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Which of the following best approximates

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by VJesus12 » Sat Feb 17, 2018 7:53 am
Which of the following best approximates (0.2)·(0.3)·(0.4)·(0.5)=?

A. 0.1
B. 0.01
C. 0.001
D. 0.0001
E. 0.00001

The OA is the option B.

Is there a method to solving this PS question in a fast way? Experts, I'd be thankful for your help. <i class="em em-disappointed"></i>
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by EconomistGMATTutor » Sat Feb 17, 2018 8:36 am
VJesus12 wrote:Which of the following best approximates (0.2)·(0.3)·(0.4)·(0.5)=?

A. 0.1
B. 0.01
C. 0.001
D. 0.0001
E. 0.00001

The OA is the option B.

Is there a method to solving this PS question in a fast way? Experts, I'd be thankful for your help. <i class="em em-disappointed"></i>
Hi Vjesus12.

Let's take a look at your question.

Let's rewrite the numbers as follows:

0.2 = 2*10^(-1)
0.3 = 3*10^(-1)
0.4 = 4*10^(-1)
0.5 = 5*10^(-1)

Now, $$\left(0.2\right)\cdot\left(0.3\right)\cdot\left(0.4\right)\cdot\left(0.5\right)=2\cdot10^{-1}\cdot3\cdot10^{-1}\cdot4\cdot10^{-1}\cdot5\cdot10^{-1}$$ $$120\cdot10^{-4}=0.012\approx0.01$$ Hence, the correct answer is the option B.

I hope it helps you.

I'm available if you'd like a follow-up.

Regards.
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by Brent@GMATPrepNow » Sat Feb 17, 2018 10:16 am
VJesus12 wrote:Which of the following best approximates (0.2)·(0.3)·(0.4)·(0.5)=?

A. 0.1
B. 0.01
C. 0.001
D. 0.0001
E. 0.00001
Another approach:

(0.2)(0.3)(0.4)(0.5) = (2/10)(3/10)(4/10)(5/10)
= 120/10000
= 12/1000

ASIDE: Notice that 12/1000 is pretty close to 10/1000
10/1000 = 1/100 = 0.01

So, 12/1000 is closest to 0.01

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by [email protected] » Sat Feb 17, 2018 10:18 am
Hi VJesus12,

We're asked to find the answer that best approximates (0.2)(0.3)(0.4)(0.5). You can approach the 'math' behind this question in a variety of ways - and if you recognize some of the patterns involved, then you could potentially save some time in the process.

To start, if we ignore the decimal points for a moment, then we're multiplying (2)(3)(4)(5); that's the same as 5! (so if you have that value memorized, you know that 5! = 120).

Next, there are 4 numbers - and each includes one decimal point. By extension, the product of those 4 values should have 4 decimal points (even if some of the latter digits are 0s).

If we combine 120 and 4 decimal places, then we get....

0.0120

Final Answer: B

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by Scott@TargetTestPrep » Sun Jun 23, 2019 10:23 am
VJesus12 wrote:Which of the following best approximates (0.2)·(0.3)·(0.4)·(0.5)=?

A. 0.1
B. 0.01
C. 0.001
D. 0.0001
E. 0.00001
Since 2 x 3 x 4 x 5 = 120 and each original factor has one decimal place, the product will have four decimal places. That is, (0.2) x (0.3) x (0.4) x (0.5) = 0.0120 = 0.012.

The closest value to 0.012 is 0.01.

Answer: B

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