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The OA is correct.mmslf75 wrote:Is X^2 * Y^4 an integer divisible by 9 ?
1. X is an integer divisible by 3
2. X*Y is an integer divisble by 9
OA : E
Source : GMATClub
Query :
Doesnt St1 all by itself anwer the question ??
Yah, the "an integer" part is irrelevant; only integers are divisible by integers. For some reason a lot of questions have that kind of redundancy built in (another common example is that a question will describe a number as an "even integer", when "even" already implies "integer", at least for GMAT level math).papgust wrote:Stuart, i was particularly confused with the statement "Is X^2 * Y^4 an integer divisible by 9?" which made me think that statement 1 could be sufficient to answer.
So it's kinda dangerous when playing with these kind of questions,,Stuart Kovinsky wrote:Yah, the "an integer" part is irrelevant; only integers are divisible by integers. For some reason a lot of questions have that kind of redundancy built in (another common example is that a question will describe a number as an "even integer", when "even" already implies "integer", at least for GMAT level math).papgust wrote:Stuart, i was particularly confused with the statement "Is X^2 * Y^4 an integer divisible by 9?" which made me think that statement 1 could be sufficient to answer.
You also have to interpret the question correctly. "Is X^2 * Y^4 an integer divisible by 9?" doesn't imply that X^2 * Y^4 is an integer, just as "is my car a 4 year old Ford?" doesn't imply that my car is 4 years old.
Stuart,Stuart Kovinsky wrote:The OA is correct.mmslf75 wrote:Is X^2 * Y^4 an integer divisible by 9 ?
1. X is an integer divisible by 3
2. X*Y is an integer divisble by 9
OA : E
Source : GMATClub
Query :
Doesnt St1 all by itself anwer the question ??
One thing we must NEVER do in DS - make assumptions; nowhere in this question does it say that X and Y are integers.
For statement 1, even if X is a multiple of 3, Y could be .0000001, giving us a "no" answer.
We could also pick x=3 and y=1 to get a "yes" answer.
(2) is a bit more interesting, but also insufficient. We can rewrite the original as:
XY * XY * Y * Y
and we can see that even if XY is a multiple of 9, the whole thing doesn't need to be a multiple of 9. For example, we could choose:
x = 9/pi
y = pi
so that xy = 9, and we'd get:
9 * 9 * pi * pi which certainly isn't a multiple of 9.
So, (2) is also insufficient alone.
How about together? We know that X is a multiple of 3 and XY is a multiple of 9.
We can certainly get a yes answer if we pick x=3 and y=3. So the question is, can we get a no answer?
We can no longer pick 9/pi for x, since x must be a multiple of 3.
Well, what if we pick x = 6 and y = 1.5.
6 is a multiple of 3, so we satisfy (1).
6*1.5 = 9 which is a multiple of 9, so we satisfy (2).
9*9*1.5*1.5 isn't an integer, so we can also get a no answer.
Therefore, choose (E).
mehravikas wrote:Answer should be D
1. Statement 1 is sufficient itself
2. Statement 2 can be written as X*Y * X*Y^3 - We know that X*Y is divisible by 9 therefore it is sufficient
rohan_vus wrote:X and Y are not mentioned as integers so they could be any number..Your point is valid only if X and Y could have been integers
1. X is an integer divisible by 3
Take X = 3 and Y = 1.5 --> x^2*Y^4 ----> clearly not divisible by 9 even though X^2 alone is divisble by 9... NOT SUFFICIENT
- Why take the whole product 3 * 3 * 1.5^4 - isnt it divisible by 9?
2. X*Y is an integer divisble by 9 --> Assume X = 9 and Y = 1/9...X*Y is an integer but X^2*Y^4 = 81* (1/9^4)== (1/81^2)..a fraction thus NOT SUFFICIENT - your example is wrong it x*y is an integer divisible by 9 but in your example x*y = 1 which is not divisible by 9
Even if you combine X and Y..no success as X = 9 case we already considered for 2nd stmnt , which any how suffices case of stmnt 1 of X being multiple of 3..
So (E) ...
[/quote][/quote]rohan_vus wrote:X and Y are not mentioned as integers so they could be any number..Your point is valid only if X and Y could have been integers
1. X is an integer divisible by 3
Take X = 3 and Y = 1.5 --> x^2*Y^4 ----> clearly not divisible by 9 even though X^2 alone is divisble by 9... NOT SUFFICIENT
- Why take the whole product 3 * 3 * 1.5^4 - isnt it divisible by 9?
--because if you do that total is what ..its 45.5625---> a non integer.. the decimal portion will stand out as remainder when u divide by 9....
2. X*Y is an integer divisble by 9 --> Assume X = 9 and Y = 1/9...X*Y is an integer but X^2*Y^4 = 81* (1/9^4)== (1/81^2)..a fraction thus NOT SUFFICIENT - your example is wrong it x*y is an integer divisible by 9 but in your example x*y = 1 which is not divisible by 9
a mistake indeed coz of hurry , but doesnt matter ... ok X*Y = 9 lets say,., so what -- X = 6 and Y = 3/2 ..X*Y = 9 .. but X^2*Y^4 = 729/4 ...a clear non integer..even if divide a non integer by 9 its the decimal part which stand out to deny the divisibility criteria... Likeiwse there are n number of ways to illustrate this one
Even if you combine X and Y..no success as X = 9 case we already considered for 2nd stmnt , which any how suffices case of stmnt 1 of X being multiple of 3..
So (E) ...
I'm not sure how you've solved at all.mehravikas wrote:the content of the questions seems to be ambiguous. You are first calculating the product of X and Y and then dividing the total product by 9.
I am breaking the product as X * X * Y * Y * Y * Y and dividing it by 9.
So the final equation is - (X * X * Y * Y * Y * Y) / 9
If you divide by 9 before multiplying the numerator you can say that the equation is divisible by 9
I agree that with your approach the answer would be E, but consider my approach and check the answer.
I may be wrong but I think it could be solved the way I have done.
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