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hdwnkr
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The number of positive integer solutions for the equation x + y + z + 12 Sep 2016, 11:15
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Difficulty:

55% (hard)

Question Stats:

54% (01:43) correct 46% (02:06) wrong based on 35 sessions

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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
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A
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The number of positive integer solutions for the equation x + y + z + 12 Sep 2016, 11:42
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hdwnkr
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

Pls help with a shorter approach for this one
Show more

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.
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hdwnkr
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The number of positive integer solutions for the equation x + y + z + 12 Sep 2016, 11:44
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msk0657
hdwnkr
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

Pls help with a shorter approach for this one

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.
Show more

Can you pls elaborate?
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Senthil1981
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The number of positive integer solutions for the equation x + y + z + 12 Sep 2016, 11:50
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hdwnkr
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

Pls help with a shorter approach for this one
Show more


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
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The number of positive integer solutions for the equation x + y + z + 12 Sep 2016, 11:56
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hdwnkr
msk0657
hdwnkr
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

Pls help with a shorter approach for this one

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.

Can you pls elaborate?
Show more

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.
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The number of positive integer solutions for the equation x + y + z + 12 Sep 2016, 12:19
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hdwnkr
msk0657
hdwnkr
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

Pls help with a shorter approach for this one

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.

Can you pls elaborate?
Show more


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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