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Number properties

by nakul17 » Thu Oct 10, 2013 10:02 pm
If , where both s and t are prime numbers, does s@t = 1?

(1) s + t (not equal to) 4

(2) s/t (not equal to) 1

Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
EITHER statement BY ITSELF is sufficient to answer the question.
Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.[/spoiler][/list]
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by theCodeToGMAT » Thu Oct 10, 2013 10:39 pm
s@t = ts/(t+s)

For RHS to be "1" .. t&S must be same.

Statement 1:
s+t != 4
So, both are not "2"
SUFFICIENT

Statement 2:
s/t != 1
So, both are not same.
SUFFICIENT

Answer [spoiler]{D}[/spoiler]
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by Brent@GMATPrepNow » Fri Oct 11, 2013 6:12 am
nakul17 wrote:If , where both s and t are prime numbers, does s@t = 1?

(1) s + t (not equal to) 4

(2) s/t (not equal to) 1

Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
EITHER statement BY ITSELF is sufficient to answer the question.
Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.[/spoiler][/list]


Once you post a question, please take a moment to ensure that you've transcribed it correctly. There is obviously some information missing here.

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by Brent@GMATPrepNow » Fri Oct 11, 2013 7:33 am
NOTE: I added the necessary information to the question below.
nakul17 wrote:If s@t = ts/(t+s), where both s and t are prime numbers, does s@t = 1?

(1) s + t ≠ 4
(2) s/t ≠ 1
This is a great candidate for rephrasing the target question. In fact, if we spend a bit of time rephrasing the target question, we can solve the question quickly. (Aside: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100)

Target question: Does s@t = 1?
In other words, does ts/(t+s) = 1?
We can also word this as: does (t+s)/ts = 1?
Or we can write: does t/ts + s/ts = 1?
Simplify to get: does 1/s + 1/t = 1?

IMPORTANT: since s and t are prime numbers, we know that s > 2, and t > 2
When s = 2 and t = 2, it's true that 1/s + 1/t = 1
If s > 2 and t > 2, then 1/s < 0.5 and 1/t < 0.5. Since it's impossible to two values less than 0.5 to add to 1, we can see that 1/s + 1/t ≠ 1 if s > 2 and t > 2

In other words, THE ONLY WAY that 1/s + 1/t can equal 1 is if s = 2 and t = 2.
So, we can rephrase our target question as . . .
REPHRASED target question: Does s = t = 2?

Statement 1: s + t ≠ 4
If s + t ≠ 4, then it is IMPOSSIBLE for s = t = 2
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: s/t ≠ 1
If s/t ≠ 1, then it is IMPOSSIBLE for s = t = 2
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

Answer = D

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by GMATGuruNY » Fri Oct 11, 2013 10:46 am
nakul17 wrote:If s@t = st/(s+t), where both s and t are prime numbers, does s@t = 1?

(1) s + t (not equal to) 4

(2) s/t (not equal to) 1
It can be helpful to rephrase the question stem so that one variable is IN TERMS OF THE OTHER.

st/(s+t) = 1
st = s+t
st - s = t
s(t-1) = t
s = t/(t-1).

t and t-1 are CONSECUTIVE INTEGERS.
For s to be a prime number such that s = t/(t-1) -- the quotient of two consecutive integers -- only one case is possible:
t-1 = 1, implying that t=2 and that s = 2/(2-1) = 2.
Thus, s = t/(t-1) only if s=2 and t=2.

Question rephrased: Does s=t=2?

Statement 1: s+t ≠ 4.
Thus, it is not possible that s=t=2.
SUFFICIENT.

Statement 2: s/t ≠ 1.
Thus, it is not possilbe that s=t=2.
SUFFICIENT.

The correct answer is D.
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