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

Question

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!

singhabhijeet · Accepted Answer

I took a little different approach to solve this question.

p =  2^x * 3^y * 5^z

So, p = multiple of 2*3*5 = 30.

Smallest multiple in answer chose is 240.

Hence, ans: Option B.

Andrenico · Answer

x, z, and y can have the same value. I got 240 2^4+3*5, since y and z must be > than 0

grichagupta · Answer

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.

Bunuel · Answer

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

sillyboy · Answer

+1 B.

x=4
y=1
z=1

=> 2^x*3^y*5^z = 2^4 * 3^1 * 5^1 = 16*3*5 = 240

devctg · Answer

x + y + Z = 6
we can chose bigger value for x , as it is power of 2 which is smallest number out of given three values

so x =4 ; y =1 ; z = 1

then 2^x 3^y 5^z => 16*3*5 = 240

guptarahul · Answer

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

x+y+z=6 => 2^x*3^y*5^z = 2^4 * 3^1 * 5^1 = 16*3*5 = 240

rever08 · Answer

Remember words play important role. since x, y, and z are positive they cannot be 0.

sashiim20 · Answer

p = (2^x )( 3^y)(5^z)

x + y + z = 6

x, y,  and  z  are positive integers.

Smallest value of ' p ' would be when  x, y , z  would be smallest positive integers.

x = 4 
 y = 1  
 z = 1

x+y+z = 4 + 1 + 1 = 6

p = (2^4)( 3^1)(5^1) = (16)(3)(5) = 240

Answer (B)...

vasu1104 · Answer

i found the easiest way is to factorize the given choices and see which has 2,3 and 5 as a factor and which one is smallest in all.
by doing this 240 is smallest

arushi118 · Answer

p = 2^x.3^y.5^z
x+y+z = 6
z = 1 (as x, y, z are positive - none of them can be 0)

x,y -> 1,4 or 4,1 or 2,3 or 3,2
if we try with x = 4, y=1 and z=1 : we get p = 240 which is the smallest number possible.

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

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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

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