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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 10 May 2018, 11:05
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

55% (hard)

Question Stats:

53% (01:19) correct 47% (01:12) wrong based on 128 sessions

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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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C
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
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If X is a real number, is X > 7? (1) X^2 > 49 (2) [X] = 7, where Updated on: 10 May 2018, 21:55
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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amanvermagmat
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.
Show more

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.
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If X is a real number, is X > 7? (1) X^2 > 49 (2) [X] = 7, where 10 May 2018, 16:00
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DavidTutorexamPAL
amanvermagmat
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.
Show more

I think you mean -10
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If X is a real number, is X > 7? (1) X^2 > 49 (2) [X] = 7, where 10 May 2018, 21:56
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DavidTutorexamPAL
amanvermagmat
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
Show more

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

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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If X is a real number, is X > 7? (1) X^2 > 49 (2) [X] = 7, where 17 Jun 2018, 04:03
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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.
Show more


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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If X is a real number, is X > 7? (1) X^2 > 49 (2) [X] = 7, where 13 May 2024, 15:57
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