GMAT Club Around The World!!! Is x^2 less than or equal to 10y^2?

Question

Is x^2 less than or equal to 10y^2?

(1) 0 < x < 2
(2) 1 < y < 2

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Harsh9676 · Answer

IMO C

Is x^2 less than or equal to 10y^2?

Asking Whether X^2 <= 10 Y^2; its an Yes/No DS

(1) 0 < x < 2

If Y = 0 , and X = 1 then X^2 <= 10 Y^2 cannot be true

But, If Y =1 and X = then X^2 <= 10 Y^2 is true.

Two different answers, hence insufficient.

(2) 1 < y < 2

No idea about X, clearly insufficient.

Combined, we know for sure that X^2 <= 10 Y^2 is true.

Deepakjhamb · Answer

Is x^2 less than or equal to 10y^2?

(1) 0 < x < 2
(2) 1 < y < 2

lets analyze stem : x^2 <= 10 y^2 or we get( x/y)^2 <= 10 , let z = x/y , we get z^2- underoot 10 ^2 <= 0

- underoot 10 <= z <= underoot 10 is the question

statement 1 : 0 < x < 2 , now if y is very small we may fall x/y out of range in question we can have inside also if x is small so insufficient

statement 2: 1<y < 2 , if x is very great value we have out of range if x is small value we have in range also so insufficinet

if we combine both we can get values of x/y as 0<x/y< 2 now if x/y is between 0 and 2 its definitely subset of range 
- 3.xx < x/y < 3.xx so we are sure that x/y lies in range given in stem

so answer is c ) both statements combined together are sufficinet but neiother statement alone is sufficient

rocky620 · Answer

Is x^2 less than or equal to 10y^2? or Is x^2 > 10y^2?

(1) 0 < x < 2
No information about y.

Insufficient

(2) 1 < y < 2
No information about x.

Insufficient

Combining 1 & 2
0 < x < 2
so, 1<\(x^2\)<4. Minimum value of \(x^2\) can be 0 and maximum value can be 4

1 < y < 2
1<\(y^2\)<4.

Multiply by 10

10<10\(y^2\)<40. Minimum value of 10\(y^2\) can be 10 and maximum value can be 40

In both the cases the minimum value of 10\(y^2\) is greater than maximum value of \(x^2\)

so 10y^2>x^2.

Sufficient

IMO Option C

BIDJI23 · Answer

By combining the 2 conditions, we see that y is always bigger than 1. So 10*y^2 is more than 10 and x^2 will be under 4.

We need these two conditions to be certain about the answer.

PUSH C

ananya3 · Answer

IMO C Que: x^2 <= 10y^2 ? (1) 0 < x < 2 case 1: if x = 1, y = \frac{1}{5} x^2 = 1 10 * y^2 = \frac{10}{25} = \frac{2}{5} => 1 > \frac{2}{5} case 2: if x = 1, y = 2 x^2 = 1 10 * y^2 = 10 * 4 = 40 => 1 < 40 NOT SUFFICIENT (2) 1 < y < 2 case1: if x = 1, y = \frac{3}{2} x^2 = 1 10 * y^2 = 10 * \frac{9}{4} = \frac{90}{4} => 1 < 90/4 case 2: if x = 5, y=\frac{3}{2} x^2 = 25 10 * y^2 = \frac{90}{4} 25>\frac{90}{4} NOT SUFFICIENT combining 1 and 2 0 < x < 2 => 0 < x^2 < 4 1 < y < 2 => 10 < 10* y^2 < 40 => x^2 < 10*y^2 SUFFICIENT

TarunKumar1234 · Answer

Is x^2 less than or equal to 10y^2? Stat1: 0 < x < 2, not sufficient , as we need value of y Stat2: 1 < y < 2, not sufficient , as we need value of x Combining both, 0 < x < 2 & 1 < y < 2 Between 0

bidskamikaze · Answer

Is x^2 less than or equal to 10y^2?

(1) 0 < x < 2
(2) 1 < y < 2

Individual statements are not sufficient because they talk about either x or y, but not both.
Combine:
Let us assume maximum value of x and minimum value of y.
Let x = 2 and y = 1 (These values are out of range, but will suffice)
Is  x^2 <= 10 y^2 ?
4 <= 10 (yes)
So the value of  x^2  will always be less than 10 y^2 
Combining is sufficient.

Answer C.

Green2k1 · Answer

Correct Answer C

Is x^2 less than or equal to 10y^2?
 x^2 <= 10y^2
 -root (10y^2) <= x <= root (10y^2)
Approx -3y <= x <= 3y

(1) 0 < x < 2
 - do not know anything about y range
- Not Sufficient

(2) 1 < y < 2
 - don't know anything about x range
- Not Sufficient
 
Together
 when y= 1
-3y <= x <= 3y
-3 < x<3
y=2
-6<x<6

Given 0<x<2 - it is well within the range
Sufficient

manasi05 · Answer

x^2 <= 10 y^2 ?
To find the answer we will need the information about x and y both

Statement 1
0 < x < 2
Gives no information about y hence not sufficient

Statement 2
1 < y < 2
Gives no information about x hence not sufficient

Combining statement 1 and 2 we have 
0 < x < 2 from this we can find the range for x^2
0 < x^2 < 4
1 < y < 2 from this we can find the range for y^2
1 < y^2 < 4
The range for 10y^2 will be
10 < 10y^2 < 40
The range for 10y^2 is bigger than x^2 hence x^2 < 10y^2 — Hence Sufficient

So the answer will be C

MakSha · Answer

IMO option C is correct .

From each statement alone, no conclusion can be made.

when both sentences are taken together, 10y^2 is always greater than x^2 in the defined range of each variable.

GMAT Club Around The World!!! Is x^2 less than or equal to 10y^2?

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GMAT Club Around The World!!! Is x^2 less than or equal to 10y^2?

Prep Toolkit

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