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# Given that 0.0001402 x 10^q < 5^(-2), and q is an integer, which of th

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Joined: 02 Sep 2009
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Given that 0.0001402 x 10^q < 5^(-2), and q is an integer, which of th  [#permalink]

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18 Nov 2016, 02:40
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65% (hard)

Question Stats:

58% (01:32) correct 42% (01:35) wrong based on 189 sessions

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Given that 0.0001402 x 10^q < 5^(-2), and q is an integer, which of the following is the largest possible value of q?

A. 1
B. 2
C. 3
D. 4
E. 5

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Re: Given that 0.0001402 x 10^q < 5^(-2), and q is an integer, which of th  [#permalink]

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18 Nov 2016, 03:38
Bunuel wrote:
Given that 0.0001402 x 10^q < 5^(-2), and q is an integer, which of the following is the largest possible value of q?

A. 1
B. 2
C. 3
D. 4
E. 5

Given 0.0001402 * 10^q < 0.04
the largest value of q for which the given would be true is q=2, i.e., 0.01402 < 0.04
Hence B
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Re: Given that 0.0001402 x 10^q < 5^(-2), and q is an integer, which of th  [#permalink]

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29 Nov 2016, 16:37
Bunuel wrote:
Given that 0.0001402 x 10^q < 5^(-2), and q is an integer, which of the following is the largest possible value of q?

A. 1
B. 2
C. 3
D. 4
E. 5

We start by simplifying 5^(-2):

5^(-2) = 1/(5^2) = 1/25 = 0.04

Now we must determine the largest value of q that makes 0.0001402 x 10^q < 0.04.

When q = 2, then 0.0001402 x 10^2 = 0.01402, which is less than 0.04. However, when q = 3, then 0.0001402 x 10^3 =0.1402, which is greater than 0.04. Thus, the maximum integer value of q is 2.

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Re: Given that 0.0001402 x 10^q < 5^(-2), and q is an integer, which of th  [#permalink]

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29 Nov 2016, 19:15
Bunuel wrote:
Given that 0.0001402 x 10^q < 5^(-2), and q is an integer, which of the following is the largest possible value of q?

A. 1
B. 2
C. 3
D. 4
E. 5

$$5^{-2}=\frac{1}{5^2}=0.04 =4\times 10^{-2}$$

$$0.0001402 \times 10^q = 1.402 \times 10^{-4} \times 10^q = 1.402 \times 10^{q-4}$$

We have $$1.402 \times 10^{q-4}<4 \times 10^{-2} \implies 1.402 \times 10^{q-2}<4$$

Note that $$1.402 \times 10 =14.02 >4$$
Hence $$q-2 \leq 0 \implies q \leq 2$$

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Re: Given that 0.0001402 x 10^q < 5^(-2), and q is an integer, which of th  [#permalink]

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17 Aug 2018, 19:02
Given that 0.0001402 x 10^q < 5^(-2), and q is an integer, which of the following is the largest possible value of q?

A. 1
B. 2
C. 3
D. 4
E. 5

0.0001402 x 10^q < 5^(-2)

0.0001402 x 10^q <1/25
multiple both side by 25
(100/4)*0.0001402 x 10^q <1

.0000something*(10) ^q+2<1

so, q+2 can be 4 at max. so q can be 2

Re: Given that 0.0001402 x 10^q < 5^(-2), and q is an integer, which of th &nbs [#permalink] 17 Aug 2018, 19:02
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# Given that 0.0001402 x 10^q < 5^(-2), and q is an integer, which of th

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