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Re: HOT Competition: A function g is defined, for all positive integers x
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26 Aug 2020, 01:42
Question gives two constraints, so let’s take a note of each:
(1) x = positive integer
(2) x > 3
Therefore, x = {4, 5, ,6, 7, 8, ………………} – any integer from this set
Now, let us test what kind of value does g(x) give when x = even or odd to check what inference we can draw from the question stem before we jump into statement analysis
When x = even (say, x = 4), we’ll use function g(x) = 4x - 5
g (x) = 4(4) – 5 = 11 = ODD
When x = odd (say, x = 5), we’ll use function g(x) = 5x - 15
g (x) = 5(5) – 15 = 10 = EVEN
To summarize:
g(x) = 4x-5 ---à gives ODD integral values
g(x) = 5x-15 ---à gives EVEN integral values
Statement 1: Tells us that sum of two g(x) functions = ODD, which means two cases are possible
Case 1: g(g(p)) = ODD and g(p) = EVEN, or
Case 2: g(g(p)) = EVEN and g(p) = ODD
Now, unless we know which whether p = odd/even, we would not know which g(x) function is used out of g(x) = 4x-5 or g(x) = 5x-15 in statement 1, because
if p = odd
g(p) = 5p-15 -à will give EVEN value
g(g(p)) = g(EVEN) = 4(5p-15) - 5
so,
g(p) + g(g(p)) = 195
(5p-15) + 4(5p-15)-5 = 195
25P = 275
P = 11
if p = even
g(p) = 4p- 5 -à will give ODD value
g(g(p)) = g(ODD) = 5(4p-5) - 15
so,
g(p) + g(g(p)) = 195
(4p- 5) + 5(4p-5) - 15 = 195
24P = 240
P = 10
Since we get two different value of P = 10 or 11 and not a UNIQUE value, this statement is INSUFFCIENT
Eliminate option A, D
Statement 2: Tell us that
g1(g2(g3(g4(p)))) = EVEN, which implies that,
g1(ODD) = EVEN
g2(EVEN) = ODD
g3(ODD) = EVEN
g4(p) = ODD
Therefore P = EVEN. However, P could be any ODD integer from the set {4,5,6,7, 8……}, so this statement is INSUFFICIENT
Eliminate option B
Combining statement 1 & 2, we know that
P = ODD and g(x) = 5x-15 (first case in statement 1), so we can find UNIQUE value of P = 11
Both statement together are SUFFICIENT.
Correct answer - Option C
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