I dont know what is the component I should be focussing on while doing this problem
If n and y are positive integers and 450y=n^3, which of the following must be an integer??
I.y/3*2^2*5
II.y/3^2*2*5
III.y/3*2*5^2
Thanks
GMAT Prpe
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450 = 2 x 5^2 x 3^2moneyman wrote:I dont know what is the component I should be focussing on while doing this problem
If n and y are positive integers and 450y=n^3, which of the following must be an integer??
I.y/3*2^2*5
II.y/3^2*2*5
III.y/3*2*5^2
Thanks
Now 2 x 5^2 x 3^2 x y = n^3
So at minimum, y = 2^2 x 5 x 3
So y/3*2^2*5 is the minimum value which will always be integer. Got me, Max?
Correct me If I am wrong
Regards,
Amitava
Regards,
Amitava
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i tried to push numbers out for this and wound up with n=10 and y=2.2
when i plugged them into the answer choices not one of the roman numerals gave an integer. So my first answer is none will give an integer.
I tried to break this up into primes but then got lost.
can someone explain this to me in baby steps and please give qa. thanks folks!
when i plugged them into the answer choices not one of the roman numerals gave an integer. So my first answer is none will give an integer.
I tried to break this up into primes but then got lost.
can someone explain this to me in baby steps and please give qa. thanks folks!
Appetite for 700 and I scraped my plate!
Step by step:Enginpasa1 wrote:i tried to push numbers out for this and wound up with n=10 and y=2.2
when i plugged them into the answer choices not one of the roman numerals gave an integer. So my first answer is none will give an integer.
I tried to break this up into primes but then got lost.
can someone explain this to me in baby steps and please give qa. thanks folks!
Find the prime factors of 450.
450
->45*10
->9*5*2*5
-->3*3*5*2*5
--->2*3*3*5*5
The question states that 450y = n^3.
Since y and n are both positive integers, this means that 450y must be a perfect cube.
In order for 450y to be a perfect cube, we look at our current prime factors of 450:
(2) (3*3) (5*5)
Therefore, in order for 450y to be a perfect cube, we need an additional 5, an additional 3, and two additional 2's.
(2) (3*3) (5*5) * y
->(2) (3*3) (5*5) * [(2*2) (3) (5)]
-->(2*2*2) (3*3*3) (5*5*5) = perfect cube
Thus, at minimum, y must be [(2*2) (3) (5)] or 2^2 * 3 * 5.
We look at our answer choices and plug in for y.
I)
y/3*2^2*5
-> (2^2 * 3 * 5) / 3*2^2*5 = 1 (integer)
II)
y/3^2*2*5
-> (2^2 * 3 * 5) / 3^2*2*5 = 2/3 (not an integer)
III)
y/3*2*5^2
-> (2^2 * 3 * 5) / 3*2*5^2 = 2/5 (not an integer)
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Is there a way to approach this problem and not go through all of your steps. Can we force a value for y and n and then test each roman numeral?
Appetite for 700 and I scraped my plate!
To me, this approach makes the most sense, and like camitava showed, it is pretty straightforward. I would not go through my step by step method on paper; rather, a lot of it would be mental.Enginpasa1 wrote:Is there a way to approach this problem and not go through all of your steps. Can we force a value for y and n and then test each roman numeral?
The underlying process is quite simple:
1. Recognize that 450y must be a perfect cube.
2. Break 450 into its prime factors and see what y at minimum must be to create a perfect cube.
3. Glance at I, II, and III to see if this minimum value of y can cancel all the denominator values.
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A quick suggestion Enginpasa:Enginpasa1 wrote:i tried to push numbers out for this and wound up with n=10 and y=2.2
when i plugged them into the answer choices not one of the roman numerals gave an integer. So my first answer is none will give an integer.
I tried to break this up into primes but then got lost.
can someone explain this to me in baby steps and please give qa. thanks folks!
On the GMAT, more often than not, there is as much information in the options and the other parts of the question as the actual question itself.
The 3 Roman Numeral statements are CLEAR indicators that Prime factorisation is in some way or the other involved.
Any method that takes us away from that will be longer and relatively more cumbersome.
For love, not money.
thank you very much, I was surfing the web looking for such a good explanation. Good lucktmmyc wrote:Step by step:Enginpasa1 wrote:i tried to push numbers out for this and wound up with n=10 and y=2.2
when i plugged them into the answer choices not one of the roman numerals gave an integer. So my first answer is none will give an integer.
I tried to break this up into primes but then got lost.
can someone explain this to me in baby steps and please give qa. thanks folks!
Find the prime factors of 450.
450
->45*10
->9*5*2*5
-->3*3*5*2*5
--->2*3*3*5*5
The question states that 450y = n^3.
Since y and n are both positive integers, this means that 450y must be a perfect cube.
In order for 450y to be a perfect cube, we look at our current prime factors of 450:
(2) (3*3) (5*5)
Therefore, in order for 450y to be a perfect cube, we need an additional 5, an additional 3, and two additional 2's.
(2) (3*3) (5*5) * y
->(2) (3*3) (5*5) * [(2*2) (3) (5)]
-->(2*2*2) (3*3*3) (5*5*5) = perfect cube
Thus, at minimum, y must be [(2*2) (3) (5)] or 2^2 * 3 * 5.
We look at our answer choices and plug in for y.
I)
y/3*2^2*5
-> (2^2 * 3 * 5) / 3*2^2*5 = 1 (integer)
II)
y/3^2*2*5
-> (2^2 * 3 * 5) / 3^2*2*5 = 2/3 (not an integer)
III)
y/3*2*5^2
-> (2^2 * 3 * 5) / 3*2*5^2 = 2/5 (not an integer)
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