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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]

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30 Dec 2013, 13:33
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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]

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03 Jan 2014, 04:29
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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]

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12 Jun 2014, 17:52
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]

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14 Jun 2014, 02:33
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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]

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14 Jun 2014, 11:59
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]

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18 Jun 2014, 07:24
Isn't B a subset of A ?
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Re: Is the exact value of x/y less than 0.5? [#permalink]

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18 Jun 2014, 07:26
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]

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18 Jun 2014, 09:39
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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.

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Re: Is the exact value of x/y less than 0.5? [#permalink]

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18 Jun 2014, 10:24
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]

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18 Jun 2014, 10:27
himanshujovi wrote:
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]

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18 Jun 2014, 13:49
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]

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Re: Is the exact value of x/y less than 0.5?   [#permalink] 16 Sep 2015, 04:32
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