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Decimals : Problem Solving (Medium)

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Decimals : Problem Solving (Medium)

by bkk_marc » Tue Aug 30, 2011 11:09 pm
If p = 5.18r7, what is the result when p is subtracted from p rounded to the nearest thousandth?
A) -0.001

B)-0.0007

C)-0.0003

D) 0.0003

E) 0.001

Answer: D

How do we derived the answer if we don't even know what r is?
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by GMATGuruNY » Wed Aug 31, 2011 4:00 am
bkk_marc wrote:If p = 5.18r7, what is the result when p is subtracted from p rounded to the nearest thousandth?
A) -0.001

B)-0.0007

C)-0.0003

D) 0.0003

E) 0.001

Answer: D

How do we derived the answer if we don't even know what r is?
Plug in for r any digit 0-9.
Let r = 0.
Then p = 5.1807.
Rounded to the nearest thousandths, new p = 5.181.
New p - old p = 5.181 - 5.1807 = .0003.

The correct answer is D.

No reason to try different values for r.
If a different value for r could yield a result other than .0003, then there would be no correct answer.
Last edited by GMATGuruNY on Wed Aug 31, 2011 10:16 am, edited 1 time in total.
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by saketk » Wed Aug 31, 2011 7:58 am
bkk_marc wrote:If p = 5.18r7, what is the result when p is subtracted from p rounded to the nearest thousandth?
A) -0.001

B)-0.0007

C)-0.0003

D) 0.0003

E) 0.001

Answer: D

How do we derived the answer if we don't even know what r is?
Hi-- Because we need not know the value of R in this case. Since the question asks us to round the number to the nearest thousandth, the value of r (0-9) will not change your result.

Reason: when we round off the number -- its value will increase by 1.

Mitch has already explained you this by taking R=0.

Even if you take R=1,2,3, etc the result will not change..

Let r=4
then, P=5.1847
round it.. the new value will be: P=5.185
5.185-5.1847 = 0.0003
Hence answer will be [spoiler](Option D)[/spoiler] :)
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by Brian@VeritasPrep » Wed Aug 31, 2011 9:25 am
Got a PM about this one so hopefully I'm not stealing Mitch's thunder...

Just to add to what he did, I'd answer bbk_marc's question by asking the follow up "does it matter?". And initially, I don't know - but if I were on the test and I hit this situation I'd have around 2 minutes to find out, so I'd try two different numbers to see if there's a difference, and since it's a rounding problem I'd try a high number and a low number to see what happens:

r = 1

5.1817 rounds to 5.182
5.182 - 5.1817 = 0.0003

r = 9

5.1897 rounds to 5.190
5.190 - 5.1897 = 0.0003

And in doing this you'd probably notice that the 7 after the r is what counts for rounding - not r itself. Whatever r is, that 7 means you bump r up by 1, and that always leaves a difference of 0.0003.

What this means for you, strategically, on GMAT quant problems is that if you're unsure of the role of a variable, a sequence, etc., it often helps to do a quick demonstration to yourself with a small, easy-to-calculate number so that you can see for yourself what happens. Often you can find a pattern or gauge the importance or role of a variable just by testing it with a number, and that becomes your key to unlocking the problem. Most of us are a lot better at math with numbers than we are at math with letters, so when you're struggling with something that involves algebra try a "side problem" with a quick plug-in number so that you can more clearly see how the algebra works.
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