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If x and y are positive integers, what is the value of x y? 24 Jul 2022, 08:07
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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55% (hard)

Question Stats:

56% (01:44) correct 44% (01:45) wrong based on 127 sessions

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If \(x\) and \(y\) are positive integers, what is the value of \(x – y\)?

(1) The greatest common divisor of \(x\) and \(y\) is \(1\).
(2) \(\frac{13x}{y}\) is a positive integer with exactly two positive divisors.
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E
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If x and y are positive integers, what is the value of x y? 24 Jul 2022, 08:48
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1) GCD of x and y = 1
We can take any set of 2 prime numbers and their gcd will be 1 but differences will not be the same
2,3 Diff = 1
2,5 Diff = 3
2,13 Diff = 11
Not sufficient

2) 13x/y is a positive integer with exactly 2 positive divisors

This means that 13x/y is a prime number because only prime numbers have exactly 2 positive divisors

13x/y can be prime if y=13 and x is any prime number
x=2,y=13 Diff=11
x=5,y=13 Diff=8
Not sufficient

Both combined
GCD of x and y is 1 and 13x/y is a prime number
x=2,y=13 Diff=11
x=5,y=13 Diff=8
Not sufficient

Answer - E

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If x and y are positive integers, what is the value of x y? 24 Jul 2022, 11:16
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av1901
1) GCD of x and y = 1
We can take any set of 2 prime numbers and their gcd will be 1 but differences will not be the same
2,3 Diff = 1
2,5 Diff = 3
2,13 Diff = 11
Not sufficient

2) 13x/y is a positive integer with exactly 2 positive divisors

This means that 13x/y is a prime number because only prime numbers have exactly 2 positive divisors

13x/y can be prime if y=13 and x is any prime number
x=2,y=13 Diff=11
x=5,y=13 Diff=8
Not sufficient

Both combined
GCD of x and y is 1 and 13x/y is a prime number
x=2,y=13 Diff=11
x=5,y=13 Diff=8
Not sufficient

Answer - E

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What if x=y then ans must be B.
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If x and y are positive integers, what is the value of x y? 24 Jul 2022, 12:44
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figjam786
av1901
1) GCD of x and y = 1
We can take any set of 2 prime numbers and their gcd will be 1 but differences will not be the same
2,3 Diff = 1
2,5 Diff = 3
2,13 Diff = 11
Not sufficient

2) 13x/y is a positive integer with exactly 2 positive divisors

This means that 13x/y is a prime number because only prime numbers have exactly 2 positive divisors

13x/y can be prime if y=13 and x is any prime number
x=2,y=13 Diff=11
x=5,y=13 Diff=8
Not sufficient

Both combined
GCD of x and y is 1 and 13x/y is a prime number
x=2,y=13 Diff=11
x=5,y=13 Diff=8
Not sufficient

Answer - E

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What if x=y then ans must be B.
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Even if we consider x=y, still other cases will also work so we have multiple answers for x-y, that is why statement is not sufficient
Statement is only sufficient if it gives only 1 answer under any and all circumstances
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If x and y are positive integers, what is the value of x y? 25 Jul 2022, 09:30
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BrentGMATPrepNow
If \(x\) and \(y\) are positive integers, what is the value of \(x – y\)?

(1) The greatest common divisor of \(x\) and \(y\) is \(1\).
(2) \(\frac{13x}{y}\) is a positive integer with exactly two positive divisors.
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Given: \(x\) and \(y\) are positive integers

Target question: What is the value of \(x – y\)?

Statement 1: The greatest common divisor of \(x\) and \(y\) is \(1\)
There are several values of x and y that satisfy statement 1. Here are two:
Case a: If x = 1 and y = 1, then the greatest common divisor of x and y is 1. In this case, the answer to the target question is x - y = 1 - 1 = 0
Case b: If x = 1 and y = 2, then the greatest common divisor of x and y is 1. In this case, the answer to the target question is x - y = 1 - 2 = -1
Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: \(\frac{13x}{y}\) is a positive integer with exactly two positive divisors.
In other words, \(\frac{13x}{y}\) is a prime number.
There are several values of x and y that satisfy statement 2. Here are two:
Case a: If x = 1 and y = 1, then 13x/y = (13)(1)/(1) = 13, which is prime. In this case, the answer to the target question is x - y = 1 - 1 = 0
Case b: If x = 5 and y = 13, then 13x/y = (13)(5)/(13) = 5, which is prime. In this case, the answer to the target question is x - y = 5 - 13 = -8
Since we can’t answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
There are several values of x and y that satisfy BOTH statements. Here are two:
Case a: x = 1 and y = 1. In this case, the answer to the target question is x - y = 1 - 1 = 0
Case b: x = 5 and y = 13.In this case, the answer to the target question is x - y = 5 - 13 = -8

Answer: E
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If x and y are positive integers, what is the value of x y? 16 Dec 2023, 03:52
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