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Which of the following is equal to 2^k*5^(k-1)?

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Which of the following is equal to 2^k*5^(k-1)? [#permalink]

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New post 05 Jun 2007, 19:37
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A
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E

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99,999^2 - 1^2 =

A. 10^10 - 2
B. (10^5 – 2)^2
C. 10^4(10^5 – 2)
D. 10^5(10^4 – 2)
E. 10^5(10^5 – 2)


Which of the following is equal to (2^k)(5^(k − 1))?

A. 2(10^k − 1)
B. 5(10^k − 1)
C. 10^k
D. 2(10^k )
E. 10^(2k − 1)
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Re: PS [#permalink]

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New post 05 Jun 2007, 20:36
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jet1445 wrote:
99,999^2 - 1^2 =

A. 10^10 - 2
B. (10^5 – 2)^2
C. 10^4(10^5 – 2)
D. 10^5(10^4 – 2)
E. 10^5(10^5 – 2)



E. 8-)
= 99,999^2 - 1^2
= (10^5 - 1)^2 - 1
= (10^5)^2 - 2 (10^5) + 1 - 1
= 10^5 (10^5 - 2)

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Re: PS [#permalink]

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New post 05 Jun 2007, 20:45
jet1445 wrote:
Q18: Which of the following is equal to (2^k)(5^(k − 1))?

A. 2(10^k − 1)
B. 5(10^k − 1)
C. 10^k
D. 2(10^k )
E. 10^(2k − 1)


= (2^k) {5^(k − 1)}
= (2^k) (5^k) / 5
= 10^k/5

none???????? seems the answeres have typo. :roll: :roll: :roll:

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 [#permalink]

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New post 06 Jun 2007, 04:02
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Himalayan I did it that way too, but unfortunately to match the answer I had to redo it slightly differently

2^k * 5 ^(k-1)
= 2 * 2^(k-1) * 5 ^(k-1)
= 2 * 10^(k-1)

which is option A

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Re: 99,999^2 - 1^2 = A. 10^10 - 2 B. (10^5 2)^2 C. [#permalink]

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New post 16 Feb 2012, 21:02
For second question Ans. should be (10^k)/5

Further help appreciated.
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Re: 99,999^2 - 1^2 = A. 10^10 - 2 B. (10^5 2)^2 C. [#permalink]

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New post 16 Feb 2012, 21:18
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Baten80 wrote:
For second question Ans. should be (10^k)/5

Further help appreciated.


(10^k)/5 is a correct solution, though as it's not listed among the answer choices then we should manipulate with given expression in another way.

Which of the following is equal to 2^k*5^(k-1)?
A. 2*10^(k-1)
B. 5*10^(k-1)
C. 10^k
D. 2*10^k )
E. 10^(2k-1)

\(2^k*5^{k-1}=(2*2^{k-1})*5^{k-1}=2*10^{k-1}\).

Answer: A.

99,999^2 - 1^2 =
A. 10^10 - 2
B. (10^5 – 2)^2
C. 10^4(10^5 – 2)
D. 10^5(10^4 – 2)
E. 10^5(10^5 – 2)

Apply \(a^2-b^2=(a+b)(a-b)\):

\(99,999^2-1^2 =(99,999+1)(99,999-1)=10^5(10^5-2)\)

Answer: E.

Hope it's clear.
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Re: Which of the following is equal to 2^k*5^(k-1)? [#permalink]

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New post 04 Jun 2012, 11:31
Bunuel,
Can you please explain how (2^k)*(5^(k-1)) equals (2*(2^k-1))*5^k-1

I have seen this logic on 2 other problems now and this one step is causing me to miss questions. If you could please explain you get that it would help me a lot!

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Re: Which of the following is equal to 2^k*5^(k-1)? [#permalink]

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New post 04 Jun 2012, 11:46
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wjf9838 wrote:
Bunuel,
Can you please explain how (2^k)*(5^(k-1)) equals (2*(2^k-1))*5^k-1

I have seen this logic on 2 other problems now and this one step is causing me to miss questions. If you could please explain you get that it would help me a lot!


Operations involving the same bases:
Keep the base, add or subtract the exponent (add for multiplication, subtract for division)
\(a^n*a^m=a^{n+m}\)

\(\frac{a^n}{a^m}=a^{n-m}\)

So, \(2*2^{k-1}=2^1*2^{k-1}=2^{1+k-1}=2^k\).

For more on exponents check Number Theory chapter of Math Book: math-number-theory-88376.html

Hope it helps.
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PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Which of the following is equal to 2^k*5^(k-1)? [#permalink]

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Re: Which of the following is equal to 2^k*5^(k-1)? [#permalink]

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Re: Which of the following is equal to 2^k*5^(k-1)?   [#permalink] 15 May 2015, 06:57
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