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TANCET 2020 Solved Papers

Question Numbers: 21-40

PART II

DIRECTIONS: Data sufficiency problems consist of a question and two statements, labelled (I) and (II), in which certain data are given. You have to decide whether the data given in the statements is sufficient for answering the question. Use the data given, plus your knowledge of mathematics and every day facts, to mark your answer as

a. If the question can be answered with the help of statement I alone,

b. If the question can be answered with the help of statement II, alone,

c. If both, statement I and statement II are needed to answer the question, and

d. If the question cannot be answered even with the help of both the statements.

Question : 39 of 100

Marks: +1, -0

What is the number x ?

I. The LCM of

x

and 18 is 36.

II. The HCF of

x

and 18 is 2.

If the question can be answered with the help of statement I alone,
If the question can be answered with the help of statement II, alone,
If both, statement I and statement II are needed to answer the question, and
If the question cannot be answered even with the help of both the statements.

Validate

Solution:

Concept:

For two numbers,

\text{LCM} \times \text{HCF} = \text{product of the numbers}

Explanation:

From statement I alone:

\text{LCM}(x, 18) = 36

gives possible values

x = 4, 12, 36

So statement I alone is not sufficient.

From statement II alone:

\text{HCF}(x, 18) = 2

gives many possible even values of

x

So statement II alone is not sufficient.

Using both statements:

\text{LCM} \times \text{HCF} = x \times 18

36 \times 2 = 18x

x = 4

Thus both statements together are needed.

Answer:

Both statement I and statement II are needed to answer the question.

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