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Comparing fractions

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Source: — Data Sufficiency |
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by shankar.ashwin » Mon Nov 07, 2011 7:20 am
Statement 1:

n > 1/7 - Can be any number - Insuff

Statement 2:

n < 3/10 - Again no lower limit here - Insuff

Together;

1/7 < n < 3/10 - We cannot define it within 1/8 < n < 1/6. So E IMO
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by gb » Mon Nov 07, 2011 7:26 am
o-------------------------->
<----------------------------------------o
---------------0---------.125------.142------.166----.3----

1/8 = .125
1/6 = .166
1/7 = .142
3/10 = .3

1. n > 2/7 - 1/7 => n> 1/7

See the number line. Some portion satisfy the equation and some does not. So leave A

2. n < 2/5 - 1 / 10 => n < 3/10

Again some portion satisfied and some not. So, Leave B

Now lets try C. The overlapping portion of A and B will define the region for the equation and then you cna take a descision. So, its C.
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by neelgandham » Mon Nov 07, 2011 7:50 am
Is 1/8 < n < 1/6?

(1) n + 1/7 > 2/7
Implies, n > 1/7, i.e. n can be 1/6, 1, 7, 8 Insufficient !

(2) n + 1/10 < 2/5
Implies n < 3/10, i.e. n can be -1, -2, 1/7, 1/8 etc Insufficient !

From 1 and 2 (1/7)<n<(3/10) Insufficient !
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by GMATGuruNY » Mon Nov 07, 2011 8:21 am
studentps2011 wrote:Is 1/8 < n < 1/6?

(1) n + 1/7 > 2/7

(2) n + 1/10 < 2/5
Try to plug in extreme values that satisfy both statements.

Statement 1: n > 1/7.
Statement 2: n < 3/10.
Combined: 1/7 < n < 3/10.

The lower limit is 1/7:
Let n = 1/(6.9).
1/8 < 1/(6.9) < 1/6.

The upper limit is 3/10:
Let n = 3/11.
Since 3/11 = 18/66 and 1/6 = 11/66, n > 1/6.

Thus, it cannot be determined whether 1/8 < n < 1/6.
INSUFFICIENT.

The correct answer is E.
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by studentps2011 » Mon Nov 07, 2011 8:44 am
gb wrote:o-------------------------->
<----------------------------------------o
---------------0---------.125------.142------.166----.3----

1/8 = .125
1/6 = .166
1/7 = .142
3/10 = .3

1. n > 2/7 - 1/7 => n> 1/7

See the number line. Some portion satisfy the equation and some does not. So leave A

2. n < 2/5 - 1 / 10 => n < 3/10

Again some portion satisfied and some not. So, Leave B

Now lets try C. The overlapping portion of A and B will define the region for the equation and then you cna take a descision. So, its C.
When we combine the statements, we get that n is between 0.142 and 0.3. So it can be 0.15 (less than 0.166) or 0.2 (greater than 0.166). Hence E.
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by Dauren » Fri Oct 24, 2014 7:49 pm
Hello,

If n<3/10, then n is definitely with the range such that 1/8 < n <1/6. Then the answer should be B.

Is this logic faulty?
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by [email protected] » Fri Oct 24, 2014 10:07 pm
Hi Dauren,

One of the aspects of DS questions that you need to think about is the issue of consistency.

Here, we're asked if 1/8 < N < 1/6? This is a YES/NO question. If it makes you more comfortable, you can convert the fractions into decimals - then the questions becomes.....is .125 < N < .1666666.

Fact 1: N + 1/7 > 2/7

This means that N > 1/7, meaning that N > .142857.....
If N = .15, then the answer to the question is YES
If N = 1, then the answer to the question is NO
Fact 1 is INSUFFICIENT

Fact 2: N + 1/10 < 2/5

This means that N < 3/10, meaning that N < .3
If N = .15, then the answer to the question is YES
If N = 0, then the answer to the question is NO
Fact 2 is INSUFFICIENT

Combined, we know....
.142857..... < N < .3
If N = .15, then the answer to the question is YES
If N = .2, then the answer to the question is NO
Combined, INSUFFICIENT

Final Answer: E

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by Matt@VeritasPrep » Mon Oct 27, 2014 11:24 am
Dauren wrote:Hello,

If n<3/10, then n is definitely with the range such that 1/8 < n <1/6. Then the answer should be B.

Is this logic faulty?
Unfortunately yes: n < 3/10 gives all sorts of possibilities, such as n = 0, n = -1, n = -1,000,000, etc.
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