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Nishan

· started a discussion

· 1 Months ago

the answer as explained is confusing (Question:101374.0)

we need both the statements to answer the given question. statement 2 only tells that the product of the two numbers is 4 but x+y = 5 is deduced from the first statement

Question:

DIRECTIONS: In each of the following questions, a question is followed by information given in two statements. You have to study the question along with the statements and decide, the information given in which of the statements (s) is necessary to answer the question?


Question:

The H.C.F. of two numbers is 17. What are the values of the two numbers?


Statements:

I. The sum of the two numbers is 85.

II. The L.C.M. of the two numbers is 68.
Options:
A) If the question can be answered by using statement I alone but not by using statement II alone
B) If the question can be answered by using statement II alone but not by using statement I alone
C) If the question can be answered by using either of the statements alone
D) If the question can be answered by using both the statements together but not by either of the statements alone
E) If the question can be answered by using both the statements together but not by either of the statements alone
Solution:

Let the two numbers be 17x and 17y where x and y are co-primes.

From statement I, 17x + 17y = 85. ⇒ x + y = 5

The pairs of (x y) satisfying x + y = 5 is (1,4) and (2, 3). 

So the numbers are 17, 68 or 34, 51.

So statement I alone is not sufficient.

From statement II, 17xy = 68 ⇒ xy = 4

So the only pair of (x, y) satisfying x+y = 5 is (1, 4). So the numbers are 17 and 68.

As the unique value of the numbers can be found, statement II alone is sufficient.

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