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Is 0.4 < x < 0.8?

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by M7MBA » Thu May 31, 2018 1:42 am

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty—

Is 0.4 < x < 0.8?

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

The OA is the option B.

How can I conclude here that the correct answer is the option B? Could anyone show me what is the best approach to solve it? Thanks.
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Source: — Data Sufficiency |
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by Vincen » Thu May 31, 2018 3:08 am
Hello M7MBA.

I will give you my solution.

Question
Is 0.4 < x < 0.8?
First statement
(1) 407x < 376
Here we have $$407x<376\ \ \Rightarrow\ \ x<\frac{376}{407}\approx0.9$$ This is NOT SUFFICIENT because we can have that x=0.7 or we can get that x=0.2.

Second statement
(2) 1400x > 1240
Here we have $$1400x>1240\ \ \ \Rightarrow\ \ x>\frac{1240}{1400}=\frac{31}{35}>\frac{28}{35}=0.8\ $$ Hence, we have that x>0.8, therefore the answer to the original question is NO.

In conclusion, this statement SUFFICIENT.

Therefore, the correct answer is the option B.

I hope it helps.

Regards.
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by Brent@GMATPrepNow » Thu May 31, 2018 4:56 am
M7MBA 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
Brent Hanneson - Creator of GMATPrepNow.com
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by Jeff@TargetTestPrep » Sun Jun 03, 2018 4:58 pm
M7MBA 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

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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