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Difficulty:
75%
(hard)
Question Stats:
43% (01:36) correct
57%
(01:42)
wrong
based on 184
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Is square root of a positive integer x an integer?
(1) The sum of distinct factors of x is odd
(2) x has an odd number of distinct factor
(1) The sum of distinct factors of x is odd
(2) x has an odd number of distinct factor
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
Data Sufficiency Forum
03 Jun 2013, 07:29
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summer101
Tips about the perfect square:
1. The number of distinct factors of a perfect square is ALWAYS ODD. The reverse is also true: if a number has the odd number of distinct factors then it's a perfect square;
2. The sum of distinct factors of a perfect square is ALWAYS ODD. The reverse is NOT always true: a number may have the odd sum of its distinct factors and not be a perfect square. For example: 2, 8, 18 or 50;
3. A perfect square ALWAYS has an ODD number of Odd-factors, and EVEN number of Even-factors. The reverse is also true: if a number has an ODD number of Odd-factors, and EVEN number of Even-factors then it's a perfect square. For example: odd factors of 36 are 1, 3 and 9 (3 odd factor) and even factors are 2, 4, 6, 12, 18 and 36 (6 even factors);
4. Perfect square always has even powers of its prime factors. The reverse is also true: if a number has even powers of its prime factors then it's a perfect square. For example: \(36=2^2*3^2\), powers of prime factors 2 and 3 are even.
Similar questions to practice:
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if-x-is-an-integer-that-has-exactly-three-positive-divisors-132710.html
Hope it helps.
05 Jun 2013, 03:07
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Is square root of a positive integer x an integer?
Is \(\sqrt{x}=integer\)? --> is \(x=integer^2\)? So, the question basically asks whether x is a perfect square.
(1) The sum of distinct factors of x is odd. If x=1 (1 has one distinct factor: 1), then x IS a prefect square but if x=2 (2 has two distinct factor: 1 and 2 --> 1+2=3=odd), then x is NOT a prefect square. Not sufficient.
(2) x has an odd number of distinct factor. According to the properties above, x must be a perfect square. Sufficient.
Answer: B.
Hope it's clear.
Is \(\sqrt{x}=integer\)? --> is \(x=integer^2\)? So, the question basically asks whether x is a perfect square.
(1) The sum of distinct factors of x is odd. If x=1 (1 has one distinct factor: 1), then x IS a prefect square but if x=2 (2 has two distinct factor: 1 and 2 --> 1+2=3=odd), then x is NOT a prefect square. Not sufficient.
(2) x has an odd number of distinct factor. According to the properties above, x must be a perfect square. Sufficient.
Answer: B.
Hope it's clear.
