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Re: Variable in Exponent DS problem [#permalink]
07 Dec 2010, 17:50

Expert's post

tonebeeze wrote:

I would appreciate it if someone could walk me through this problem. Thanks

Is 5^k less than 1000?

1. 5^k+1 > 3000 2. 5^k-1 = 5^k -500

I am assuming the question is:

Is 5^k less than 1000?

1. 5^{k+1} > 3000 2. 5^{k-1} = 5^k -500

5^4 = 625 and 5^5 = 3125 (even if you do not know this, it is fine. You don't need to calculate. Just observe that 625*5 will be greater than 3000)

Statement 1: 5^{k+1} > 3000 This means k + 1 is greater than 4 so k is greater than 3 (It doesnt mean that k + 1 is at least 5 because the question doesn't say that k is an integer. k + 1 could be 4.999 making k = 3.999) Since k can take values less than 4 and more than 4, 5^k could be less than 1000 or more than 1000. Not sufficient.

Statement 2: 5^{k-1} = 5^k -500 Re-arrange: 500 = 5^k -5^{k-1} 5^3 *4 = 5^{k-1}(5 - 1) Hence k - 1 = 3 and k = 4 So 5^k = 625 which is less than 1000. Answer is 'Yes'. Sufficient.

Re: Variable in Exponent DS problem [#permalink]
03 Jan 2011, 07:29

Expert's post

m990540 wrote:

Can you go over how you went from 500 = 5^k -5^{k-1} to 5^3 *4 = 5^{k-1}(5 - 1)?

Thanks so much in advance!

Left hand side: 500 = 5*100 = 5*25*4 = 5^3*4 (Since your concern is the power of 5, separate 5s from the rest)

Right hand side: 5^k -5^{k-1} = 5^{k - 1} ( 5 - 1)(Take 5^{k - 1} common. e.g. if you have 5^4 - 5^3, you can take 5^3 common and you will be left with (5 - 1))

Re: Variable in Exponent DS problem [#permalink]
22 May 2014, 22:11

VeritasPrepKarishma wrote:

tonebeeze wrote:

I would appreciate it if someone could walk me through this problem. Thanks

Is 5^k less than 1000?

1. 5^k+1 > 3000 2. 5^k-1 = 5^k -500

I am assuming the question is:

Is 5^k less than 1000?

1. 5^{k+1} > 3000 2. 5^{k-1} = 5^k -500

5^4 = 625 and 5^5 = 3125 (even if you do not know this, it is fine. You don't need to calculate. Just observe that 625*5 will be greater than 3000)

Statement 1: 5^{k+1} > 3000 This means k + 1 is greater than 4 so k is greater than 3 (It doesnt mean that k + 1 is at least 5 because the question doesn't say that k is an integer. k + 1 could be 4.999 making k = 3.999) Since k can take values less than 4 and more than 4, 5^k could be less than 1000 or more than 1000. Not sufficient.

Statement 2: 5^{k-1} = 5^k -500 Re-arrange: 500 = 5^k -5^{k-1} 5^3 *4 = 5^{k-1}(5 - 1) Hence k - 1 = 3 and k = 4 So 5^k = 625 which is less than 1000. Answer is 'Yes'. Sufficient.

Answer (B)

I can't get why are we talking about decimals in the first statement. I don't know if I'm doing something wrong here...

I did it like this 5^{k+1} > 3000 k+1 \geq 5 k \geq 4

Re: Variable in Exponent DS problem [#permalink]
23 May 2014, 01:12

Expert's post

b2bt wrote:

VeritasPrepKarishma wrote:

tonebeeze wrote:

I would appreciate it if someone could walk me through this problem. Thanks

Is 5^k less than 1000?

1. 5^k+1 > 3000 2. 5^k-1 = 5^k -500

I am assuming the question is:

Is 5^k less than 1000?

1. 5^{k+1} > 3000 2. 5^{k-1} = 5^k -500

5^4 = 625 and 5^5 = 3125 (even if you do not know this, it is fine. You don't need to calculate. Just observe that 625*5 will be greater than 3000)

Statement 1: 5^{k+1} > 3000 This means k + 1 is greater than 4 so k is greater than 3 (It doesnt mean that k + 1 is at least 5 because the question doesn't say that k is an integer. k + 1 could be 4.999 making k = 3.999) Since k can take values less than 4 and more than 4, 5^k could be less than 1000 or more than 1000. Not sufficient.

Statement 2: 5^{k-1} = 5^k -500 Re-arrange: 500 = 5^k -5^{k-1} 5^3 *4 = 5^{k-1}(5 - 1) Hence k - 1 = 3 and k = 4 So 5^k = 625 which is less than 1000. Answer is 'Yes'. Sufficient.

Answer (B)

I can't get why are we talking about decimals in the first statement. I don't know if I'm doing something wrong here...

I did it like this 5^{k+1} > 3000 k+1 \geq 5 k \geq 4

k= 4 then 5^4 = 625 k=5 then 5^5 = 3000 (approx)

5^{k+1} > 3000 --> 5*5^{k} > 3000 --> 5^{k} > 600. Now, we are NOT told that k is an integer, thus we cannot say that k\geq{4}. For example, 5^{3.99}\approx{615}, thus k could be 3.99.

Is 5^k less than 1,000?

Is 5^k<1,000?

(1) 5^(k+1) > 3,000 --> 5^k>600 --> if k=4 then the answer is YES: since 600<(5^4=625)<1,000 but if k=10, for example, then the answer is NO. Not sufficient.

(2) 5^(k-1) = (5^k) - 500 --> we can solve for k and get the single numerical value of it, hence this statement is sufficient. Just to illustrate: 5^k-5^{k-1}=500 --> factor out 5^{k-1}: 5^{k-1}(5-1)=500 --> 5^{k-1}=125 --> k-1=3 --> k=4. Sufficient.