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# M01-28

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Math Expert
Joined: 02 Sep 2009
Posts: 52231

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15 Sep 2014, 23:16
00:00

Difficulty:

25% (medium)

Question Stats:

67% (00:45) correct 33% (00:47) wrong based on 212 sessions

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Is $$\frac{143}{z}$$ an integer?

(1) $$z$$ is a prime number

(2) $$8 \lt z \lt 17$$

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Math Expert
Joined: 02 Sep 2009
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15 Sep 2014, 23:16
Official Solution:

Statement (1) by itself is not sufficient. 143 is not divisible by every prime number. For example, it is divisible by 11 but not by 2 or 3.

Statement (2) by itself is not sufficient. S2 does not tell us whether z is an integer; and therefore, 143 may or may not be divisible by z.

Statements (1) and (2) combined are sufficient. $$z$$ is a prime number between 8 and 17. 11 and 13 are the prime numbers between 8 and 17. These primes are both divisors of 143.

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07 Aug 2015, 19:19
Hello

Could you please let me know how to derive case of non integer value to denominator that would divide equally with 143?

I was unable to point any?

thanks
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17 Aug 2015, 02:19
WillGetIt wrote:
Hello

Could you please let me know how to derive case of non integer value to denominator that would divide equally with 143?

I was unable to point any?

thanks

If z = 143/10 = 14.3, then 143/(143/10) = 10.
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31 Oct 2016, 01:37
Hi,

Why is E not the correct answer? Even if we conclude that 11 and 13 are the values of Z we haven't found a unique value. Isn't this condition insufficient ?
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31 Oct 2016, 01:39
Saumyos wrote:
Hi,

Why is E not the correct answer? Even if we conclude that 11 and 13 are the values of Z we haven't found a unique value. Isn't this condition insufficient ?

The question asks whether 143/z is an integer, not what is the value of z.
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Joined: 05 Sep 2016
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03 Nov 2016, 03:21
hi
why s1 is not sufficient??
factors of 143 are: 1, 11, 13 and 143, and 11 and 13 are prime numbers which satisfy the s1.
thnks
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03 Nov 2016, 03:24
FTR wrote:
hi
why s1 is not sufficient??
factors of 143 are: 1, 11, 13 and 143, and 11 and 13 are prime numbers which satisfy the s1.
thnks

The question asks whether 143/z is an integer. (1) says that z i prime. If z is 11 or 13 then the answer is YES but if z is any other prime, say 2, then the answer is NO.
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23 Oct 2017, 18:25
I think this is a poor-quality question and I don't agree with the explanation. My confusion in the answer comes from that "Z" can be 11 or 13 for both 1 & 2. One of the values is not canceled out by either of the solutions thus it is not sufficient. Why is C correct?
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23 Oct 2017, 20:23
I think this is a poor-quality question and I don't agree with the explanation. My confusion in the answer comes from that "Z" can be 11 or 13 for both 1 & 2. One of the values is not canceled out by either of the solutions thus it is not sufficient. Why is C correct?

You should read the question carefully.

The question asks whether 143/z is an integer, not what is the value of z. For both value of z, 143/z IS an integer.
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Re: M01-28 &nbs [#permalink] 23 Oct 2017, 20:23
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# M01-28

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