If x, y, and z are consecutive positive integers, with x

Question

If x, y, and z are consecutive positive integers, with x < y < z and x + y + z an even number, which of the following could be the value of z ?

(A) 1 
(B) 2 
(C) 4 
(D) 5 
(E) 8

nick1816 · Answer

(x,y,z) can be (odd, even , odd) or (even, odd, even)
Case 1 O+E+O=E
Case 2 E+O+E= O 
Since x+y+z= even, z must be odd.
Also x<y<z, hence z>2

z=5

cantaffordname · Answer

We can substitute it with the number, since x< y < z so if we put z as 5, (answer choice D) then y and x has to be 4 and 3 respectively. We have given information that the sum is even, hence the sum of this number is 12 which is even.

If we try 8( answer choice e) we get 21 as total. You can try with each choice.

IMO answer is D.

Correct me if i am wrong.

Posted from my mobile device

Lampard42 · Answer

The stem gives that y=x+1 and z=x+2; among x,x+1,x+2 two are odd and one is even (then only it will full fill the criteria of the sum being even). so x and x+2 must be odd. only D is odd. IMO D

firas92 · Answer

Since x, y and z are consecutive and x+y+z=even, x & z must be odd

In the answer choices, only A and D are odd

If z=1, x=-1 which is not possible since we are given that x is a positive integer

Therefore z=5

Answer is  (D)

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Kinshook · Answer

If z is positive integer y = z-1 and x = z-2 given that z>2
x+y+z = 3z-3 = even no 
3z = odd => z = odd and >2

Only D 5 satisfies both conditions
IMO D

CareerGeek · Answer

Least value of x = 1, y = 2 & z = 3 {Since they are positive integers}
Also, x = z - 2, y = z - 1

--> x + y + z = z - 2 + z - 1 + z
= 3z - 3 --> This is only even when z is odd {3*odd - 3 = odd - odd = Even}

Only Option feasible = 5

IMO Option D

Given, 
v:o = 2:3
 o:w = 7:5

Take LCM of common ingredient oil = LCM(3, 7) = 21
--> v:o = 2:3 = 14:21
--> o:w = 7:5 = 21:15
--> v:o:w = 14:21:15
--> Values of v = 14k, o = 21k, w = 15k for any constant k.

I. The dressing will contain more water than vinegar. -  YES

II. At least 25% of the dressing will be vinegar. 
% Vinegar =  \frac{14k}{(14k + 21k + 15k)} *100 =  \frac{14}{50} *100 = 28% -  YES

III. If you have equal volumes of each ingredient, the amount of dressing you can mix will be limited by the amount of oil.
Equal Volumes of each --> v = o = w = 14k
--> It will be limited by vinegar (Least value) -  NO

IMO Option D

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Archit3110 · Answer

for three no x+y+z=even
possible when ; e+e+e= even and o+o+e
out of given options 
IMO D; would only correct.

kitipriyanka · Answer

As x,y and z are consecutive nos, say x=p, y=p+1, z=p+2

Now p+p+1+p+2= Even no
3p+3=Even
3(p+1)= Even
Therefore, p+1 is even
Hence z=p+2 is odd

And only odd answer is 5
Hence D

bumpbot · Answer

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If x, y, and z are consecutive positive integers, with x < y < z and x

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