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x , y and z are three consecutive odd integers. If x + y

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x , y and z are three consecutive odd integers. If x + y  [#permalink]

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New post 23 Oct 2019, 11:39
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x , y and z are three consecutive odd integers. If x + y = z + 9 , what is the value of z ?

a. 13
b. 15
c. 17
d. 19
e. none of those

Posted from my mobile device
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Posts: 1827
Re: x , y and z are three consecutive odd integers. If x + y  [#permalink]

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New post 23 Oct 2019, 11:52
Unless the question tells you that x, y and z are three consecutive odd integers in increasing order, there's more than one solution. If we do know x < y < z, then y = x + 2, and z = x + 4, since consecutive odd integers are 2 apart. Substituting into the given equation, we have

x + (x+2) = (x + 4) + 9
2x + 2 = x + 13
x = 11

Since z = x + 4, we find z = 15.

But if we don't know x < y < z, then it might be that z = 3, x = 5, and y = 7, for example. What is the source of the question?
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Re: x , y and z are three consecutive odd integers. If x + y  [#permalink]

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New post 23 Oct 2019, 12:10
jackfr2 wrote:
x , y and z are three consecutive odd integers. If x + y = z + 9 , what is the value of z ?

a. 13
b. 15
c. 17
d. 19
e. none of those

Posted from my mobile device


First few consecutive Odd Numbers are - \(1, 3, 5, 7, 9, 11, 13, 15, 17, 19..........................\)

Now we know, \(x + y = z + 9\)

Or, \(x + y - z = 9\)

Check the values using options...

(A) If z = 13 , x + y = 9 + 11 => 20 & x + y - z = 7
(B) If z = 15, x + y = 11 + 13 => 24 & x + y - z = 9 ( We do not need to go further )

I will mark my Answer as (B) and move on to the next question..
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Re: x , y and z are three consecutive odd integers. If x + y  [#permalink]

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New post 23 Oct 2019, 19:52
jackfr2 wrote:
x , y and z are three consecutive odd integers. If x + y = z + 9 , what is the value of z ?

a. 13
b. 15
c. 17
d. 19
e. none of those

Posted from my mobile device



what is the value of z? should be what is CAN BE the value of z? or what is the MAXIMUM POSSIBLE value of z?

Now z can be the smallest of three as there is NO order given..
so x and y will be z+2 or z+4 in any order....\(z+2+z+4=z+9....z=3\)

Now z can be the average or in center of three ..
so x and y will be z-2 or z+2 in any order....\(z+2+z-2=z+9....z=9\)

Also z can be the greatest of three ..
so x and y will be z-2 or z-4 in any order....\(z-4+z-2=z+9....z=15\)

what is CAN BE the value of z? --- ONLY 15 is given in choices, so B or
what is the MAXIMUM POSSIBLE value of z?---- 15 is the answer

B
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Re: x , y and z are three consecutive odd integers. If x + y   [#permalink] 23 Oct 2019, 19:52
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