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a = 4/39. What is the value of 10^6a - a?

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a = 4/39. What is the value of 10^6a - a? [#permalink] a = 4/39. What is the value of 10^6a - a?   17 Jul 2020, 00:34
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[GMAT math practice question]

\(a = \frac{4}{39}\). What is the value of \(10^6a - a\)?

A. \(10,2500\)

B. \(102,510 \)

C. \(102,555\)

D. \(102,564\)

E. \(102,573\)
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D
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Re: a = 4/39. What is the value of 10^6a - a? [#permalink] a = 4/39. What is the value of 10^6a - a?   17 Jul 2020, 00:56
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(4000000 -4)/39

Subtraction ends with 6 .

The no. 6 comes as a multiple of 9 when we multiply by 4.

The only option that has 4 as unit digit is D.
D!

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Re: a = 4/39. What is the value of 10^6a - a? [#permalink] a = 4/39. What is the value of 10^6a - a?   19 Jul 2020, 00:17
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\(a(10^6-1)\)
\(a*9999999\)
= 4/13*333333
= 4*25641
= 102564
D
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Re: a = 4/39. What is the value of 10^6a - a? [#permalink] a = 4/39. What is the value of 10^6a - a?   19 Jul 2020, 01:06
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MathRevolution wrote:
[GMAT math practice question]

\(a = \frac{4}{39}\). What is the value of \(10^6a - a\)?

A. \(10,2500\)

B. \(102,510 \)

C. \(102,555\)

D. \(102,564\)

E. \(102,573\)



\(10^6a - a=(10^6-1)*a=99999*\frac{4}{39}\)
Now, we know this is an integer as the choices are integer....

The denominator 39 is a multiple of 3, while the numerator 99999*4 is a multiple of 4 and 9.
Thus, the answer should be a multiple of 4 and 9/3 or 3.
Multiple of 4 - A and D left
A is not a multiple of 3, while D is a multiple of 4 and 3 both.

D
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a = 4/39. What is the value of 10^6a - a? [#permalink] a = 4/39. What is the value of 10^6a - a?   19 Jul 2020, 01:08
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MathRevolution wrote:
[GMAT math practice question]

\(a = \frac{4}{39}\). What is the value of \(10^6a - a\)?

A. \(102,500\)

B. \(102,510 \)

C. \(102,555\)

D. \(102,564\)

E. \(102,573\)


1. If we observe the answer options, then we see that the options are very close and hence we have to be careful with approximations

2. \(a\) can be pulled out as common from \(10^6a - a\) to give us \(a\)(\(10^6 - 1\))

3. Now, approximate the part inside the parenthesis to \((10^6 - 1)\) ~ \(10^6 = 10^6\)

4. Glance at the answer options and start the long division of \(\frac{4}{39} = 0.10256\)...STOP! as this matches option D

Ans. D
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Re: a = 4/39. What is the value of 10^6a - a? [#permalink] a = 4/39. What is the value of 10^6a - a?   19 Jul 2020, 19:22
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=>

\(10^6a - a = a(10^6 - 1) = \frac{4}{39} · 999,999 = \frac{4}{13} · 333,333\\
= 4 · 25641 = 102,564\)

Therefore, D is the correct answer.
Answer: D
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Re: a = 4/39. What is the value of 10^6a - a? [#permalink] a = 4/39. What is the value of 10^6a - a?   28 Dec 2023, 12:59
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Re: a = 4/39. What is the value of 10^6a - a? [#permalink]
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