GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 08 Dec 2019, 05:30

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

What is the decimal equivalent of (2/5)^5 ?

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 59592
What is the decimal equivalent of (2/5)^5 ?  [#permalink]

Show Tags

07 Mar 2019, 01:49
00:00

Difficulty:

35% (medium)

Question Stats:

70% (01:18) correct 30% (01:05) wrong based on 92 sessions

HideShow timer Statistics

What is the decimal equivalent of $$(\frac{2}{5})^5$$ ?

A. 0.00016
B. 0.00032
C. 0.00256
D. 0.00512
E. 0.01024

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 59592
Re: What is the decimal equivalent of (2/5)^5 ?  [#permalink]

Show Tags

07 Mar 2019, 01:50
Bunuel wrote:
What is the decimal equivalent of $$(\frac{2}{5})^5$$ ?

A. 0.00016
B. 0.00032
C. 0.00256
D. 0.00512
E. 0.01024

Similar questions to practice:
https://gmatclub.com/forum/what-is-the- ... 40712.html
https://gmatclub.com/forum/what-is-the- ... 23591.html
https://gmatclub.com/forum/what-is-the- ... 51352.html
_________________
VP
Joined: 31 Oct 2013
Posts: 1491
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: What is the decimal equivalent of (2/5)^5 ?  [#permalink]

Show Tags

07 Mar 2019, 01:54
Bunuel wrote:
What is the decimal equivalent of $$(\frac{2}{5})^5$$ ?

A. 0.00016
B. 0.00032
C. 0.00256
D. 0.00512
E. 0.01024

Given,

$$(\frac{2}{5})^5$$

= $$(0.4)^5$$

= (0.4) (0.4) (0.4) (0.4) (0.4) (0.4)

=0.01024.

Intern
Joined: 09 Apr 2018
Posts: 13
Re: What is the decimal equivalent of (2/5)^5 ?  [#permalink]

Show Tags

07 Mar 2019, 01:57
1
(2/5)^5 can be written as (4/10)^5

Which is:

2^10
100000

Intern
Joined: 08 Jan 2017
Posts: 21
Location: India
GMAT 1: 630 Q45 V31
GMAT 2: 670 Q48 V34
GPA: 4
WE: Engineering (Computer Software)
What is the decimal equivalent of (2/5)^5 ?  [#permalink]

Show Tags

07 Mar 2019, 02:00
1
On multiplying numerator and denominator by 2^5:
(2/5)^5 * (2/2)^5
We get numerator as = 2^10
denominator as = (2*5)^5

2^10 = 1024
(2*5)^5 = 10 ^5

Ans: 0.01024

Tip: Always try to convert denominator as multiple of 10.
Intern
Joined: 16 Oct 2016
Posts: 5
Re: What is the decimal equivalent of (2/5)^5 ?  [#permalink]

Show Tags

07 Mar 2019, 02:02
1
=(2/5)^{5}
=(4/10)^{5}
=4^{5}/10^{5}
=1024/10^{5}
=0.01024
Intern
Joined: 30 Nov 2015
Posts: 34
Location: United States (CO)
WE: Information Technology (Consumer Products)
Re: What is the decimal equivalent of (2/5)^5 ?  [#permalink]

Show Tags

09 Mar 2019, 14:40
Some good explanation above.
I will throw another idea out there-

We know we can write the term as $$(\frac{4}{10}) ^5$$

Which means $$(\frac{4*4*4*4*4}{100000})$$

Cyclicity of 4 is 2. Meaning- If you keep multiplying 4 by 4, the units digits keep changing between 6 and 4. Since the power is 5 it's cyclicity is 2m+1 which tells us the unit's digit will be 4.
Or you can just multiple 4 to itself 5 times in your head (keeping track of just the unit's digit- 4*4 = 16 ; 6*4 = 24; 4*4 = 16 ; 6*4 = 24 ) Unit's digit is 4.

Option E is the only option with unit's digit 4.
Re: What is the decimal equivalent of (2/5)^5 ?   [#permalink] 09 Mar 2019, 14:40
Display posts from previous: Sort by