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If X is a real number, is X > 7? (1) X^2 > 49 (2) [X] = 7, where

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amanvermagmat
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If X is a real number, is X > 7? (1) X^2 > 49 (2) [X] = 7, where [#permalink] New post   10 May 2018, 11:05
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If X is a real number, is X > 7?

(1) X^2 > 49

(2) [X] = 7, where [X] denotes the greatest integer less than or equal to X.
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DavidTutorexamPAL
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If X is a real number, is X > 7? (1) X^2 > 49 (2) [X] = 7, where [#permalink] New post   Updated on: 10 May 2018, 21:55
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amanvermagmat wrote:
If X is a real number, is X > 7?

(1) X^2 > 49

(2) [X] = 7, where [X] denotes the greatest integer less than or equal to X.


We'll try using numbers at the edge of our range to generate contradictory answers.
This is an Alternative approach.

(1) Putting in X = 10 gives x^2 = 100 > 49. But, putting in x = -10 gives the same result. So we don't know if x > 7.
Insufficient.

(2) So if x = 7 then [x] = 7 but if x = 7.5 then we also get [x]=7.
Insufficient.

Combined. (2) tells us that 7<=x<8 and (1) tells us that x > 7 or x < -7. So x > 7 must be true.
Sufficient.

(C) is our answer.

Originally posted by DavidTutorexamPAL on 10 May 2018, 14:36.
Last edited by DavidTutorexamPAL on 10 May 2018, 21:55, edited 1 time in total.
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Re: If X is a real number, is X > 7? (1) X^2 > 49 (2) [X] = 7, where [#permalink] New post   10 May 2018, 16:00
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DavidTutorexamPAL wrote:
amanvermagmat wrote:
If X is a real number, is X > 7?

(1) X^2 > 49

(2) [X] = 7, where [X] denotes the greatest integer less than or equal to X.


We'll try using numbers at the edge of our range to generate contradictory answers.
This is an Alternative approach.

(1) Putting in X = 10 gives x^2 = 100 > 49. But, putting in x = 10 gives the same result. So we don't know if x > 7.
Insufficient.

(2) So if x = 7 then [x] = 7 but if x = 7.5 then we also get [x]=7.
Insufficient.

Combined. (2) tells us that 7<=x<8 and (1) tells us that x > 7 or x < -7. So x > 7 must be true.
Sufficient.

(C) is our answer.


I think you mean -10
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DavidTutorexamPAL
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Re: If X is a real number, is X > 7? (1) X^2 > 49 (2) [X] = 7, where [#permalink] New post   10 May 2018, 21:56
Mo2men wrote:
DavidTutorexamPAL wrote:
amanvermagmat wrote:
If X is a real number, is X > 7?

(1) X^2 > 49

(2) [X] = 7, where [X] denotes the greatest integer less than or equal to X.


We'll try using numbers at the edge of our range to generate contradictory answers.
This is an Alternative approach.

(1) Putting in X = 10 gives x^2 = 100 > 49. But, putting in x = 10 gives the same result. So we don't know if x > 7.
Insufficient.

(2) So if x = 7 then [x] = 7 but if x = 7.5 then we also get [x]=7.
Insufficient.

Combined. (2) tells us that 7<=x<8 and (1) tells us that x > 7 or x < -7. So x > 7 must be true.
Sufficient.

(C) is our answer.


I think you mean -10


You're right, that was a typo on my part.
Thanks!
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mrinalsharma1990
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Re: If X is a real number, is X > 7? (1) X^2 > 49 (2) [X] = 7, where [#permalink] New post   17 Jun 2018, 03:43
Mo2men wrote:
DavidTutorexamPAL wrote:
amanvermagmat wrote:
If X is a real number, is X > 7?

(1) X^2 > 49

(2) [X] = 7, where [X] denotes the greatest integer less than or equal to X.


We'll try using numbers at the edge of our range to generate contradictory answers.
This is an Alternative approach.

(1) Putting in X = 10 gives x^2 = 100 > 49. But, putting in x = 10 gives the same result. So we don't know if x > 7.
Insufficient.

(2) So if x = 7 then [x] = 7 but if x = 7.5 then we also get [x]=7.
Insufficient.

Combined. (2) tells us that 7<=x<8 and (1) tells us that x > 7 or x < -7. So x > 7 must be true.
Sufficient.

(C) is our answer.


I think you mean -10


Combined. (2) tells us that 7<=x<8 and (1) tells us that x > 7 or x < -7. So x > 7 must be true.
Sufficient.
I did not understand how x greater than equal to 7 and less than 8 and eventually by combining 1&2 become greater than 7.
Could you please explain.
TIA.
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DavidTutorexamPAL
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Re: If X is a real number, is X > 7? (1) X^2 > 49 (2) [X] = 7, where [#permalink] New post   17 Jun 2018, 04:03
mrinalsharma1990 wrote:
Combined. (2) tells us that 7<=x<8 and (1) tells us that x > 7 or x < -7. So x > 7 must be true.
Sufficient.
I did not understand how x greater than equal to 7 and less than 8 and eventually by combining 1&2 become greater than 7.
Could you please explain.
TIA.



Hi,

Because (1) tells us that x has to be larger than 7.

More explicitly, (1) tells us that x has to be greater than 7 or smaller than -7.
But based on (2), we know that x can't be smaller than -7.
That means that (1) tells us that x has to be larger than 7.
And we're done!

It's also true that (2) tells us that x is smaller than 8 but we don't actually care about this; we only care that it is larger than 7.

Hope that helps!
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Re: If X is a real number, is X > 7? (1) X^2 > 49 (2) [X] = 7, where [#permalink] New post   18 Aug 2022, 06:12
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Re: If X is a real number, is X > 7? (1) X^2 > 49 (2) [X] = 7, where [#permalink]
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