GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
What is the sum of the digits of integer x, where x = 4^10 x
[#permalink]
05 Nov 2017, 01:34
05 Nov 2017, 01:34
2
Bookmarks
00:00
Question Stats:
80% (01:46) correct
20% (00:39) wrong based on 20 sessions
Hide Show timer Statistics
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
Kudos for correct solution.
(A) 13
(B) 11
(C) 10
(D) 8
(E) 5
Kudos for correct solution.
Re: What is the sum of the digits of integer x, where x = 4^10 x
[#permalink]
05 Nov 2017, 06:23
05 Nov 2017, 06:23
2
We can rearrange the expression for x as \(2^7*(2*5)^{13}\) so that \((2*5)^{13}\) is equal to 1 followed by 13 zeros so that when it is multiplied by any number is equal to that number followed by 13 zeros. Then, \(2^7 = 128\) so that multiplied by the power of 10 becomes 128 and 13 zeros. Since we have to sum the digit of this number, we get 1+2+8+13*0 = 11.
Answer B
Answer B
Target Test Prep Representative
Joined: 09 May 2016
Status:Head GRE Instructor
Affiliations: Target Test Prep
Posts: 183
Given Kudos: 114
Location: United States
Re: What is the sum of the digits of integer x, where x = 4^10 x
[#permalink]
09 Jan 2018, 10:17
09 Jan 2018, 10:17
Expert Reply
Bunuel wrote:
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
(A) 13
(B) 11
(C) 10
(D) 8
(E) 5
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
