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ian7777
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n, w, x, y, and z are all positive integers. If Updated on: 25 Jul 2004, 10:00
Originally posted by ian7777 on 25 Jul 2004, 09:10.
Last edited by ian7777 on 25 Jul 2004, 10:00, edited 1 time in total.
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n, w, x, y, and z are all positive integers. If n=(3^w)(5^x)(7^y)(11^z), and if n is divisible by both 7,425 and 4,235, what is the minimum* value of (wxyz)/3?

A) 3
B) 4
C) 9
D) 12
E) 27

Note: this is an adaptation of a problem from a real test with Quant score of 50.

*the word "minimum" was added later after realizing that is the most correct way to ask this question. See Dookie's post.



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n, w, x, y, and z are all positive integers. If 25 Jul 2004, 09:33
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The best answer is B.

Approach:

1.Factorise 7425 ad 4235
7425=5x5x3x3x3x11
4235=5x7x11x11

2. so the LCM of 7425 and 4235 is 3^3 x 5^2 x 7^1 x 11^2

3. so w=3, x=2, y=1 and z=2

4. so, wxyz/3 = 12/3 =4.
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n, w, x, y, and z are all positive integers. If 25 Jul 2004, 09:37
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Sorry to have not logged in earlier. The Guest was me.

The best answer is B.

Approach:

1.Factorise 7425 ad 4235
7425=5x5x3x3x3x11
4235=5x7x11x11

2. so the LCM of 7425 and 4235 is 3^3 x 5^2 x 7^1 x 11^2

3. so w=3, x=2, y=1 and z=2
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n, w, x, y, and z are all positive integers. If Updated on: 25 Jul 2004, 10:12
Originally posted by Dookie on 25 Jul 2004, 09:38.
Last edited by Dookie on 25 Jul 2004, 10:12, edited 1 time in total.
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B.

7425 = 5*5*3*3*3*11
4235 = 11*11*7*5

W = 3
X = 2
Y = 1
Z = 2

Therefore, the answer is 4.

I think that the question should be: "What COULD be the value".
N could also be divisible by other greater numbers, so W,X,Y,Z could be different...
Ian, what do you think ?
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ian7777
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n, w, x, y, and z are all positive integers. If 25 Jul 2004, 09:59
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Dookie,

you're right. My bad. The question should read,

"which of the following is the MINIMUM value of wxyz/3?"

sorry about that...I've changed the problem.

by the way, please check your prime factorization of 7425...
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n, w, x, y, and z are all positive integers. If 25 Jul 2004, 10:39
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Thanks, i fixed the typo.
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n, w, x, y, and z are all positive integers. If 27 Aug 2006, 09:57
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n, w, x, y, and z are all positive integers. If n=(3^w)(5^x)(7^y)(11^z), and if n is divisible by both 7,425 and 4,235, what is the minimum* value of (wxyz)/3?

A) 3
B) 4
C) 9
D) 12
E) 27
Found this question posted long long ago
I think it is very interesting
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haas_mba07
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n, w, x, y, and z are all positive integers. If 27 Aug 2006, 10:10
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B) 4

Although tedious, you just need to find the LCM of 7425 & 4235 and get the following:

LCM(7425, 4325) = 3x3x3 x 5x5 x 7 x 11x11

Giving w=2, x=2, y=1, z=2;
wxyz/3 = 4
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n, w, x, y, and z are all positive integers. If 27 Aug 2006, 10:22
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B for me too ..
7425 = 3^3 * 5 ^2 * 11
4235 = 5 * 7 * 11 ^2 ..
pick the gretaest powers of each prime number ...
theus
w = 3, x = 2, y = 1, z = 2 ...
wxyz/3 = 3*2*1*2/3 = 4 ..



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