What is the sum of the digits of integer x, where x = 4^10* 5^13?

Question

What is the sum of the digits of integer x, where  x = 4^{10} * 5^{13} ?

(A) 13

(B) 11

(C) 10

(D) 8

(E) 5

JeffTargetTestPrep · Accepted Answer

We can simplify the given equation:

x = 4^10 x 5^13

x = 2^20 x 5^13

x = 2^7 x 2^13 x 5^13

x = 2^7 x 10^13

x = 128 x 10^13

We see that x is the number 128 followed by 13 zeros. Thus, the sum of the digits of x is 1 + 2 + 8 = 11.

Answer: B

GMATisLovE · Answer

Answer is B as follows

x = 4^{10} * 5^{13} = 2^{20}*5^{13} = 10^{13}*2^7 = 10^{13}*128 
Sum of the digits = 1+2+8 = 11

Hence B

spc11 · Answer

X= 2^20*5^13
= 10^13 *2^7
= 128*10^13

Sum of digits = 11
Option B

Sent from my A0001 using  GMAT Club Forum mobile app

roninmanutd · Answer

Since we are looking for the sum of the digits we can simplify this problem by removing the trailing zeros (zeros at the end of the number). Trailing zeros are added to a number when multiplied by 10.

Remember 10 = 2 * 5
Thus, in our problem 4^10*5^13 or: 
2^20 * 5^13

As you can see we have the pair 2*5 thirteen times. We can remove 2^13 and 5^13 and work with the rest which is 2^7 = 128

1+2+8 = 11

celo700 · Answer

we can use the concept of cyclicity to find out the units digit.
units digit of 4^10 is 6 and units digit of 5^13 is 5
6+5 = 11
units digit 1.
(This method works because there is no repetition of units digit in the options.)

ScottTargetTestPrep · Answer

We can rewrite the expression as:

2^20 x 5^13

2^7 x 2^13 x 5^13

2^7 x 10^13

128 x 10^13

This is the number 128 followed by 13 zeros, so the sum of the digits is 1 + 2 + 8 = 11 (note: the 13 zeros will not contribute anything to the sum).

Answer: B

MBAaustralia · Answer

B)

2^7 is 128

Sum of digits is equal to 11.

Posted from my mobile device

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

What is the sum of the digits of integer x, where x = 4^10* 5^13?

Prep Toolkit

Top 5 GMAT Debrief Videos

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

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

What is the sum of the digits of integer x, where x = 4^10* 5^13?

Prep Toolkit

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

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards