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Senior Manager  Status: Up again.
Joined: 31 Oct 2010
Posts: 458
Concentration: Strategy, Operations
GMAT 1: 710 Q48 V40 GMAT 2: 740 Q49 V42 What is the tenth digit to the right of the decimal point  [#permalink]

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27 00:00

Difficulty:   75% (hard)

Question Stats: 50% (01:42) correct 50% (01:35) wrong based on 877 sessions

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What is the tenth digit to the right of the decimal point, in the decimal expansion of (1/5)^10
(A) 0
(B) 2
(C) 4
(D) 6
(E) 8

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Re: Powers PS: Manhattan GMAT Challenge Problem Showdown  [#permalink]

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$$(\frac{1}{5})^{10}$$

$$\frac{1}{5^{10}}$$

$$\frac{1}{(\frac{10}{2})^{10}}$$

$$\frac{2^{10}}{{10}^{10}}$$

$$\frac{1024}{{10}^{10}}$$

$$1024*10^{-10}$$

$$.0000001024$$

Tenth digit to the right of decimal is 4.

Ans: "C"
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Re: Powers PS: Manhattan GMAT Challenge Problem Showdown  [#permalink]

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(1/5)^10 is same as (2/10)^10. 10th digit after decimal in this is same as unit's digit in 2^10
2^10 = 2^5*2^5 - 32*32 whose units digit would be 4
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Re: Powers PS: Manhattan GMAT Challenge Problem Showdown  [#permalink]

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2
Hi fluke,

but, inasmuch as I know tenth digit to the right of the decimal point is a first number after the decimal point. Please correct if I am wrong!
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Re: Powers PS: Manhattan GMAT Challenge Problem Showdown  [#permalink]

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feruz77 wrote:
Hi fluke,

but, inasmuch as I know tenth digit to the right of the decimal point is a first number after the decimal point. Please correct if I am wrong!

You are talking about the 'tenths' digit which is right after the decimal point.
'The tenth digit to the right of the decimal' is the digit that appears after 9 digits to the right of the decimal point.
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Senior Manager  Joined: 23 Oct 2010
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GMAT 1: 690 Q47 V38 Re: Powers PS: Manhattan GMAT Challenge Problem Showdown  [#permalink]

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3
(1/5)^10 is (0.2)^10

we know that 2^5=32 .we have (2^5) *(2^5) or 32*32=1024 since we have 10 zeros , our result is
0.0000001024

so 10th digit is 4
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Manager  Joined: 08 Oct 2010
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Re: Powers PS: Manhattan GMAT Challenge Problem Showdown  [#permalink]

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VeritasPrepKarishma wrote:
feruz77 wrote:
Hi fluke,

but, inasmuch as I know tenth digit to the right of the decimal point is a first number after the decimal point. Please correct if I am wrong!

You are talking about the 'tenths' digit which is right after the decimal point.
'The tenth digit to the right of the decimal' is the digit that appears after 9 digits to the right of the decimal point.

Hi Karishma,

Thanks for reply. Such kind of things make GMAT very tricky. I appreciate your help.
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Re: Powers PS: Manhattan GMAT Challenge Problem Showdown  [#permalink]

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Manager  Joined: 26 Apr 2011
Posts: 201
Re: Powers PS: Manhattan GMAT Challenge Problem Showdown  [#permalink]

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Hi Karishma,
Thanks for making it clear . very confusing language.
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Re: What is the tenth digit to the right of the decimal point  [#permalink]

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SVP  Joined: 06 Sep 2013
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Concentration: Finance
Re: What is the tenth digit to the right of the decimal point  [#permalink]

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gmatpapa wrote:
What is the tenth digit to the right of the decimal point, in the decimal expansion of (1/5)^10
(A) 0
(B) 2
(C) 4
(D) 6
(E) 8

Yeah actually 1/5 = 0.2 = 2*10^-1

so 2^10 * 10^-10

2 has sequence 2,4,8,6.

Hence digit will be 4

Hope it helps

Cheers!
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Re: What is the tenth digit to the right of the decimal point  [#permalink]

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so, this is about Tenth vs Tenths! Tricky
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What is the tenth digit to the right of the decimal point  [#permalink]

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1/5=0.2
Now the question becomes what is 10th digit of (0.2)¹⁰
for calculation remove decimal
2X2X2=8-a
2X2X2=8-b
(2X2X2)X2=8X2-c
8X8=64-a&b
64X8X2=1024-a&b&c
10th place after decimal
0.0000001024
Ans=4
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Re: What is the tenth digit to the right of the decimal point  [#permalink]

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jlgdr wrote:
gmatpapa wrote:
What is the tenth digit to the right of the decimal point, in the decimal expansion of (1/5)^10
(A) 0
(B) 2
(C) 4
(D) 6
(E) 8

Yeah actually 1/5 = 0.2 = 2*10^-1

so 2^10 * 10^-10

2 has sequence 2,4,8,6.

Hence digit will be 4

Hope it helps

Cheers!
J hi

is it possible to find out the tenth digit of the expression without further simplification made to "2^10"....?
anybody out there ....?

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Joined: 03 Sep 2018
Posts: 7
What is the tenth digit to the right of the decimal point  [#permalink]

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1
1
Analysis (30 seconds): The question is asking me to find the 10th digit of $$0.2^1^0$$, the answer choices look familiar, possibly the pattern of final digits for powers of 2. I have absolutely no idea how to calculate the actual value of this so I'm going to go ahead and assume two things : 1) I can ignore the fact that the number is a decimal and focus on the 2, and 2) the 10th digit is actually the last digit (because I'm confident GMAC don't actually want me to compute the value of $$0.2^1^0$$). In order to solve this I'll quickly refresh my memory on the pattern of end digits for powers of 2 and then see what the 10th power would yield.

Strategy: Find the pattern, Count to 10

Find the pattern (30 seconds):
$$2^0 = 0$$
$$2^1 = 2$$
$$2^2 = 4$$
$$2^3 = 8$$
$$2^4 = 16$$
$$2^5 = 32$$
Looks like the pattern is: [2,4,8,6] with the exception of 0.

Count to 10 (10 seconds):
Using [2,4,8,6] as the pattern and starting from index 1 I can see that the 10th power will give me an end digit of 4.

Total Time: 1:10
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Re: What is the tenth digit to the right of the decimal point  [#permalink]

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_________________ Re: What is the tenth digit to the right of the decimal point   [#permalink] 22 Oct 2019, 06:37
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