sum of two odd integers to be odd, then the case of 3 odd numbers is ruled out, hence at least one of them must be even. Sufficient.


Answer: B


Hi Bunuel - isn't it possible that one of the integers a,b,c is zero? The question doesn't state that the integers are either positive or distinct numbers. In the case that they aren't and a=0 while b=c, then wouldn't we have the case that a*b*c = 0 and thus both statements are insufficient? This is the answer I got, so if you could please explain I'd be really grateful.

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Re: M27-13 [#permalink]

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New post 24 Nov 2017, 08:25
Udsey1234 wrote:
Bunuel wrote:
Official Solution:


In order for the product of the integers to be even, at least one of them must be even.

(1) \(b\) is halfway between \(a\) and \(c\). On the GMAT we often see such statement and it can ALWAYS be expressed algebraically as \(b=\frac{a+c}{2}\). Now, does that mean that at least one of them is even? Not necessarily: \(a=1\), \(b=3\) and \(c=5\), of course it's also possible that for example \(b= 4 = even\), for \(a=1\) and \(c=7\). Not sufficient.

(2) \(a = b - c\). Re-arrange: \(a+c=b\). Since it's not possible the sum of two odd integers to be odd, then the case of 3 odd numbers is ruled out, hence at least one of them must be even. Sufficient.


Answer: B


Hi Bunuel - isn't it possible that one of the integers a,b,c is zero? The question doesn't state that the integers are either positive or distinct numbers. In the case that they aren't and a=0 while b=c, then wouldn't we have the case that a*b*c = 0 and thus both statements are insufficient? This is the answer I got, so if you could please explain I'd be really grateful.


ZERO:

1. 0 is an integer.

2. 0 is an even integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even.

3. 0 is neither positive nor negative integer (the only one of this kind).

4. 0 is divisible by EVERY integer except 0 itself.


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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: M27-13   [#permalink] 24 Nov 2017, 08:25
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