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If x is the lowest common multiple of 15, 18, and 24 and y is the grea

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If x is the lowest common multiple of 15, 18, and 24 and y is the grea  [#permalink]

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New post 19 Apr 2016, 02:16
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If x is the lowest common multiple of 15, 18, and 24 and y is the greatest common factor of 15, 18, and 24, what is the value of x^2 – 2xy + y^2?

A. 115^2
B. 250^2
C. 357^2
D. 463^2
E. 500^2

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If x is the lowest common multiple of 15, 18, and 24 and y is the grea  [#permalink]

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New post 19 Apr 2016, 03:50
1
1
Bunuel wrote:
If x is the lowest common multiple of 15, 18, and 24 and y is the greatest common factor of 15, 18, and 24, what is the value of x^2 – 2xy + y^2?

A. 115^2
B. 250^2
C. 357^2
D. 463^2
E. 500^2


hi,

Two ways..


1)straight elimination
all terms 15, 18 and 24 are multiple of 3 and 9 in one number..
so their HCF, y and LCM, x should also be multiple of 3..
so all terms in \(x^2 – 2xy + y^2\) should be multiple of 3..
look for a choice which is a multiple of 3..
ONLY C is left

2)lets find the HCF and LCM first..
\(15= 3*5....
18=2*3^2...
24=2^3*3..\)

\(HCF = 3..
LCM = 2^3*3^2*5\)

now
\(x^2 – 2xy + y^2 = (x-y)^2 = (2^3*3^2*5-3)^2=357^2\)
C
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: If x is the lowest common multiple of 15, 18, and 24 and y is the grea  [#permalink]

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New post 19 Apr 2016, 10:15
chetan2u wrote:
Bunuel wrote:
If x is the lowest common multiple of 15, 18, and 24 and y is the greatest common factor of 15, 18, and 24, what is the value of x^2 – 2xy + y^2?

A. 115^2
B. 250^2
C. 357^2
D. 463^2
E. 500^2


hi,

Two ways..


1)straight elimination
all terms 15, 18 and 24 are multiple of 3 and 9 in one number..
so their HCF, y and LCM, x should also be multiple of 3..
so all terms in \(x^2 – 2xy + y^2\) should be multiple of 3..
look for a choice which is a multiple of 3..
ONLY C is left

2)lets find the HCF and LCM first..
\(15= 3*5....
18=2*3^3...
24=2^3*3..\)

\(HCF = 3..
LCM = 2*3^6*5\)

now
\(x^2 – 2xy + y^2 = (x-y)^2 = (2*3^6*5-3)^2=357^2\)
C


Your answer appears correct but your Greatest Common Factor isn't. I don't know how you got the answer correct given your work. you have 2*3^6*5...... it should be 5*3^2*2^3 (which equals 360).
Your GCF equals to 7290.
Also, 18 GCF is not 2*3^3..... it is 3^2*2

If you work it out, you will see that answer is (3-360)^2.... which is (-357)^2...which is in turn 357^2. Hope this helps
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Re: If x is the lowest common multiple of 15, 18, and 24 and y is the grea  [#permalink]

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New post 19 Apr 2016, 13:34
1
LCM of
15 = 3 x 5
18 = 3 x 3 x 2
24 = 3 x 2 x 2 x 2

is 3 x 2 x 5 x 3 x 2 x 2 = 360

GCF of 15, 18 and 24 = 3 (as seen above)

so X = 360 and Y =3

X^2 – 2XY + Y^2 = (X - Y)^2 = (360-3)^2 = 357^2

Correct Option : C
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Re: If x is the lowest common multiple of 15, 18, and 24 and y is the grea  [#permalink]

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New post 19 Apr 2016, 18:21
chetan2u wrote:
Bunuel wrote:
If x is the lowest common multiple of 15, 18, and 24 and y is the greatest common factor of 15, 18, and 24, what is the value of x^2 – 2xy + y^2?

A. 115^2
B. 250^2
C. 357^2
D. 463^2
E. 500^2


hi,

Two ways..


1)straight elimination
all terms 15, 18 and 24 are multiple of 3 and 9 in one number..
so their HCF, y and LCM, x should also be multiple of 3..
so all terms in \(x^2 – 2xy + y^2\) should be multiple of 3..
look for a choice which is a multiple of 3..
ONLY C is left

2)lets find the HCF and LCM first..
\(15= 3*5....
18=2*3^3...
24=2^3*3..\)

\(HCF = 3..
LCM = 2*3^6*5\)

now
\(x^2 – 2xy + y^2 = (x-y)^2 = (2*3^6*5-3)^2=357^2\)
C

i think highlighted part is wrong....
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Posts: 7106
Re: If x is the lowest common multiple of 15, 18, and 24 and y is the grea  [#permalink]

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New post 19 Apr 2016, 19:06
sashaman14 wrote:
chetan2u wrote:
Bunuel wrote:
If x is the lowest common multiple of 15, 18, and 24 and y is the greatest common factor of 15, 18, and 24, what is the value of x^2 – 2xy + y^2?

A. 115^2
B. 250^2
C. 357^2
D. 463^2
E. 500^2


hi,

Two ways..


1)straight elimination
all terms 15, 18 and 24 are multiple of 3 and 9 in one number..
so their HCF, y and LCM, x should also be multiple of 3..
so all terms in \(x^2 – 2xy + y^2\) should be multiple of 3..
look for a choice which is a multiple of 3..
ONLY C is left

2)lets find the HCF and LCM first..
\(15= 3*5....
18=2*3^3...
24=2^3*3..\)

\(HCF = 3..
LCM = 2*3^6*5\)

now
\(x^2 – 2xy + y^2 = (x-y)^2 = (2*3^6*5-3)^2=357^2\)
C


Your answer appears correct but your Greatest Common Factor isn't. I don't know how you got the answer correct given your work. you have 2*3^6*5...... it should be 5*3^2*2^3 (which equals 360).
Your GCF equals to 7290.
Also, 18 GCF is not 2*3^3..... it is 3^2*2

If you work it out, you will see that answer is (3-360)^2.... which is (-357)^2...which is in turn 357^2. Hope this helps


Hi,
The answer is correct and GCF is also correct as 3..
However there are few typo in LCMs, which I have corrected..
I have corrected the errors..

But you should not get confused in GCF and LCM..
GCF is HCF, which is the greatest common factor

Quote:
Also, 18 GCF is not 2*3^3..... it is 3^2*2

here these are not GCF BUT factors..
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: If x is the lowest common multiple of 15, 18, and 24 and y is the grea  [#permalink]

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New post 28 Nov 2016, 11:11
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Re: If x is the lowest common multiple of 15, 18, and 24 and y is the grea  [#permalink]

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Re: If x is the lowest common multiple of 15, 18, and 24 and y is the grea &nbs [#permalink] 11 Dec 2017, 05:12
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