Please help with question below
If x, y and z are integers and xyz is divisible by 8, is x even?
1) yz is divisible by 4
2) x,y,z are all not divisible by 4
Statement 1
We do not know anything about x
Not Sufficient
Statement 2
I am a bit confused with the language of the question. Is it suggesting that only possible value of x y z is restricted to 2 each? Hence the statement is sufficient?
But possible values of x y z can be
x=6 y=2 z=2
x=3 y=6 z=2
So why is the answer B
If x, y and z are integers and xyz is divisible by 8
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- fiza gupta
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(2) second statement implies that not all x,y,z are divisible by 4
to make xyz divisible by 8 all hhas to be multiple of 2.
SUFFICIENT
to make xyz divisible by 8 all hhas to be multiple of 2.
SUFFICIENT
Last edited by fiza gupta on Tue Nov 01, 2016 9:53 am, edited 1 time in total.
Fiza Gupta
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Hi melguy,
The wording in Fact 2 is a bit clunky, but if the intent of this question is that the correct answer is supposed to be B, then here is how you're meant to interpret Fact 2:
To start, we know that X, Y and Z are all INTEGERS and that (X)(Y)(Z) is divisible by 8. This means that when we prime-factor (X)(Y)(Z) we'll have AT LEAST three 2s. We're asked if X is EVEN. This is a YES/NO question.
1) (Y)(Z) is divisible by 4.
IF...
X=2, Y=2, Z=2, then the answer to the question is YES.
X=1, Y=4, Z=4, then the answer to the question is NO.
Fact 1 is INSUFFICIENT
2) X, Y and Z are all NOT divisible by 4
Since this Fact states that the variables are "all not divisible by 4", then whatever these three variables are... none of them is divisible by 4. Thus, none is a multiple of 4, although they could all be even. Remember though - we're told that (X)(Y)(Z) is divisible by 8, so there has to be three 2s in the prime-factorization of that product. If none of the variables is divisible by 4, then each variable could contain no more than one 2 in its prime-factorization. With three variables and three 2s needed, each variable MUST contain one 2 - which means that each variable MUST be EVEN. The answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT
Final Answer: B
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Rich
The wording in Fact 2 is a bit clunky, but if the intent of this question is that the correct answer is supposed to be B, then here is how you're meant to interpret Fact 2:
To start, we know that X, Y and Z are all INTEGERS and that (X)(Y)(Z) is divisible by 8. This means that when we prime-factor (X)(Y)(Z) we'll have AT LEAST three 2s. We're asked if X is EVEN. This is a YES/NO question.
1) (Y)(Z) is divisible by 4.
IF...
X=2, Y=2, Z=2, then the answer to the question is YES.
X=1, Y=4, Z=4, then the answer to the question is NO.
Fact 1 is INSUFFICIENT
2) X, Y and Z are all NOT divisible by 4
Since this Fact states that the variables are "all not divisible by 4", then whatever these three variables are... none of them is divisible by 4. Thus, none is a multiple of 4, although they could all be even. Remember though - we're told that (X)(Y)(Z) is divisible by 8, so there has to be three 2s in the prime-factorization of that product. If none of the variables is divisible by 4, then each variable could contain no more than one 2 in its prime-factorization. With three variables and three 2s needed, each variable MUST contain one 2 - which means that each variable MUST be EVEN. The answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
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Hi melguy,melguy wrote:Please help with question below
If x, y and z are integers and xyz is divisible by 8, is x even?
1) yz is divisible by 4
2) x,y,z are all not divisible by 4
Statement 1
We do not know anything about x
Not Sufficient
Statement 2
I am a bit confused with the language of the question. Is it suggesting that only possible value of x y z is restricted to 2 each? Hence the statement is sufficient?
But possible values of x y z can be
x=6 y=2 z=2
x=3 y=6 z=2
So why is the answer B
As far as the question "If x, y and z are integers and xyz is divisible by 8, is x even?" is concerned, it is clear that it does not suggest that each of x, y, and z are 2. All it implies: (1) x, y and z are integers. (2) [x.y.z] is a multiple of 8.
Till we see a statement, we have to only think that at least one among x, y, and z is even. x can be even or odd.
Let us see each statement one by one.
S1: Given that yz is divisible by 4.
If x is a multiple of 2 (even), xyz is a multiple of 8, thus the answer is YES.
However, if yz itself is a multiple of 8, x may or may not be even; it may be odd. The answer is NO. Insufficient.
S2: Given that x, y, and z are all not divisible by 4, we have to think of how will the product of x, y, and z would be a multiple of 8 = 2^3?
We can deduce that each of x, y, and x must be a multiple of 2, so that x.y.z would be a multiple of 8 = 2^3. Thus, x is even. Sufficient.
Hope this helps!
-Jay
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Be careful. Your second example (x=3 y=6 z=2) does not meet the given condition that xyz is divisible by 8.melguy wrote:Please help with question below
If x, y and z are integers and xyz is divisible by 8, is x even?
1) yz is divisible by 4
2) x,y,z are all not divisible by 4
Statement 1
We do not know anything about x
Not Sufficient
Statement 2
I am a bit confused with the language of the question. Is it suggesting that only possible value of x y z is restricted to 2 each? Hence the statement is sufficient?
But possible values of x y z can be
x=6 y=2 z=2
x=3 y=6 z=2
So why is the answer B
Here, xyz = (3)(6)(2) = 36, and 36 is not divisible by 8
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We are given that x, y, and z are integers and xyz is divisible by 8. We need to determine whether x is even, i.e., whether x is divisible by 2.melguy wrote:Please help with question below
If x, y and z are integers and xyz is divisible by 8, is x even?
1) yz is divisible by 4
2) x,y,z are all not divisible by 4
Statement One Alone:
yz is divisible by 4.
We don't have enough information to determine whether x is even. For example, if yz = 4, then x could be 2, so that xyz = 8 is divisible by 8. However, if yz = 8, then x could be 3, so that xyz = 24 is divisible by 8. In the former case, x is even; in the latter case, x is odd. Statement one alone is not sufficient to answer the question.
Statement Two Alone:
x, y, z are all not divisible by 4.
Notice that 4 = 2^2 and 8 = 2^3. If x, y, and z are not divisible by 4, in order for the product, xyz, to be divisible by 8, each variable has to be divisible by 2. Thus, x must be even.
Answer: B
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