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If x and y are both positive numbers, is x greater than 75% of y?

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If x and y are both positive numbers, is x greater than 75% of y?  [#permalink]

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New post 22 Aug 2016, 02:50
11
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A
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C
D
E

Difficulty:

  75% (hard)

Question Stats:

53% (01:48) correct 47% (02:05) wrong based on 222 sessions

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Re: If x and y are both positive numbers, is x greater than 75% of y?  [#permalink]

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New post 22 Aug 2016, 05:37
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Top Contributor
Bunuel wrote:
If x and y are both positive numbers, is x greater than 75% of y?

(1) 5x > 4y + 1
(2) x = 6


Target question: Is x greater than 75% of y?

Given: x and y are both positive numbers

Let's REPHRASE the target question as.....
REPHRASED target question: Is 0.75y < x?

Aside: I like to arrange my inequalities so that the larger value is on the right (just like on the number line)

Statement 1: 5x > 4y + 1
Rearrange to get: 4y + 1 < 5x
Divide both sides by 5 to get: 0.8y + 0.2 < x

IMPORTANT: Since y is POSITIVE (given), we know that 0.75y < 0.8y
Since 0.8y is ALREADY bigger than 0.75y, we can be certain that 0.75y < 0.8y + 0.2
Given all of this, we can COMBINE the inequalities to see that 0.75y < 0.8y + 0.2 < x
So, we can conclude that 0.75y < x
PERFECT
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: x = 6
No information about y.
Statement 2 is NOT SUFFICIENT

Answer =

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Re: If x and y are both positive numbers, is x greater than 75% of y?  [#permalink]

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New post 22 Aug 2016, 04:25
Bunuel wrote:
If x and y are both positive numbers, is x greater than 75% of y?

(1) 5x > 4y + 1
(2) x = 6



Given to find x > 3/4(y)

Stat 1: 5x > 4y + 1...let's say x = 1 and y = 1 then 5 > 4 + 1...here x is greater than y....5x > 4y + 1...if 5x value has to be greater than 4y+1..then x must be greater than y.

if x = 2 and y = 1, then 10 > 4 + 1.... Sufficient..

Stat 2: x = 6..we don't have info about y.

IMO option A is correct answer...

OA please...will correct if I missed anything..
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Re: If x and y are both positive numbers, is x greater than 75% of y?  [#permalink]

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New post 23 Aug 2016, 11:54
Bunuel wrote:
If x and y are both positive numbers, is x greater than 75% of y?

(1) 5x > 4y + 1
(2) x = 6


Q: is x > 0.75y?

Let's begin with statement (2), the question becomes: is 6 > 0.75y? Yes or no depending on the value of y. if y = 4, then is 6 > 3/4 * 4? ===> is 6 > 3? YES:

but if y = 12, then is 6 > 3/4 * 12? ===> is 6 > 9? NO. Not sufficient.

Statement (1) 5x > 4y + 1 ===> divide both sides of the inequality by 5 ===> x > 0.8y + 0.2 . YES
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Re: If x and y are both positive numbers, is x greater than 75% of y?  [#permalink]

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New post 08 Oct 2018, 04:22
since 5x>4y+1
using number line
5x>y
x>.2y
now to the question
x>75/100y?
x>(3/4)y?
x>.75y?
from statement 1 x>.2y
hence x>.75y
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Re: If x and y are both positive numbers, is x greater than 75% of y?   [#permalink] 08 Oct 2018, 04:22
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