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# If x and y are integers and 3x > 8y, is y > −18?

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Director
Joined: 11 Feb 2015
Posts: 615
If x and y are integers and 3x > 8y, is y > −18?  [#permalink]

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17 Jul 2018, 07:45
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00:00

Difficulty:

95% (hard)

Question Stats:

42% (03:23) correct 58% (02:39) wrong based on 36 sessions

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If $$x$$ and $$y$$ are integers and $$3x > 8y$$, is $$y > −18$$?
1. $$−9 < x < 20$$
2. $$y = \frac{(x-42)}{5}$$

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Manish

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Director
Joined: 11 Feb 2015
Posts: 615
Re: If x and y are integers and 3x > 8y, is y > −18?  [#permalink]

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17 Jul 2018, 07:54
1

If x and y are integers and 3x > 8y, is y > −18?

Step 1: Analyze the Question Stem
This is a Yes/No question with two integer variables. Simplify the inequality given in the stem, 3x > 8y, to get $$y < \frac{3x}{8}$$.

Step 2: Evaluate the Statements
Statement (1): The possible values of x are limited by the range of this inequality, so examine the endpoints of the range. If x > −9, the least value that is permissible for x is −8. Since y is less than $$\frac{3x}{8}$$ it follows that y < −3. Some values of y could be > −18, but there is no lower limit for y, so it could also be < −18. There is no need to evaluate the upper boundary of x. Statement (1) is insufficient, so eliminate choices (A) and (D).

Statement (2): Simplify the equation by multiplying both sides by 5 to get 5y = x − 42. Add 42 to both sides and x = 5y + 42.
Substitute this value for x into the inequality 3x > 8y: to get 3(5y + 42) > 8y or y > -18

Statement (2) is sufficient to answer definitively yes.

Choice (B) is correct.
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Manish

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Re: If x and y are integers and 3x > 8y, is y > −18? &nbs [#permalink] 17 Jul 2018, 07:54
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