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Is the exact value of x/y less than 0.5?

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Is the exact value of x/y less than 0.5? [#permalink] New post 30 Dec 2013, 12:33
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Is the exact value of x/y less than 0.5?

(1) When x and y are rounded to the nearest ten, x is 30, and y is 70.

(2) When x and y are rounded to the nearest unit, x is 32, and y is 65.
[Reveal] Spoiler: OA

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Re: Is the exact value of x/y less than 0.5? [#permalink] New post 03 Jan 2014, 03:29
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teabecca wrote:
Is the exact value of x/y less than 0.5?

(1) When x and y are rounded to the nearest ten, x is 30, and y is 70.

(2) When x and y are rounded to the nearest unit, x is 32, and y is 65.


We need to find whether x/y<0.5

From St 1, we have Possible range of x = 25 to 35
Y = 65 to 75
Now the range of x/y will be between min x/max y and max x/min y------> 25/75 and 35/65
Clearly the x<y can have value more or less than 0.5
A& D ruled out

From St 2 we have Possible value of x 31.5 to 32.5 and for y = 64.5 to 65.5

31.5/65.5 <x/y< 32.5/65.5
Again it can value more than or less than 0.5

Combining we get that
X is between 31.5 and 32.5 and Y is more than 65 (Y can have any value above 65 till 74.9999) and for all possible values of Y, X/Y will be less than 0.5

Ans C
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Re: Is the exact value of x/y less than 0.5? [#permalink] New post 12 Jun 2014, 16:52
teabecca wrote:
Is the exact value of x/y less than 0.5?

(1) When x and y are rounded to the nearest ten, x is 30, and y is 70.

(2) When x and y are rounded to the nearest unit, x is 32, and y is 65.





statement 1
25 \leq x \leq 34
65 \leq y \leq 74

lowest value of x/y = 25/74 = 0.33
Highest Value of x/y = 34/65 = 0.52

Hence Insufficient

Statement 2 =
31.5 \leq x \leq 32.4
64.5\leq x \leq 65.4

Lowest value of x/y = 0.48
Highest value of x/y = 0.50

hence insufficient

1+ 2

Now can anybody explain how to get the value of x and y using both 1 and 2
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Re: Is the exact value of x/y less than 0.5? [#permalink] New post 14 Jun 2014, 01:33
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qlx wrote:
teabecca wrote:
Is the exact value of x/y less than 0.5?

(1) When x and y are rounded to the nearest ten, x is 30, and y is 70.

(2) When x and y are rounded to the nearest unit, x is 32, and y is 65.





statement 1
25 \leq x \leq 34
65 \leq y \leq 74

lowest value of x/y = 25/74 = 0.33
Highest Value of x/y = 34/65 = 0.52

Hence Insufficient

Statement 2 =
31.5 \leq x \leq 32.4
64.5\leq x \leq 65.4

Lowest value of x/y = 0.48
Highest value of x/y = 0.50

hence insufficient

1+ 2

Now can anybody explain how to get the value of x and y using both 1 and 2


Combine 1 and 2.
31.5 \leq x \leq 32.4
65 \leq y \leq 65.4
=> x/y < 32.4/65 < 32.5/65 = 1/2. Here you go!
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Re: Is the exact value of x/y less than 0.5? [#permalink] New post 14 Jun 2014, 10:59
Icerockboom wrote:
qlx wrote:
teabecca wrote:
Is the exact value of x/y less than 0.5?

(1) When x and y are rounded to the nearest ten, x is 30, and y is 70.

(2) When x and y are rounded to the nearest unit, x is 32, and y is 65.





statement 1
25 \leq x \leq 34
65 \leq y \leq 74

lowest value of x/y = 25/74 = 0.33
Highest Value of x/y = 34/65 = 0.52

Hence Insufficient

Statement 2 =
31.5 \leq x \leq 32.4
64.5\leq x \leq 65.4

Lowest value of x/y = 0.48
Highest value of x/y = 0.50

hence insufficient

1+ 2

Now can anybody explain how to get the value of x and y using both 1 and 2


Combine 1 and 2.
31.5 \leq x \leq 32.4
65 \leq y \leq 65.4
=> x/y < 32.4/65 < 32.5/65 = 1/2. Here you go!


Thanks Buddy , I see that we have to take the overlapping values of x from both statements and overlapping values of Y from Both statements.
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Re: Is the exact value of x/y less than 0.5? [#permalink] New post 18 Jun 2014, 06:24
Isn't B a subset of A ?
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Re: Is the exact value of x/y less than 0.5? [#permalink] New post 18 Jun 2014, 06:26
WoundedTiger wrote:
teabecca wrote:
Is the exact value of x/y less than 0.5?

(1) When x and y are rounded to the nearest ten, x is 30, and y is 70.

(2) When x and y are rounded to the nearest unit, x is 32, and y is 65.


We need to find whether x/y<0.5

From St 1, we have Possible range of x = 25 to 35
Y = 65 to 75

Now the range of x/y will be between min x/max y and max x/min y------> 25/75 and 35/65
Clearly the x<y can have value more or less than 0.5
A& D ruled out

From St 2 we have Possible value of x 31.5 to 32.5 and for y = 64.5 to 65.5

31.5/65.5 <x/y< 32.5/65.5
Again it can value more than or less than 0.5

Combining we get that
X is between 31.5 and 32.5 and Y is more than 65 (Y can have any value above 65 till 74.9999) and for all possible values of Y, X/Y will be less than 0.5

Ans C


Shouldn't the possible range be from 25 to 34 and 65 to 74 because the moment the number becomes 35 , it will round up to 40
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Re: Is the exact value of x/y less than 0.5? [#permalink] New post 18 Jun 2014, 08:39
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himanshujovi wrote:
WoundedTiger wrote:
teabecca wrote:
Is the exact value of x/y less than 0.5?

(1) When x and y are rounded to the nearest ten, x is 30, and y is 70.

(2) When x and y are rounded to the nearest unit, x is 32, and y is 65.


We need to find whether x/y<0.5

From St 1, we have Possible range of x = 25 to 35
Y = 65 to 75

Now the range of x/y will be between min x/max y and max x/min y------> 25/75 and 35/65
Clearly the x<y can have value more or less than 0.5
A& D ruled out

From St 2 we have Possible value of x 31.5 to 32.5 and for y = 64.5 to 65.5

31.5/65.5 <x/y< 32.5/65.5
Again it can value more than or less than 0.5

Combining we get that
X is between 31.5 and 32.5 and Y is more than 65 (Y can have any value above 65 till 74.9999) and for all possible values of Y, X/Y will be less than 0.5

Ans C


Shouldn't the possible range be from 25 to 34 and 65 to 74 because the moment the number becomes 35 , it will round up to 40


Is the exact value of x/y less than 0.5?

(1) When x and y are rounded to the nearest ten, x is 30, and y is 70:

25 \leq x < 35.
65 \leq y < 75.

We can get x/y to be less than 1/2 as well as more than 1/2. Not sufficient.

(2) When x and y are rounded to the nearest unit, x is 32, and y is 65:

31.5\leq x < 32.5.
64.5 \leq y < 65.5.

We can get x/y to be less than 1/2 as well as more than 1/2. Not sufficient.

(1)+(2) 31.5\leq x < 32.5 and 65 \leq y < 65.5. The minimum value of y (65) is more than twice as large as the maximum value of x (<32.5). So, x/y < 1/2. Sufficient.

Answer: C.
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Re: Is the exact value of x/y less than 0.5? [#permalink] New post 18 Jun 2014, 09:24
I agree on the answer. My query is around rounding concept


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Re: Is the exact value of x/y less than 0.5? [#permalink] New post 18 Jun 2014, 09:27
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Re: Is the exact value of x/y less than 0.5? [#permalink] New post 18 Jun 2014, 12:49
I believe woundedtiger's solution had this problem


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Re: Is the exact value of x/y less than 0.5?   [#permalink] 18 Jun 2014, 12:49
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