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Difficulty:
95%
(hard)
Question Stats:
32% (02:17) correct
68%
(01:59)
wrong
based on 773
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History
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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).
(1) x is more close to 10^(-4) than to 10^(-1).
(2) x is more close to 10^(-3) than to 10^(-1).
Smita04
10^(-4), 10^(-3), 10^(-2), and 10^(-1) are positioned on the number line as follows:
-(0.0001)-(0.001)---------(0.01)---------------------------------------------------------------------------------(0.1)-
The question asks which of the two middle numbers x is closer to.
(1) indicates that x is closer to the first number than to the fourth. However, x could still be anywhere between the two middle numbers. Not sufficient.
(2) indicates that x is closer to the second number than to the fourth. However, x could still be anywhere between the two middle numbers. Not sufficient.
(1)+(2) x could still be anywhere between the two middle numbers. Therefore, we cannot determine which number x is closer to. Not sufficient.
Answer: E.
P.S. You could consider these simpler numbers for easier manipulation:
-(1)-(10)---------(100)---------------------------------------------------------------------------------(1000)-
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General Discussion
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
_________________
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
stne
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 13364 times ]
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Bunuel
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
_________________
- Stne
stne
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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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.
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.
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))
Therefore answer is E.
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))
Therefore answer is E.
This is the way I solved it (please help me understand the error if my technique/answer is incorrect)
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)
Therefore, the answer is E.
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)
Therefore, the answer is E.
Answer E.
Question can be quickly solved by multiplying each of \(10^{-4}\), \(10^{-3}\),\(10^{-2}\),\(10^{-1}\) with \(10^4\) => 1, 10, 100, 1000
then statements will read as
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 \(10^{-3}\))
So still insufficient. Answer (E)
Question can be quickly solved by multiplying each of \(10^{-4}\), \(10^{-3}\),\(10^{-2}\),\(10^{-1}\) with \(10^4\) => 1, 10, 100, 1000
then statements will read as
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 \(10^{-3}\))
So still insufficient. Answer (E)
Posts: 938
the key to soving the question is figuring out all the given possibilities
(1) x is more close to 10^(-4) than to 10^(-1).
it could be 10^-3.5 then it's closer to 10^-3
However if it's 10^-2.1 then it's closer to 10^-2
Cleraly insuff
(2) x is more close to 10^(-3) than to 10^(-1).
it could be 10^-2.1 in that clase it will be close to 10^-2
it could be 10^-3.5 then it's closer to 10^-3
Clearly INsuff
when 1 and 2 is combined we get
it could be 10^-2.1 and 10^2.6
clearly INSuff
Hence IMO E
(1) x is more close to 10^(-4) than to 10^(-1).
it could be 10^-3.5 then it's closer to 10^-3
However if it's 10^-2.1 then it's closer to 10^-2
Cleraly insuff
(2) x is more close to 10^(-3) than to 10^(-1).
it could be 10^-2.1 in that clase it will be close to 10^-2
it could be 10^-3.5 then it's closer to 10^-3
Clearly INsuff
when 1 and 2 is combined we get
it could be 10^-2.1 and 10^2.6
clearly INSuff
Hence IMO E
Posts: 2
Smita04
7 and 1 -> which one is closer to x?
middle of two numbers is 4 so, if x > 4 it is closer to 7
if x < 4 it is closer to 1.
same logic here, but we have to rewrite every number with the same power. the smallest power is -4, so our common power gonna be -4.
10^(-2) = 100*10^(-4)
10^(-3) = 10*10^(-4)
[100*10^(-4) + 10*10^(-4)]/2 = 55*10^(-4)
the question is x < 55*10^(-4) ?
(1) x < 500.5*10^(-4) | it can be 50*10^(-4), it can be 60*10^(-4) too ------ insufficient
(2) x < 505*10^(-4) | it can be 50*10^(-4), it can be 60*10^(-4) too ------ insufficient
(1)(2) is the same as (1) ------ insufficient
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