DS - Question

[neeg]

If d is a positive integer, is sq.rt. d an integer?

(1)Sq.rt.9d is an integer
(2)Sq.rt.10d is an integer

[Anurag@Gurome]

If d is a positive integer, is sq.rt. d an integer?

(1)Sq.rt.9d is an integer
(2)Sq.rt.10d is an integer

[Note : I suspect the actual question says ".. is not an integer." because if √(10d) is an integer, then it is not possible for √d to be an integer which is contradictory to statement 1. I am replying assuming the correction. Otherwise, if the question is considered as posted, both statements will be sufficient to answer the question.]

Statement 1: √(9d) = (√9)*(√d) = 3√d is an integer ---> √d must be an integer

Sufficient

Statement 2: √(10d) = (√10)*(√d) is not an integer
Now, √d may or may not be an integer. For example, consider the following two cases,

• d = 1 ---> √(10d) is not an integer but √d is an integer
  d = 2 ---> √(10d) as well as √d is not an integer

Not sufficient

The correct answer is A.

[neeg]

Yes, it was an error in typing the statements. Statement (2) should have read as sq rt 10d is NOT an integer. Thanks for the solution as I understand the solution now.