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p is equal to the product of 2^x, 3^y, and 5^z. If x, y, and z are pos [#permalink]

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01 Feb 2017, 06:24

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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

Hi, I was working on this questions below and I assumed that x, y and z had to be 3 different numbers. But apparently I was wrong. I haven't been using math for a long time, but I remember we would always use different letters to refer to different values. So I thought: 1+2+3=6 was correct. However, based on the final answer, it seems that the correct assumption is x+y+z = 6 = 1+1+4=6. So x= 1 and y also =1

I would be wrong then if I assume in other math problems that different letters refer to different values? Thanks!

Re: p is equal to the product of 2^x, 3^y, and 5^z. If x, y, and z are pos [#permalink]

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01 Feb 2017, 08:12

MaggieSG, Thank you for posting this question. I made a mistake of considering x =6, y=0 and z=0 only to realize that the question clearly states POSITIVE INTEGERS and 0 is neither positive nor negative. Hence, lesson learnt. Need to keep this fact in mind while solving questions such as this.

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

Hi, I was working on this questions below and I assumed that x, y and z had to be 3 different numbers. But apparently I was wrong. I haven't been using math for a long time, but I remember we would always use different letters to refer to different values. So I thought: 1+2+3=6 was correct. However, based on the final answer, it seems that the correct assumption is x+y+z = 6 = 1+1+4=6. So x= 1 and y also =1

I would be wrong then if I assume in other math problems that different letters refer to different values? Thanks!

Unless it is explicitly stated otherwise, different variables CAN represent the same number.
_________________

Re: p is equal to the product of 2^x, 3^y, and 5^z. If x, y, and z are pos [#permalink]

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19 May 2017, 01:58

MaggieSG 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

Hi, I was working on this questions below and I assumed that x, y and z had to be 3 different numbers. But apparently I was wrong. I haven't been using math for a long time, but I remember we would always use different letters to refer to different values. So I thought: 1+2+3=6 was correct. However, based on the final answer, it seems that the correct assumption is x+y+z = 6 = 1+1+4=6. So x= 1 and y also =1

I would be wrong then if I assume in other math problems that different letters refer to different values? Thanks!

As we want to make number as small as possible, so we will take power of smallest number i.e 2, as greater as we can take. so we take, x=4 y=1 z=1

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