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# S95-39

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Math Expert
Joined: 02 Sep 2009
Posts: 54437

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16 Sep 2014, 01:50
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Difficulty:

35% (medium)

Question Stats:

65% (00:30) correct 35% (00:56) wrong based on 43 sessions

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If $$r$$, $$s$$, and $$t$$ are nonzero numbers, is $$rt = 14$$?

(1) $$r^2st = 14rs$$

(2) $$\frac{t}{2} = \frac{7}{r}$$

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Joined: 02 Sep 2009
Posts: 54437

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16 Sep 2014, 01:50
Official Solution:

We must determine if $$rt = 14$$, given that $$r$$, $$s$$, and $$t$$ are nonzero numbers.

Statement 1 says that $$r^2st = 14rs$$. We can divide both sides of the equation by $$rs$$, like so: $$\frac{r^2st}{rs} = \frac{14rs}{rs}$$. The $$rs$$ in the numerator and denominator on each side divide to 1, leaving us with $$rt = 14$$. Therefore, statement 1 alone is sufficient to answer the question. Eliminate answer choices B, C, and E. The correct answer choice is either A or D.

Statement 2 says that $$\frac{t}{2} = \frac{7}{r}$$. Cross-multiply to obtain $$t \times r = 7 \times 2$$, or $$rt = 14$$. Statement 2 alone is also sufficient to answer the question.

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Joined: 24 Oct 2015
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03 Aug 2017, 01:58
Hi Bunuel, I was wondering how with statement 1, we can simply divide by 'rs' and conclude the answer. What if r is negative? In that case, there would be one negative sign remaining in the LHS post division by 'rs', leaving us with -> -rt=14.

Could you please clarify? Thanks a ton!
Math Expert
Joined: 02 Sep 2009
Posts: 54437

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03 Aug 2017, 08:49
1
ShivaniD wrote:
Hi Bunuel, I was wondering how with statement 1, we can simply divide by 'rs' and conclude the answer. What if r is negative? In that case, there would be one negative sign remaining in the LHS post division by 'rs', leaving us with -> -rt=14.

Could you please clarify? Thanks a ton!

We are concerned about the sign when dealing with inequalities: we should keep the sign if we multiply by a positive value and flip the sign when we multiply by a negative value.

For equations we can multiply/divide by a variable regardless of its sign (providing it's not 0).

Hope it's clear.
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05 Aug 2017, 19:47
Bunuel This problem seemed so straight forward and simple that I thought it was too good to be true. So since we are solving for the product of "r" and "t", we really only need to find that product in our statements. In statement 1, since "s" and the extra "r" are factored out from both sides, we get the product of "r" and "t"- and it doesn't matter what their exact values are because it answers the question: is rt=14. Same concept with statement 2 except there is no "s" or extra "r" to worry about. Am I thinking of this question correctly? Thanks!
Re: S95-39   [#permalink] 05 Aug 2017, 19:47
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# S95-39

Moderators: chetan2u, Bunuel

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