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Is the positive square root of x an integer? (1) x has exactly three f 21 Sep 2022, 04:28
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

35% (medium)

Question Stats:

59% (01:02) correct 41% (01:29) wrong based on 39 sessions

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Is the positive square root of x an integer?

(1) x has exactly three factors.
(2) x < 16

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A
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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Is the positive square root of x an integer? (1) x has exactly three f 21 Sep 2022, 23:34
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Is the positive square root of x an integer?

(1) x has exactly three factors.
(2) x < 16
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Solution:

Pre-Analysis:
  • We are asked if \(\sqrt{x}\) is an integer or not
  • Which means we are asked if \(x\) is a perfect square or not
  • This is a Yes - No question

Statement 1: x has exactly three factors
  • We know that if an integer has an odd number of factors, then the number is a perfect square
  • Similarly, if we know x has 3 factors, we can be sure that x is a perfect square
  • Thus, statement 1 alone is sufficient and we can eliminate options B, C and E

Statement 2: \(x < 16\)
  • If x = 9, then it is perfect square
  • If x = 10, then it is not perfect square
  • Thus, statement 2 alone is not sufficient


Hence the right answer is Option A
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