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Math Expert V
Joined: 02 Sep 2009
Posts: 58445

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Difficulty:   25% (medium)

Question Stats: 68% (01:02) correct 32% (01:07) wrong based on 251 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 V
Joined: 02 Sep 2009
Posts: 58445

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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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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
Math Expert V
Joined: 02 Sep 2009
Posts: 58445

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1
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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Intern  B
Joined: 22 May 2016
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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 ?
Math Expert V
Joined: 02 Sep 2009
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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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Intern  B
Joined: 06 Sep 2016
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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
Math Expert V
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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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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?
Math Expert V
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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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Manager  S
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Good question, it test your ability to pay attention to detail.

Is 143/z an integer, Yes or NO.

1) Insufficient, z can be any prime number which is 143/2 = 71.5 not an integer, 143/13 = 11 is an integer
2) Insufficient, Z is 9,10,11,12,13,14,15,16, 143/10 = 14.3, not an integer but 143/11 = 13, is an integer

Combine 1) Z is a prime number and 2) between 8 and 17, which leads only two possible choices for Z = 11 or 13.

Plug back into the original question is "is 143/z an integer." Can get a solid yes.

143/11 = 13 and 143/13 = 11, both results are integers M01-28   [#permalink] 09 Apr 2019, 11:34
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