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Intern  Joined: 01 Feb 2017
Posts: 1
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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1
5 00:00

Difficulty:   55% (hard)

Question Stats: 61% (01:32) correct 39% (01:38) wrong based on 288 sessions

HideShow timer Statistics 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!

Originally posted by MaggieSG on 01 Feb 2017, 07:24.
Last edited by Bunuel on 01 Feb 2017, 08:07, edited 1 time in total.
Renamed the topic and edited the question.
Intern  B
Joined: 20 Jan 2017
Posts: 1
Re: If x+y+z = 6, 1+1+4=6 is possible?  [#permalink]

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x, z, and y can have the same value. I got 240 2^4+3*5, since y and z must be > than 0
Intern  S
Joined: 13 Dec 2016
Posts: 42
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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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.
Math Expert V
Joined: 02 Sep 2009
Posts: 55804
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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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!

Unless it is explicitly stated otherwise, different variables CAN represent the same number.
_________________
Manager  G
Joined: 04 Dec 2016
Posts: 53
Location: India
GPA: 3.8
WE: Operations (Other)
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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1
+1 B.

x=4
y=1
z=1

=> 2^x*3^y*5^z = 2^4 * 3^1 * 5^1 = 16*3*5 = 240 B
Joined: 30 May 2015
Posts: 35
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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1
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
Manager  B
Joined: 02 Aug 2013
Posts: 64
Location: India
WE: Programming (Consulting)
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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2
1
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.
Manager  S
Status: Gmat lover
Joined: 27 Mar 2017
Posts: 84
Location: India
Schools: IIMA , IIMA PGPX"18
GMAT 1: 710 Q49 V39 GPA: 3.91
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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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 x+y+z=6

=> 2^x*3^y*5^z = 2^4 * 3^1 * 5^1 = 16*3*5 = 240
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Manager  S
Joined: 21 Jul 2017
Posts: 190
Location: India
GMAT 1: 660 Q47 V34 GPA: 4
WE: Project Management (Education)
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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Remember words play important role. since x, y, and z are positive they cannot be 0.
Director  V
Joined: 04 Dec 2015
Posts: 740
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)
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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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

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

$$x + y + z = 6$$

$$x, y,$$ and $$z$$ are positive integers.

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

$$x = 4$$
$$y = 1$$
$$z = 1$$

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

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

Non-Human User Joined: 09 Sep 2013
Posts: 11448
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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_________________ Re: p is equal to the product of 2^x, 3^y, and 5^z. If x, y, and z are pos   [#permalink] 17 Sep 2018, 10:35
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