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Problem solving ?

by Pugalenthi » Sat May 12, 2012 7:03 am
p is equal to the product of 2^x, 3^y, and 5^z. If x, y, and z are positive integers and x+y+z = 6, what is the smallest possible value of p?
(A) 64
(B) 240
(C) 360
(D) 640
(E) 900

https://www.gmatdaily.com/20120511-gmat- ... e-day.html
The answer is B. I am wondering why A is not the answer. Here is my logic...x could be 6 and y and z could be zero...then 2^6*3^0*5^0 =64. What am I missing? Please let me know
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by Brent@GMATPrepNow » Sat May 12, 2012 7:31 am
Pugalenthi wrote:p is equal to the product of 2^x, 3^y, and 5^z. If x, y, and z are positive integers and x+y+z = 6, what is the smallest possible value of p?
(A) 64
(B) 240
(C) 360
(D) 640
(E) 900

https://www.gmatdaily.com/20120511-gmat- ... e-day.html
The answer is B. I am wondering why A is not the answer. Here is my logic...x could be 6 and y and z could be zero...then 2^6*3^0*5^0 =64. What am I missing? Please let me know
Your strategy of minimizing the values of y and z, while also maximizing the value of x is perfect.
The only thing you missed is the word "positive."
So, the best we can do is x=4, y=1, and z=1

We get (2^4)(3^1)(5^1) =[spoiler] 240 = B[/spoiler]

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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