Is 0.4 < x < 0.8 ? (1) 407x < 376 (2) 1400x > 1240

Hi Bunuel ,

Is this really a 700 level Question ?

45% of the users answered this question incorrectly, so the answer to your question is yes.

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)

B it is

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.

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

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

376/407 ~ 0.9 --> Not sufficient
1240/1440 --. 31/35 --> x > 0.8 sufficient
Hence B

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

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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