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# What is the least integer z for which (0.000125)(0.0025)(0.00000125)

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What is the least integer z for which (0.000125)(0.0025)(0.00000125)  [#permalink]

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30 Jul 2018, 22:02
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What is the least integer z for which $$(0.000125)(0.0025)(0.00000125)*10^z$$ is an integer?

A. 18
B. 10
C. 0
D. −10
E. −18

NEW question from GMAT® Quantitative Review 2019

(PS00774)

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Re: What is the least integer z for which (0.000125)(0.0025)(0.00000125)  [#permalink]

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30 Jul 2018, 22:33
5
1
Bunuel wrote:
What is the least integer z for which $$(0.000125)(0.0025)(0.00000125)*10^z$$ is an integer?

A. 18
B. 10
C. 0
D. −10
E. −18

NEW question from GMAT® Quantitative Review 2019

(PS00774)

OA: A
$$(0.000125)(0.0025)(0.00000125)*10^z= 125*10^{-6}*25*10^{-4}*125*10^{-8}*10^z$$
$$=125*25*125*10^{-6-4-8+z}$$
$$=125*25*125*10^{-18+z}$$

$$125*25*125$$ will end with $$5$$ as unit's digit, there will be no $$0$$ at unit's place.So for $$z$$ to be minimum,$$-18+z$$ should be equal to $$0$$.
$$-18+z=0$$
$$z=18$$
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##### General Discussion
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What is the least integer z for which (0.000125)(0.0025)(0.00000125)  [#permalink]

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Updated on: 03 Dec 2018, 23:43

Solution

Given:
• We are given an expression: $$(0.000125)(0.0025)(0.00000125)∗10^z$$

To find:
• We need to find the least integer z such that $$(0.000125)(0.0025)(0.00000125)∗10^z$$ is an integer

Approach and Working:

• $$(0.000125)(0.0025)(0.00000125)∗10^z$$ can be written as $$(125* 10^{-6})(25*10^{-4})(125* 10^{-8})* 10^z$$
• = $$125*25*125* 10^{-6-4-8+z}$$
• For $$125*25*125* 10^{-6-4-8+z}$$ to be an integer, the power of 10 in $$10^{-6-4-8+z}$$ must be an integer, which is greater than or equal to 0
o Implies, -6 - 4 - 8 + z ≥ 0
o z ≥ 18

Hence, the correct answer is option A.

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Originally posted by EgmatQuantExpert on 30 Jul 2018, 22:56.
Last edited by EgmatQuantExpert on 03 Dec 2018, 23:43, edited 1 time in total.
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Re: What is the least integer z for which (0.000125)(0.0025)(0.00000125)  [#permalink]

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30 Jul 2018, 23:59
2
Bunuel wrote:
What is the least integer z for which $$(0.000125)(0.0025)(0.00000125)*10^z$$ is an integer?

A. 18
B. 10
C. 0
D. −10
E. −18

NEW question from GMAT® Quantitative Review 2019

(PS00774)

This question needs no calculation. Just think.

If we use negative exponent as a value of z we won't get integer in this case. Eliminate D and E. For the same reason o can't be the value of z as we need integer.

We are left with A and B. If anyone calculate the fraction he gets 18 decimal points. A is the best answer.

The best answer is A.
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Re: What is the least integer z for which (0.000125)(0.0025)(0.00000125)  [#permalink]

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31 Jul 2018, 02:32
= 125 ∗ 25 ∗ 125 ∗ 10^(−6−4−8+z)
= 125 ∗ 25 ∗ 125 ∗ 10^(−18+z)

For the above value to be integer, we need a a value of Z that equals 0, therefore 18
-18 + z = 0
-18 + 18 = 0

Hence, A.
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Re: What is the least integer z for which (0.000125)(0.0025)(0.00000125)  [#permalink]

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31 Jul 2018, 07:37
Bunuel wrote:
What is the least integer z for which $$(0.000125)(0.0025)(0.00000125)*10^z$$ is an integer?

A. 18
B. 10
C. 0
D. −10
E. −18

NEW question from GMAT® Quantitative Review 2019

(PS00774)

$$(0.000125)(0.0025)(0.00000125)*10^z$$

$$= (\frac{125}{10^6})(\frac{25}{10^4})(\frac{125}{10^8})10^z$$

$$= (\frac{5^3}{10^6})(\frac{5^2}{10^4})(\frac{5^3}{10^8})10^z$$

$$= \frac{5^8}{10^{18}}10^z$$

Now, if $$z = 18$$, then we will have an Integer with value $$5^8$$, Answer must be (A)
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Re: What is the least integer z for which (0.000125)(0.0025)(0.00000125)  [#permalink]

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10 Aug 2018, 19:09
Bunuel wrote:
What is the least integer z for which $$(0.000125)(0.0025)(0.00000125)*10^z$$ is an integer?

A. 18
B. 10
C. 0
D. −10
E. −18

0.000125 = 5^3 x 10^-6

0.0025 = 5^2 x 10^-4

0.00000125 = 5^3 x 10^-8

So the product equals 5^8 x 10^-18 x 10^z. We see that if z = 18, then the product will be an integer.

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Re: What is the least integer z for which (0.000125)(0.0025)(0.00000125)   [#permalink] 10 Aug 2018, 19:09
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