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

Question

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

M36-117

Bunuel · Accepted Answer

Official Solution:

If  x^2y^3 = 200 , what is the value of  xy  ? 
 
Factorize:  200=5^2*2^3=x^2*y^3 .
 
(1)  y  is an integer
 
If  y=1 , then  x=\sqrt{200}  or  x=-\sqrt{200}  and in this case  xy=\sqrt{200}  or  -\sqrt{200} 
 
Of course there are infinitely many other solutions possible.
 
Not sufficient.
 
(2)  x  is an integer
 
If  x=1 , then  y=\sqrt {200}  and in this case  xy=\sqrt {200}  
 
If  x=2 , then  y=\sqrt {50}  and in this case  xy=2\sqrt {50}  
 
Of course there are infinitely many other solutions possible.
 
Not sufficient.
 
(1)+(2) Since both  x  and  y  are integers, then  y  must be 2 but because of even power,  x  could be 5 or -5. So,  xy  could be 10 or -10. Not sufficient.

Answer: E

GMATinsight · Answer

x^2y^3 = 200

i.e.  x^2*y^3 = 2^3*5^2

Statement 1 : y is an integer

Case 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 integer

Case 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 statements

Case 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

sujoykrdatta · Answer

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 =  ³ * 10²  , where x =  10  and y =     ...(ii)

Or

#3.  200 =  ² * 1³ , where x =     and y =  1  ...(iii)

#4.  200 =  ² *  ³  , where x =     and y =     ...(iv)

Thus, there can be multiple ways of expressing 200.

Let's now look at the 2 statements:

St1.  y is an integer 
Both (i) and (iii) are valid - Insufficient

St2.  x is an integer 
Both (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

Posted from my mobile device

Staphyk · Answer

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

Posted from my mobile device

freedom128 · Answer

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)

Posted from my mobile device

exc4libur · Answer

x^2(y^3) = 200 = 2*100 = 5^2(2^3)

(1) y is an integer   insufic

y=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   insufic

x=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)   insufic

x,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)

CareerGeek · Answer

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

BhishmaNaidu99 · Answer

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

lacktutor · Answer

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.

Posted from my mobile device

QuantMadeEasy · Answer

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

unraveled · Answer

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.

debjit1990 · Answer

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

Archit3110 · Answer

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

eakabuah · Answer

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.

ostrick5465 · Answer

(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.

TheGraceful · Answer

Hi  Bunuel ,

In the explanation here powers are looking very clear:  x^2y^3 = 200 ,
However in the question those are NOT: x^2y^3 = 200, 
It made me interprete : x^(2y)^3 = 200

please help correcting those - so they appear what they actually meant.

Bunuel · Answer

Mathematically x^2y^3 can mean one and only one thing:  x^2y^3 . Nothing else! If it were  x^{(2y)^3}  it would have been written as x^(2y)^3. Still edited.

TheGraceful · Answer

Thanks  Bunuel , for the edit and more for clarifying a doubt.

sanjitscorps18 · Answer

x^2 * y^3 = 200

(1) y is an integer
Let's say y = 10, then x = 1/√5
Let's say y = 5, then x = √8/√5
--> Insufficient

(2) x is an integer
Let's say x = 10, then y = cube root of 2
Let's say x = 5, then y = 2
--> Insufficient

Using (1) and (2) we get x and y both are integers
200 = 5^2 * 2^3
But also we can have 
200 = (-5)^2 * 2^3
So if we put this in the question stem x can be -5 or 5 hence insufficient

Option E

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards