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154 - Data Sufficiency

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by phoenix9801 » Sat Jul 10, 2010 10:30 pm
Hi, can someone please help to explain by step-by-step instructions (in detail) in the most simplest way and clear to understand. Would Greatly appreciate it.

1-

If n is a positive integer and k =5.1 * 10 ^n, what is the value of K?

(1) 6,000 < k < 500,000

(2) K^2 = 2.601 * 10^9


(note th answer is D But I am having trouble to understand statement 1)



2-

If n is a positive integer, is the value of b - a at least twice the value of 3^n - 2^n?

(1) a= 2^n+1 and b=3^n+1

(2) n =3

(note the answer is A, but I having trouble to understand the first part statement 1 especially how to combine them together)
Last edited by phoenix9801 on Mon Jul 12, 2010 2:11 pm, edited 1 time in total.
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Source: — Data Sufficiency |
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by albatross86 » Sat Jul 10, 2010 11:42 pm
Question 1

n is a +ve integer. k = 5.1 * 10^n. k =?

1. 6,000 < k < 500,000

k can only take values like this:

n = 1 => k = 5.1 * 10 = 51
n = 2 => k = 5.1 * 100 = 510
And so on.

So after 6,000, the next immediate value of k is 51,000 (Since 5,100 is less than 6,000). The next value after this is 510,000 but this is greater than our upper limit of 500,000.

So the only possible value of k is 51,000.
SUFFICIENT

2. k^2 = 2.601 * 10^9

You can easily find the positive square root of this number (since we know that k must be positive looking at our original expression of k) and thus obtain k

SUFFICIENT

Pick D.


Question 2

n is a positive interger. IS (b-a) atleast = 2*(3^n - 2^n) ?

1. a = 2^(n+1) and b = 3^(n+1)

=> b - a = 3^(n + 1) - 2^(n + 1)
= 3* 3^n - 2* 2^n ...........[This is using the rule that x^(m + n) = x^m * x^n]
= 3^n + 2*3^n - 2*2^n .....[Splitting up the first term of 3x into x + 2x]
= 3^n + 2*(3^n - 2^n)

Thus b - a is greater than 2*(3^n - 2^n) by an amount = 3^n ....[which is positive]

SUFFICIENT

2. n = 3

This gives no information about a or b.

INSUFFICIENT

Pick A.
~Abhay

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by phoenix9801 » Mon Jul 12, 2010 2:13 pm
albatross86 wrote:Question 1

n is a +ve integer. k = 5.1 * 10^n. k =?

1. 6,000 < k < 500,000

k can only take values like this:

n = 1 => k = 5.1 * 10 = 51
n = 2 => k = 5.1 * 100 = 510
And so on.

So after 6,000, the next immediate value of k is 51,000 (Since 5,100 is less than 6,000). The next value after this is 510,000 but this is greater than our upper limit of 500,000.

So the only possible value of k is 51,000.
SUFFICIENT

2. k^2 = 2.601 * 10^9

You can easily find the positive square root of this number (since we know that k must be positive looking at our original expression of k) and thus obtain k

SUFFICIENT

Pick D.


Question 2

n is a positive interger. IS (b-a) atleast = 2*(3^n - 2^n) ?

1. a = 2^(n+1) and b = 3^(n+1)

=> b - a = 3^(n + 1) - 2^(n + 1)
= 3* 3^n - 2* 2^n ...........[This is using the rule that x^(m + n) = x^m * x^n]
= 3^n + 2*3^n - 2*2^n .....[Splitting up the first term of 3x into x + 2x]
= 3^n + 2*(3^n - 2^n)

Thus b - a is greater than 2*(3^n - 2^n) by an amount = 3^n ....[which is positive]

SUFFICIENT

2. n = 3

This gives no information about a or b.

INSUFFICIENT

Pick A.

Hi, Can you substitute number for example if you use by picking numbers N=2, the is 19 at least twice of 5, would it be considered sufficient???
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