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# How many digits are in (8×10^14)(10×10^10)?

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Math Expert
Joined: 02 Sep 2009
Posts: 53063
How many digits are in (8×10^14)(10×10^10)?  [#permalink]

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25 Apr 2016, 23:53
00:00

Difficulty:

25% (medium)

Question Stats:

69% (00:45) correct 31% (01:02) wrong based on 236 sessions

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How many digits are in (8×10^14)(10×10^10)?

A. 24
B. 25
C. 26
D. 27
E. 28

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Joined: 01 Jul 2010
Posts: 62
Location: India
GMAT 1: 660 Q43 V38
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Re: How many digits are in (8×10^14)(10×10^10)?  [#permalink]

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26 Apr 2016, 05:41
1
The question simplfies to (8×10^14)(10^11)
=> 8*10^25
=> Will contain 25 zeros +1 digit 8
=>26

Ans C
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Re: How many digits are in (8×10^14)(10×10^10)?  [#permalink]

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30 Dec 2017, 22:21
Bunuel wrote:
How many digits are in (8×10^14)(10×10^10)?

A. 24
B. 25
C. 26
D. 27
E. 28

Bunuel can you help me in this. Though I know the concept, still I am counting it as 27.

(8×10^14) ; 10^14 means fourteen "0s" and one "1" So total 15 digits ; 8 does not change the number of digits

(10×10^10) ; 10^11 means 12 digits

So 15+12 = 27
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Math Expert
Joined: 02 Sep 2009
Posts: 53063
Re: How many digits are in (8×10^14)(10×10^10)?  [#permalink]

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30 Dec 2017, 22:30
QZ wrote:
Bunuel wrote:
How many digits are in (8×10^14)(10×10^10)?

A. 24
B. 25
C. 26
D. 27
E. 28

Bunuel can you help me in this. Though I know the concept, still I am counting it as 27.

(8×10^14) ; 10^14 means fourteen "0s" and one "1" So total 15 digits ; 8 does not change the number of digits

(10×10^10) ; 10^11 means 12 digits

So 15+12 = 27

You cannot add like that. For example, 10 has 2 digits but 10*10 does not have 2 + 2 = 4 digits it has 3 digits.

You should do the following way: (8×10^14)(10×10^10) = 8*10^25 --> 10^25 has 26 digits. Multiplying it by 8 does not change the number of digits.

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Re: How many digits are in (8×10^14)(10×10^10)?  [#permalink]

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30 Dec 2017, 22:39
Bunuel wrote:
QZ wrote:
Bunuel wrote:
How many digits are in (8×10^14)(10×10^10)?

A. 24
B. 25
C. 26
D. 27
E. 28

Bunuel can you help me in this. Though I know the concept, still I am counting it as 27.

(8×10^14) ; 10^14 means fourteen "0s" and one "1" So total 15 digits ; 8 does not change the number of digits

(10×10^10) ; 10^11 means 12 digits

So 15+12 = 27

You cannot add like that. For example, 10 has 2 digits but 10*10 does not have 2 + 2 = 4 digits it has 3 digits.

You should do the following way: (8×10^14)(10×10^10) = 8*10^25 --> 10^25 has 26 digits. Multiplying it by 8 does not change the number of digits.

Can we deduce that number less than 10 does not change the number of digits ever?
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"Do not watch clock; Do what it does. KEEP GOING."

Math Expert
Joined: 02 Sep 2009
Posts: 53063
Re: How many digits are in (8×10^14)(10×10^10)?  [#permalink]

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30 Dec 2017, 22:47
QZ wrote:
Bunuel wrote:
QZ wrote:

Bunuel can you help me in this. Though I know the concept, still I am counting it as 27.

(8×10^14) ; 10^14 means fourteen "0s" and one "1" So total 15 digits ; 8 does not change the number of digits

(10×10^10) ; 10^11 means 12 digits

So 15+12 = 27

You cannot add like that. For example, 10 has 2 digits but 10*10 does not have 2 + 2 = 4 digits it has 3 digits.

You should do the following way: (8×10^14)(10×10^10) = 8*10^25 --> 10^25 has 26 digits. Multiplying it by 8 does not change the number of digits.

Can we deduce that number less than 10 does not change the number of digits ever?

It won't if you have a*10^n, where a is a single digit integer. But for other cases it might not be true. For example, 3*400.
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Math Expert
Joined: 02 Aug 2009
Posts: 7334
Re: How many digits are in (8×10^14)(10×10^10)?  [#permalink]

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30 Dec 2017, 22:56
QZ wrote:
Bunuel wrote:
QZ wrote:
How many digits are in (8×10^14)(10×10^10)?

A. 24
B. 25
C. 26
D. 27
E. 28

Bunuel can you help me in this. Though I know the concept, still I am counting it as 27.

(8×10^14) ; 10^14 means fourteen "0s" and one "1" So total 15 digits ; 8 does not change the number of digits

(10×10^10) ; 10^11 means 12 digits

So 15+12 = 27

You cannot add like that. For example, 10 has 2 digits but 10*10 does not have 2 + 2 = 4 digits it has 3 digits.

You should do the following way: (8×10^14)(10×10^10) = 8*10^25 --> 10^25 has 26 digits. Multiplying it by 8 does not change the number of digits.

Can we deduce that number less than 10 does not change the number of digits ever?

Hi..
You can't take that as a rule..
It depends on other factors too..
8*10^2.... 8 will not effect
8*20^2.... 8 will effect...

Why you have gone wrong is that you have separated the 10s..
(8*10^14)(10*10^11)....
Although you have correctly solved 10*10^11, you have added an extra digit of 1 from 10^14..
10*10^11 could have meant 10 - 2 digits and 10^10- 10 zeroesand 1 digit for '1', so 10+1=11 digits
Total 2+11=13digits.. but is it so ...NO
It is 12 digits because 10*10^10=10^11, meaning 12 digits
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

GMAT Expert

Re: How many digits are in (8×10^14)(10×10^10)?   [#permalink] 30 Dec 2017, 22:56
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