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Is 0.4 < x < 0.8 ?

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Is 0.4 < x < 0.8 ?  [#permalink]

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New post Updated on: 16 Aug 2015, 12:03
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Is 0.4 < x < 0.8 ?

(1) 407x < 376
(2) 1400x > 1240

Originally posted by RudeyboyZ on 16 Aug 2015, 11:40.
Last edited by Bunuel on 16 Aug 2015, 12:03, edited 1 time in total.
Edited the question.
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Re: Is 0.4 < x < 0.8 ?  [#permalink]

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New post 16 Aug 2015, 12:13
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Is 0.4 < x < 0.8 ?

(1) 407x < 376 --> x < 376/407 --> x is less than some number which is approximately 0.9, so this statement is not sufficient to say whether x is 0.4 < x < 0.8. Not sufficient.

(2) 1400x > 1240 --> x > 1240/1400. Now, (1240/1400 = 31/35) > (8/10 = 28/35), so x is out of the range (0.4, 0.8). Sufficient.

Answer: B.

Hope it's clear.
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Re: Is 0.4 < x < 0.8 ?  [#permalink]

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New post 24 Oct 2015, 13:25
1: Round 407 down to 400 and the answer will be .94. So, original x < .94. Insufficient
2. Round down 1240 to 1200 and the fraction will be x > 6/7, which is .85. Sufficient
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Re: Is 0.4 < x < 0.8 ?  [#permalink]

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New post 30 Oct 2015, 23:18
Hi Bunuel ,

Is this really a 700 level Question ?
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Is 0.4 < x < 0.8 ?  [#permalink]

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New post 31 Oct 2015, 03:34
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Re: Is 0.4 < x < 0.8 ?  [#permalink]

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New post 31 Oct 2015, 11:46
Is 0.4 < x < 0.8 ?

(1) 407x < 376
(2) 1400x > 1240

_____________________

Does x lie in between 0.4 and 0.8
1) 407 x - 376 < 0
x < 376/407
x < 0.92
Not Sufficient

2) x> 1240/1400
x > 0.88
Sufficient (The value will never lie in between 0.4 ad 0.8)

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Re: Is 0.4 < x < 0.8 ?  [#permalink]

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New post 01 Nov 2015, 09:46
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Is 0.4 < x < 0.8 ?

(1) 407x < 376
(2) 1400x > 1240

We will use the point that if the range of the condition includes that of the condition, the condition is sufficient.

In the original condition, there is one variable (x), and 2 equations are given from the 2 conditions; there is high chance (D) will be our answer.
From condition 1, x<376/407=0.92..... This makes the condition insufficient as the range of the condition does not include this range
In condition 2, x>1240/1400=0.885. This condition, on the other hand, is sufficient, as it answers the question 'no' straightaway.
The answer is therefore (B).

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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Is 0.4 < x < 0.8 ?  [#permalink]

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New post 30 Apr 2016, 03:46
I did it differently, requiring easy calculation:-

rephrase this to 1< 10x/4 < 2
Now in B : x > 1240/1400. Hence 10x/4> 12400/5600 which is greater than 2. SO this is suff
In A : x < 376/407 : 10x/4 < 3760/1626 i.e less than something just greater than 2. So it may lie between 1 and 2. Not suff. Ans:B
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Re: Is 0.4 < x < 0.8 ?  [#permalink]

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New post 31 May 2018, 06:01
Top Contributor
RudeyboyZ wrote:
Is 0.4 < x < 0.8 ?

(1) 407x < 376
(2) 1400x > 1240


Target question: Is 0.4 < x < 0.8?

Statement 1: 407x < 376
Divide both sides of the inequality by 407 to get: x < 376/407
Convert to a decimal to get: x < 0.92
There are several values of x that satisfy statement 1. Here are two:
Case a: x = 0.6. In this case, the answer to the target question is YES, x IS between 0.4 and 0.8
Case b: x = 0.1. In this case, the answer to the target question is NO, x is NOT between 0.4 and 0.8
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 1400x > 1240
Divide both sides of the inequality by 1400 to get: x > 1240/1400
Simplify to get: x > 124/140
Simplify more: x > 31/35
Convert to decimal: x > 0.88
If x > 0.88, there are NO VALUES of x such that 0.4 < x < 0.8
In other words, the answer to the target question is NO, x is definitely NOT between 0.4 and 0.8
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent
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Re: Is 0.4 < x < 0.8 ?  [#permalink]

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New post 31 May 2018, 09:54
376/407 ~ 0.9 --> Not sufficient
1240/1440 --. 31/35 --> x > 0.8 sufficient
Hence B
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Re: Is 0.4 < x < 0.8 ?  [#permalink]

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New post 01 Jun 2018, 11:33
RudeyboyZ wrote:
Is 0.4 < x < 0.8 ?

(1) 407x < 376
(2) 1400x > 1240


We need to determine if x is between 0.4 and 0.8.

Statement One Alone:

407x < 376

We see that:

x < 376/407

Notice that 376/407 > 1/2. So if x = 1/2, then x is between 0.4 and 0.8. However, if x = 0, then x is not between 0.4 and 0.8. Statement one alone is not sufficient.

Statement Two Alone:

1400x > 1240

We see that:

x > 1240/1400 = 124/140 = 31/35 > 28/35 = 4/5 = 0.8

Since x > 0.8, then it is not between 0.4 and 0.8. Statement two alone is sufficient.

Answer: B
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Re: Is 0.4 < x < 0.8 ?  [#permalink]

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New post 04 Aug 2018, 09:08
Hey Guys,

Is there an easier to go about the ugly division in the first statement. I see that statement 2 can be divided easily but any ideas how to solve the 1st statement quickly.

Thanks.
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Re: Is 0.4 < x < 0.8 ? &nbs [#permalink] 04 Aug 2018, 09:08
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