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09 Jul 2006, 04:21
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The number q is a positive integer. Is the square root of q an integer as well?
(1) 2 and 5 are factors of q
(2) The tens digit of q is 5.
(1) 2 and 5 are factors of q
(2) The tens digit of q is 5.
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09 Jul 2006, 23:53
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"C" for me
(1) 2 and 5 are factors of q.
This statement implies that the number should be a mulitple of 2 and 5 which in turn implies that the units digit should be 0. Some sample numbers (10, 20, 30, 100, etc etc )
Nothing can be concluded from this.
(2) The tens digit of q is 5.
Sample numbers -- 51, 52, 53, 256, etc etc . 256 is sqr(16). Nothing can be concluded from this.
Combining both the conditions --- The units digit should be 0 and the tens digit should be 5. Hence the numbers should be either 50 or 150, 250, etc etc. Now squares of all the digits from 1-9 does not have a 0 in their units place. (4, 9, 16, 25, 36, 49, 64, 81). Only the number 10 can lead to a number which has 0 in the units place.
Any number which has 0 in the units place and should have a perfect square root should be a multiple of 10^2 = 100 which in turn means that the number should have a 0 in the tens place as well. If a number has 0 in the units place and a non-zero number in the tens place can never have an integer as its square root.
Hope I am clear with my explanation.
(1) 2 and 5 are factors of q.
This statement implies that the number should be a mulitple of 2 and 5 which in turn implies that the units digit should be 0. Some sample numbers (10, 20, 30, 100, etc etc )
Nothing can be concluded from this.
(2) The tens digit of q is 5.
Sample numbers -- 51, 52, 53, 256, etc etc . 256 is sqr(16). Nothing can be concluded from this.
Combining both the conditions --- The units digit should be 0 and the tens digit should be 5. Hence the numbers should be either 50 or 150, 250, etc etc. Now squares of all the digits from 1-9 does not have a 0 in their units place. (4, 9, 16, 25, 36, 49, 64, 81). Only the number 10 can lead to a number which has 0 in the units place.
Any number which has 0 in the units place and should have a perfect square root should be a multiple of 10^2 = 100 which in turn means that the number should have a 0 in the tens place as well. If a number has 0 in the units place and a non-zero number in the tens place can never have an integer as its square root.
Hope I am clear with my explanation.
jainvik7
Great work; yours is the OA and OE!
