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### Discussion :: Problems on Numbers

1. What is the number?

I. The sum of the two digits is 8. The ratio of the two digits is 1 : 3.

II. The product of the two digit of a number is 12. The quotient of two digits is 3

2.  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

Explanation :

Let the tens and units digit be x and y respectively. Then,

I. x + y = 8 and $$\frac {X } { Y }$$=$$\frac { 1 } {3 }$$

I gives, 4y = 24        y = 6.

So, x + 6 = 8        x = 2.

II. xy = 12  and$$\frac {X } { Y }$$=$$\frac { 3 } {1 }$$

II gives, x2 = 36        x = 6.

So, 3y = 6        y = 2

Therefore, Either I or II alone sufficient to answer.

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