Bunuel wrote:
2a + b = 12, and |b| ≤ 12
How many ordered pairs (a, b) are solutions of the above system such that a and b both are integers?
(A) 9
(B) 10
(C) 11
(D) 12
(E)13
Solution:
- Given\( |b| ≤12\) means the possible values of b are\( -12, -11, -10, -9....... -3, -2, -1, 0, 1, 2, 3, .....10, 11,12\)
- Also,\(2a+b=12\) or\(a=\frac{12-b}{2}=6-\frac{b}{2}\)
- The value of a will be integral for every even integral (positive or negative) value ofb
- So,\( b=-12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10,12\) will all lead to integer pair(a,b)
Hence the right answer is OptionE
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Statistics : Posted by SaquibHGMATWhiz • on 13 Apr 2021, 08:00 • Replies 3 • Views 1834
