If x

Question

If x < y < z and y - x > 5, where x is an even integer and y and z are odd integers, what is the least possible value of z - x?

A. 6
B. 7
C. 8
D. 9
E. 10

PS25302.01

KarishmaB · Accepted Answer

Think about it this way: x < y < z
Difference between y and x is more than 5 so it is at least 6. But x is even and y is odd so their difference would be odd. Hence the diff between them will be at least 7. 
Now z is greater than y by at least 2 (since z is odd too), hence diff between x and z is at least 9.

Answer (D)

Abhii46 · Answer

y-x is >5. y is odd and x is even then y-x will be odd. Lowest possible value of y-x is 7.
For lowest possible value of z-x, y and z should be close, it means y and z are consecutive odd integers or z = y + 2.
Hence z-x = y + 2 - x = 7 + 2 = 9.

Bunuel · Answer

We want to minimize  z-x , so we need to maximize  x .

Say  z=11=odd , then max value of  y  will be 9 (as  y  is also odd). Now, since  y-5>x  -->  9-5>x  -->  4>x , then max value of  x  is 2 (as  x  is even).

Hence, the least possible value of  z-x  is 11-2=9.

Answer: D.

palsays · Answer

If x < y < z and y-x > 5, where x is an even integer and y and z are odd integers, what is the least possible value of z - x?

A. 6
B. 7
C. 8
D. 9
E. 10

Y is odd and X is even, so (y - x) has to be odd. ( Y - X ) > 5 means ( Y - X ) can have a value of 7.

Y - X = 7; Y = X + 7

Main equation will become,
X < X + 7 < Z

Subtract X from all,

0 < 7 < Z - X

Since Z is odd and X is even, (Z - X) has to be odd.

As (Z - X) > 7, the least possible value of Z-X will be 9. ANSWER.

- Ravender Singh

greatps24 · Answer

Z-x will be odd. therefore, option A, C, E is eliminated.

y-x> 5, if x= 2 then Y> 7 (8, 9 etc). so minimum value from z-x is 9

maddyboiler · Answer

I did it like this and i am getting 7 as the answer. Kindly tell me where i went wrong. Given x5 From the first equation i subtracted x so 05 We now that z-x is odd so the next odd number is 7.

Bunuel · Answer

You got z-x>5 but we also have y-x>5, so the least value of y-x is 7 and since z>y then the least value of z-x is 9.

Levry · Answer

We have: 1) x5 3) x=2k (x is an even number) 4) y=2n+1 (y is an odd number) 5) z=2p+1 (z is an odd number) 6) z-x=? least value z-x=2p+1-2k=2p-2k+1=2(p-k)+1 - that means that z-x must be an ODD number. We can eliminate answer choices A, C and E we are asked to find the least value, so we have to pick the least numbers since y is odd and x is even, y-x must be odd. since y-x>5, the least value for y-x must be 7, the least value for x must be 2, and, thus, the least possible value for y must be 9 (y-2=7, y=9) 2<9

sdas · Answer

Question asks least possible value, thus we can substitute by least possible numbers to get to answer

A, C and E are out since they are even

Left with B and E

y-x>5 which means least value of y-x=7 (since y is odd and x is even, result will be odd)
Work back: y= 5 (least value) x= -2 (least value). thus y-x = 5 - (-2) = 7 (least possible odd integer greater than 5)

Since z> y, thus least possible value of z = 7
Therefore, z-x = 7 - (-2) = 9

Correct choice D

sayansarkar · Answer

ACE are out as they are even. z = odd and x is even therefore Z-X is odd. out of B or D we need to see that we have to get the minimum value of z-x so we have to minimize z and maximize x. Hence z-x is 9

Abhishek009 · Answer

From  where x is an even integer   &  least possible value of z - x?

we can have x < y as 2 < 7 ,  where y - x = 5

From x < y < z and  y and z are odd integers

We have x < y < z = 2 < 7 < 9

So,  least possible value of z - x?    = 9 - 2 => 7

stonecold · Answer

here let y be 13 => then x will be 8 atleast and z will be 15 atleast => 9 is the difference 
thus D .

mehraumang · Answer

Since y-x>5; let us assume x to be -4 (even no); such that we get the least value of y.
Hence y has to be either 1 or 3, but since y=1 give y-x=5, this. Ant be right. Thus we can conclude y to be 3
Therefore next available odd integer is z=5
Z-x = 5-(-4)=9

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AD2GMAT · Answer

x=0; y=5; z=7 - if we take this set of values, then all the conditions satisfy and the answer becomes 7.
Where did I go wrong?

KarishmaB · Answer

y - x needs to be greater than 5. 
If x = 0, y = 5, then y - x = 5

So this set of values does not satisfy the conditions.

gps5441 · Answer

Easy one. Not sure if it is a 700 level question.
Given x < y < z and y-x > 5 and x is even and y&z are odd.
y-x>5. Now y is odd and x is even, therefore, Y can be 7, 9, 11.... and x is even and can be 0,2,4...
let us plug in a set of values
7-0>5
9-0>5
9-2>5
One more condition mentioned is z>y and is odd therefore z can be 9, 11, 13....
we now have
0<7<9 and z-x=9-0=9
2<9<11 and z-x=11-2=9 Answer D

ScottTargetTestPrep · Answer

Since y < z and y and z are odd integers, the smallest value that z can be, in terms of y, is z = y + 2.

We know that y - x > 5, so we might think that the minimum difference between y and x would be 6. However, this is impossible. Since x is even and y is odd, their difference cannot be an even number (because even – odd = odd). Thus, we see that the smallest difference between even number x and odd number y is not 6, but rather it is 7. So we have y - x = 7.

Therefore, the smallest difference between z and x is:

z - x = (y + 2) - x = (y - x) + 2 = 7 + 2 = 9.

Answer: D

babloorudra · Answer

Please correct me if my process is wrong:

x= even , Y & Z are Odd. Z-X has to be Odd. y>x+5. So Y has to be 7 & or 7+ (considering smallest even value for x,i.e 0). To obtain the least value of Z-x, Z has to be reduced and X has to be maximised. Since Z > Y, Min value for Z is 9. thus 9-0= 9.

Pritishd · Answer

1. x = even, y = odd and z = odd 2. x , y and z are integers 3. Subtracting x in x < y < z yields 0 < y - x < z - x ( Why? because we are asked to find the value of z - x ) 4. Re-arranging y - x > 5 to y > x + 5 5. Least value that x can take is 0 6. Substitute in 4 and we get that the least value of y - x will be 7 7. Substitute y - x in 3 to get 0 < 7 < z - x 8. Now z (odd) - x (even) will be odd so the smallest odd >7 is 9 ( Why? because we are asked for the least value) 9. 0 < y - x < z - x is 0 < 7 < 9 Ans D

If x < y < z and y - x > 5, where x is an even integer and y and z are

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