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21 Apr 2022, 01:30
Kudos
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
43% (02:21) correct
57%
(02:04)
wrong
based on 77
sessions
History
Date
Time
Result
Not Attempted Yet
How many ways are there to write 2016 as the sum of twos and threes, ignoring order? (For example, 1008 · 2 + 0 · 3 and 402 · 2 + 404 · 3 are two such ways.)
(A) 236
(B) 336
(C) 337
(D) 403
(E) 672
Are You Up For the Challenge: 700 Level Questions
(A) 236
(B) 336
(C) 337
(D) 403
(E) 672
Are You Up For the Challenge: 700 Level Questions
30 Apr 2022, 22:45
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To find: The number of ways in which 2016 can be expressed as the sum of 2s and 3s.
Let us start with the maximum number of 3s and the minimum number of 2s.
2016 = 0 * 2 + 672 * 3
Let us increase the number of 2s and correspondingly decrease the number of 3s.
Removing two 3s and correspondingly increasing the number of 2s by 3 will keep the sum intact.
Here is a listing of the iterations
2016 = 0 * 2 + 672 * 3
2016 = 3 * 2 + 670 * 3
2016 = 6 * 2 + 668 * 3
2016 = 9 * 2 + 666 * 3
.
.
.
.
2016 = 1005 * 2 + 2 *3
2016 = 1008 * 2 + 0 * 3
This covers all the possibilities.
The number of rows in the above iteration is the answer to the question - in how many ways can 2016 be expressed as a sum of 2s and 3s.
Notice that we started with 672 3s and reduced it by 2 in every subsequent row till we reached 0 3s.
So, the number of possibilities is the count of even numbers from 0 to 672
= \(\frac{672}{2}\) + 1
We add the 1 at the end to include the possibility of having 0 3s.
CHOICE-C 337 is the answer
Let us start with the maximum number of 3s and the minimum number of 2s.
2016 = 0 * 2 + 672 * 3
Let us increase the number of 2s and correspondingly decrease the number of 3s.
Removing two 3s and correspondingly increasing the number of 2s by 3 will keep the sum intact.
Here is a listing of the iterations
2016 = 0 * 2 + 672 * 3
2016 = 3 * 2 + 670 * 3
2016 = 6 * 2 + 668 * 3
2016 = 9 * 2 + 666 * 3
.
.
.
.
2016 = 1005 * 2 + 2 *3
2016 = 1008 * 2 + 0 * 3
This covers all the possibilities.
The number of rows in the above iteration is the answer to the question - in how many ways can 2016 be expressed as a sum of 2s and 3s.
Notice that we started with 672 3s and reduced it by 2 in every subsequent row till we reached 0 3s.
So, the number of possibilities is the count of even numbers from 0 to 672
= \(\frac{672}{2}\) + 1
We add the 1 at the end to include the possibility of having 0 3s.
CHOICE-C 337 is the answer
General Discussion
16 Mar 2025, 03:35
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