If x is a k-digit integer and x =(4^9)*(5^17), what is the value of k?

Question

If x is a k-digit integer and x = (4^9)(5^17), what is the value of k?

(A) 16
(B) 17
(C) 18
(D) 19
(E) 20

Bunuel · Accepted Answer

No approximation there.

x = (4^9)(5^{17})=

= (2^{18})(5^{17})=

= 2(2^{17})(5^{17})=

= 2(10^{17})  
 
So, x is 2 followed by 17 zeros (200,000,000,000,000,000), making it an 18-digit number.

Answer: E.

Abhishek009 · Answer

x = (4^9)(5^{17})

x = (2^{18})(5^{17})

Or,  x = (10^{17})2

10^{17}  will have  17  , 0 's multiplied by 2 will have 1 more digit, ie 18 digits, Answer must be (E) 18

gmatophobia · Answer

x  =  4^{9}*5^{17}

x  =  2^{18}*5^{17}

x  =  2^{1}*10^{17}

Let's take a smaller value of the power to understand the pattern

x  =  2^{1}*10^{2}  = 200 ; in this case x is 3 digit integer.

x  =  2^{1}*10^{3}  = 2000 ; in this case x is 4 digit integer.

Therefore the number of digits = value of the exponent + 1

In this case,

number of digits in x= 17 + 1 = 18

Option C

JeffTargetTestPrep · Answer

x = (4^9)(5^17) = (2^18)(5^17) = (2)(2 × 5)^17

x = (2)(10)^17

Multiplying an integer by (10)^17 simply attaches 17 zeros to the last digit of the integer.

Since 2 is a one-digit integer, the number of digits in question is:

1 + 17 = 18

Answer: C

ruis · Answer

Hi Abhi, thank you for your approach. One question I have is why do we need to multiply 10^17*2...
The property says x^a * y^a = (x*y)^a
I understand the solving until 2^18 * 5^17 = 10^17 --> We are using approximation right? in order to have the same exponent.

ruis · Answer

That´s amazing, thank you so much Bunuel! You saved me a huge misunderstanding there

Carcass · Answer

Bunuel

When I saw this question in the gmat focus the answer choices were

A. 16
B. 17
C. 18
D. 19
E. 20

Bunuel · Answer

Edited the options. Thank you!

Peachesncream · Answer

Can anyone suggest similar questions for practice please, thank you.

Bunuel · Answer

bumpbot · Answer

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If x is a k-digit integer and x =(4^9)*(5^17), what is the value of k?

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If x is a k-digit integer and x =(4^9)*(5^17), what is the value of k?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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My Rewards