Problems on Numbers

Q1:
What is the two-digit number?
I.  The difference between the two digits is 9.
 II.  The sum of the digits is equal to the difference between the two digits.

A I alone sufficient while II alone not sufficient to answer

B II alone sufficient while I alone not sufficient to answer

C Either I or II alone sufficient to answer

D Both I and II are not sufficient to answer

E Both I and II are necessary to answer

ANS:E - Both I and II are necessary to answer

Let the tens and unit digits be x and y respectively. Then,  I. x - y = 9. II. x + y = x - y. From I and II, we get x - y = 9 and x + y = 9. On solving, we get x = 9 and y = 0.  Required number is 90. Thus, both I and II are needed to get the answer.  Correct answer is (E).



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