If x, y, z are positive integers, is x+y+z divisible by 7? I. x+y+z is an even number, II. x=4y-11,z=2y+4

Correct Answer is : if the statement II alone is sufficient to answer the question.

if the statement 1 alone is sufficient to answer the question.

if the statement II alone is sufficient to answer the question.

if both the statements I and II are sufficient to answer the question but neither statement alone is sufficient.

if both the statements I and II together are not sufficient to answer the question and additional data is required.

Correct Answer is : if the statement II alone is sufficient to answer the question.

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AP ICET 2016 Paper

Question : 8 of 200

Marks: +1, -0

x+y+z

x+y+z

x=4y-11,z=2y+4

if the statement 1 alone is sufficient to answer the question.
if the statement II alone is sufficient to answer the question.
if both the statements I and II are sufficient to answer the question but neither statement alone is sufficient.
if both the statements I and II together are not sufficient to answer the question and additional data is required.

Solution:

x, y, z are positive integers.

I. Given : x + y + z is even.

\Rightarrow x+y+z=2,4,6,8,10,12,14,16,\ldots

Of these, only multiples of 14 are divisible by 7 while others are not.

∴ I alone is not sufficient.

II. Given :

x=4y-11

and

z=2y+4

Adding the two we get,

x+z=6y-7

\Rightarrow x+y+z=7y-7=7(y-1)

Since 7 is a factor,

x+y+z

is divisible by 7.

∴ II alone is sufficient.

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