If x and y are positive odd integers, and x

Question

If x and y are positive odd integers, and x < y, what is the value of y – x?

(1) The greatest common divisor of x and y is 1. 
(2) The least common multiple of x and y is 91

BrentGMATPrepNow · Answer

Given : x and y are positive odd integers, and x < y

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

Statement 1 : The greatest common divisor (GCD) of x and y is 1.  
There are infinitely many pairs values of x and y that satisfy statement 1. Here are two: 
 Case a : x = 1 and y = 3. In this case, the answer to the target question is  y - x = 3 - 1 = 2 
 Case b : x = 1 and y = 4. In this case, the answer to the target question is  y - x = 5 - 1 = 4 
Since we can’t answer the  target question  with certainty, statement 1 is NOT SUFFICIENT

Statement 2 : The least common multiple (LCM) of x and y is 91 
To get a better idea of what this statement is telling us, let's first find the prime factorization of 91.
We get: 91 = (7)(13)
At this point, I can identify some of pairs of values of x and y that satisfy statement 2. Here are two: 
 Case a : x = 1 and y = 91. In this case, the answer to the target question is  y - x = 91 - 1 = 90 
 Case b : x = 7 and y = 13. In this case, the answer to the target question is  y - x = 13 - 7 = 6 
Since we can’t answer the  target question  with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined    
  STRATEGY: At this point, it's a good idea to see if we can  reuse  any of the counterexamples we used in statements 1 or 2.  
I can see that the x and y values I used to show that statement 2 is insufficient ALSO satisfy statement 1. 
So, the same counterexamples will satisfy the two statements COMBINED. 
In other words, 
 Case a : x = 1 and y = 91 (notice that the GCD = 1, and the LCM = 91). In this case, the answer to the target question is  y - x = 91 - 1 = 90 
 Case b : x = 7 and y = 13 (notice that the GCD = 1, and the LCM = 91). In this case, the answer to the target question is  y - x = 13 - 7 = 6 
Since we can’t answer the  target question  with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent

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If x and y are positive odd integers, and x < y, what is the value of

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