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If w + x + y = 42, what is the value of xyz? (1) x and y are consecuti

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If w + x + y = 42, what is the value of xyz? (1) x and y are consecuti  [#permalink]

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New post 27 Mar 2019, 12:51
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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

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Re: If w + x + y = 42, what is the value of xyz? (1) x and y are consecuti  [#permalink]

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New post 27 Mar 2019, 17:45
1
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 2

We 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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Re: If w + x + y = 42, what is the value of xyz? (1) x and y are consecuti  [#permalink]

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New post 27 Mar 2019, 17:54
1
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


Equation 1:\(w+x+y=42\)
Statement 1: x and y are consecutive odd integers. i.e. either \(x=y+2 or y=x+2.\) Putting x=y+2 in eqn 1.\(w+x+x+2=42. w+2x=42\). x can have different values. so can w. e.g. w= 40, x=1, y=3 or w=36,x=3, y=5. Insuff
Statement 2: w=2x, putting it in eqn, \(2x+x+y=42. 3x + y=42\), x and y are odd and again can have different values. x=3, y=31, w=4 or x=5, w=10 y=27. Insuff,

1+2
\(2x+x+2+x=42. 4x =40. x= 10.\) but x isn't odd now. Insuff.

IMO, Option E.
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Re: If w + x + y = 42, what is the value of xyz? (1) x and y are consecuti  [#permalink]

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New post 28 Mar 2019, 13:24
1
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


#1
x & y are consective odd integers
so if x = x and y = x+2
so
w+x+y=42 ;
w+x+x+2= 42
w+2x= 40
now x,y ; 19,17 and w = 4
or x,y; 17,15 and w= 8
insufficient
#2
w=2x
so 3x+y= 42
again insufficient
as we get x=13 and y=3
from 1 & 2
we can write
2x+2x=40
x= 10
so w= 20 and x,y = 9,11
sufficient
IMO C
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Re: If w + x + y = 42, what is the value of xyz? (1) x and y are consecuti   [#permalink] 28 Mar 2019, 13:24
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