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# If z is a positive integer and y = 6.038x10^z, what is the value of z?

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Math Expert
Joined: 02 Sep 2009
Posts: 51215
If z is a positive integer and y = 6.038x10^z, what is the value of z?  [#permalink]

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21 Jul 2016, 22:46
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Difficulty:

45% (medium)

Question Stats:

67% (01:35) correct 33% (01:36) wrong based on 136 sessions

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If z is a positive integer and $$y = 6.038 * 10^{z}$$, what is the value of z?

(1) $$6500 < y < 65,000$$

(2) $$10^{4}< y < 10^{5}$$

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If z is a positive integer and y = 6.038x10^z, what is the value of z?  [#permalink]

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22 Jul 2016, 01:12
1
Bunuel wrote:
If z is a positive integer and $$y = 6.038 * 10^{z}$$, what is the value of z?

(1) $$6500 < y < 65,000$$

(2) $$10^{4}< y < 10^{5}$$

Given y = 6.038 * 10^{z}

if Z = 3 then we get y = 6038 then this value is not in the range 6500 < y < 65,000.

Stat 1: if Z = 4 then we get y = 60380 then this value within the limit 6500 < y < 65,000.

if Z = 5 then we get y as 603800 which is greater than maximum limit 65,000...this can't be the value. Sufficient..we get unique result.

Stat 2 : 10^{4}< y < 10^{5} i.e. 10000 < y < 100000 in order to make sure Y value is within the range.

Let's check the value of Z
if Z = 3 then we get y = 6038 then this value is not 10000 < y < 100000 limit.

if Z = 4 then 60380 suits in the limit 10000 < y < 100000.

if z = 5 then 603800 it exceeds 100000.... Sufficient..we get unique result.

IMO D is correct option..

OA please..will correct if I missed anything..
CEO
Joined: 11 Sep 2015
Posts: 3237
Re: If z is a positive integer and y = 6.038x10^z, what is the value of z?  [#permalink]

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24 Feb 2018, 14:11
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Top Contributor
Bunuel wrote:
If z is a positive integer and $$y = 6.038 * 10^{z}$$, what is the value of z?

(1) $$6500 < y < 65,000$$

(2) $$10^{4}< y < 10^{5}$$

Target question: What is the value of z?

Given: z is a positive integer and y = (6.038)(10^z)
Since z is a positive integer, let's see how different values of z affect the value of y
Case a: z = 1: y = (6.038)(10^1) = (6.038)(10) = 60.38
Case b: z = 2: y = (6.038)(10^2) = (6.038)(100) = 603.8
Case c: z = 3: y = (6.038)(10^3) = (6.038)(1,000) = 6,038
Case d: z = 4: y = (6.038)(10^4) = (6.038)(10,000) = 60,380
Case e: z = 5: y = (6.038)(10^5) = (6.038)(100,000) = 603,800
Case e: z = 6: y = (6.038)(10^6) = (6.038)(1,000,000) = 6,038,000
.
.
.

So, y can equal 60.38 or 603.8 or 6,038 or 60,380 or 603,800 or 6,038,000 or . . . etc

Statement 1: 6500 < y < 65,000
Only one possible value of y lies between 6500 and 65,000
That value is 60,380 (case d)
So, y MUST equal 60,380, which mean z MUST equal 4
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: 10^4 < y < 10^5
10^4 = 10,000 and 10^5 = 100,000
Only one possible value of y lies between 10,000 and 100,000
That value is 60,380 (case d)
So, y MUST equal 60,380, which mean z MUST equal 4
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent
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Re: If z is a positive integer and y = 6.038x10^z, what is the value of z? &nbs [#permalink] 24 Feb 2018, 14:11
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