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# If s and t are positive integers and s/t = 39.12, then which one of th

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Math Expert
Joined: 02 Sep 2009
Posts: 64174
If s and t are positive integers and s/t = 39.12, then which one of th  [#permalink]

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17 Apr 2019, 20:32
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If s and t are positive integers and s/t = 39.12, then which one of the following could t equal?

(A) 8
(B) 13
(C) 15
(D) 60
(E) 75

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Posts: 4876
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Re: If s and t are positive integers and s/t = 39.12, then which one of th  [#permalink]

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26 Feb 2020, 14:26
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Top Contributor
Bunuel wrote:
If s and t are positive integers and s/t = 39.12, then which one of the following could t equal?

(A) 8
(B) 13
(C) 15
(D) 60
(E) 75

First take 39.12 and convert into a FRACTION to get 3912/100
In other words, s/t = 3912/100

So, as you can see, t COULD equal 100 (this is why the question asks, "Which of the following COULD t equal?")
Since 100 isn't one of the answer choices, we'll keep going

Simplify the fraction to get: 978/25
Since 25 isn't one of the answer choices, we'll keep going

At this point we can see that, if we take 978/25 and multiply numerator and denominator by 3, we get the equivalent fraction 2934/75
So, t COULD equal 75

Cheers,
Brent
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Re: If s and t are positive integers and s/t = 39.12, then which one of th  [#permalink]

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17 Apr 2019, 20:47
1
Bunuel wrote:
If s and t are positive integers and s/t = 39.12, then which one of the following could t equal?

(A) 8
(B) 13
(C) 15
(D) 60
(E) 75

$$s/t=3912/100=978/25=978*3/25*3=X/75$$

Option E
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Joined: 27 Mar 2019
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Re: If s and t are positive integers and s/t = 39.12, then which one of th  [#permalink]

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19 Apr 2019, 05:42
kunalcvrce wrote:
Bunuel wrote:
If s and t are positive integers and s/t = 39.12, then which one of the following could t equal?

(A) 8
(B) 13
(C) 15
(D) 60
(E) 75

$$s/t=3912/100=978/25=978*3/25*3=X/75$$

Option E

Could you please explain following step: 978*3/25*3=X/75[/m]

I don't understand why you multiplied everything by 3.

Thanks
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Joined: 03 Dec 2014
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Re: If s and t are positive integers and s/t = 39.12, then which one of th  [#permalink]

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19 Apr 2019, 05:49
i could not understand the solution,any alternate method ?
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Joined: 21 Feb 2019
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Re: If s and t are positive integers and s/t = 39.12, then which one of th  [#permalink]

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19 Apr 2019, 05:59
Flixus16 he multiplied the fraction set forth above by 3 to get 75 as multiple of 25. The reasoning behind is that you need 25 or a multiple of it. Hence, 25*3= 75.
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Re: If s and t are positive integers and s/t = 39.12, then which one of th  [#permalink]

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26 Feb 2020, 12:40
[quote="Bunuel"]If s and t are positive integers and s/t = 39.12, then which one of the following could t equal?

(A) 8
(B) 13
(C) 15
(D) 60
(E) 75

Bunuel, could you please explain why this doesn't align with the very similar (almost exact) question that has s/t=64.12? The solution for that question shows that simplifying 12/100 to 3/25 results in the solution having to be a multiple of 3. In that problem, there was only 1 answer with a multiple of 3.

In this situation, it is the same simplification of 12/100 into 3/25. However for this problem that thought process does not work the same as there are several options for multiples of 3. Why is there a different approach here if the problem is exactly the same?
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If s and t are positive integers and s/t = 39.12, then which one of th  [#permalink]

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27 Feb 2020, 20:32
Bunuel wrote:
If s and t are positive integers and s/t = 39.12, then which one of the following could t equal?

(A) 8
(B) 13
(C) 15
(D) 60
(E) 75

s/t = 39.12 = 39 12/100 = 39 3/25

Hence, answer choice must be a multiple of 25. Only choice (E) satisfies this condition.

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Re: If s and t are positive integers and s/t = 39.12, then which one of th  [#permalink]

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28 Feb 2020, 09:11

Solution

Given
• s and t are positive integers
• s/t = 39.12

To find
• Find one of the possible value of t

Approach and Working out

• s=39 t + 0.12 t
• S and t are integer.
o So, 0.12 t must also be an integer.
o 0.12 t= 12/100 t = 3/25t
o For 3/25 t to be an integer, t must be divisible by 25.

Hence, option E is the correct answer.

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Re: If s and t are positive integers and s/t = 39.12, then which one of th  [#permalink]

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29 Feb 2020, 05:30
Bunuel wrote:
If s and t are positive integers and s/t = 39.12, then which one of the following could t equal?

(A) 8
(B) 13
(C) 15
(D) 60
(E) 75

We can create the equation:

s/t = 39 + 12/100

s/t = 39 + 3/25

Since s/t = Q + r/t, we see that t must be a multiple of 25, so t could be 75.

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Re: If s and t are positive integers and s/t = 39.12, then which one of th   [#permalink] 29 Feb 2020, 05:30