How many multiples of 4 lie between 4^4 and 4^5, inclusive?

Question

How many multiples of  4  lie between  4^4  and  4^5 , inclusive?

A. 128  
 B. 129  
 C. 192  
 D. 193  
 E. 256

BrentGMATPrepNow · Accepted Answer

Here's a slightly different solution.

4^4 = ( 4³ )( 4 ) = ( 64 )( 4 )
4^5 = ( 4⁴ )( 4 ) = ( 256 )( 4 )

So, we want the multiples of  4  from ( 64 )( 4 ) to ( 256 )( 4 ) inclusive. 
The multiples of  4  are: ( 64 )( 4 ), ( 65 )( 4 ), ( 66 )( 4 ), ( 67 )( 4 ), ( 68 )( 4 ), . . . ( 256 )( 4 )

A nice rule says:   the number of integers from x to y inclusive equals y - x + 1  
So, the number of integers from  64  to  256  inclusive =  256  -  64  + 1 = 193

Answer: D

Cheers,
Brent

GMATBusters · Answer

Let the number of multiples of 4 between 4^4 and 4^5 is N.

Hence 4^4 +4(N+1) = 4^5

Or, (N+1) = (4^5-4^4)/4

Or, (N+1) = 4^4(4-1)/4

Or, (N+1) = 4^3 *3

Or, (N+1) = 192

Or, N = 191.

Since both extreme values are to be included, add 2 to N.

Hence number of multiples of 4 between 4^4 and 4^5 INCLUSIVE is 191+2 =193

imtisalsiddiqui · Answer

4^4= 256 & 4^5=1024

1024-256/4=192

192+1 = 193

aserghe1 · Answer

GMATPrepNow

Right when I was wondering how this problem can be solved without performing any calculations...

JeffTargetTestPrep · Answer

4^4 = 256

4^5 = 1,024

We use the formula for the number of multiples: (greatest multiple of 4 - least multiple of 4)/4 + 1. The number of multiples of 4 from 256 to 1,024, inclusive, is:

(1,024 - 256)/4 + 1 = 193

Answer: D

JeffTargetTestPrep · Answer

4^4 = 256

4^5 = 1,024

We use the formula for the number of multiples: (greatest multiple of 4 - least multiple of 4)/4 + 1. The number of multiples of 4 from 256 to 1,024, inclusive, is:

(1,024 - 256)/4 + 1 = 193

Answer: D

MathRevolution · Answer

=>
Since we are including the end points, the number of multiples of 4 is

\frac{( 4^5 – 4^4 )}{4} + 1 = \frac{4^4(4-1)}{4} + 1 = 4^3*3 + 1 = 64 * 3 + 1 = 193.

Therefore, D is the answer.

Answer : D

SSM700plus · Answer

4^4  = 256

4^5  = 1024.

(1024 - 256)/4 = 192

192 +1 = 193.

Ans - 193

Parvezahmed2210 · Answer

Given range is 
4^5-4^4
= 4^4 (4-1)

Now to find out the multiples of 4 we need to divide 4^4*3 by 4

Therefore, 4^3*3 =64*3= 192.

Since the question says its inclusive therefore we need to add +1.

Total number is 192+1=193

To further clarify inclusive formula :

How many numbers from 1 to 10 inclusive?

It is: (10-1)+1 =10

Posted from my mobile device

laddaboy · Answer

Considering an arithmetic progression with starting term as 4^4 and 4^5 as last term , with difference obviously being 4 (since they need to be multiples of 4)

Last term = First term + (n-1)*d

4^5 = 4^4 + (n-1) * 4

Dividing by 4

4^4 = 4^3 + (n-1)

4^4-4^3 = n -1 
4^3 (4-1) = n- 1
64*3 = n -1 
=> n = 193

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How many multiples of 4 lie between 4^4 and 4^5, inclusive?

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How many multiples of 4 lie between 4^4 and 4^5, inclusive?

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