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# Which of the two values 10^(-2) and 10^(-3), is x more close

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Which of the two values 10^(-2) and 10^(-3), is x more close [#permalink]

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22 Mar 2012, 03:49
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Which of the two values 10^(-2) and 10^(-3), is x more close to?

(1) x is more close to 10^(-4) than to 10^(-1).
(2) x is more close to 10^(-3) than to 10^(-1).
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22 Mar 2012, 06:02
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Smita04 wrote:
Which of the two values 10^(-2) and 10^(-3), is x more close to?

(1) x is more close to 10^(-4) than to 10^(-1).
(2) x is more close to 10^(-3) than to 10^(-1).

10^(-4), 10^(-3), 10^(-2) and 10^(-1) are positioned on the number line in the following way:

-(0,0001)-(0.001)---------(0.01)---------------------------------------------------------------------------------(0.1)-

Question asks which of the two middle numbers x is closer to.

(1) says that x closer to the first number than to the fourth, but it could be anywhere between the two middle numbers. Not sufficient.

(2) says that x closer to the second number than to the fourth, but it could be anywhere between the two middle numbers. Not sufficient.

(1)+(2) x could still be anywhere between the two middle numbers, so we cannot say which number x is more close to. Not sufficient.

P.S. You can consider easier numbers to manipulate with:

-(1)-(10)---------(100)---------------------------------------------------------------------------------(1000)-
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Re: Which of the two values 10^(-2) and 10^(-3), is x more close [#permalink]

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25 Jun 2013, 04:47
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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Tough and tricky PS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125956.html

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Re: Which of the two values 10^(-2) and 10^(-3), is x more close [#permalink]

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09 Jul 2013, 03:32
can anybody help with the above solution please.

number line = $$\frac{1}{10000}---- \frac{1}{1000} -- | --\frac{1}{100} ----\frac{1}{10}$$

(1) x is more closer to $$\frac{1}{10000}$$ than to $$\frac{1}{10}$$

for this to be true shouldn't x have to be to the left of the center marked as $$|$$ above and if x is the left of the center ,then shouldn't x be closer to $$\frac{1}{1000}$$than to $$\frac{1}{100}$$

I fail to see how x can be anywhere between $$\frac{1}{1000}$$ and $$\frac{1}{100}$$and still be closer to $$\frac{1}{10000}$$ than to $$\frac{1}{10}$$

lets say x is between $$\frac{1}{1000}$$ and $$\frac{1}{100}$$ but just slightly to the left of $$\frac{1}{100}$$, say x = $$\frac{1}{101}$$
now here x lies as shown $$\frac{1}{1000} -- | -- \frac{1}{101} --\frac{1}{100}$$ so here it looks x is between $$10^{-3}$$ and $$10 ^{-2}$$ but closer to $$\frac{1}{10},$$ so this doesn't satisfy statement 1

lets say x =$$\frac{1}{999}$$here the position of x = $$\frac{1}{10000}---- \frac{1}{1000} --\frac{1}{999} --- | --\frac{1}{100} ----\frac{1}{10}$$

so here statement 1 holds and x is closer to $$\frac{1}{10000}$$ .

So it seems to me for statement 1 to hold x has to be to the left of the center , marked as $$|$$in the number line, and in that case x will be closer to $$\frac{1}{1000}$$ than to $$\frac{1}{100}$$, anywhere to the right of $$|$$ and x becomes closer to $$\frac{1}{10}$$ violating statement1 , so x has to be to the left of $$|$$ for statement 1 to be true. so I am getting A as sufficient . Can anybody assist please?

thanks
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- Stne

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Which of the two values 10^(-2) and 10^(-3), is x more close [#permalink]

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09 Jul 2013, 04:10
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stne wrote:
can anybody help with the above solution please.

number line = $$\frac{1}{10000}---- \frac{1}{1000} -- | --\frac{1}{100} ----\frac{1}{10}$$

(1) x is more closer to $$\frac{1}{10000}$$ than to $$\frac{1}{10}$$

for this to be true shouldn't x have to be to the left of the center marked as $$|$$ above and if x is the left of the center ,then shouldn't x be closer to $$\frac{1}{1000}$$than to $$\frac{1}{100}$$

I fail to see how x can be anywhere between $$\frac{1}{1000}$$ and $$\frac{1}{100}$$and still be closer to $$\frac{1}{10000}$$ than to $$\frac{1}{10}$$

lets say x is between $$\frac{1}{1000}$$ and $$\frac{1}{100}$$ but just slightly to the left of $$\frac{1}{100}$$, say x = $$\frac{1}{101}$$
now here x lies as shown $$\frac{1}{1000} -- | -- \frac{1}{101} --\frac{1}{100}$$ so here it looks x is between $$10^{-3}$$ and $$10 ^{-2}$$ but closer to $$\frac{1}{10},$$ so this doesn't satisfy statement 1

lets say x =$$\frac{1}{999}$$here the position of x = $$\frac{1}{10000}---- \frac{1}{1000} --\frac{1}{999} --- | --\frac{1}{100} ----\frac{1}{10}$$

so here statement 1 holds and x is closer to $$\frac{1}{10000}$$ .

So it seems to me for statement 1 to hold x has to be to the left of the center , marked as $$|$$in the number line, and in that case x will be closer to $$\frac{1}{1000}$$ than to $$\frac{1}{100}$$, anywhere to the right of $$|$$ and x becomes closer to $$\frac{1}{10}$$ violating statement1 , so x has to be to the left of $$|$$ for statement 1 to be true. so I am getting A as sufficient . Can anybody assist please?

thanks

Which of the two values 0.01 and 0.001, is x more close to?

(1) x is more close to 0.0001 than to 0.1.
(2) x is more close to 0.001 than to 0.1.

Relative positioning on the number line might help:

Attachment:

Number line.png [ 18.55 KiB | Viewed 6188 times ]

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Re: Which of the two values 10^(-2) and 10^(-3), is x more close [#permalink]

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Updated on: 17 Aug 2013, 03:26
Bunuel wrote:
stne wrote:
can anybody help with the above solution please.

number line = $$\frac{1}{10000}---- \frac{1}{1000} -- | --\frac{1}{100} ----\frac{1}{10}$$

(1) x is more closer to $$\frac{1}{10000}$$ than to $$\frac{1}{10}$$

for this to be true shouldn't x have to be to the left of the center marked as $$|$$ above and if x is the left of the center ,then shouldn't x be closer to $$\frac{1}{1000}$$than to $$\frac{1}{100}$$

I fail to see how x can be anywhere between $$\frac{1}{1000}$$ and $$\frac{1}{100}$$and still be closer to $$\frac{1}{10000}$$ than to $$\frac{1}{10}$$

lets say x is between $$\frac{1}{1000}$$ and $$\frac{1}{100}$$ but just slightly to the left of $$\frac{1}{100}$$, say x = $$\frac{1}{101}$$
now here x lies as shown $$\frac{1}{1000} -- | -- \frac{1}{101} --\frac{1}{100}$$ so here it looks x is between $$10^{-3}$$ and $$10 ^{-2}$$ but closer to $$\frac{1}{10},$$ so this doesn't satisfy statement 1

lets say x =$$\frac{1}{999}$$here the position of x = $$\frac{1}{10000}---- \frac{1}{1000} --\frac{1}{999} --- | --\frac{1}{100} ----\frac{1}{10}$$

so here statement 1 holds and x is closer to $$\frac{1}{10000}$$ .

So it seems to me for statement 1 to hold x has to be to the left of the center , marked as $$|$$in the number line, and in that case x will be closer to $$\frac{1}{1000}$$ than to $$\frac{1}{100}$$, anywhere to the right of $$|$$ and x becomes closer to $$\frac{1}{10}$$ violating statement1 , so x has to be to the left of $$|$$ for statement 1 to be true. so I am getting A as sufficient . Can anybody assist please?

thanks

Which of the two values 0.01 and 0.001, is x more close to?

(1) x is more close to 0.0001 than to 0.1.
(2) x is more close to 0.001 than to 0.1.

Relative positioning on the number line might help:

Thank you finally got it !
didn't realize that there was so much in between 0.00 and .02

Well if I have understood the diagram above correctly then for statement 1 to be true x need not necessarily have to be in between .001 and .01 in fact for statement 1 to hold x could also be to the left of .001 and slightly to the right of .01 as we can see from the figure,Even if x is slightly to the right of .01 and to the left of .001, x could still be closer to .00001 than to .1

is this deduction correct?

So statement 1 holds if x is anywhere in between .001 and.01 and also holds if x is left of .001 and slightly to the right of .01.
So we can see that we cannot say for sure whether x is closer to .001 or .01, hence insufficient.

Please do correct if x cannot also be slightly to the right of .01

Thank you
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- Stne

Originally posted by stne on 09 Jul 2013, 05:16.
Last edited by stne on 17 Aug 2013, 03:26, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 45251
Re: Which of the two values 10^(-2) and 10^(-3), is x more close [#permalink]

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09 Jul 2013, 05:51
stne wrote:
Bunuel wrote:
stne wrote:
can anybody help with the above solution please.

number line = $$\frac{1}{10000}---- \frac{1}{1000} -- | --\frac{1}{100} ----\frac{1}{10}$$

(1) x is more closer to $$\frac{1}{10000}$$ than to $$\frac{1}{10}$$

for this to be true shouldn't x have to be to the left of the center marked as $$|$$ above and if x is the left of the center ,then shouldn't x be closer to $$\frac{1}{1000}$$than to $$\frac{1}{100}$$

I fail to see how x can be anywhere between $$\frac{1}{1000}$$ and $$\frac{1}{100}$$and still be closer to $$\frac{1}{10000}$$ than to $$\frac{1}{10}$$

lets say x is between $$\frac{1}{1000}$$ and $$\frac{1}{100}$$ but just slightly to the left of $$\frac{1}{100}$$, say x = $$\frac{1}{101}$$
now here x lies as shown $$\frac{1}{1000} -- | -- \frac{1}{101} --\frac{1}{100}$$ so here it looks x is between $$10^{-3}$$ and $$10 ^{-2}$$ but closer to $$\frac{1}{10},$$ so this doesn't satisfy statement 1

lets say x =$$\frac{1}{999}$$here the position of x = $$\frac{1}{10000}---- \frac{1}{1000} --\frac{1}{999} --- | --\frac{1}{100} ----\frac{1}{10}$$

so here statement 1 holds and x is closer to $$\frac{1}{10000}$$ .

So it seems to me for statement 1 to hold x has to be to the left of the center , marked as $$|$$in the number line, and in that case x will be closer to $$\frac{1}{1000}$$ than to $$\frac{1}{100}$$, anywhere to the right of $$|$$ and x becomes closer to $$\frac{1}{10}$$ violating statement1 , so x has to be to the left of $$|$$ for statement 1 to be true. so I am getting A as sufficient . Can anybody assist please?

thanks

Which of the two values 0.01 and 0.001, is x more close to?

(1) x is more close to 0.0001 than to 0.1.
(2) x is more close to 0.001 than to 0.1.

Relative positioning on the number line might help:

Thank you finally got it !
didn't realize that there was so much in between .01 and .1

Well if I have understood the diagram above correctly then for statement 1 to be true x need not necessarily have to be in between .001 and .01 in fact for statement 1 to hold x could also be to the left of .001 and slightly to the right of .01 as we can see from the figure,Even if x is slightly to the right of .01 and to the left of .001, x could still be closer to .00001 than to .1

is this deduction correct?

So statement 1 holds if x is anywhere in between .001 and.01 and also holds if x is left of .001 and slightly to the right of .01.
So we can see that we cannot say for sure whether x is closer to .001 or .01, hence insufficient.

Please do correct if x cannot also be slightly to the right of .01

Thank you

Yes, x could be to the right of 0.01.

As, for the positioning of the points: it was also provided here: which-of-the-two-values-10-2-and-10-3-is-x-more-close-129498.html#p1063210
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Re: Which of the two values 10^(-2) and 10^(-3), is x more close [#permalink]

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10 Jul 2013, 09:45
Which of the two values 10^(-2) and 10^(-3), is x more close to?
Is x closer to 10^-3 than 10-2?
Is x < (1/2)(1/100+1/1000)?
Is x < 11/2000?

1. x is more close to 10^(-4) than to 10^(-1).
x<(1/2)(1/10+1/10000)
x< (1001/20000)
This doesn't tell us if x <11/2000 since 1001/20000 > 11/2000. Not sufficient.

2. x is more close to 10^(-3) than to 10^(-1).
x<(1/2)(1/10+1/1000)
x<101/2000
Still doesn't tell us if x< 11/2000. Not sufficient.

1 and 2. 2 follows from 1 so no new information is introduced by combining them. Not sufficient. Answer is E.

My method is probably not the best way to do it because there's room for error doing the arithmetic and it may take too long on the actual test. But I don't like drawing number lines.
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Re: Which of the two values 10^(-2) and 10^(-3), is x more close [#permalink]

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04 Jun 2014, 14:27
Quick solution: draw a number line, plug in X = 10^(-2) and X = 10^(-3), and realize that both scenarios satisfy both statements.

Thus, even given both statements you cannot distinguish between the two most extreme cases X = 10^(-2) (where X must be closer to 10^(-2)) and X = 10^(-3) (where X must be closer to 10^(-3))

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Re: Which of the two values 10^(-2) and 10^(-3), is x more close [#permalink]

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10 Sep 2014, 22:01

Convert everything to 10^(-4).

So the question becomes "Which of the two values 100 X 10^(-4) and 10 X 10^(-4), is x more close to?"

(1) x is more close to 1 X 10^(-4) than to 10,000 X 10^(-4).

- So X could be 55 X 10^(-4), it is closer to 1 X 10^(-4) as stat. 1 requires, but right in between 100 X 10^(-4) and 10 X 10^(-4)
- If X is 56 X 10^(-4), it is closer to 100 X 10^(-4)
- If X is 54 X 10^(-4), it is closer to 10 X 10^(-4)

- Insufficient

(2) x is more close to 10 X 10^(-4) than to 1000 X 10^(-4)
- Once again, X could be 55 X 10^(-4) and we can use the same analysis as above.

(1) + (2) - Use 55 X 10^(-4) once again, which satisfies both (1) and (2) and still not clarify whether X is closer to 100 X 10^(-4) or 10 X 10^(-4)

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Which of the two values 10^(-2) and 10^(-3), is x more close [#permalink]

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02 Nov 2017, 11:47

Question can be quickly solved by multiplying each of $$10^{-4}$$, $$10^{-3}$$,$$10^{-2}$$,$$10^{-1}$$ with $$10^4$$ => 1, 10, 100, 1000

Statement 1: 10000x is more close to 1 than to 1000
Statement 2: 10000x is more close to 10 than to 1000

for 10000x = 20, 10000x = 70 both statements are satisfied.

but 10000 x = 20 (10000x closer to 10 => x is closer to $$10^{-3}$$ than to $$10^{-2}$$), and if 10000x = 70(10000x is closer to 100 => x is closer to $$10^{-2}$$ than to $$10^{-3}$$)

Which of the two values 10^(-2) and 10^(-3), is x more close   [#permalink] 02 Nov 2017, 11:47
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