Question: If a(a + 2) = 24 and b(b + 2) = 24, where a ≠ b, then a + b =
(A) −48
(B) −2
(C) 2
(D) 46
(E) 48
Correct Answer: B
Solution and Explanation:
Approach Solution 1:
Given:
a(a + 2) = 24
b(b + 2) = 24
Condition: a ≠ b
Find: The value of (a+b)
Let us consider the arithmetic equation:
a(a + 2) = 24 and b(b + 2) = 24
i.e. Product of two consecutive Even Integers = 24
If we break the results as per the equation, the results can be:
a(a+2)=24 is 4(4+2) = 24
4(6) = 24 which is true.
For the second part, we consider the value as -6
b(b + 2) = 24
-6*(-6+2) = 24 which is true.
Hence, either 4*(4+2) = 24 or -6*(-6+2) = 24
i.e. if a = 4 then b = -6
or if a = -6 then b = 4
But in each case a+b = -6+4 = -2
Approach Solution 2:
Given:
a(a + 2) = 24
b(b + 2) = 24
Condition: a ≠ b
Find: The value of (a+b)
Considering the equation:
a(a + 2) = 24 and b(b + 2) = 24
i.e. a(a+2)=b(b+2)
i.e. \(a^2+2a-b^2-2b= 0\)
i.e. \(a^2-b^2=-2(a-b)\)
Providing the formula for \(a^2-b^2\)
(a−b)∗(a+b) = −2(a−b)
(a+b) = −2
Approach Solution 3:
From the given information,
a(a+2)=24 → a2+2a=24 →
a2+2a−24=0 → (a+6)(a−4)=0
Therefore, a=−6 or a=4
Similarly, for the equation in variable "b"
So, a and b take the values -6 and 4
So, their sum is (−6+4=−2)
“If a(a + 2) = 24 and b(b + 2) = 24, Where a ≠ b, Then a + b =”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.
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