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# If x is a positive integer, is x^(1/2) greater than 20?

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If x is a positive integer, is x^(1/2) greater than 20?  [#permalink]

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01 Nov 2015, 09:24
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If x is a positive integer, is $$\sqrt{x}$$ greater than 20?

(1) x is divisible by 30
(2) x is divisible by 50

Kudos for a correct solution.

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Re: If x is a positive integer, is x^(1/2) greater than 20?  [#permalink]

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01 Nov 2015, 11:05
2
Bunuel wrote:
If x is a positive integer, is $$\sqrt{x}$$ greater than 20?

(1) x is divisible by 30
(2) x is divisible by 50

Kudos for a correct solution.

to be divisible by 30 .
x can be 30 ,60 ,90 or we can say it can be multiple of 30

to be greater than x^(1/2) greater than 20 it can be or not be

so ns

point b.
to be divisible by50 .
x can be 50 ,100 or 150 we can say it can be multiple of 50

so not suffi

lcm of 50 and 30 is 150
it can be 150 ,300,450 ,600
150^ is close to 13

600^ is greater than 20 .. so not suff

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Re: If x is a positive integer, is x^(1/2) greater than 20?  [#permalink]

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01 Nov 2015, 12:30
x is a positive integer, is x√ greater than 20?
It is given that x is positive. we can take the square on both side and hence the question is "is x > 400?"

1) x is divisible by 30 - there are many numbers less than and greater than 400 are divisible by 30. So x can be less or greater than 400.

2) x is divisible by 50 - there are many numbers less than and greater than 400 are divisible by 50. So x can be less or greater than 400.

lets combine both the equations 1 & 2 to find out if the answer is C or E?

X is such a number which is divisible by both 30 & 50.
150 is divisible by both 30 & 50. => X<400
600 is divisible by both 30 & 50, => X>400.

So x can be less or greater than 400. Hence the answer is "E".
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Re: If x is a positive integer, is x^(1/2) greater than 20?  [#permalink]

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01 Nov 2015, 12:35
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x can't be 0
1 - divisible by 30, x can be 30 - in this case, sqrt 30 is not greater than 20, if x = 900 = yes, is greater. NS
2 - divisible by 50, x can be 50 -> in this case, sqrt 50 is 5 sqrt 2 - not greater than 20. if x = 2500 - yes, is greater. NS
1+2 -> x can be 150, sqrt of 150 can be 5 sqrt 6 -> not greater than 20. x can be 1500 - and sqrt of 1500 is greater than 20. both are insufficient. E.
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Re: If x is a positive integer, is x^(1/2) greater than 20?  [#permalink]

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Updated on: 01 Nov 2015, 14:31
Sqrt(X)>20
Squaring on both sides X>400

i)factors of 30=2x3x5
30,300,420 are also divisible by 30 So we dont have single value.So not sufficient

ii)factors of 50=2x5x5
50,240,500 are also divisible by 50 and So we dont have single value.So not sufficient

Combining i) & ii)

common factors = 2x3x5x5 =150
150,450 is also divisible by 150.we dont have single value.So not sufficient.

Originally posted by iikarthik on 01 Nov 2015, 14:20.
Last edited by iikarthik on 01 Nov 2015, 14:31, edited 3 times in total.
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Re: If x is a positive integer, is x^(1/2) greater than 20?  [#permalink]

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01 Nov 2015, 14:22
iikarthik wrote:
Sqrt(X)>20
Squaring on both sides X>400

i)factors of 30=2x3x5
30 is also divisible by 30 and <400.So not sufficient

ii)factors of 50=2x5x5
50 is also divisible by 30 and <400.So not sufficient

Combining i) & ii)

common factors = 2x3x5x5 =150
150 is still <400.So not sufficient.

mate, there are some serious flaws in your way of thinking.
first of all, when analyzing statement 2, do not, do not, do not use any information from statement 1.
second, as you have pointed out, 150 is <400. This is a Yes/No DS type of question. IF you can clearly say Yes or No, then the information is sufficient. From your msg, you say that 150 is less than 400, that's why it is not sufficient. That's not true.
third, 50 is not divisible by 30, since the prime factorization is different. 30 has 3 distinct factors 2, 3, and 5, while 50 has only 2 distinct factors: 2 and 5.
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Re: If x is a positive integer, is x^(1/2) greater than 20?  [#permalink]

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01 Nov 2015, 14:30
mvictor wrote:
iikarthik wrote:
Sqrt(X)>20
Squaring on both sides X>400

i)factors of 30=2x3x5
30 is also divisible by 30 and <400.So not sufficient

ii)factors of 50=2x5x5
50 is also divisible by 30 and <400.So not sufficient

Combining i) & ii)

common factors = 2x3x5x5 =150
150 is still <400.So not sufficient.

mate, there are some serious flaws in your way of thinking.
first of all, when analyzing statement 2, do not, do not, do not use any information from statement 1.
second, as you have pointed out, 150 is <400. This is a Yes/No DS type of question. IF you can clearly say Yes or No, then the information is sufficient. From your msg, you say that 150 is less than 400, that's why it is not sufficient. That's not true.
third, 50 is not divisible by 30, since the prime factorization is different. 30 has 3 distinct factors 2, 3, and 5, while 50 has only 2 distinct factors: 2 and 5.

Thanks Mvictor for pointing out the typo and logical flaws.Hope it si correct now.

I have edited my post
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Re: If x is a positive integer, is x^(1/2) greater than 20?  [#permalink]

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02 Nov 2015, 09:01
orig condition is x>400?

1. x divisibly by 30, i.e. x=30,600etc..
not suff
2. x divisible by 50 i.e. x =50,500 etc.
not suff
combining both, x= 150, 1500 etc..
so not suff.
ANS :E
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Re: If x is a positive integer, is x^(1/2) greater than 20?  [#permalink]

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04 Nov 2015, 11:13
1
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If x is a positive integer, is x √ greater than 20?

(1) x is divisible by 30
(2) x is divisible by 50

If we modify the original condition by squaring both sides, we get x>20^2 or x>400. There is one variable (x) and 2 equations are given from the conditions, so there is high chance (D) will be our answer.

From condition 1, the answer is 'no' for x=30 but 'yes' for 1500. This is insufficient.
For condition 2, the answer is 'no' for x=50 but 'yes' for 1500. This is insufficient.
Looking at the conditions together, the answer is 'no' for x=150 but 'yes' for 1500. So the answer becomes (E).

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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Re: If x is a positive integer, is x^(1/2) greater than 20?  [#permalink]

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14 Jul 2017, 10:40
1
lcm of 50 and
30 is 150

it can be 150 ,300
,450 ,600

150^ is close to 13

600^ is greater than 20 .. so not sufficient

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Re: If x is a positive integer, is x^(1/2) greater than 20?  [#permalink]

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