If y is an integer such that 2 < y < 100 and if y is also the square of an integer, what is the value of y ?
(1) y has exactly two prime factors.
(2) y is even.
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Number properties - prime factors
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Anurag@Gurome
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Statement 1: As y has exactly two prime factors and y is also square of an integer, y must be a square of a prime number. Therefore possible values of y are 4, 9, 25 and 49.koby_gen wrote:If y is an integer such that 2 < y < 100 and if y is also the square of an integer, what is the value of y ?
(1) y has exactly two prime factors.
(2) y is even.
Not sufficient.
Statement 2: Different values of y are possible.
Not sufficient.
1 & 2 Together: Only possible value of y is 4.
Sufficient.
The correct answer is C.
Note: The statement 1 doesn't say "y has exactly two different prime factors". In which case there will be only one possible value of y in that range. Which is 36. And thus statement 1 will be sufficient.
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kevincanspain
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I would say the latter case holds, as 4 does not have two prime factors
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prachich1987
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I am not getting abovekevincanspain wrote:I would say the latter case holds, as 4 does not have two prime factors
4 has exactly 2 prime factors
4=2 X 2
Can you please explain your view?
Thanks!
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chendawg
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My thought process was this:
We know 2 < y < 100 and y is also the square of an integer. So we know that y is the square of some number less than 10 and more than 1, so we can consider 2-9.
1. y has exactly two prime factors. Primes under 10 are 2, 3, 5 and 7. Since we know Y is the square of an integer, all its factors must come in 2's. Since Y has 2 prime factors, only (2*3)^2 is under 100. Thus sufficient.
2. y is even. Y can be 2,4, etc. Insufficient.
I got A as the answer.
However, as with Anurag@Gurome's answer, it could be C, as I thought of statement one as saying 2 distinct prime factors, where it just states y has 2 prime factors.
What's OA and source?
We know 2 < y < 100 and y is also the square of an integer. So we know that y is the square of some number less than 10 and more than 1, so we can consider 2-9.
1. y has exactly two prime factors. Primes under 10 are 2, 3, 5 and 7. Since we know Y is the square of an integer, all its factors must come in 2's. Since Y has 2 prime factors, only (2*3)^2 is under 100. Thus sufficient.
2. y is even. Y can be 2,4, etc. Insufficient.
I got A as the answer.
However, as with Anurag@Gurome's answer, it could be C, as I thought of statement one as saying 2 distinct prime factors, where it just states y has 2 prime factors.
What's OA and source?
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ikaplan
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A cannot be the answer.
Statement (1) states that y has exactly 2 prime factors.
Possible values for y are 4 (2^2), 9(3^2), 16(4^2), 25(5^2) etc...
So there are more than one possible solutions for y from Statement (1), namely 4, 9, 25 etc.
Therefore, A is insufficient
Statement (1) states that y has exactly 2 prime factors.
Possible values for y are 4 (2^2), 9(3^2), 16(4^2), 25(5^2) etc...
So there are more than one possible solutions for y from Statement (1), namely 4, 9, 25 etc.
Therefore, A is insufficient
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banibhusan
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Here statement 1 says that there are exactly two prime factors of y. It doesn't mention whether they are distinct or not. So the possible answers statement 1 are 4,9,25 and 49. 36 can be ruled out because it has 2 distinct prime factors, but a total of 4 prime factors which contradicts statement 1. So its insufficient.
Now coming to statement 2, it says that y is even. Which means y can have any even integer between 2 and 100. Hence insufficient.
However if you combine statement 1 and 2, you can eliminate 9,25 and 49 from the possible answers. So the value of y would be 4 which has exactly two prime factors and its even and square of an integer.
Since I am just a beginner, plz correct me if I am wrong.
Now coming to statement 2, it says that y is even. Which means y can have any even integer between 2 and 100. Hence insufficient.
However if you combine statement 1 and 2, you can eliminate 9,25 and 49 from the possible answers. So the value of y would be 4 which has exactly two prime factors and its even and square of an integer.
Since I am just a beginner, plz correct me if I am wrong.
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ClaireSpencer
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a) is insufficient, b) is sufficient.
Eligible numbers 2<n<100 are 4,9,16,25,36,49,64,81.
1 is not a prime number.
9,25,49,81 have only one prime factor each; 3,5,7,3 respectively.
4 only has one prime factor (2) as does 64 (8^2).
The factors of 36 are 1,2,3,6,18. 2 and 3 are prime numbers.
The answer is 36.
Eligible numbers 2<n<100 are 4,9,16,25,36,49,64,81.
1 is not a prime number.
9,25,49,81 have only one prime factor each; 3,5,7,3 respectively.
4 only has one prime factor (2) as does 64 (8^2).
The factors of 36 are 1,2,3,6,18. 2 and 3 are prime numbers.
The answer is 36.
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MAAJ
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2 < y < 100
y = x^2 = x * x
y = ?
1) y has exactly 2 prime factors
x * x = y
2 * 2 = 4
3 * 3 = 9
5 * 5 = 25
7 * 7 = 49
2) y is even
x * x = y
2 * 2 = 4
4 * 4 = 16
6 * 6 = 36
8 * 8 = 64
Combining 1) and 2)
Only 2 x 2 = 4
y = x^2 = x * x
y = ?
1) y has exactly 2 prime factors
x * x = y
2 * 2 = 4
3 * 3 = 9
5 * 5 = 25
7 * 7 = 49
2) y is even
x * x = y
2 * 2 = 4
4 * 4 = 16
6 * 6 = 36
8 * 8 = 64
Combining 1) and 2)
Only 2 x 2 = 4
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Ian Stewart
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If I were to ask the question 'how many positive factors does 9 have?', the answer would be 'three': 1, 3 and 9. We would not count the '3' twice. By the same token, if I ask 'how many prime factors does 9 have?' the answer ought to be one; there is no logical reason to count the '3' twice.Anurag@Gurome wrote:Statement 1: As y has exactly two prime factors and y is also square of an integer, y must be a square of a prime number. Therefore possible values of y are 4, 9, 25 and 49.koby_gen wrote:If y is an integer such that 2 < y < 100 and if y is also the square of an integer, what is the value of y ?
(1) y has exactly two prime factors.
(2) y is even.
When a question asks 'how many prime factors does x have?', that normally means 'how many *different* prime factors does x have?' Fortunately the wording of real GMAT questions will be unambiguous -- GMAT questions will include the phrase 'distinct prime factors' so there is no possibility of misinterpretation. Still, I'm sure Statement 1 in the original post above is intended to mean "y has exactly two *distinct* prime factors" (in which case y must be 36), particularly since the upper bound of 100 seems specifically chosen so that Statement 1 will be sufficient.
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gmatters12
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I pick A
We know y=integer^2 and y is between 2and 100
So...
y can be 2^2=4
y can be 3^2=9
y can be 4^2=16
y can be 5^2=25
y can be 6^2=36
y can be 7^2=49
y can be 8^2=64
y can be 9^2=81
1) y has exactly 2 prime factors
The only one that has 2 distinct prime factors is 36 (2 and 3 are its only prime factors). All the other numbers have only one prime factor. So statement 1 is sufficient!
2) that does not tell us anything. could be 4, 16, 36, or 64. Insufficient
We know y=integer^2 and y is between 2and 100
So...
y can be 2^2=4
y can be 3^2=9
y can be 4^2=16
y can be 5^2=25
y can be 6^2=36
y can be 7^2=49
y can be 8^2=64
y can be 9^2=81
1) y has exactly 2 prime factors
The only one that has 2 distinct prime factors is 36 (2 and 3 are its only prime factors). All the other numbers have only one prime factor. So statement 1 is sufficient!
2) that does not tell us anything. could be 4, 16, 36, or 64. Insufficient
