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Is the exact value of x/y less than 0.5? (1) When x and y are rounded

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Bunuel
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Is the exact value of x/y less than 0.5? (1) When x and y are rounded [#permalink] New post   12 May 2021, 04:30
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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.
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Re: Is the exact value of x/y less than 0.5? (1) When x and y are rounded [#permalink] New post   15 May 2021, 02:15
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Bunuel 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.


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? (1) When x and y are rounded [#permalink] New post   12 May 2021, 13:00
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Bunuel 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:

We have \( 25 \leq x < 35\) and \(65 \leq y < 70\). So x/y can certainly be less than 0.5, we need to check if it is possibly greater than 0.5. The greatest x/y we can have is near 35/65 which is greater than 0.5, thus it is possibly greater than 0.5. Insufficient.

Statement 2:

We have \( 31.5 \leq x < 32.5\) and \(64.5 \leq y < 65.5\). Again x/y can certainly be less than 0.5, the greatest x/y we can have is near 32.5/64.5, which is still more than 0.5. Insufficient.

Combined:

Combined the range of x is \( 31.5 \leq x < 32.5\) and the range of y is \(65 \leq y < 65.5\). The greater x/y possible is \(\frac{x}{y} < \frac{32.5}{65}\), hence we must have \(\frac{x}{y} < \frac{1}{2}\). Sufficient.

Ans: C
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Is the exact value of x/y less than 0.5? (1) When x and y are rounded [#permalink] New post   15 May 2021, 04:27
Asked: 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<=x<35
65<=y<75
If we take x = 25 & y = 74; x/y = 25/74< .5
But if we take x = 34.x & y = 65; x/y = 34.x/65 > .5
NOT SUFFICIENT

(2) When x and y are rounded to the nearest unit, x is 32, and y is 65.
31.5<=x<32.5
64.5<=y<65.5
If we take x = 31.5 & y = 65.4; x/y = 31.5/65.4< .5
But if we take x = 32.5 & y = 64.4; x/y = 32.4/64.5 > .5
NOT SUFFICIENT

(1) + (2)
(1) When x and y are rounded to the nearest ten, x is 30, and y is 70.
25<=x<35
65<=y<75
(2) When x and y are rounded to the nearest unit, x is 32, and y is 65.
31.5<=x<32.5
65<=y<65.5
Since maximum value of x<32.5 is less than half of minimum value of y =65
(x/y) < 0.5
SUFFICIENT

IMO C
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Re: Is the exact value of x/y less than 0.5? (1) When x and y are rounded [#permalink] New post   28 May 2021, 07:53
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Bunuel 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.


Answer: Option C
Attachment:
Screenshot 2021-05-28 at 8.19.53 PM.png
Screenshot 2021-05-28 at 8.19.53 PM.png [ 673.38 KiB | Viewed 1094 times ]


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Re: Is the exact value of x/y less than 0.5? (1) When x and y are rounded [#permalink]
28 May 2021, 07:53
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