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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
54% (01:39) correct
46%
(01:59)
wrong
based on 37
sessions
History
Date
Time
Result
Not Attempted Yet
The number of positive integer solutions for the equation x + y + z + t = 25 is
A. 2024
B. 2042
C. 2204
D. 2402
E. 2420
A. 2024
B. 2042
C. 2204
D. 2402
E. 2420
hdwnkr
The number of positive integer solutions for the equatio fx1+x2+⋯+xn=k
(k-1)C(n-1) - where k is the number and n is number of variable in the equation.
25-1 C 4-1 = 24C3 = 2024.
Option A.
msk0657
Can you pls elaborate?
Senthil1981
Joined: 23 Apr 2015
Last visit: 14 Oct 2021
Posts: 225
Location: United States
Concentration: General Management, International Business
Schools: Booth PT '19 Ross Weekend"19
WE:Engineering (Consulting)
Schools: Booth PT '19 Ross Weekend"19
Posts: 225
hdwnkr
There is a formula for a similar problem that i came across.
it's \(\frac{{(n-3)(n-2)(n-1)}}{3!}\) for four variables.
n = 25 here it gives answer as A.
Here is the original link https://gmatclub.com/forum/a-how-many-positive-integer-solutions-does-the-following-3533.html
hdwnkr
This is a standard formula to find the number of positive integral solutions from the given equation. - -Fix this in your mind.
x +y +z + t = 25 , here we have four variables sum equal to 25.
This is like a number 25 identical balls getting distributed across 4 (x,y,z and t) distinct boxes or variables and where each box contains atleast one ball.
So we use the formula => (k-1) C(n-1) - this is combinations topic related formula.
Senthil1981
Joined: 23 Apr 2015
Last visit: 14 Oct 2021
Posts: 225
Location: United States
Concentration: General Management, International Business
Schools: Booth PT '19 Ross Weekend"19
WE:Engineering (Consulting)
Schools: Booth PT '19 Ross Weekend"19
Posts: 225
hdwnkr
Refer to this wiki page on this formula and other variations.
https://en.wikipedia.org/wiki/Stars_and_bars_%28combinatorics%29
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