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If x and y are distinct positive integers, what is the value of ....
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10 Sep 2015, 14:00
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If x and y are distinct positive integers, what is the value of \(x^4  y^4\)? 1. \((y^2 + x^2)(y + x)(x  y) > 100\) 2. \(x^y = y^x\)
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Re: If x and y are distinct positive integers, what is the value of ....
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10 Sep 2015, 21:04



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Re: If x and y are distinct positive integers, what is the value of ....
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12 Mar 2017, 23:51
Prajat wrote: If x and y are distinct positive integers, what is the value of \(x^4  y^4\)?
1. \((y^2 + x^2)(y + x)(x  y) > 100\) 2. \(x^y = y^x\) Hi, I could infer the answer to be "E". 1. \((y^2 + x^2)(y + x)(x  y) > 100\)
By solving, \((x^4  y^4) > 100\). The Value cannot not be decided as the set is infinite (> 100). Hence it is insufficient.2. \(x^y = y^x\)x and y being two distinct positive integers, the values can take one of the forms as below, (a) y=2, x=4 (b) y=4, x=16 etc. Hence insufficient. By combining 1 and 2, many values exist,(a) y=2, x=4, then \((x^4  y^4) > 100\) becomes 240, which is >100 (b) y=4, x=16, then \((x^4  y^4) > 100\) becomes 65280, which is also >100. so no one value can be inferred by combining 1 and 2. Hence, the answer is E.Please let me know any other alternative views. Thanks.



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Re: If x and y are distinct positive integers, what is the value of ....
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13 Mar 2017, 00:01
arichinna wrote: Prajat wrote: If x and y are distinct positive integers, what is the value of \(x^4  y^4\)?
1. \((y^2 + x^2)(y + x)(x  y) > 100\) 2. \(x^y = y^x\) Hi, I could infer the answer to be "E". 1. \((y^2 + x^2)(y + x)(x  y) > 100\)
By solving, \((x^4  y^4) > 100\). The Value cannot not be decided as the set is infinite (> 100). Hence it is insufficient.2. \(x^y = y^x\)x and y being two distinct positive integers, the values can take one of the forms as below, (a) y=2, x=4 (b) y=4, x=16etc. Hence insufficient. By combining 1 and 2, many values exist,(a) y=2, x=4, then \((x^4  y^4) > 100\) becomes 240, which is >100 (b) y=4, x=16, then \((x^4  y^4) > 100\) becomes 65280, which is also >100. so no one value can be inferred by combining 1 and 2. Hence, the answer is E.Please let me know any other alternative views. Thanks. Notice that 4^16 ≠ 16^4.
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Re: If x and y are distinct positive integers, what is the value of ....
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16 Mar 2017, 07:33
Good question!
While B might look like the answer (I spent a good amount of time trying to understand why it wasn't), C is correct.
Statement 1 gives the lowest limit of the, i.e. x^4y^4\(\) >100. Basically, the result will be a positive number greater than 100. Statement B defines a relationship between x and y such that only the numbers 2 and 4 satisfy this relationship. Butwe either X or Y could be 2 or 4. Thus, we do not know the value for each variable. If x = 2 and y = 4, then we get a negative result, but if x is 4 and y is 2, then we get a postive result that is quite large
Combining both statements, we can rule out x=2 and y=4, as we know that the result must be positive and greater than 100. This gives the correct answer, x=4 and y=2. Hence C.



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Re: If x and y are distinct positive integers, what is the value of ....
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29 May 2017, 19:06
Prajat wrote: If x and y are distinct positive integers, what is the value of \(x^4  y^4\)?
1. \((y^2 + x^2)(y + x)(x  y) > 100\) 2. \(x^y = y^x\) They key words in this problem are "distinct positive integers." Statement 1 (y^2 + x^2)(y + x)(x  y) > 10 (y^2 + x^2) (xy y^2 + x^2 yx) xy^3 y^4 + x^2y^2  y^3x + x^3y  x^2y^2 + x^4 yx^3 ( notice terms that cancel) y^4 + x^4 x^4y^4 >100 Insufficient because there are infinite variables that can satisfy this inequality Statement 2 x^y=y^x only 0,1 or 2 and 4 can satisfy this equation; however, the integers must be both positive and distinct. Therefore, the set of integers must be 2 and 4 but x and y cannot be distinguished x could be 2 or x could be 4 Statement 1 and 2 Using both statements it can be inferred that x must be 4 because x must be greater than 100. Hence "C"



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Re: If x and y are distinct positive integers, what is the value of ....
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30 Oct 2018, 19:07
If I am not mistaken, 0 and 1 does't satisfy statement 2. 0^1 not equals to 1^0 Nunuboy1994 wrote: Prajat wrote: If x and y are distinct positive integers, what is the value of \(x^4  y^4\)?
1. \((y^2 + x^2)(y + x)(x  y) > 100\) 2. \(x^y = y^x\) They key words in this problem are "distinct positive integers." Statement 1 (y^2 + x^2)(y + x)(x  y) > 10 (y^2 + x^2) (xy y^2 + x^2 yx) xy^3 y^4 + x^2y^2  y^3x + x^3y  x^2y^2 + x^4 yx^3 ( notice terms that cancel) y^4 + x^4 x^4y^4 >100 Insufficient because there are infinite variables that can satisfy this inequality Statement 2 x^y=y^x only 0,1 or 2 and 4 can satisfy this equation; however, the integers must be both positive and distinct. Therefore, the set of integers must be 2 and 4 but x and y cannot be distinguished x could be 2 or x could be 4 Statement 1 and 2 Using both statements it can be inferred that x must be 4 because x must be greater than 100. Hence "C"




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