wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

A positive integer is called "Panache” if it can be written as a sum of distinct positive powers of 4, and "Elan" if it can be written as a sum of distinct positive powers of 6. From the given number, which of the following can we write as a sum of a "Panache” number and an "Elan" number?


A

2012

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

2013

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

2011

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

none of these.

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D

none of these.


Suppose that 2013 = a + b, where a is "Panache” and b is an "Elan". Then 'a' must be a sum of some of the powers of 4 less than 2013, namely 1, 4, 16, 64, 256, and 1024. Similarly, b must be a sum of some of the numbers 1, 6, 36, 216, and 1296. So, a + b must be a sum of some distinct entries from the list 1, 1, 4, 6, 16, 36, 64, 216, 256, 1024, 1296. If we use both 1024 and 1296, we get at least 1024+1296 = 2320 which is too big. But if we omit one of them, the most we can get 1 + 1 + 4 + 6 + 16 + 36 + 64 + 216 + 256 + 1296 = 1896; which is too small. So there is no way to achieve a sum of 2011, 2012 and 2013.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Highest Power and Summation
QUANTITATIVE APTITUDE
Watch in App
Join BYJU'S Learning Program
CrossIcon