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If x and y are positive integers such that 3x + 4y = 24, what is the value of x + y?
A) 4
B) 5
C) 6
D) 7
E) 8
A) 4
B) 5
C) 6
D) 7
E) 8
01 Feb 2025, 09:41
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Gmat750aspirant
If x and y are positive integers such that 3x + 4y = 24, what is the value of x + y?
A) 4
B) 5
C) 6
D) 7
E) 8
Both 4y and 24 are multiples of 4, meaning 3x must also be a multiple of 4. This implies that x must be a multiple of 4. Testing the smallest positive multiple, x = 4, gives 3(4) + 4y = 24, which simplifies to y = 3. Thus, x = 4 and y = 3, giving x + y = 7.A) 4
B) 5
C) 6
D) 7
E) 8
Answer: D.
01 Feb 2025, 10:26
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Gmat750aspirant
If x and y are positive integers such that 3x + 4y = 24, what is the value of x + y?
A) 4
B) 5
C) 6
D) 7
E) 8
A) 4
B) 5
C) 6
D) 7
E) 8
Method 1:
The easiest values of x and y that work are x = 8 and y = 0
Since y=0 isn't positive, we reduce x by the coefficient of y and increase y by the coefficient of x to get: x=4, y=3 - these values satisfy the equation.
(Think why this method works)
Here both are positive integers.
So answer = 4+3 = 7
Method 2
3x + 4y = 24
A) Divide by 3: x + 4y/3 = 8
=> x + y < 8
B) Divide by 4: 3x/4 + y = 6
=> x + y > 6
Thus the only value is 7
Method 3:
We can use the method shown by Bunuel
