Decimal

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Hello Experts,


Dint get the explanation give, pls help!

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HI shibsriz,

First off, this fraction has a denominator that is BIGGER than the numerator, so the fraction has to be LESS than 1. This eliminates options D and E.

In situations such as these, if you can't spot an "elegant" way to approach the questions, then there's nothing wrong with doing the "brute force" math...

1/1.001 = 1000/1001

Are you comfortable doing that division by hand. Thankfully, you KNOW (from the answer choices) that the first 2 digits of the decimal will both be 9. It's just a matter of doing enough work to figure out that final digit.

GMAT assassins aren't born, they're made,
Rich

[GMATGuruNY]

1/1.001

= 1000/1001

= 10³/(10³ + 1)

= (10³)(10³ - 1) / (10³ + 1)(10³ - 1)

= (10³)(999) / (10� - 1)

≈ (10³)(999) / (10�)

= 999 * 10¯³

= 0.999.

The correct answer is C.

[Brent@GMATPrepNow]

Which of the following is CLOSEST to 1/1.001?
A) 0.997
B) 0.998
C) 0.999
D) 1.000
E) 1.001

The words "CLOSEST to" let us know we can use some estimation.

1/1.001 = 1000/1001 [multiplied top and bottom by 1000]
= (1001 - 1)/1001 [rewrote 1000 as 1001 - 1]
= 1001/1001 - 1/1001
= 1 - 1/1001

ASIDE: Notice that 1/1001 is VERY CLOSE to equalling 1/1000, so we can say that...
1 - 1/1001 ≈ 1 - 1/1000
≈ 1 - 0.001
≈ 0.999

Answer: C

Cheers,
Brent

[GMATinsight]

Another approximation approach (Useful in various questions)

[Jeff@TargetTestPrep]

Which of the following is closest to (1)/(1.001)?

A. 0.997
B. 0.998
C. 0.999
D. 1.000
E. 1.001

We can convert 1.001 to a fraction and we have:

1/[(1001/1000)] = 1000/1001

It is obvious that this number is just a little smaller than 1 (which makes it just a little greater than 0.999), so the answer is either D or C. We must decide which. We will compare the difference between 1 and 1000/1001 to the difference between 1000/1001 and 0.999 = 999/1000.

1 - 1000/1001 = 1000/1000 - 1000/1001

= 1001000/1001000 - 1000000/1001000

= 1000/1001000

= 1/1001

1000/1001 - 999/1000 = 1000000/1001000 - 999999/1001000

= 1/1001000

Since the difference between 1000/1001 and 999/1000 is much smaller than the difference between 1 and 1000/1001, 1000/1001 is closer to 999/1000 = 0.999 than any other choice.

Answer: C