AP ICET 2017 Shift 1 Paper

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Directions for Questions Numbers 1 to 20
In questions numbered 1 to 20. a question is followed by data in the form of two statements labelled as I and II. You must decide whether the data given in the statements are sufficient to answer the questions. Using the data make anappropriate choice from (1) to (4) as per the following guidelines:

Question : 10 of 200

Marks: +1, -0

(x^{3}+y^{3})^{1/3}

an integer
I.

x^3+y^3

is a multiple of 125
II.

x^3+y^3

is equal to the volume of the cuboid whose dimensions are 16 cm. 125 cm and 27 cm

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

Validate

Solution:

I.When

x^3+y^3=125×8

(x^3+y^3)^{1/3}=5×2=10

← It is an integer.
When

(x^3+y^3)=125×2,(x^3+y^3)^{1/3}

=5(2)^{1/3}

← It is not an integer
Thus, it may or may not be an integer
Hence, it is not sufficient.
II. Volume of cuboid

=16×125×27=x^3+y^3

∴(x^3+y^3)^{1/3}=(2×8×125×27)^{1/3}

=(2)^{1/3}(2×5×3)

←It is not an integer.
Hence, II alone is sufficient.

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