SajjadAhmad wrote:
If \(w + x + y = 42\), what is the value of \(xyz?\)
(1) \(x\) and \(y\) are consecutive odd integers
(2) \(w = 2x\)
Source: McGraw-Hill's GMAT
First: I assume that there's a typo in the problem. Should the question read "what is the value of wxy?" Otherwise, each statement is definitely insufficient, both alone and together, since we have no information about the value of z.
Let's assume that the question should actually read "what is the value of wxy?".
My first instinct is to test cases, because I don't know very much about the values of w, x, or y, other than the fact that they sum to 42.
Statement 1: Let's start coming up with sets of numbers that fit this statement, and also have w + x + y = 42. Also, let's keep them as simple as possible, since we'll have to multiply them together.
x = -1
y = 1
w = 42
-1 + 1 + 42 = 42, and -1 and 1 are consecutive odd integers. The product is (-1)(1)(42) = -42.
x = 1
y = 3
w = 38
1 + 3 + 38 = 42, and 1 and 3 are consecutive odd integers. The product is (1)(3)(38), which definitely doesn't equal -42.
So, this statement is insufficient.
Statement 2:
w = 2x. It's easiest to start by choosing any value for x - let's choose something super easy first:
x = 0
w = 2(0) = 0
So, y must equal 42, and the product is (0)(0)(42) = 0.
Or,
x = 1
w = 2(1) = 2
So, y must equal 42-2-1 = 39, and the product is (1)(2)(39) which definitely doesn't equal 0.
So, this statement is insufficient.
Statements 1 and 2We now know three things:
w + x + y = 42
w = 2x
x and y are consecutive odd integers
If x and y are consecutive odd integers, it's also true that one of them is 2 greater than the other one. Either x = y + 2, or y = x + 2.
Either way, there are three equations, so we can solve for all three variables:
w + x + y = 42
w = 2x
x = y + 2
--> 2x + x + x - 2 = 42
--> 4x = 44
--> x = 11, w = 22, y = 9
The product is (11)(22)(9).
Alternatively,
w + x + y = 42
w = 2x
y = x + 2
--> 2x + x + x + 2 = 42
--> 4x = 40
--> x = 10
However, we already know that x is odd, so that can't be correct. The only correct possible solution is (11)(22)(9), so both statements together are sufficient and the answer is C.
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