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If x^2y^3 = 200, what is xy ? (1) y is an integer (2) x is an integer
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24 Jan 2020, 00:44
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Competition Mode Question If x^2y^3 = 200, what is xy ? (1) y is an integer (2) x is an integer Are You Up For the Challenge: 700 Level Questions
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Re: If x^2y^3 = 200, what is xy ? (1) y is an integer (2) x is an integer
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24 Jan 2020, 01:27
Quote: If x^2y^3 = 200, what is xy ?
(1) y is an integer (2) x is an integer \(x^2y^3 = 200\) i.e. \(x^2*y^3 = 2^3*5^2\) Statement 1: y is an integerCase 1: y = 2 and x = 5 Case 2: \(y = 2*3^2\) and \(x = 5/3^3\) i.e. Different values of x*y KEY: Nowhere is it given that x also is an Integer NOT SUFFICIENT Statement 2: x is an integerCase 1: y = 2 and x = 5 Case 2: \(y = 2/3^2\) and \(x = 5*3^3\) i.e. Different values of x*y KEY: Nowhere is it given that y also is an Integer NOT SUFFICIENT Combining the two statementsCase 1: y = 2 and x = +5 Case 1: y = 2 and x = 5 i.e. x*y may be either +10 or 10 hence NOT SUFFICIENT Answer: Option E
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Re: If x^2y^3 = 200, what is xy ? (1) y is an integer (2) x is an integer
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24 Jan 2020, 01:40
Solution:x²y³ = 200 Observe that 200 can be factorised as: #1. 2³ * 5² where x = 5 and y = 2 ... (i) However, we can also say that: #2. \(200 = [2^\frac{1}{3}]³ * 10² \), where x = \(10\) and y = \([2^\frac{1}{3}]\) ...(ii) Or #3. \(200 = [200^\frac{1}{2}]² * 1³\), where x = \([200^\frac{1}{2}]\) and y = \(1\) ...(iii) #4. \(200 = [50^\frac{1}{2}]² * [4^\frac{1}{3}]³ \), where x = \([50^\frac{1}{2}]\) and y = \([4^\frac{1}{3}]\) ...(iv) Thus, there can be multiple ways of expressing 200. Let's now look at the 2 statements: St1. y is an integerBoth (i) and (iii) are valid  Insufficient St2. x is an integerBoth (i) and (ii) are valid  Insufficient Combining: Since both x and y are integers apparently it seems that only (i) is correct. However, the trick here is that it doesn't say x and y are positive integers. Thus, another possible solution is: 2³ * (5)² where x = 5 and y = 2 Thus, even after combining the statements, we have: xy = 10 or 10 Hence, the [banswer is E[/b] Posted from my mobile device
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Re: If x^2y^3 = 200, what is xy ? (1) y is an integer (2) x is an integer
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24 Jan 2020, 02:08
If x^2y^3 = 200, what is xy?
(1) y is an integer x^2= 200/(y^3) where y = any integer except zero (0) Say y= 2 , x^2= 200/8 = 25 x= +/ 5 Now xy=(5)(2)=10 or xy = (5)(2)=10 (Not Sufficient)
(2) x is an integer But x can be +ve or ve integer y^3= 200/(x^2) When x= 5 , y^3 =200/25 = 8 y= 2 .: xy = 10 When x= 5, y= 2 .: xy =10 (Not sufficient)
(1+2) we still don’t know wether x= +ve or ve ,though we know x and y are both integers as (/+5)^2•(2)^3 =200
Hit that E
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Re: If x^2y^3 = 200, what is xy ? (1) y is an integer (2) x is an integer
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24 Jan 2020, 03:23
1)+2) x and y are both integers and (xy)^2.y=200
If y=2, then (xy)^2=100 and (xy)=10 or 10. x could be  5 or 5. We don't know whether xy is  10 or 10. NOT SUFFICIENT
FINAL ANSWER IS (E)
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Re: If x^2y^3 = 200, what is xy ? (1) y is an integer (2) x is an integer
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24 Jan 2020, 04:46
Quote: If x^2y^3 = 200, what is xy ?
(1) y is an integer (2) x is an integer x^2(y^3) = 200 = 2*100 = 5^2(2^3) (1) y is an integer insuficy=1: x^2=200…x=√200,…xy=√200 y=2: x^2=200/8=25…x=√25=5…xy=10 (2) x is an integer insuficx=1: y^3=200…y=cube√200=2(cube√25)…xy=2(cube√25) x=2: y^3=200/4=50…y=cube√50…xy=2(cube√50) (1&2) insuficx,y=integers then x^2(y^3) = 5^2(2^3) = (5^2)(2^3) xy=5(2)=10, or xy=5(2)=10 Ans (E)



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Re: If x^2y^3 = 200, what is xy ? (1) y is an integer (2) x is an integer
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24 Jan 2020, 05:01
Given, \(x^2y^3 = 200\) > Many values of \(x\) & \(y\) are possible > Possible values of \((x, y) = {(5, 2), (5, 2), (1, 200^{1/3}), (200^{1/2}, 1), . . . . } \)
(1) \(y\) is an integer > Possible values of \((x, y) = {(5, 2), (5, 2), (200^{1/2}, 1), . . . . }\) > No Definite value of \(x*y\) > Insufficient
(2) \(x\) is an integer > Possible values of \((x, y) = {(5, 2), (5, 2), (1, 200^{1/3}), . . . . }\) > No Definite value of \(x*y\) > Insufficient
Combining (1) & (2), > Possible values of \((x, y) = {(5, 2), (5, 2)}\) > Possible values of \(x*y = 5*2\) or \((5)*2\) > No Definite value of \(x*y\) > Insufficient
Option E



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Re: If x^2y^3 = 200, what is xy ? (1) y is an integer (2) x is an integer
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24 Jan 2020, 10:19
If \(x^2y^3 = 200\), what is xy ?
(Statement1): y is an integer If y=2, then x could be 5 or —5 —> xy could be 10 or —10 Insufficient
(Statement2): x is an integer If x= 5, then y = 2 —> xy = 10 If x =—5, then y =2 —> xy = —10 Insufficient
Taken together 1&2, It will have the same values of xy as statement1 and statement2 do. ( 10 or —10)
Insufficient
The answer is E.
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Re: If x^2y^3 = 200, what is xy ? (1) y is an integer (2) x is an integer
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25 Jan 2020, 06:11
If \(x^2y^3 = 200\), what is xy ? (1) y is an integer \(x^2y^3 = 200\) = \(2^3*5^2\) Thus, y = 2 and x = 5 OR 5 xy = 10 OR 10 INSUFFICIENT. (2) x is an integer Thus, y = 2 and x = 5 OR 5 xy = 10 OR 10 INSUFFICIENT. Together 1 and 2 Thus, y = 2 and x = 5 OR 5 xy = 10 OR 10 INSUFFICIENT. Answer E.
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Re: If x^2y^3 = 200, what is xy ? (1) y is an integer (2) x is an integer
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25 Jan 2020, 09:04
Ans: E
a)y=int if y=1, we can get one value for x..not sufficient b)same as a..not sufficient
combined..not sufficient
x^2y^3=200=5^2*2^3=(5)^2*2^3 not sifficient



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If x^2y^3 = 200, what is xy ? (1) y is an integer (2) x is an integer
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Updated on: 27 Jan 2020, 01:57
Given x^2*y^3 = 200 ,
X^2*y^3 = 5^2 * 2 ^ 3.
from statement 1 ,
y is integer ,
we don't know about the value of x , it can be non integer and this can has many solutions ,
for example , x = 1/200 and y =200. Not sufficient .
From statement 2 , .
if x is an integer , same as above we can have different values of y , so we can't find the values.
OPTION E



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Re: If x^2y^3 = 200, what is xy ? (1) y is an integer (2) x is an integer
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24 Jan 2020, 20:45
If x^2*y^3 = 200, what is xy ? Prime factorization of 200 is 2^3*5^2 (1) y is an integer When y = 5, x = 2, xy = 10 When y = 1 , x = sqrt(200), xy = sqrt(200) Insufficient (2) x is an integer Similarly When x = 2, y = 5, xy = 10 When x = 1 , y = sqrt(200), xy = sqrt(200) Insufficient (1)+(2) Only possibility When x = 2, y = 5, xy = 10 Sufficient C is correct
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If x^2y^3 = 200, what is xy ? (1) y is an integer (2) x is an integer
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Updated on: 26 Jan 2020, 23:29
not know whether x y are integers such that x^2y^3 = 200 #1 y is an integer not know if x is an integer as well ; insufficient as x = fraction or root value #2 x is an integer not know if y is an integer as well ; insufficient as y = fraction or root value insufficient from 1 & 2 if both x & y are integers then only possiblity ; 5^2 * 2^3 ; = 200 or value of x & y can be fraction as well insufficient IMO e
If x^2y^3 = 200, what is xy ?
(1) y is an integer (2) x is an integer
Originally posted by Archit3110 on 25 Jan 2020, 09:04.
Last edited by Archit3110 on 26 Jan 2020, 23:29, edited 1 time in total.



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Re: If x^2y^3 = 200, what is xy ? (1) y is an integer (2) x is an integer
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25 Jan 2020, 14:36
Given that x^2y^3 = 200, we are to determine the value of xy. It is worth noting that x and y are not restricted in any way. So, x and y can be integers, rational or irrational numbers.
Statement 1: y is an integer. Clearly insufficient because y can be 2, and y^3=8, implying x=5. Hence xy=10 However, when y=3, then y^3=27, implying x=√(200/27). xy=3*√(200/27) = 30*√(2/27) ≠ 10.
Statement 2: x is an integer. Clearly insufficient because x can be 5, implying y is 2. xy=10 However when x=2, then y=(50)^(1/3). xy=50*2^(1/3) ≠ 10
1+2 By combining both statements, we can now conclude that x=5 and y=2, and that xy=10.
The answer is C.



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Re: If x^2y^3 = 200, what is xy ? (1) y is an integer (2) x is an integer
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26 Jan 2020, 09:35
(1) Not suff to solve (2) Not suff to solve Combine (1) & (2) There are countless pairs of solutions of xy. => Not suff
Choice E.




Re: If x^2y^3 = 200, what is xy ? (1) y is an integer (2) x is an integer
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