gmatpapa wrote:
Is rst ≤ 1?
(1) rs + rt = 5
(2) r + st = 2
(A) Statement (1) ALONE is sufficient, but statement (2) is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.
The question is testing you on the following concept:
If the sum of two non negative numbers is constant, their product is greatest when the numbers are equal. e.g. if a + b = 10, then ab is maximum when a = b = 5. Maximum value of ab = 5*5 = 25
Stmnt 1: Given rs + rt is constant, the maximum value of rs*rt will be when rs = rt = 5/2. Maximum value of \(r^2st= (5/2)*(5/2) = 25/4.\)
But we get no information about maximum value of rst so not sufficient.
Stmnt 2: Given r + st = 2, then maximum value of r*st will be when r = st = 1.
Maximum value of rst = 1 i.e. rst <= 1. Sufficient.
Answer (B).
Note here that though they haven't said that the numbers are non-negative, we can easily see that the product can be less than 1. We only need to worry about the product greater than 1. In that case, since the sum is positive and product we need is positive, we only need to worry about positive numbers.
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Karishma
Veritas Prep GMAT Instructor
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